Since Fe-based high temperature superconductor was discovered in 2008, its material exploration and physical properties have been widely and in depth studied. However, the 1111 system, which was discovered first to have the highest T_{c} in the bulk material, has long been lacking in large-size and high-quality single-crystalline sample. This seriously restricts the in-depth study of the physical problems relating to this material system. In recent years, the great progress of single crystal growth of the fluorine-based 1111 system CaFeAsF has been made. One has successfully grown the high-quality CaFeAsF parent phase and Co doped superconducting single crystal with millimeter size at ambient pressure by using CaAs as the flux. On this basis, several research groups have studied the physical properties of this system by different experimental means and obtained some important results. For example, Dirac Fermions have been detected in CaFeAsF single crystal by measuring the quantum oscillation and optical conductivity. A high-field-induced metal-insulator transition was reported in CaFeAsF, which is closely related to the quantum limit. This review is intended to make a preliminary summary of the progress of this area, including crystal growth, quantum oscillation, infrared spectrum, magnetoresistance under strong field, high pressure regulation, anisotropy, superconducting fluctuations, etc.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Diffusion mechanisms of four intrinsic point defects in rutile TiO_{2}, titanium interstitial (Ti_{I}), titanium vacancy (V_{ti}), oxygen interstitial (O_{I}) and oxygen vacancy (V_{O}) are studied in the framework of density functional theory with quantum ESPRESSO suite. Diffusion processes are simulated by defect movement between two stable atomic configurations through using the climbing image nudged elastic band (CI-NEB) method. The initial and final atomic structure in the minimum energy path (MEP) are constructed with 3×3×4 perfect supercell matrix of 216 atoms. Considering that oxygen atoms build up TiO_{6} octahedron and half of the octahedral centers are occupied by Ti atoms in rutile, interstitial defect is constructed by adding one Ti or O atom to the empty oxygen octahedral center, and vacancy defect is constructed by removing one atom from crystal lattice grid. Structural relaxation is performed before performing the NEB calculation with gamma k point sampling in irreducible Brillouin zone with an energy cutoff of 650 eV. As rutile TiO_{2} has tetragonal symmetry (P4_{2}/mnm), the diffusion channel along the[100] direction is equivalent to the[010] direction. Then, the diffusion paths along the direction parallel to c axis ([001] direction) and perpendicular to the c axis ([100] or[110] direction) are chosen to find the minimum diffusion energy path of Ti_{I} and O_{I}. As for V_{Ti} and V_{O}, diffusion paths are established from the vacancy site to nearest lattice site of the same kind. Calculation results exhibit significant anisotropy of energy barrier and diffusion mechanism. Of all defect species, Ti_{I} diffusion along the[001] direction through interstitial mechanism has the lowest activation barrier of 0.5057 eV. In addition, diffusions along the[100] and[110] direction through kick-out mechanism show higher energy barriers of 1.0024 eV and 2.7758 eV, respectively. Compared with Ti_{I}, O_{I} shows small barrier discrepancy between different diffusion directions, which is 0.859 eV along[001] and 0.902 eV along[100] direction. For vacancy defects, diffusion can occur only through the vacancy mechanism. The activation barrier energy of symmetrically inequivalent diffusion path of V_{O} is 0.735 eV along the[110] direction, 1.747 eV along the[001] direction, and 1.119 eV from the TiO_{6} apex site to the equator site. On the other hand, V_{Ti} has two inequivalent paths with much larger diffusion energy barriers:2.375 eV along the[111] direction and 3.232 eV along the[001] direction. In summary, the Ti_{I} interstitial diffusion along the[001] direction (parallel to the c axis) has the lowest activation barrier in rutile TiO_{2}, which is in excellent agreement with former experimental and theoretical data.

Nanocapillaries in various materials have received considerable attention due to the rapid growth of the nanotechnology.Recent studies have focused on the transmission of ions through the nanocapillary. The pioneer work,the transmission of 3-keV Ne^{7+} through polyethylene terephthalate nanocapillaries based on guiding effect has been reported by Stolterfoht et al.(2002 Phys.Rev.Lett.88 133201),indicating that the selforganized charge patches on the capillary walls,which inhibits close contact between the ions and the inner capillary walls,deflecting the trajectories of ions,and thus the ions transmit along the direction of the capillary axis.For the high-energy region (E/Q > 1 MV),Hasegawa et al.(2011 J.Appl.Phys.110 044913) measured the outgoing angle and energy distribution of 2 MeV H^{+} ions transmitted through a tapered glass capillary.The results indicated that the main transport mechanism of the MeV ions in a tapered glass capillary is the multiple random inelastic collisions below the surface. In the medium-energy region (E/Q from dozens of kV to hundreds of kV),Zhou et al.(2016 Acta Phys.Sin.65 103401) measured the transmission features of the 100-keV protons transmitted through a polycarbonate (PC) membrane at a tilt angle of+1°,the transmitted particles were located around the direction along the incident beam,not along the capillary axis,the transport mechanism of the 100-keV protons in the nanocapillary is the charge-patch-assisted collective scatterings on the surface.With the nanocapillary membranes at different tilt angles,the transverse momentum of the incident ions are different.What is the transmission mechanism of the ions in nanocapillary membranes at different tilt angels? In the present study,we measure the time evolution of the angular distribution,charge state distribution and relatively transmission rate of 30-keV He^{2+} ions with 500 pA transmitting through a polycarbonate nanocapillary membrane at different incident angles (-0.5°,-1°,-1.5°,-2.5°).It is found that for the small tilt angles (-0.5°,-1°,-1.5°) the transmitted He^{2+} ions are located around the direction of incident beam,not along the capillary axis,and the directions of the transmitted H^{0} atoms change from the direction of capillary axis to the direction of incident beam gradually,during the experimental period,the charge exchange is observed.The charge patches in the capillaries overcome the transverse momentum of the incident ions,the ions are transmitted by specular scatterings on the inner surface of capillary,and the main transport mechanism of ions in the nanocapillary at the small tilt angles is the charge-patch-assisted collective scatterings on the surface.For a large tilt angle (-2.5°),the transmitted He^{2+} ions are located in the direction of the incident beam,and He^{0} atoms are always in the direction of capillary axis,the charge patches cannot overcome the transverse momentum of the incident ions,and the main transport mechanism of ions in the nanocapillary at the large tilt angles is the multiple random inelastic collisions below the surface.This finding increases the knowledge of charged ions through nanocapillary at different tilt angles within dozens of keV energies in many scientific fields.

The nuclear spin-polarized ^{3}He gas has been in depth studied and widely used in various scientific experiments. The polarized ^{3}He gas can be used as a polarized neutron target to study the reaction of neutrons with charged particles or photon beams. On the other hand, spin polarized ^{3}He gas is a good probe for detecting the new interactions in the supernormal model, and has many other applications as follows:the spin-dependent interaction can be studied quantitatively by measuring the NMR frequency shift but the spin-dependent interaction can also be studied by measuring the relaxation time of polarized ^{3}He gas; the polarized ^{3}He gas can be applied to magnetometers and magnetic resonance imaging (MRI); the highly polarized ^{3}He gas can be used as a neutron spin filter for neutron polarization and polarization analysis because of the high correlation between the absorption cross section of the neutron in polarized ^{3}He nucleus and the spin orientation. At present, the three major domestic sources of neutron, CMRR, CARR, and CSNS, are used to study the neutron polarization and polarization analysis techniques based on spin polarized ^{3}He gas. The longitudinal (or spin-lattice) relaxation time (i.e., T_{1}) of ^{3}He is a key parameter that limits the polarizability of ^{3}He gas. In order to reduce the effect of magnetic field gradient on the longitudinal relaxation time of polarized ^{3}He gas, large-sized Helmholtz coils are usually constructed to provide the main magnetic field where the uniformity in the magnetic field central region reaches 10^{-4} cm^{-1}. To obtain enough magnetic field uniformity, some magnetic field systems even exceed 1.5 m in size. However, it is expected to have a small magnetic field configuration from the view of practicality and convenience. For the common size (<0.1 m×0.1 m×0.1 m) of ^{3}He cells, Merritt coil and Saddle coil can effectively reduce the size of the magnetic field apparatus. However, for electron scattering experiments of ^{3}He cells, the chamber length can be 40 cm. The system length exceeds 1 m even by using the Merritt coil. In this work, a new six-coil system for ^{3}He polarization is obtained. Within the coils, the magnetic field gradient satisfies the requirement that √|▽B_{x}|^{2}+|▽B_{y}|^{2}/B_{0} < 10^{-4} cm^{-1} in more than 30% area, which is better than all the existing coils used in polarized ^{3}He experiments and can be applied to the future ^{3}He instruments. For other experiments that require magnetic field to have a large uniform area, the new six-coil system is also a good option.

