Hydrogen is the lightest and most abundant element in the universe. Ever since Wigner and Huntington's prediction that pressure induced metallization might happen in solid hydrogen, understanding the hydrogen phase diagram has become one of the greatest challenges in condensed matter and high pressure physics. The light mass of hydrogen means that the nuclear quantum effects could be important in describing this phase diagram under high pressures. Numerical evaluations of their contributions to the structural, vibrational, and energetic properties, however, are difficult and up to now most of the theoretical simulations still remain classical. This is particularly true for the energetic properties. When the free-energies of different phases are compared in determining the ground state structure of the system at a given pressure and temperature, most of the theoretical simulations remain classical. When nuclear quantum effects must be taken into account, one often resorts to the harmonic approximation. In the very rare case, the anharmonic contributions from the nuclear statistical effects are considered by using a combination of the thermodynamic integration and the at initio molecular dynamics methods, which helps to include the classical nuclear anharmonic effects. Quantum nuclear anharmonic effects, however, are completely untouched. Here, using a self-developed combination of the thermodynamic integration and the at initio path-integral molecular dynamics methods, we calculated the free-energies of the high pressure hydrogen at 100 K from 200 GPa to 300 GPa. The harmonic lattice was taken as the reference and the Cmca phase of the solid hydrogen was chosen. When the bead number of the path-integral (P) equals one, our approach reaches the so-called classical limit. Upon increasing P until the results are converged, our approach reaches the limit when both classical and quantum nuclear anharmonic effects are included. Therefore, by comparing the free-energy of the harmonic lattice and the thermodynamic integration results at P equals one, we isolate the classical nuclear anharmonic effects. By comparing the thermodynamic integration results at P equals one and with those when they are converged with respect to P, we isolate the quantum nuclear anharmonic effects in a very clean manner. Our calculations show that the classical nuclear anharmonic contributions to the free-energy are negligible at this low temperature. Those contributions from the quantum nuclear anharmonic effects, however, are as large as ～15 meV per atom. This value also increases with pressure. This study presents an algorithm to quantitatively calculate the quantum contribution of the nuclear motion to free-energy beyond the often used harmonic approximation. The large numbers we got obtained also indicate that such quantum nuclear anharmonic effects are important in describing the phase diagram of hydrogen, at/above the pressures studied.

Dirac cones and Dirac points are found at the K (K') points in the Brillouin zones of electronic and classical waves systems with hexagonal or triangular lattices. Accompanying the conical dispersions, there are many intriguing phenomena including quantum Hall effect, Zitterbewegung and Klein tunneling. Such Dirac cones at the Brillouin zone boundary are the consequences of the lattice symmetry and time reversal symmetry. Conical dispersions are difficult to form in the zone center because of time reversal symmetry, which generally requires the band dispersions to be quadratic at k=0. However, the conical dispersions with a triply degenerate state at k=0 can be realized in two dimensional (2D) photonic crystal (PC) using accidental degeneracy. The triply degenerate state consists of two linear bands that generate Dirac cones and an additional flat band intersecting at the Dirac point. If the triply degenerate state is derived from the monopolar and dipolar excitations, effective medium theory can relate this 2D PC to a double zero-refractive-index material with effective permittivity and permeability equal to zero simultaneously. There is hence a subtle relationship between two seemingly unrelated concepts: Dirac-like cone and zero-refractive index. The all-dielectric “double zero”-refractive-index material has advantage over metallic zero-index metamaterials which are usually poorly impedance matched to the background and are lossy in high frequencies. The Dirac-like cone zero-index materials have impedances that can tune to match the background material and the loss is small as the system has an all-dielectric construction, enabling the possibility of realizing zero refractive index in optical frequencies. The realization of Dirac-like cones at k=0 can be extended from the electromagnetic wave system to acoustic and elastic wave systems and effective medium theory can also be applied to relate these systems to zero-index materials. The concept of Dirac/Dirac-like cone is intrinsically 2D. However, using accidental degeneracy and special symmetries, the concept of Dirac-like point can be extended from two to three dimensions in electromagnetic and acoustic waves. Effective medium theory is also applicable to these systems, and these systems can be related to isotropic media with effectively zero refractive indices. One interesting implication of Dirac-like cones in 2D PC is the existence of robust interface states. The existence of interface states is not a trivial problem and there is usually no assurance that localized state can be found at the boundary of photonic or phononic crystal. In order to create an interface state, one usually needs to decorate the interface with strong perturbations. Recently, it is found that interface state can always be found at the boundary separating two semi-infinite PCs which have their system parameters slightly perturbed from the Dirac-like cone formation condition. The assured existence of interface states in such a system can be explained by the sign of the surface impedance of the PCs on either side of the boundary which can be derived using a layer-by-layer multiple scattering theory. In a deeper level, the existence of the interface state can be accounted for by the geometric properties of the bulk band. It turns out that the geometric phases of the bulk band determine the surface impedance within the frequency range of the band gap. The geometric property of the momentum space can hence be used to explain the existence of interface states in real space through a bulk-interface correspondence.