Applying the active control of electric field to the preparation of micro-droplets via the traditional microfluidic technology has attracted great attention because it can effectively improve the controllability of the preparing process. Therefore, a full understanding of mechanism for the regulation and control of microdroplets's generation by the microfluidic technology and electric field will provide interesting possibilities for the active control of producing required microdroplets in the practical applications. A transient theoretical model is developed via the coupling of phase-field method and electrostatic model to numerically investigate the generation of the single-phase droplets in a co-flow microfluidic device under the control of a uniform direct-current electric field. Via the numerical simulations based on the transient model, the control mechanisms of the electric field on dynamic behaviors of the droplets generation are revealed, and the influences of flow and electric parameters on the droplets generation characteristics are elucidated. The results indicate that the electrostatic field is able to generate an electric field force toward the inner phase fluid in the normal direction of the interface between two-phase fluids with different electric parameters. The electric field force enhances the necking and breaking of the inner fluid interface, which accelerates the droplets' generation, increases droplet deformation degree, and reduces droplet size. As the electric capillary number increases under the same hydrodynamic capillary number, the droplet formation pattern is transformed from dripping regime with only a single droplet formed per cycle to another dripping regime with one main droplet formed together with the following satellite droplets per cycle. In addition, according to the numerical results in this work, we organize a regime diagram to quantitatively represent the respective regime of these two flow patterns as a function of hydrodynamic capillary number and electric capillary number. The regime diagram indicates that with the increase in hydrodynamic capillary number and electric capillary number, the viscous drag force and electric field force are strengthened, which induces the formation of a slender liquid thread of inner fluid at the later stage of the necking process. This contributes to triggering the Rayleigh-Plateau instability on the liquid thread of inner fluid, and thus facilitating the generation of satellite droplets via the breakup of the liquid thread.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Vanadium dioxide (VO_{2}) is well known for its metal-insulator transition (MIT) at 341 K.Normally,the VO_{2} presents a metallic rutile (R) phase above the T_{c},but an insulator (monoclinic,M) phase below the T_{c}.Besides the thermally driven mode,the phase transition can also be triggered electrically,which is common in electron devices like field effect transistors and actuators.Due to the electron correlation,the Mott transition associated with electronelectron interaction as well as the Peierls transition involving electron-lattice interaction are both believed to drive the transition of VO_{2},although the actual MIT mechanism is still under debate in condensed matter physics.The Coulomb screening of the electron hopping can be broken by injecting enough carriers.However,the issue is more complicated in the electrically-triggered MIT of VO_{2} due to the Joule heat of current and the carrier injection of field effect.In this work, we study the electrically induced MIT in VO_{2} nanowires by in-situ transmission electron microscopy (TEM).We build a closed circuit under the TEM by using in-situ electric TEM holder to capture the changes of VO_{2} in electron structure and phase structure simultaneously.An alternating bias voltage is applied to the VO_{2} nanowire while the selected area electron diffraction (SAED) patterns of VO_{2} nanowire are recorded using Gatan Oneview^{®} fast camera.The current rises or drops suddenly in the current-voltage curve (I-V curve),indicating a phase transition,through which the SAED pattern of nanowire is recoded every 5 ms.By correspondence analysis between the SAED patterns and the I-V data at every moment,a transition state of insulating R phase is observed,which is obviously different from the normal state of the metallic R phase or the insulating M phase.The existence of the insulating R phase indicates that electron structure transforms prior to the phase transition.The decoupling phenomenon reveals a predominant role of electron-electron interaction.Moreover,by feedback strategy of the circuit,the current through the metallic nanowire of VO_{2} remains unchanged,and thus keeping the Joule heating in the nanowire constant,the phase transition from metal to insulator does not happen until the voltage decreases to about 1 V.When phase transition to insulator happens in voltage stepdown,even stronger Joule heating is generated because of the increased resistance of VO_{2} nanowire.Therefore,the VO_{2} phase transition is triggered electrically by the carrier injection instead of the Joule heating.The injecting of enough carriers can break the screening effect to activate the electron hopping and initiate the phase transition.The deduction is confirmed by the decoupling phenomenon in the insulating R phase.Additionally,the polarized shift rather than the phase transition of the VO_{2} nanowire is observed in the non-contact electric field mode,which also supports the cause of the carrier injection for the electric induced MIT.The results prove the electron-correlation-driven MIT mechanism, or so called Mott mechanism,and open the new way for electron microscopy used to study the electron correlated MIT.

The excessive leakage current, commonly observed in GaN Schottky barrier diodes (SBDs), severely degrades device electrical performance and long-term reliability. This leakage current relates to the dislocation-related conductive states as observed by microscopy. Up to now, various transport models have been proposed to explain the leakage current, but none of them can clearly describe in physics the electrically active dislocations. One just equivalently regarded the electric defect as a continuum conductive defect state within the forbidden band, without considering the microscopic electrical properties of the dislocations. Here in this work, on the basis of numerical simulation, we propose a phenomenological model for the electrically active dislocations to explain the leakage conduction of the GaN Schottky diodes, which are fabricated on a freestanding bulk substrate n-GaN wafer with a low dislocation density of about 1.3×10^{6} cm^{-2}. In this model, we emphasize that the acceptor-like traps at the core of dislocations could capture electrons from the nearby donor-like traps, resulting in a high Coulomb potential and a decreasing potential at the donor-like sites. In this case, the core of dislocations would be negatively charged, and not favor the electron transport due to a strong Coulomb scattering effect, while the shallow donor-like traps around them can lead to a significant tunneling leakage component. This model is consistent well with the common observation of the localized currents at the edges of the surface V-defects in GaN. The shallow donor-like defects in GaN induced by the substitution of oxygen for nitrogen (O_{N}), rather than the nitrogen vacancies, act as the dominant donor impurities responsible for the significant leakage current, which has a density on the order of 10^{18} cm^{-3} and an activation energy of about 47.5 meV, because 1) it has been demonstrated that during the material growth, oxygen diffusion toward the surface pits of dislocations via nitrogen vacancies could produce an exponentially decayed distribution with a density of at least 10^{17} cm^{-3}, in good agreement with our derivation; 2) by the first principle calculation, the thermal activation energy of the oxygen-related donors is determined to be about 50 meV, which is very close to our derived 47.5 meV. According to this model, we propose that reducing the O_{N} defect density during device growth is a feasible method to suppress the high leakage current in GaN-based SBDs. In addition, this study can also improve our understanding of the leakage current in other GaN-based devices.

Fe_{3}O_{4} nanomaterials have received great attention due to their many applications in tumor diagnosis and tumor heat therapy based on their good biocompatibility, magnetic targeting ability and superparamagnetic properties to avoid magnetic reunion in the process of magnetic targeting. Most of superparamagnetic nanoparticles obtained by traditional methods exhibit lower saturation magnetization (MS), because of their small particle sizes. Enlarging the particle size is favorable to increase the MS of magnetic particles. However, the superparamagnetism of the particle could be lost with the increase of particle size. This is not favorable to the targeting delivery of magnetic particles. For this purpose, in this paper, novel Fe_{3}O_{4} nano-microspheres with mesoporous hollow structure are successfully synthesized by a facile hydrothermal method from the FeCl_{3}6 H_{2}O, sodium citrate, urea, and polyacrylamide as additive, the reaction temperature is 200℃ and reaction time is 12 h. The crystal structure and purity of the resulting products are examined by powder X-ray diffraction (XRD). The morphologies of the products are studied by using scanning electron microscopy (SEM) and transmission electron microscopic (TEM). The magnetic properties of Fe_{3}O_{4} nano-microspheres are evaluated with a vibrating sample magnetometer. The morphology evolution process and possible formation mechanism of Fe_{3}O_{4} nano-microspheres are investigated. The findings are as follows:all XRD peaks of the hollow Fe_{3}O_{4} nano-microspheres could be assigned to the spinel-type Fe_{3}O_{4}. The SEM and TEM images reveal that the products are mesoporous hollow Fe_{3}O_{4} nano-microspheres and possess hierarchical structure, in which large microspheres (160 nm) are self-assembled by smaller Fe_{3}O_{4} initial crystals (18 nm). It is found that the synthetic time of Fe_{3}O_{4} nano-microspheres is considerable for the formation of the Fe_{3}O_{4} hierarchical structure, and that the dispersion and sphericity of Fe_{3}O_{4} nano-microspheres are the best when reaction time is 12 h. The formation of hierarchical hollow structure is believed to be due to the Ostwald ripening process, in which the initial crystals redissolve and regrow. Furthermore, the magnetic measurement results show that as-prepared hollow Fe_{3}O_{4} nano-microspheres exhibit typical superparamagnetic properties whose initial crystal size is in the range of superparamagnetic region. Meanwhile, MS is about 73.3 emu/g at room temperature, which is significantly greater than that of traditional small superparamagnetic nanoparticles and compact solid nano-microspheres. The high saturation magnetization of hollow Fe_{3}O_{4} nano-microspheres originates from a high crystallinity with primary grain, lager size and hierarchical structure. The results indicate that the as-prepared Fe_{3}O_{4} hollow nano-microspheres are dispersed, water-soluble, homogeneous in particle diameter, and superparamagnetic, and can be used in targeted anticancer drug delivery and tumor heat therapy.