Detonation is a kind of self-propagating supersonic combustion where the chemical reaction is rapid and violent under an extreme condition. The leading part of a detonation front is pre-shocked by a strong shock wave propagating into the explosive and triggering chemical reaction. The combustion system can be regarded as a kind of chemical reactive flow system. Therefore, the fluid modeling plays an important role in the studies on combustion and detonation phenomena. The discrete Boltzmann method (DBM) is a kind of new fluid modeling having quickly developed in recent thirty years. In this paper we review the progress of discrete Boltzmann modeling and simulation of combustion phenomena.
Roughly speaking, the discrete Boltzmann models can be further classified into two categories. In the first category the DBM is regarded as a kind of new scheme to numerically solve partial differential equations, such as the Navier-Stokes equations, etc. In the second category the DBM works as a kind of novel mesoscopic and coarse-grained kinetic model for complex fluids. The second kind of DBM aims to probe the trans- and supercritical fluid behaviors or to study simultaneously the hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) behaviors. It has brought significant new physical insights into the systems and promoted the development of new methods in the fields. For example, new observations on fine structures of shock and detonation waves have been obtained; The intensity of TNE has been used as a physical criterion to discriminate the two stages, spinodal decomposition and domain growth, in phase separation; Based on the feature of TNE, some new front-tracking schemes have been designed. Since the goals are different, the criteria used to formulate the two kinds of models are significantly different, even though there may be considerable overlaps between them. Correspondingly, works in discrete Boltzmann modeling and simulation of combustion systems can also be classified into two categories in terms of the two kinds of models. Up to now, most of existing works belong to the first category where the DBM is used as a kind of alternative numerical scheme. The first DBM for detonation [Yan, et al. 2013 Front. Phys. 8 94] appeared in 2013. It is also the first work aiming to investigate both the HNE and TNE in the combustion system via DBM. In this review we focus mainly on the development of the second kind of DBM for combustion, especially for detonation. A DBM for combustion in polar-coordinates [Lin, et al. 2014 Commun. Theor. Phys. 62 737] was designed in 2014. It aims to investigate the nonequilibrium behaviors in implosion and explosion processes. Recently, the multiple-relaxation-time version of DBM for combustion [Xu, et al. 2015 Phys. Rev. E 91 043306] was developed. As an initial application, various non-equilibrium behaviors around the detonation wave in one-dimensional detonation process were preliminarily probed. The following TNE behaviors, exchanges of internal kinetic energy between different displacement degrees of freedom and between displacement and internal degrees of freedom of molecules, have been observed. It was found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave. Even locally, the system viscosity (or heat conductivity) results in two competing trends, i.e. to increase and decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses to the corresponding driving forces. The ideas to formulate DBM with the smallest number of discrete velocities and DBM with flexible discrete velocity model are presented.