Materials with perpendicular magnetic anisotropy have been intensively investigated due to their potential applications in the nonvolatile magnetic memory and spin-torque oscillators. Hear in this paper, we report a special interesting spin-transfer-driven magnetic behavior in perpendicularly magnetized (Co/Ni) -based spin-valve nano-pillars due to the reduced symmetry of easy axis in the free layer. The micromagnetic simulations indicate that a dip in the average magnetization curve can take place due to the reduced symmetry such as tilt of the magnetic field as well as the easy axis of the free and polarizer layers. In order to further clarify the physics mechanism of the dip, we carry out a series of new simulation studies. In our simulations, we consider a spin-valve nano-pillar with perpendicular anisotropy free layer and a 3° tilted polarizer layer. A negative perpendicular magnetic field and a positive perpendicular current are both applied simultaneously. In the average magnetization curves <m_{z}> as a function of the magnetic field with various currents, three dips are observed. Note that although the spin-transfer torque is essential to the appearance of the dips, the position of the dips is less affected by the current in a certain current range. For three dips, we notice that the <m_{z}> values are almost identical at a special magnetic field for different currents. At this special magnetic field, the magnetization oscillation modes in the free layer are similar to each other for different currents. The corresponding frequency spectra show that the amplitude of the main frequency peak decreases with the increasing of current due to the enhanced spin-transfer torque. In addition, the frequency shows a blue-shift with the increasing of applied current. Our simulations show that the main frequency f_{1} corresponding to the highest peak is approximately equal to the precession frequency of the local magnetization in the free layer. Several high-order frequency peaks are also observed in the frequency spectrum with f_{n}=nf_{1}, where n is an integer. Therefore the periodic oscillation of <m_{z}> is a harmonic oscillation. Further simulations indicate that the dip appearance is also affected by the thickness of free layer. The spin-transfer torque effect decreases with the thickness of the free layer increasing. As a consequence, the dips shift to a low magnetic field range with the increase of the thickness. And for larger thickness t=8.0 nm, no dip appears. This result suggests that the spin-transfer torque is necessary for the dip, rather than the unique effect factor, to occur. In the dip region, the magnetic oscillation modes of the free layer show interesting frequency spectrum characters:harmonic frequency or inter-harmonic frequency. As a consequence, the periodic oscillation of the free layer is accompanied by the harmonic waves.

Considering hydrogen-like impurity and the thickness effect,the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot (QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well (PCPW) and an asymmetric Gaussian functional confinement potential well (AGFCPW) serving as the transverse and longitudinal confinement potential,respectively.Based on the above two states,a two-level system is constructed.Then,the electron quantum transition affected by a magnetic field is discussed in terms of the two-level system theory.The numerical calculations indicate that the electron transition probability Q deceases with the range R_{0} of the PCPW decreasing.With R_{0} decreasing,the amplitude of the transition probability Q decreases greatly when R_{0} is small (R_{0} < 2.5r_{p}),but the decrease becomes small when R_{0} is large (R_{0} > 2.5r_{p}).The transition probability Q decreases with the dielectric constant ratio η increasing.For different values of the well width L of the AGFCPW,the change forms of the transition probability Q with the well width L are different:the transition probability Q decreases monotonically with the decreasing of the well width L when L is large (L > 1.3r_{p}), which is similar to the trend of the transition probability Q changing with the range R_{0} of the PCPW,but the oscillation of the transition probability Q is small with the decreasing of the well width L when L is small (L < 1.3r_{p}).Whereas, both changes are consistent basically when the range of the confinement potential (the value of R_{0} or L) is large since the AGFCPW can be approximated by the PCPW when z/L ≪ 1.For the electronic state and its change in the QD with a confinement potential,in any case,the results are rough without regard to the influence arising from the thickness of the QD.This shows that the AGFCPW is more accurate than the PCPW in reflecting the real confinement potential. This conclusion is in accordance with the experimental results.In addition,the transition probability Q decreases with increasing V_{0}.The amplitude of the transition probability Q decreasing with increasing the dielectric constant ratio η is enlarged with reducing the coupling strength α.This indicates that the phonon (the polarization of the medium) effect cannot be ignored when investigating the change of the electronic state in the QD.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency ω_{c}.The external magnetic field is a kind of inducement causing the quantum transition of electronic state.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency ω_{c},and is affected dramatically by the coupling strength α:with increasing the coupling strength α,the oscillation period of Q increases,but the oscillation amplitude decreases.In a word,the transition probability of the electron is influenced significantly by some physical quantities,such as the coupling strength α,the dielectric constant ratio η,the resonant frequency of the magnetic field ω_{c},the well depth V_{0}, and the well width L of AGFCPW.

With the development of modern micro-processing technology, the basic theory and relevant applications for surface plasmon have formed a new research direction which is known as surface plasmon photonics. The traditional plasmonic materials are noble metals, such as gold and silver, but they have some limitations that may hinder their application in plasmonic devices, such as lack of the chemical stability in air, difficulty in modulating by external field, large optical losses in the infrared wavelength range, etc. It has been demonstrated that transparent conducting oxides are a good candidate of plasmonic materials working in the infrared frequency range because of their low optical loss and tenability. Here in this work, the quasi-three dimensional silica nano-sphere array is prepared by nano-imprint lithography. Indium tin oxide (ITO) film is deposited on the array. The transmission properties are measured and the excitation modes of surface plasmons are analyzed for the samples obtained. Then, we focus on the effect of annealing treatment on characteristics of surface plasmon resonance for ITO thin films. The carrier concentration and carrier mobility of the ITO thin films annealed under different conditions are changed, and the corresponding surface plasmon resonance characteristics are investigated. The main results obtained in this work are as follows. 1) Mono-disperse SiO_{2} spheres, quasi-ordered monolayer SiO_{2} mask and ITO films with high transmittance (≥ 85%) and high electrical conductivity are obtained. Experimental results show that a surface plasma resonance at a wavelength of 1780 nm is excited for the glass/sphere/ITO system. 2) The grain size of ITO thin film after being annealed turns large, resulting in the increased optical transmittance of samples. 3) The carrier concentration of ITO film annealed in the air decreases, leading the resonance peak of surface plasmon to be red-shifted. 4) The carrier concentration of ITO thin film annealed in vacuum increases and the resonance peak is blue-shifted. These results obtained in this work contribute to the application of surface plasmon devices fabricated by ITO materials.

Suppression of the secondary electron (SE) multipactor is a key issue for improving the performance of high power microwave devices and particle accelerators. The decrease of the SE emission yield (SEY) by using certain surface morphology is one of the effective methods. To optimize the surface morphology, we simulate the SE emissions of different surface structures by using the Monte Carlo method. The effects of geometric parameters, such as duty ratio of area, depth-to-height ratio, pattern and its arrangement on SEY are investigated. For surface morphology with patterns of square, round and triangle, and for both convex and concave structures, the corresponding values of SEY first decrease and then become steady with the increase of duty ratio of area and depth-to-height ratio. For convex structures, the values of SEY are different for different pattern shapes, in which triangle pattern has the smallest SEY. However, the value of SEY is nearly independent of arrangement of pattern. For concave structures, on the other hand, the value of SEY is scarcely different for different patterns or different arrangements. In general, a convex structure has a better suppression effect than a concave structure if other geometric parameters are identical. The “shading effect” from side wall of structure is found to be the intrinsic reason of the suppression effect.

In this paper, the hybrid physical model is established based on the equivalent circuit for describing dynamic radio-frequency (RF) field buildup and the particle-in-cell (PIC) method for describing two-sided multipactor discharge in plate cavity. By using our built 1D3V-PIC code for multipactor discharge and fully equivalent circuit code for RF field buildup, the influence of multipactor discharge on the dynamic process of RF field buildup is numerically investigated and analyzed in detail under the condition of cavity with different Q-values. The numerical results could be concluded as follows. Under the condition of no multipactor discharge in dynamic process of RF field buildup, the higher the Q-value, the longer the buildup-time is. The input energy is equal to the sum of stored energy and consumed energy in cavity, the speed of energy storing is higher than the speed of energy consuming at the beginning stage of RF field buildup and then the speed of energy storing becomes lower than the speed of energy consuming. When the process of RF field buildup is finished, the average power of input is equal to the average power of consumed power in cavity. Under the condition of multipactor discharge loading in dynamic process of RF field buildup, the higher the Q-value, the later the start-time is and the longer the interaction time-interval of multipactor discharge is. The bigger the area of secondary electron emission, the higher the peak-value of secondary electron current is. The failure of RF field-buildup is caused by the continuous loading of multipactor discharge. The higher the Q-value or the bigger the area of secondary electron emission, the lower the probability of RF field buildup success is. The simulated results could partly provide a reference for engineering design.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

The atomic-level structure of metallic glasses (MGs) is one of the most fundamental and challenging topics in condensed matter physics. Unlike crystalline metals or alloys, the MGs are lacking in a well-defined description of structure order, which is a major obstruction for relating its structure to physical properties. Obviously, it is vitally important to have an in-depth understanding of the atomic packing scheme in MGs. Due to the limitations of experimental characterization methods, it is hard to obtain the atomic packing scheme of MGs in experiment. Computational simulation on an atomic scale has become an important method of characterizing the atomic structure of MGs. The La-based La–Ni–Al glass forming system is well-known for its good glass-forming ability, distinctive β relaxation peak that is well separated from α relaxation, and liquid-liquid transition at a temperature around 1000 K. Many efforts have been made to investigate these novel properties. However, the atomic structure of this system is rarely studied. In this paper, the atomic structure evolution from liquids to glass states in La-based binary MGs La_{65}Ni_{35} and La_{65}Al_{35} are studied via ab initio molecular dynamics based on the density functional theory. The local structures are systematically analyzed by the radical distribution function, partial radical distribution function (PRDF), Voronoi tessellation method, and bond-type method in Honeycutt-Andersen. The results indicate that the PRDF of Ni–Ni is much weaker than that of Al–Al, which indicates the Ni–Ni avoidance in La_{65}Ni_{35}. The major peaks of PRDFs are always smaller than the sum of efficient radius of the two kinds of atoms, especially for La–Ni pairs. Atomic structure of the two systems are coincident with dense atomic packing scheme and the difference between major Voronoi polyhedron types (<0, 3, 6, 0> for La_{65}Ni_{35} and <0, 2, 8, 1>, <0, 2, 8, 0> for La_{65}Al_{35}) in local structures is controlled by their ratio of solute to solvent atomic size. The high five-fold local symmetry structure gradually increases in both systems with the decrease of temperature, which validates its pivotal part in hindering crystallization. The electronic structure is studied with the partial density of states. It is found that the significant bond-shortening between La and Ni is due to the strong hybridization between Ni-3d and La-5d electrons and this result may play a key role in understanding composition related structure and properties in MGs.