As a kind of new modeling of combustion system, mathematically, the second kind of DBM is composed of the discrete Boltzmann equation(s) and a phenomenological reactive function; physically, it is equivalent to a hydrodynamic model supplemented by a coarse-grained model of the TNE behaviors. Being able to capture various non-equilibrium effects and being easy to parallelize are two features of the second kind of DBM. Some more realistic DBMs for combustion are in progress. Combustion process has an intrinsic multi-scale nature. Typical time scales cover a wide range from 10^-13 to 10^-3 second, and typical spatial scales cover a range from 10^-10 to 1 meter. The hydrodynamic modeling and microscopic molecular dynamics have seen great achievements in combustion simulations. But for problems relevant to the mesoscopic scales, where the hydrodynamic modeling is not enough to capture the nonequilibrium behaviors and the molecular dynamics simulation is not affordable, the modeling and simulation are still keeping challenging. Roughly speaking, there are two research directions in accessing the mesoscopic behaviors. One direction is to start from the macroscopic scale to smaller ones, the other direction is to start from the microscopic scale to larger ones. The idea of second kind of DBM belongs to that of the first direction. It will contribute more to the studies on the nonequilibrium behaviors in combustion phenomena.

In the past 60 years’ development of photovoltaic semiconductors, the number of component elements has increased steadily, i.e., from silicon in the 1950s, to GaAs and CdTe in the 1960s, to CuInSe₂ in the 1970s, to Cu(In, Ga) Se₂ in the 1980s, to Cu₂ZnSnS₄ in the 1990s, and to recent Cu₂ZnSn(S, Se)₄ and CH₃NH₃PbI₃. Whereas the material properties become more flexible as a result of the increased number of elements, and multinary compound semiconductors feature a dramatic increase of possible point defects in the lattice, which can significantly influence the optical and electrical properties and ultimately the photovoltaic performance. It is challenging to characterize the various point defects and defect pairs experimentally. During the last 20 years, first-principles calculations based on density functional theory (DFT) have offered an alternative method of overcoming the difficulties in experimental study, and widely used in predicting the defect properties of semiconductors. Compared with the available experimental methods, the first-principles calculations are fast, direct and exact since all possible defects can be investigated one by one. This advantage is especially crucial in the study of multinary compound semiconductors which have a large number of possible defects. Through calculating the formation energies, concentration and transition (ionization) energy levels of various possible defects, we can study their influences on the device performance and then identify the dominant defects that are critical for the further optimization of the performance. In this paper, we introduce the first-principles calculation model and procedure for studying the point defects in materials. We focus on the hybrid scheme which combines the advantages of both special k-points and Γ-point-only approaches. The shortcomings of the presentcalculation model are discussed, with the possible solutions proposed. And then, we review the recent progress in the study of the point defects in two types of multinary photovoltaic semiconductors, Cu₂ZnSn(S,Se)₄ and H₃NH₃PbI₃.
The result of the increased number of component elements involves various competing secondary phases, limiting the formation of single-phase multinary compound semiconductors. Unlike ternary CuInSe₂, the dominant defect that determines the p-type conductivity in Cu₂ZnSnS₄ is Cu-on-Zn antisite (CuZn) defect rather than the copper vacancy (V_Cu). However, the ionization level of CuZn is deeper than that of VCu. The self-compensated defect pairs such as [₂CuZn+SnZn] are easy to form in Cu₂ZnSnS₄, which causes band gap fluctuations and limits the V_oc of Cu₂ZnSnS₄ cells. Additionally the formation energies of deep level defects, SnZn and V_S, are not sufficiently high in Cu₂ZnSnS₄, leading to poor lifetime of minority carriers and hence low V_oc. In order to enhance the formation of V_Cu and suppress the formation of CuZn as well as deep level defects, a Cu-poor/Zn-rich growth condition is required. Compared with Cu₂ZnSnS₄, the concentration of deep level defects is predicted to be low in Cu₂ZnSnSe₄, therefore, the devices fabricated based on the Se-rich Cu₂ZnSn(S,Se)₄ alloys exhibit better performances.
Unlike Cu₂ZnSnS₄ cells, the CH₃NH₃PbI₃ cells exhibit rather high V_oc and long minority-carrier life time. The unusually benign defect physics of CH₃NH₃PbI₃ is responsible for the remarkable performance of CH₃NH₃PbI₃ cells. First, CH₃NH₃PbI₃ shows that flexible conductivity is dependent on growth condition. This behavior is distinguished from common p-type photovoltaic semiconductor, in which the n-type doping is generally difficult. Second, in CH₃NH₃PbI₃, defects with low formation energies create only shallow levels. Through controlling the carrier concentration (Fermi level) and growth condition, the formation of deep-level defect can be suppressed in CH₃NH₃PbI₃. We conclude that the predicted results from the first-principles calculations are very useful for guiding the experimental study.