Organic solar cells (OSCs) have attracted intensive attention in recent years due to their distinct advantages of rich material resources, easy fabrication, and good flexibility. The standard structure of OSCs consists of an anode, an active layer and a cathode. Indium tin oxide (ITO) is often used as a transparent anode. However, the indium in ITO is not only very low in content, but also can penetrate into other layers of OSCs and affect the battery life. The ITO is not suitable for flexible OSCs because of its brittleness. Therefore, researchers have been trying to find alternatives to ITO, which should have transparent and flexible electrodes. The multilayer film consisting of MoO_{3}/Ag/MoO_{3} is a very promising candidate as an alternative of ITO to work as the transparent anode in OSCs. However, in MoO_{3}/Ag/MoO_{3} based thin OSCs structure, the absorption of light is quite poor. Here, we introduce a short-pitch metallic grating in which there are used the surface plasmon polaritons (SPPs) to enhance the light absorption of the active layer. The finite-difference frequency-domain method is used to solve the Maxwell's equations and semiconductor equations for revealing the optical and electrical properties of OSCs. As is well known, the contradiction between the long light absorption path and the short exciton diffusion length results in a relatively low power conversion efficiency (PCE) of the OSCs. Metallic gratings can be introduced into conventional OSCs for improving the light absorption due to the surface plasmon resonance. The light absorption can be enhanced compared with that in the conventional OSCs without metallic gratings. At the same time, the small periodic structure is introduced into the MoO_{3}/Ag/MoO_{3} anode-based OSCs. The small spacing between gratings creates a strong interaction between two adjacent metal nanowalls. These nanostructures and metal nanostructures will further enhance the light absorption. In this work, it is proposed that short-pitch metallic gratings be introduced into the MoO_{3}/Ag/MoO_{3} anode-based OSCs for improving the light absorption and PCE. It is found that the light absorption of plasmonic structure with short-pitch metallic gratings can be greatly enhanced compared with standard structure without metallic gratings. Meanwhile, with an optimal groove width of 4 nm, PCE is improved by 49% compared with the case with the planar structure. These results contribute to better developing the ITO free OSCs.

It is of great significance to obtain the information about the stress of load-bearing ferromagnetic members quickly in order to maintain the safety of the infrastructure. The key point is to accurately and quickly determine the characterization parameters which change sensitively and linearly with the stress. Among the existing electromagnetic methods of determining axial stress in ferromagnetic members, exciting coils are usually adopted to exert a time-varying magnetic field on the ferromagnetic members, which will induce the problems of winding coils, coil heating, and eddy current that influences the test results. What is worse is that it is inevitable to compare the experimental data point by point to determine the adequate magnetic parameter characterizing the stress, which influences the fast determining of the axial stress in ferromagnetic members. In order to break through these limitations, in this paper we propose a method of determining the axial stress in ferromagnetic members by using superficial magnetic flux density obtained from static magnetization in permanent magnets. In this method, permanent magnetizers are adopted to excite the overall damping and local uniform spatially-varying constant magnetic field on ferromagnetic members. A testing probe including Hall chip array is adopted to measure the superficial axial and radial magnetic flux density to determine the axial stress of the ferromagnetic member. The principle is elaborated to choose the adequate superficial magnetic flux density fast and precisely for characterizing the axial stress in ferromagnetic members. According to the theory of demagnetizing field, the continuity of the tangential magnetic field strength and Gauss's law for magnetism, the relational equation between the derivative of superficial axial magnetic flux density with the stress and the derivative of superficial radial magnetic flux density with the stress is established. Then, an experiment is conducted to verify the proposed method. The experimental results show that according to this relational equation, the superficial magnetic flux density with the highest stress sensitivity can be determined quickly and accurately. What is more, the linearity of the superficial magnetic flux density varying with the stress is good, and the goodness of the corresponding linear fitting R^{2} is greater than 0.98. It means that the determined superficial magnetic flux density can be used as a feature parameter to characterize the stress in ferromagnetic members. The proposed method of determining the axial stress in this paper can provide a new way of on-line detecting the working stress in ferromagnetic components.

Deep-level trapping effect is one of the most critical issues that restrict the performance improvement of GaN-based microwave power devices. It is of very importance for material growth and device development to study the trapping behavior in the device. In the past decades, there have been made a lot of efforts to characterize and investigate the deep-level trapping phenomena. However, most of the previous researches focused on the large-scale devices. For pursuing higher frequency, the devices need to be scaled down. Consequently, it becomes more difficult to characterize the deep-level traps in small-scale GaN-based devices, since none of the traditional characterization techniques such as capacitance-voltage (C-V) measurement and capacitance deep-level transient spectroscopy (C-DLTS) are applicable to small devices. Pulsed I-V measurement and transient simulation are useful techniques for analyzing trapping effects in AlGaN/GaN high electron mobility transitors (HEMTs). In this work, AlGaN/GaN metal-oxide-semiconductor HEMTs (MOSHEMTs) with very short gate length (L_{g}=80 nm) are fabricated. Based on the pulsed I-V measurement and two-dimensional transient simulation, the influence of deep-level trap on the dynamic characteristic of short-gate AlGaN/GaN MOSHEMT is investigated. First, the pulsed I-V characteristics of AlGaN/GaN MOSHEMT with different quiescent bias voltages are studied. In addition, the current collapse induced by the trapping effect is extracted as a function of the quiescent bias voltage. Furthermore, the transient current of AlGaN/GaN MOSHEMT is simulated with the calibrated model, and the simulation exhibits a similar result to the measurement. Moreover, the physical mechanism of trapping effect in the device is analyzed based on the experimental data and simulation results. It is shown that the current collapse of AlGaN/GaN MOSHEMT varies non-monotonically with the increase of the gate quiescent bias voltage, which results from the combination effect of the gate leakage injection-related and hot electron injection-related mechanism. In the off state, the current collapse is mainly induced by the traps below the gate, which is dominated by the gate leakage injection mechanism, leading to the decrease of current collapse with the increase of the gate bias voltage. In the on state, the hot electron injection mechanism becomes the dominant factor for trapping effect in the drain access region, resulting in the increase of current collapse. The results in this work indicate that the trap-induced current collapse can be further suppressed by improving the quality of gate dielectric to minimize the gate reverse leakage and by reducing the trap density in the epitaxial layer.

In the past decade, fluorescence lifetime imaging microscopy (FLIM) has been widely used in biomedical research and other fields. As the fluorescence lifetime is unaffected by probe concentration, excitation intensity and photobleaching, the FLIM has the advantages of high specificity, high sensitivity and capability of quantitative measurement in monitoring microenvironment changes and reflecting the intermolecular interactions. Despite decades of technical development, the FLIM technology still faces some challenges in practical applications. For example, its resolution is still difficult to overcome the diffraction limit and the trade-off among imaging speed, image quality and lifetime accuracy needs to be considered. In recent years, a great advance in FLIM and its application has been made due to the rapid development of hardware and software and their integration with other optical technologies. In this review, we first introduce the principle and characteristics of FLIM technology based on time domain and frequency domain. We then summarize the latest progress of FLIM technology:1) imaging speed enhancement based on hardware improvement such as optimized time-correlated single photon counting module, single photon avalanche diode array detector, and acousto-optic deflector scanner; 2) lifetime measurement accuracy improvement by the proposed algorithms such as maximum likelihood estimate, Bayesian analysis and compressed sensing; 3) imaging quality enhancement and spatial resolution improvement by integrating FLIM with other optical technologies such as adaptive optics for correcting the aberration generated in the optical path, special illumination for equipping wide-field FLIM with optical sectioning ability, and super-resolution techniques for exceeding the resolution limit. We then highlight some recent applications in biomedical studies such as signal transduction or plant cell growth, disease diagnosis and treatment in cancers, Alzheimer's disease and skin diseases, assessment for toxicity and treatment efficiency of nanomaterials developed in the past few years. Finally, we present a short discussion on the current challenges and provide an outlook of the future development of enhanced imaging performance for FLIM technology. We hope that our summary on the state-of-the-art FLIM, our commentary on future challenges, and some proposed avenues for further advances will contribute to the development of FLIM technology and its applications in relevant fields.

Nickel-based superalloy is mainly used for fabricating the important high temperature parts including the turbine disk, turbine baffle, compressor disk, and other critical components. Ceramic inclusions in powder metallurgy (PM) superalloy could promote fatigue crack initiation, and thus accelerating the crack propagation under certain conditions. In this case, the ultra-clean nickel-based superalloy powder is critical for PM superalloy components. Generally, there are two well-known methods of fabricating superalloy powders, i.e., argon gas atomization (AA) and plasma rotating electrode process (PREP). Electrode induction melting gas atomization (EIGA) process is a newly developed method of preparing ultra-clean metal powders. The EIGA process is a completely crucible-free melting and atomization process developed by ALD vacuum technologies. In this process, a slowly rotating prealloyed bar is fed into a conical induction coil. The end of the bar is inductively heated and molten alloys falls into an atomizer where the liquid alloy is atomized with a high-pressure inert gas. The EIGA prepared powders possess the advantages of AA (more fine powders) and PREP (ultra-clean powders) processes. Generally, there are two key issues in EIGA process, and the free-fall gas atomizer design is one of the critical issues for the powder yield and quality. Free-fall gas atomizers are some of the first two fluid atomizer designs to be used for molten metal atomization. In a simple open (unconfined stream) design a melt stream falls from a tundish exit via gravity into the convergence of focused atomization gas jets where it is disintegrated. The gas-melt interaction is complex, and it is difficult to characterize the interaction process directly. To have a good understanding of the atomisation technology, the physical break-up process instead of correlating the gas dynamics with droplet fragmentation indirectly must be able to be examined. And it will be desirable, if we input the atomization parameters, we can obtain the particles' distributions directly. In this work, a computational fluid dynamic approach to simulating the primary and secondary atomization processes is developed by using the volume of fluid method and discrete phase model. By integrating the metal stream break-up (in primary atomization) with the flow field and particles distribution simulation (in second atomization), this numerical simulation method is able to provide the direct assessment for the atomisation process. To verify the method performance, the melt stream is initialized into a 4 mm-diameter stream, which is then injected into the gas flow field for further fragmentation. The experimental results show that the simulated particles' diameter distribution is consistent with the experimental results in the same conditions.

The influence of diffusion and defects of crystal surface on the crystal vibration mode are an important and basic subject in surface physics research. The frequency of lattice vibration corresponds to the energy band of the system. Since the vibrations of the atoms in the crystal lattice are not isolated from each other, and the crystal lattice is periodic, thereby forming a lattice wave in the crystal. The lattice wave represents that all the atoms in the crystal vibrate at an identical frequency, which is often called a vibration mode. The lattice chain model has been studied as the vibrating mode of phonon and the energy-band in solid state physics. The vibrating modes of the lattice chain model have been analyzed with the Newton equation and the Born-von-Karman boundary condition in the literaure. In general, it is difficult to solve this problem due to the complex nonlinear characteristic of the interactions between the matter particles and the environment. Noting the complicacy in directly diagonalizing quantum Hamiltonian operator of a long chain, we introduce the invariant eigenoperator method (IEO) for deriving the energy gap of a given crystal lattice without solving its eigenstates in the Heisenberg picture. The Heisenberg equation is as important as the Schrödinger equation. However, it has been seldom used for directly deriving the energy-gap in previous studies. Following the Heisenberg's original idea that most observable physical quantity in quantum mechanics is energy spectrum, Hong-yi Fan, one of the authors of the present paper, developed the IEO method. This method provides a natural result of combining both the Schrödinger operator and the Heisenberg equation. Using the IEO method, we study the vibration modes of crystal lattice, which are affected by absorbing an atom with mass m_{0}, which is different from the mass of atom in the crystal. Moreover, the attractive potential constantβ_{0} of the lattice surface differs from the inner constantβ. With the help of invariant eigen-operator method, we deduce the vibration mode ω=√(2β(1-cosh α))/ħm, where α=ln[-(mβ_{0}+m_{0}(-2β+β_{0})+√β_{0}√-4 mm_{0}β+(m+m_{0})^{2}β_{0})/2m_{0}β]. Our numerical results show that vibration mode ω depends not only on the absorption potential and the mass of the absorbed atom, but also on the mass of the lattice atom and the inner potential. In general, by discussing the vibration modes via some numerical solutions or approximate methods, we show the relations between the system vibration modes with different parameters which describe the environment influences. These results can deepen our understanding of quantum Brownian motion and demonstrate the applicability of the IEO method.

Quantum phase gate is a necessary quantum component for quantum coding and quantum computing. Compared with the traditional gate circuit, quantum phase gate has the characteristics of unitarity and reversibility. Therefore, we construct a model of mutual coupling between a single Λ -type three-level atom and two superconducting resonators, which is connected by a capacitor. By separately controlling the disconnection time and connection time of the two superconducting resonators in the model as well as by controlling the magnetic flux of the superconducting quantum interference device (SQUID) to make a certain transition energy level of the Λ -type three-level atom equal the relevant resonance energy level, the interaction between the two levels can be achieved and the system can be manipulated. Afterwards, we propose four control schemes for implementing the controlled-Z gate through a three-step operation, and two operation schemes for implementing swap gate through a four-step operation. At the same time, the numerical simulations of fidelity are implemented for the first operation scheme for controlling the Z-gate. The results of fidelity discussion show that the fidelity of this scheme is 96.67% through the running time of 20.83 ns, thus it proves that this scheme is theoretically feasible. The increase in the three attenuation parameters, i.e., attenuation rate, relaxation rate, and phase shift ratio, will reduce the fidelity of the system, while the increase in coupling strength will cut down the time of system operation, thus reducing the influence of attenuation parameters and improving the system fidelity.In this paper we present a quantum phase gate scheme in which two superconducting resonators and a Λ -type three-level atom are coupled with two capacitors. Since the experimental setup is simplified, it is important to reduce the coherence between devices. In addition, the solution has no restriction on the strength of the classic pulse principally, through which the system operates faster and the fidelity of the phase gate is improved effectively.

Spiral waves are a particular form of propagating waves, which rotate around a center point known as a rotor. Spiral waves have been found to play an important role in cardiac arrhythmia. Using voltage-sensitive dye imaging, one can find that spiral waves and plannar waves can occur in the mammalian cortex in vivo. The electrode array conduces to discovering that the seizures may manifest as recurrent spiral waves which propagate in the neocortex. However, the formation mechanism of the ordered waves and its potential function in the nervous system remain uncertain. In order to understand the formation mechanism of the ordered waves, we construct a double-layer two-dimensional -network of neuron, which is composed of nearest-neighbor excitatory coupling and long-range inhibitory coupling layers. The inhibitory grid points account for 25% of total number of grid points in the network. We propose a modified Hindmarsh-Rose neuron model to study whether differently ordered waves can occur spontaneously in the chaotic neuronal network evolving from the initial state with a random phase distribution. The numerical simulation results show that when the inhibitory coupling strength is small the spontaneous formation of ordered wave does not generally appear in the network. The larger inhibitory coupling strength, the more easily the system generates an ordered wave for sufficiently large strength of excitatory coupling. The appearance of differently ordered waves is closely related to the initial state of the system and coupling strength. As the excitatory and inhibitory coupling strengths are appropriately selected, the system can spontaneously generate the maze pattern, planar wave, single spiral wave, multiple spiral wave, paired spiral waves rotating in the opposite directions, two-arm spiral wave, target wave and inward square wave and so on. The probability for spontaneously forming a single spiral wave is far less than that for forming a small spiral wave. The occurrence probabilities of spiral wave, maze pattern and inward square wave reach 27.5%, 21.5% and 10%, respectively. The maze pattern is composed of many plane waves with different propagation directions. The occurrence probabilities of other ordered waves are quite small. These results conduce to understanding the self-organization phenomena occurring in the cerebral cortex.

Due to the novel physical properties induced by the strong spin orbit coupling and band inversions in the energy band structure, two-dimensional topological insulator has become a hot research point in the field of condensed matter physics and material science in recent years. Particularly, two-dimensional topological insulator may host exotic Majorana fermionic excitations in its edge state if superconductivity is introduced. Bi thin film with (111) orientation proves to be a two-dimensional topological insulator both in theory and in experiment. However, the topological nature of Bi thin film with (110) orientation has not yet been confirmed. In this study, high quality Bi(110) thin films are successfully prepared on superconductor NbSe_{2} surfaces, by the molecular beam epitaxial technology at ambient temperature and a low deposition rate (~24℃,~3 min/bilayer). The morphologies and electronic properties of the samples are studied by using scanning tunneling microscopy and spectroscopy. The experimental results reveal that the growth mode changes from bilayer (BL) in BL mode to monolayer (ML) in ML mode. Such transition takes place at a critical height of about 4 BLs. The mechanism of the growth mode transition is believed to be induced by the drastic variation of the surface energies of the thin films with different thickness values. Due to the large coverage of Bi(110) film on the NbSe_{2} substrate, it is almost impossible to find the exposed areas of NbSe_{2} substrate surface in practice. Especially on the sample with a large number of layers of Bi thin film, it is hard to directly determine the number of layers for each film. Hence, the critical thickness could be only estimated by controlling the deposition time and growth rate combining with the measurements of stage height of the film. The nearly identical local density of states wherever measured in the interior of a terrace or at the step edges can be discerned from the dI/dV spectra, which is thus hard to corroborate with non-trivial topology in either BL or ML thick Bi(110) film. The superconductivity induced by proximity effect from the superconducting substrate NbSe_{2} is also observed on the thin films. Through Bardeen-Cooper-Schrieffer type data fitting, the superconducting gap on the Bi thin film is estimated at about 0.5 meV. In addition, the quantum well state, which is often observed in thin films, is also revealed from the Bi(110) thin films, whose characteristic is equal energy spacing between peaks in dI/dV spectra. Noticeably, the spectral shapes of BL and ML are similar, and the local density of states from adjacent film layers displays an approximate πup phase shift.