The spin-orbit coupling (SOC) in the 5d transition metal element is expected to be strong due to the large atomic number and ability to modify the electronic structure drastically. On the other hand, the Coulomb interaction in 5d transition is non-negligible. Hence, the interplay of electron correlations and strong spin-orbit interactions make the 5d transition metal oxides (TMOs) specially interesting for possible novel properties. In this paper, we briefly summarize our theoretical studies on the 5d TMO. In section 2, we systematically discuss pyrochlore iridates. We find that magnetic moments at Ir sites form a non-colinear pattern with moment on a tetrahedron pointing to all-in or all-out from the center. We propose that pyrochlore iridates be Weyl Semimetal (WSM), thus providing a condensed-matter realization of Weyl fermion that obeys a two-component Dirac equation. We find that Weyl points are robust against perturbation and further reveal that WSM exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which is impossible to realize in purely two-dimensional band structures. In section 3, based on density functional calculation, we predict that spinel osmates (AOs₂O₄,A=m Ca,Sr) show a large magnetoelectric coupling characteristic of axion electrodynamics. They show ferromagnetic order in a reasonable range of the on-site Coulomb correlation U and exotic electronic properties, in particular, a large magnetoelectric coupling characteristic of axion electrodynamics. Depending on U, other electronic phases including a 3D WSM and Mott insulator are also shown to occur. In section 4, we comprehensively discuss the electronic and magnetic properties of Slater insulator NaOsO₃, and successfully predict the magnetic ground state configuration of this compound. Its ground state is of a G-type antiferromagnet, and it is the combined effect of U and magnetic configuration that results in the insulating behavior of NaOsO₃ We also discuss the novel properties of LiOsO₃, and suggest that the highly anisotropic screening and the local dipole-dipole interactions are the two most important keys to forming LiOsO₃-type metallic ferroelectricity in section 5. Using density-functional calculations, we systematically study the origin of the metallic ferroelectricity in LiOsO₃. We confirm that the ferroelectric transition in this compound is order-disorder-like. By doing electron screening analysis, we unambiguously demonstrate that the long-range ferroelectric order in LiOsO₃ results from the incomplete screening of the dipole-dipole interaction along the nearest-neighboring Li-Li chain direction.

The advent of the era of nano-structures has also brought about critical issues regarding the determination of stable structures and the associated properties of such systems. From the theoretical perspective, it requires to consider systems of sizes of up to tens of thousands atoms to obtain a realistic picture of thermodynamically stable nano-structure. This is certainly beyond the scope of DFT-based methods. On the other hand, conventional semi-empirical Hamiltonians, which are capable of treating systems of those sizes, do not possess the rigor and accuracy that can lead to a reliable determination of stable structures in nano-systems. During the last dozen years, extensive effort has been devoted to developing methods that can handle systems of nano-sizes on the one hand, while possess first principles-level accuracy on the other. In this review, we present just such a recently developed and well-tested semi-empirical Hamiltonian, referred in the literature as the SCED-LCAO Hamiltonian. Here SCED is the acronym for self-consistent/environment-dependent while LCAO stands for linear combination of atomic orbitals. Compared to existing conventional two-center semiempirical Hamiltonians, the SCED-LCAO Hamiltonian distinguishes itself by remedying the deficiencies of conventional two-center semi-empirical Hamiltonians on two important fronts: the lack of means to determine charge redistribution and the lack of involvement of multi-center interactions. Its framework provides a scheme to self-consistently determine the charge redistribution and includes multi-center interactions. In this way, bond-breaking and bond-forming processes associated with complex structural reconstructions can be described appropriately. With respect to first principles methods, the SCED-LCAO Hamiltonian replaces the time-consuming energy integrations of the self-consistent loop in first principles methods by simple parameterized functions, allowing a speed-up of the self-consistent determination of charge redistribution by two orders of magnitudes. Thus the method based on the SCED-LCAO is no more cumbersome than the conventional semi-empirical methods on the one hand and can achieve the first principle-level accuracy on the other. The