The reflected neutrons from the wall of the reactor have a significant effect on the waveform of the fast burst reactor. The leakage neutrons from the reactor core have a certain probability that they will come back. Their return time displays a continuous distribution because of the difference in energy among the reflected neutrons. In the stable state, the influence of the reflected neutrons is not obvious. However, in a prompt state, it is obvious because the reflected neutrons are not synchronized with the neutrons in the reactor core, which leads to some strange phenomena in experiment. For example, in the process of erupting a fission burst in a metal reactor, the number of neutrons in core increases very rapidly, while the return time of reflected neutrons lags behind, which causes the falling edge to slow down. The two-region kinetic model, which divides the reactor core into a fission region and a reflected region, is generally used to study the reflected reactor. The traditional two-region kinetic model only takes into account the interaction probability between the two regions but the time property of the interaction is not considered at all. Therefore, the traditional two-region model can well describe the stable state process rather than the prompt one. In the early stage, the delayed neutron approximation method was used to study the reflected neutron problem of metal burst reactors. Although some parameters were obtained to be in accordance with the experimental results, there existed a significant difference in behavior between delayed neutrons and reflected neutrons. In this paper, we present a time-dependent two-region model which can effectively describe the behavior of the reflected neutrons in both stable and prompt states. Firstly, we use the Monte-Carlo method to calculate the returning behavior of one leakage neutron from the reactor core. The equivalent eigen source is obtained by solving the kinetic equation with the Monte-Carlo calculating result. This source, including time information, causes the same effect as that of one leakage neutron in the reactor. Secondly, we establish the kinetic equation with reflection effect by introducing the eigen source. In short, the reflected neutrons are treated as an equivalent neutron source. The waveform acquired through solving the equation is consistent with the experiment data of CFBR-Ⅱ, which reasonably describes the experimental phenomenon of falling edge slow-down and plateau power increase.

The inhomogeneous burnup equation is often used for describing the time evolution of nuclides' depletion in nuclear systems which have a significant nuclide migration effect. However, lots of burnup calculations codes only deal with the homogeneous cases instead of the inhomogeneous ones, among them there are a few codes that can work only when the inhomogeneous term of the equation is constant. Based on the condition that the inhomogeneous term can be approximated by finite-order Taylor expansion, two methods are introduced to solve the inhomogeneous burnup equation whose inhomogeneous term is time dependent. For the first method, the transmutation trajectory analysis method is used to decompose the connections between nuclides into linear chains, for one chain the analytical solution is derived strictly by using the Laplace transform. For the second method, a solution of the inhomogeneous equation in the form of summation of infinite matrix series is first derived, and then the sum function of the series is found. Furthermore, the different-order nearly-best rational approximation function of the sum function is found by using Carathéodory-Fejér method. The error between the sum function and the rational function fluctuates in a certain range without exceeding a limit value, while the maximum error decreases exponentially with the order of rational function increasing. By adopting the nearly-best rational approximation, the summation of infinite matrix series converts into a finite expansion of matrix fraction, which is much easier to deal with. These two methods are implemented in the burnup calculation code JBURN and numerical tests are done through using two examples. The first example is a small-scale matrix example and the result shows that the results from the two methods agree well in at least 6 decimal precision together with the results from the reference solution. The second example is a large-scale problem based on real nuclides' reaction database, and the result shows that less than 1% among all nuclides have a deviation larger than 10% between two methods, while about 8% nuclides have a deviation larger than 0.01% and the remaining ones have a deviation smaller than 0.01%. These results validate the correctness and accuracy for each of the two methods. Finally, this paper provides a possible implementation process for solving inhomogeneous burnup equations which have other time-dependent forms of inhomogeneous term.

A systematical knowledge of the satellite and hypersatellite structures of X-ray transitions is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed explanation of the complex structures of X-ray satellites and hypersatellites are crucial for understanding the X-ray emission mechanism and the hollow atom formation mechanism. In this paper, the K_{α} and K_{β} X-ray satellite and hypersatellite structure are theoretically studied for hollow argon atoms with the relativistic multiconfiguration Dirac-Fock (MCDF) method, which includes the Breit and quantum electro-dynamics (QED) corrections. To check the applicability of the method, the transition energies and rates of the diagram lines for Ar are calculated,. and the results are in agreement with previously published data. Then the MCDF calculations of the transition energies and probabilities of K_{α 1, 2} (K →L_{3, 2}) and K_{β 1, 3} (K → M_{3, 2}) X-ray satellites and hypersatellites, which originate from the argon atoms with additional vacancies in the L shell, are carried out. To obtain the overall profile of the K X-ray spectrum, the diagram lines are integrated with the satellites and hypersatellites on the assumption that the intensity is proportional to the corresponding transition probability and each discrete line has a Gaussian distribution profile with a full width at half maximum (FWHM) value of 20 eV. From the convoluted profile, we can obtain the dependence of the average transition energy and relative transition intensity of the satellites and hypersatellites on the initial hollow configuration. It is found that the transition energy shift increases linearly with the number of spectator vacancies in the L shell increasing. For instance, the energy shift of the K_{α} satellite caused by L-shell hole is about 20 eV, and that of the K_{β} satellite is 48 eV. While for hypersatellite, the energy shift increases greatly due to the double ionization in the K shell. The energy shift increment of K_{α} and K_{β} hypersatellites corresponding to L vacancy are 21 and 52 eV, respectively. Finally, four simple empirical formulae for estimating the energy shifts of the K_{α}, K_{β} X-ray satellites and hypersatellite for Ar atom with any number of L-shells vacancies are deduced by using the least square method. These results are useful in explaining various K X-ray spectra and better understanding the collision process.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

In the hypersonic flight, the air surrounding an aircraft under the effect of high temperature will be ionized. The ionized gas is called plasma. Because of the influence of interaction between electromagnetic wave, in some cases the communication will be interrupted. High temperature effect is an important characteristic of the plasma. Therefore, the study of terahertz wave propagation in high temperature plasma is of great significance. In this paper, the transmission of terahertz wave in a high temperature plasma slab is studied. Generally, high temperature plasma is an anisotropic medium. The electromagnetic wave propagates in anisotropic high-temperature plasma and forms left-hand circular polarization mode or right-hand circular polarization (RCP) mode. It is found that the RCP wave can exhibit some novel characteristics, such as the forbidden band transmission characteristics, which is discovered in this paper. The transmission characteristics of terahertz wave in high temperature plasma are studied analytically. The results show that when the frequency of terahertz wave is lower than plasma frequency, the wave cannot be propagated in high temperature plasma, and it shows a stopband characteristic. When the frequency is higher, it can be transmitted through the plasma, and it presents a passband characteristic. These are consistent with the propagation characteristics of electromagnetic waves in cold plasma. However, some characteristics in high temperature plasma are different from those in the cold plasma. In high temperature plasma, the transmission characteristics are influenced by the electron temperature and external magnetic field. When the two parameters are chosen appropriately, a sharp transmission peak will be produced in the stopband. This phenomenon has never been found in cold plasma models before. And the paper will discuss this problem by the two influencing factors. It is also found that the frequency of the transmission peak is affected by magnetic field, and the peak amplitude is influenced by electron temperature. The electron temperatures at high transmittance (transmittance is about 1) under different applied magnetic fields are calculated. In order to study the law embodied in the data, the method of data fitting is adopted. And the formula of transmission peak frequency is obtained by curve fitting. The fitting results show that the transmission peak frequency is proportional to the external magnetic field. The relationship between peak electron temperature and external magnetic field is exponential. Finally, the fitting formula is verified by the finite-difference time-domain method. The numerical results are in good agreement with the analytical solution results, which proves the correctness of the work.

Due to unnoticeable changes in complex refractive index of tissue under varied pathological and physiological states, the traditional optical coherence tomography (OCT) is deficient in molecular characterization. In this paper, the stimulated-emission based optical coherence tomography is proposed, which provides both molecular contrast and scattering contrast OCT imaging simultaneously. Based on the established ultra-high resolution spectral domain OCT system, a pump-probe spectral domain OCT system with a single wide-bandwidth light source is developed through an added modulated pump beam via spectrum splitting. In addition, the theory about the stimulated-emission signal and the image formulation under the modulated pump beam is presented. The coherent detection of the transient stimulated emission is realized by the developed pump-probe spectral domain OCT system. With the stimulated-emission OCT signal and the traditional OCT signal obtained at the same time, molecular contrast OCT images of the samples consisting of nitride powder are reconstructed successfully.

The development of nanoscale single-molecule localization and tracking technology for multiple bio-molecules in intact cells has important significance for studying the dynamic process in life process. Since most of cells are several microns in depth, but the focal depth of traditional optical microscopes are less than one micron, the limited depth of field is the main drawback of conventional single molecular localization microscopy that prevents observation and tracking of multiple molecules in intact cells. In this paper, based on the wavefront coding technique, a new type of holographic phase plate with high efficiency is proposed and designed to extend the depth of field of single molecular localization microscopy, which combines the distorted multi-value pure-phase grating (DMVPPG) with the double-helix point spread function (DH-PSF). The DMVPPG can be used to realize multiplane imaging of several tens of layers of a sample in a single detection plane. And the DH-PSF is an engineered point spread function which encodes the lateral and axial position with high precision of a molecule in the center of its two lobes and the angle between them respectively. Using the combined holographic phase plate, the molecules in dozens layers of a whole cell can be simultaneously imaged on the same detection plane with DH-PSF. Not only can the axial resolving power be improved, but the imaging depth can also be extended without scanning. Adding such a holographic phase plate to the imaging path, the limited imaging depth problem in single-molecule-localization microscopy can be solved without sacrificing the localization accuracy. The proposed new type of holographic phase plate can also be implemented with a spatial light modulator. In the following numerical simulation experiments, the designed holographic phase plate is composed of 600×600 pixels with a pixel size of 10 μm. The distance between two adjacent focal planes is designed to be 0.5 μm. Such a holographic phase plate is placed on the Fourier transform plane of the detection light path. When an emitter is located on the focal plane, it can be imaged as two lobes without rotation in a center area of the field of view. If an emitter is -6 μm away from the focal plane, the DH-PSF appears in the upper-left area of the field of view. Simulation results demonstrate that a total of 25 sample layers can be simultaneously imaged on the single detection plane and the 12 μm detection range can be achieved, thus proving the feasibility of this method.

Continuous variable (CV) audio-band frequency squeezed states at the fiber telecommunication wavelength is an important quantum resource for the practical applications based on optical fiber. As is well known, the optical power attenuation and phase diffusion effect of light at 1.3 μm in standard telecommunication fibres are low and small, respectively. The audio-band frequency squeezed light at 1.34 μm can be utilized to realize quantum precision measurement, such as quantum-enhanced sensing in the low-frequency range, laser interferometer for gravitational wave detection. In this paper, CV audio-band frequency vacuum squeezed states at 1.3 μm are experimentally generated by using a type-I degenerate optical parametric oscillator (DOPO) below the threshold. A home-made continuous-wave single-frequency dual-wavelength (671 nm and 1.34 μm) Nd:YVO_{4}/LBO laser is used as a pump source for DOPO based on a type-I quasi-phase-matched periodically poled KTiOPO_{4} (PPKTP) crystal. Mode cleaners with a finesse of 400 and linewidth of 0.75 MHz are used to filter the noise of lasers at 671 nm and 1.34 μm, respectively. The intensity noises of the two lasers reach a shot noise level for analysis frequencies higher than 1.0 MHz and their phase noises reach shot noise level for analysis frequencies higher than 1.3 MHz, respectively. The low noise single-frequency 671 nm laser is utilized as a pump of the DOPO. The threshold power of the DOPO is 450 mW. In order to detect the audio-band frequency vacuum squeezed states, the power of local oscillator of a homodyne detector system is optimized to 60 μupW. Furthermore, the effect of common mode rejection ratio (CMRR) of detectors is discussed in detecting the audio-band frequency vacuum squeezed states. Improvement of CMRR of detectors is a good way to detect the audio-band frequency vacuum squeezed states effectively. When the phase matching temperature of PPKTP crystal is controlled at 53℃ by using a home-made temperature controller and the pump power is 95 mW, the vacuum squeezed states are generated at analysis frequency ranging from 8-100 kHz. A maximum measured squeeze of 5.0 dB is obtained at analysis frequency of 36 kHz. A 3.0 dB squeezed light is obtained at an audio-band frequency of 8 kHz.

In order to study the spherical aberration of thermal lens when the laser crystal is pumped with the pump light distributed differently and the pump light under the end-pumping condition, in this paper we establish a single-ended pump and constant temperature thermal model to analyze the working characteristics of the Nd:YVO_{4} crystal. The steady state heat conduction equation and Zernike polynomials are solved, and the relationship between thermal spherical aberration and distribution of pump laser is established. The model is used in simulation, and the simulation results are further analyzed theoretically, showing that under the same pump power, the spherical aberration is greatest when the pump beam is of 2-order super-Gaussian distribution. The spherical aberration decreases with the increase of pump distribution coefficient k (except the Gaussian distribution). With the increase of pump power, the influence of pump distribution coefficient k on spherical aberration is aggravated gradually, and the difference in spherical aberration caused by different values of distribution coefficient k increases gradually. The range of strongest laser power of the 2-order super-Gaussian distribution pump is analyzed and simulated. Under same pump power, the maximum range of the strongest laser power of 2-order super-Gaussian distribution pump is 0.3-0.63 times the Gauss radius. The research methods and conclusions obtained in this paper have universal applicability and can be used for quantitatively analyzing the temperature distributions, thermal deformations, optical path difference distributions, and spherical aberration distributions of other laser crystals. At the same time, this study also provides a theoretical reference for improving spherical aberration from the perspective of changing the distribution of pump light and the laser output characteristics.

The high power supercontinuum from femtosecond filamentation has attracted great attention for recent years due to its various applications. In our previous researches, we have used microlens array to obtain filament-array in fused silica and to generate the high spectral power supercontinuum. To further improve the ability to generate the high power supercontinuum by using microlens array, in this work we adopt flattened femtosecond laser beam with a flat-top energy distribution to generate filament-array in fused silica and supercontinuum. By using a laser beam shaping system consisting of aspherical lenses, the Gaussian intensity distribution of initial femtosecond laser beam is converted into a flat-top distribution. The flattened laser beam is focused by a microlens array into a fused silica block, and consequently a filament array is formed in the block. Our experimental results show that compared with the filaments formed by a Gaussian laser beam, the filaments formed by the flattened beam have a uniform distribution and almost the same onset due to the initial uniform energy distribution across the section of the laser beam. Furthermore, the spectral stability of supercontinuum emission is used to evaluate the damage of the fused silica block. It is demonstrated that the flattened beam with a pulse energy of 1.9 mJ does not induce permanent damage to the fused silica block, while the Gaussian beam with a relatively low pulse energy of 1.46 mJ leads to the damage to the block. Therefore, a higher incident laser pulse energy is allowed in the case of flattened laser beam, and consequently stronger supercontinuum generation than in the case of the Gaussian laser beam can be expected. In our experiments, the relative spectral intensity of flattened beam generated supercontinuum in the visible range is about twice higher than that for the Gaussian beam case. The conversion efficiencies of the supercontinuum for the two kinds of laser beams are further analyzed. The conversion efficiencies are 49% and 55% for the cases of Gaussian and flattened beams respectively. In this work, we demonstrate the formation of filament array with uniform distribution in fused silica, and, as a proof of principle, we also demonstrate the high power supercontinuum generation with high conversion efficiency from the filamentation, by using flattened femtosecond laser beam as the incident laser and microlens array as the focusing element. This approach provides a way to obtain a high power femtosecond supercontinuum source which is of great importance in many applications such as some absorption spectroscopies based on coherent supercontinuum light.

In inertial confinement facilities, the irradiation uniformity of the lasers is highly required to suppress the laser plasma instabilities. In order to realize the ultrafast smoothing of the focal spot, a novel scheme by using an optical Kerr medium and a high-power pump laser is proposed. The principle of the ultrafast beam smoothing scheme is to change the refractive index of the Kerr medium with the pump laser, which appends a spatiotemporal wavefront to the main laser beam in the beamline. The dynamic wavefront modulation of the main laser beam further makes the speckles within the focal spot redistributed rapidly and complicatedly, which contributes to the smoothing of the focal spot. A Gaussian beam with a temporal profile of a Gaussian pulse train is obliquely incident on the optical Kerr medium at a small angle. As a result, the spherical wavefront of the main laser beam is rapidly changed in the direction perpendicular to the propagation direction of the main laser beam. Thus the transverse and the radial redistribution of the speckles within the focal spot are both generated simultaneously. Comparing with the simple radial smoothing scheme, the spherical phase of the main laser beam always changes perpendicularly to the propagation direction in the novel scheme, and thus achieving a more stable beam smoothing effect. Besides, the phase gradient in the center region of the main laser beam changes greatly over time, making the irradiation uniformity on the focal plane further improved. The optimal deflection angle in the optical Kerr medium of the pump laser is obtained. By controlling the deflection angle of the pump laser, the spatial period of the pump laser in the transverse direction is set to be equal to the waist diameter of the main laser, which is identical with one color cycle in the typical smoothing by spectral dispersion technique. Moreover, a relatively low control precision of the deflection angle of the pump laser is required.

Acoustic wave propagation in polydisperse bubbly liquids is relevant to diverse applications, such as ship propellers, underwater explosions, and biomedical applications. The simulation of bubbly liquids can date back to Foldy who presented a general theory. In the linear regime, two frequently used models for bubbly liquids are based on the continuum theory and on the multiple scattering theory. Under the homogenization-based assumption, models based on the volume-averaged equations or on the ensemble-averaged equations are designed to find the solutions of a given two-phase flow. The effective wave number is derived through the linearization of these equations. A second approach to the problem of linear wave propagation utilizes the multiple scattering theory. Bubbles are treated as point-like scatterers, and the total field at any location can be predicted by multiple scattering of scatterers. However, in most of experimental researches, the comparison between the approaches and the experimental results is not satisfactory for frequencies near the peak of phase speed and attenuation. In fact, the discrepancies between measurements and approaches are irregular, and the explanations of these discrepancies need further studying. We indicate that such a discrepancy should be attributed to an implicit assumption in these approaches:the bubbles are spatially uniform distribution and statistically independent of each other. In contrast, the complex bubble structures can be observed in many practical bubbly liquids which have important consequences for the acoustic wave propagation. In this paper, our intent is to model the effect of small bubble cluster on linear-wave propagation in bubbly liquids using the self-consistent method. The quasi-crystal approximation is applied to the self-consistent method, and the effective wave number is derived. According to the experimental results, the small clusters of bubbles often exist in bubbly liquids. Therefore, a three-dimensional random model, the Neyman-Scott point process, is proposed to simulate bubbly liquid with the cluster structure. Using this method, we study the influence of such a phenomenon on acoustic dispersion and attenuation relation. A formula for effective wavenumber in clustered bubbly liquid is derived. Compared with the results from the equation of Commander and Prosperetti[J. Acoust. Soc. Am.85 732 (1989)], our results show that the clustering can suppress peaks in the attenuation and the phase velocity, each of which is a function of frequency. Further, we provide a numerical method. A clustered bubbly liquid is simulated with strict mathematical method and the statistical information is obtained through ratio-unbiased statistical approach. Using such a method, we quantificationally analyze the influence of estimated value on predictions.