parameters and parametric functions for SCED-LCAO Hamiltonian are carefully optimized to model electron-electron correlations and multi-center interactions in an efficient fitting process including a global optimization scheme. To ensure the transferability of the Hamiltonian, the data base chosen in the fitting process contains large amount of physical properties, including (i) the binding energies, the bond lengths, and the symmetries of various clusters covering not only the ground state but also the excited phases, (ii) the binding energies as a function of atomic volume for various crystal phases including also the high pressure phases, and (iii) the electronic band structures of the crystalline systems. In particular, the data bases for excited phases of clusters and high pressure phases in bulk systems are more important when performing molecular dynamics simulations where correct transferable phases are required, such as the excited phases. The validity and the robustness of the SCED-LCAO Hamiltonian have been tested for more complicated Si-, C-, and B-based systems. The success of the SCED-LCAO Hamiltonian will be elucidated through the following applications: (i) the phase transformations of carbon bucky-diamond clusters upon annealing, (ii) the initial stage of growth of single-wall carbon nanotubes (SWCNTs), (iii) the discovery of bulky-diamond SiC clusters, (iv) the morphology and energetics of SiC nanowires (NWs), and (v) the self-assembly of stable SiC based caged nano-structures. A recent upgrade of the SCED-LCAO Hamiltonian, by taking into account the effect on the atomic orbitals due to the atomic aggregation, will also be discussed in this review. This upgrade Hamiltonian has successfully characterized the electron-deficiency in trivalent boron element captured complex chemical bonding in various boron allotropes, which is a big challenge for semi-empirical Hamiltonians.

The highly stable optical short-pulse generator with high repetition rate is widely applied in many fields of optical communications, such as optical packet switching systems, high-speed analog-to-digital converter systems, wavelength division multiplexing networks, high-speed optical sampling systems and optical time division multiplexing networks. The optical short-pulse generator which is adopted in such systems mentioned above should possess high stability, low timing jitter, the tunability of the repetition-rate, and narrow pulse width. So far, most of the optical short pulses have been generated from the actively mode-locked lasers and the phase-modulated continuous wave lasers. However, both of the two methods require an additional microwave signal source. Consequently, the stability of such an optical short-pulse generator is strictly limited by the phase noise and stability of the additional microwave signal source. Since the concept of an optoelectronic oscillator which includes the generation of low noise optical pulses together with an ultra-low phase noise microwave signal was proposed by Yao in 1996, the optical short-pulse generator based on the optoelectronic oscillator has attracted much attention in recent years. According to this approach, Lasri demonstrated a novel, self-starting optoelectronic oscillator based on an electro-absorption modulator in a fiber-extended cavity for generating an optical pulse stream with high-rate and ultra-low jitter capabilities in 2003. In the scheme, the repetition rate of the generated optical pulses is 10 GHz, and the phase noise is-115 dBc/Hz at 10 kHz. Devgan demonstrated an optoelectronic oscillator by using a gain-switched vertical-cavity surface-emitting laser in a fiber-feedback configuration in 2006. The structure can generate a 2-GHz optical pulse stream with 750-fs timing jitter (over 100 Hz-10 MHz range). In the present paper, a novel optical short-pulse generator with tunable repetition rate and ultra-low timing jitter based on optoelectronic oscillator is demonstrated. The optoelectronic oscillator system can generate the microwave signal with ultra-low phase noise. The continuous wave light directly modulated by this microwave signal is phase modulated twice, and then the optical pulses with remarkable chirping rate are achieved. By optimizing the length of the dispersion compensating fiber, the optical pulses are further compressed. In this experiment, by utilizing a YIG tunable filter, the high-quality and tunable microwave signal within 8-12 GHz is achieved, which demonstrates the tunability of the repetition rate of the optical pulses. When the frequency of the microwave signal (i.e., the repetition rate of the optical pulses) is 9.6 GHz, the measured pulse width and the phase noise are 3.7 ps and-130.1 dBc/Hz at 10 kHz, respectively. Therefore, the timing jitter of the short optical pulse is calculated to be 60.1 fs (over 100 Hz to 1 MHz).