Various line array configurations are evaluated for the source localization performance based on the analysis of mode decomposition matrix in this paper. The guideline of array shape design focuses on improving the localization performance of matched filed processing, meanwhile reducing the difficulty of deploying equipment in practical experiments. In the shallow water environment, when the environment is well known, the source localization result can be obtained by matched field processing algorithms effectively, but the source localization performance is affected by the array parameters, such as array length, the number of sensors, and the configurations of various horizontal and vertical line arrays. The modal decomposition method provides a useful insight into the questions of how many modes are needed and how to design the array to resolve the modes. Therefore, the method of utilizing a normal mode acoustic propagation model to decompose mode is proposed by vertical line array, horizontal line array and combined array respectively. Then we can evaluate the source localization performance of various line array configurations by studying the characteristic of normal mode decomposition matrix, thus establishing a qualitative or even quantitative relationship between each other. The more the normal mode decomposition matrix tends to be diagonalized, the better performance of line array localization will be obtained. Simulation results show that the localization performance of matched field processing with the combined arrays will be severely degraded when the mode amplitudes cannot be accurately deduced by one of the sub-arrays. Considering the requirements for the practical experiments and various environments, the source localization performance of short vertical line array and combined array are mainly discussed in this paper. The combined array can increase the azimuth and depth information of the source and realize three-dimensional target detection while the vertical array provides range-depth information and the horizontal array provides bearing information. Simulation result indicates that the design guidelines based on the normal mode decomposition are appropriate for arrays employed for matched filed processing. Meanwhile, the combined arrays perform better than the short vertical array, which is benefited by the horizontal array's suppressing the side lobes, which leads the ratio of peak to sidelobe to increase, and thus improving the location accuracy. The values of localization accuracy of combined arrays are all above 90% according to the simulation experiment. Take the practical application into account, the combined array is undoubtedly a compromise choice for the localization performance and the test complexity.

In this paper, the experiments about the boundary layer transition on a 7° half-angle straight cone are carried out in a Mach 6 low-noise wind tunnel. The wall fluctuation pressure is measured by the transducer with megahertz response frequency, and the development process of the disturbance in the hypersonic boundary layer is investigated. The peaks in power spectrum density of the fluctuation pressure are related to the second mode wave, which is indicated through verifying the existence of the longitudinal acoustic second mode waves reflected between the relative sonic line and the solid wall by the flow visualization result. The wavelength and the characteristic frequency of the second mode wave in the hypersonic boundary layer are found to be greatly influenced by Reynolds number. The characteristic frequency of the second mode wave changes from 55 kHz to about 226 kHz when the Reynolds number increases from 2×10^{6} m^{-1} to 8×10^{6} m^{-1}. The second mode wave appears at the position closer to the upstream with a higher disturbance growth speed under higher unit Reynolds number. As the second mode wave propagates downstream, its characteristic frequency gradually decreases. The freestream noise level also has a great influence on the development of the disturbance wave. The characteristic frequency of the second mode wave decreases significantly in a relatively quiet environment. The cross-correlation analysis results show that the propagation velocity of the second mode wave in the boundary layer is about 0.8-0.9 times the local mainstream velocity. The wavelength of the second mode wave is about 5.01 mm at the location from X=380 mm to X=440 mm when the unit Reynolds number is 5×10^{6} m^{-1}. At 1° angle of attack, the development of the boundary layer on the windward side and the leeward side of the cone are significantly different. The characteristic frequency of the second mode wave in the leeward surface is almost the same as the result at zero angle of attack under the same unit Reynolds number. However, the position of the second mode wave is greatly advanced. Results show that the disturbance development in the boundary layer of the leeward surface is accelerated, and the second mode wave appears at the position closer to the upstream. The velocity of the second mode wave in the leeward surface rapidly increases when it propagates downstream. While on the windward side, the disturbance development is inhibited and the second mode wave has a higher characteristic frequency. The wavelength of second mode wave also decreases obviously.

In hypersonic flight, a very high temperature area can form ahead of the nose of aerocraft due to the shock aerodynamic heating, which leads to air weakly ionized. Many researchers have demonstrated that it is effective to control flow by utilizing the interaction between weakly ionized air and a magnetic field. Most of previous researches focus on magnetohydrodynamic (MHD) heat shield, because the Lorentz force can increase the shock stand-off distance, further reduce convective heat flux. In this study, the MHD force effect is mainly considered, and the MHD drag characters under different types of magnetic field are discussed. The numerical simulation of hypersonic hemispherical flow field with external magnetic field is carried out by using a low magnetic-Reynolds MHD model. Three kinds of simple ideal magnetic fields (axial, radial and circle uniformly distributed magnetic field) are compared and analyzed. The influence and mechanism of the structure of the flow field, the aerodynamic drag and the Lorentz resistance of different magnetic fields are analyzed. It is found that under the radial ‘extrusion’ effect of the axial magnetic field, the shock wave shape is protruded and a ‘saturation phenomenon’ of pressure exists on the wall; the radial magnetic field has the axial ‘extrusion’ effect, the larger magnetic field intensity will lead to the formation of the high temperature area of the shoulder, and the induced electric field in the circle magnetic field leads to the poor effect of increasing resistance. Then the flow fields of two special magnetic fields (dipole magnetic field and solenoid magnetic field) are compared, and the radial ‘dilatation’ effect is found to be different from the ideal magnetic field. Compared with the Lorentz force under the different magnetic fields, the Lorentz force in the radial magnetic field is found to be concentrated in the high temperature area of the shoulder, and the Lorentz force is generally small under the circle magnetic field. The direction near the standing point will have an adverse effect, i.e., the resistance increases. In the specially distributed magnetic field, the direction of Lorentz force near the shoulder is approximately parallel to that of the shoulder, while the direction near the standing point is approximately perpendicular to the axis. Compared with the dipole magnetic field, the solenoid magnetic field with high Lorentz force region is close to the shoulder, so it will have good resistance enhancement effect. The influence of the dipole magnetic field on the wall pressure is weak. The effect of increasing resistance, caused by the magnetic field induced electric field, evolves from weak to strong in the following sequence:radial magnetic field, solenoid magnetic field, axial magnetic field, dipole magnetic field and circle magnetic field.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Induced spatial incoherence technology is a beam-smoothing method with its own unique advantages for laser driven inertial confinement fusion. However, simply using the induced spatial incoherent method will induce a strong near-field intensity spatial modulation, which will threaten the safety of the operation and severely limit the maximum output capability of the device. This is also one of the main technical obstacles to applying induced spatial incoherence to a high-power laser device used for fusion. In this paper, a technique of smoothing the near-field spatial intensity modulation caused by induced spatial incoherence is introduced. By using a two-lens filter system, a homogeneous and stable near-field intensity distribution can be obtained on the premise of reserving the innate advantages of induced spatial incoherence (better far-field smoothing characteristics), thereby avoiding the damage to devices and limitation to output capacity in high power laser system using induced spatial incoherence. Based on the theoretical modeling and numerical analysis, using modulation degree, softening factor, and transmittance as evaluation parameters, the near-field light characters with three kinds of filter apertures, such as square, round, and Gaussian, are compared and analyzed. Finally, in a typical optimization result there are used 16×16 induced spatial incoherent divisions and a square aperture with 0.8 times diffraction limit width. In this case, the near-field intensity distribution is uniform, and at the same time, good smoothing effect on far-field and a high energy utilization rate are ensured. On this basis, according to the actual application of the device, the influence of the collimation error on the near-field intensity distribution is further analyzed. The results show that as long as the collimation error is less than 0.1 times the diffraction limit, the near-field quality will not be affected. The simulation analysis of the focal spot obtained by induced spatial incoherence shows that the addition of the filtering system can further improve the low frequency uniformity of the focal spot.

Quantum entanglement the most important part of quantum information theory, represents the intrinsic property of quantum states. It is a magical physical phenomenon in the form of nonlocality in the multi quantum system. The entanglement entropy as a measure of quantum information, has become an important tool, which provides a new research method for various subjects in physics. The study of the notion of quantum entanglement can provide a tool for understanding the cosmological features.
In this work, we consider the cosmological applications of the entanglement in order to understand the cosmological dynamics from the entanglement point of view. The relation between the quantum information theory and the cosmology is studied. Employing Fermi normal coordinates (FNC) and conformal Fermi coordinates, we establish a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker universe and entanglement. Assuming that the entanglement entropy in a geodesic ball is maximized in a fixed volume and the entanglement is the basic element of the spacetime, we derive Friedmann equations from the first law of entanglement. Friedmann equations are first derived in the Fermi normal coordinate system, where the diamond size l is much smaller than the local curvature length, but still much larger than Planck scale l_{p}. If the diamond size is comparable to the UV scale l_{UV}, the quantum gravity effect becomes strong. Then we extend the discussion about the area deficit of the geodesic ball so that a freely falling observer can report observations and local experiments. In the cosmological context, the FNC are only valid on a scale much smaller than the Hubble horizon. Then we relax the small ball limitation by introducing conformal Fermi coordinates (CFCs). In the CFC system, we mainly focus on the flat universe with vanishing curvature of the space k=0. The Friedmann equations are derived in the CFC system. From the first law of entanglement the emergence of gravity can be described by the change in entanglement δ<S_{A}> caused by matter δ<H_{A}> angle.
In this paper, we study the cosmology in a new framework with the viewpoint that spacetime geometry is viewed as an entanglement structure of the microscopic quantum state, and derive the Friedmann equations for the universe from the first law of entanglement We also briefly review the first law of entanglement. The study shows that there is a basic relation between the gravitation and quantum entanglement, which is valid for the solution of the gravitational field equation.