Refraction is an important factor influencing radiative transfer since it can change both the propagation path and polarization state of electromagnetic wave. In order to discuss the influence of atmospheric refraction on radiative transfer process, a Monte Carlo vector radiative transfer model, which takes atmospheric refraction into account, is introduced. By using this model, photon random movement in uniform atmospheric layer and at the interfaces between adjacent layers is simulated, Stokes vectors and degrees of polarizations of both directly transmitted and diffuse light, and irradiance at the specific layer is also calculated. The model is validated under two conditions: with taking atmospheric refraction into account, and comparing the simulation results with those in the literature; with taking refraction index distributed homogeneously in space, in which case the model is validated against DISORT and RT3. So, the results indicates that our model is accurate and reliable. The influences of atmospheric refraction on the Stokes vectors of diffuse light in different directions are discussed for pure molecular atmosphere, with only Rayleigh scattering considered. Simulations are performed respectively for different solar zenith angles, for different atmospheric profiles, for aerosols with different types and particle shapes, and for clouds with different base heights and optical depths, and correspondingly, the effect of atmospheric refraction on radiative transfer process is discussed as well. Simulation results show that Stokes vector of diffuse light is influenced by atmospheric refraction to a certain extent, especially for light with a zenith angle ranging from 70° to 110°, and with the increasing of solar zenith angle, the influence becomes stronger. When atmospheric profile changes, the effect of atmospheric refraction on polarized radiance field is also changed, for which the possible reason is that deference between atmospheric profiles leads to the variation of refraction index profile. When aerosol and cloud are taken into account, the influence of atmospheric refraction is reduced because of the decreasing of the ratio between side-scattering energy and backward scattering energy. Comparing the simulation results for different aerosol particles shows that the influences of atmospheric refractions in mineral and sea salt aerosol are much stronger than that in water soluble aerosol, besides, there is also great discrepancy among results for aerosols with different shapes. This phenomenon may be explained by the differences in scattering ability and spatial distribution of scattering energy among different aerosols. For cloud, there is no significant difference in result among different cloud base heights, while with the increasing of cloud optical depth, the influence of atmospheric refraction on polarized radiance is gradually weakened.

We propose a scheme for generating a genuine χ-type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. With the help of the Circuit quantum electrodynamics system composed of Δ-type three-level artificial atoms and transmission line resonator, our scheme also has long coherence time and storage time. Meanwhile, the Δ-type three-level artificial atom used in the scheme is different from natural atom and has cyclic transitions. Furthermore, our scheme is easy to control and flexible. Through a suitable choice of the Rabi frequencies and detunings of the classical fields, we can use this system to implement the selective coupling between two arbitrary qubits. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and the decays of transmission line resonator. We also analyze the performance and the experimental feasibility of the scheme, and show that our scheme is feasible under existing experimental conditions.

Dielectric elastomeric actuators (DEAs) have been intensely studied in the recent decades. Their attractive features include large deformation(380%), large energy density(3.4 J/g), light weight, fast response(< 1 ms), and high efficiency (80%-90%). They can be used in medical devices, space robotices and energy harvesters. The core part of DEAs is a dielectric elastomeric film with two electordes. When pre-stretched forces are exerted on the film in plane direction and voltage is applied across its thickness, the film achieves a large deformation. Usually the effect of electric field is described by Maxwell stress εE₂, and the effect of mechanical field is described by free energy function models (such as Neo-Hookean model, Arruda-Boyce model and Gent model). There are deviations in varying degree between every models and tests of dielectric elastomer. No model works perfectly.
In the present paper, a new free energy function model is given to reduce the deviation. According to the main models above, an undetermined parameter C(λ₁, λ₂) is introduced. and λ_i (∂W/∂λ_i)= C(λ ₁, λ ₂)(λ_i²-λ ₁^-2 λ₂^-2), σ_pi = C(λ ₁, λ ₂)(λ _pi²-λ _p1^-2λ_p2^-2)(λ_i/λ _pi), i = 1, 2, are assumed. The new λ_i (∂ W/∂λ_i) and σ_pi are substituted into the equation of equilibrium of dielectric elastomer film σ_pi + εE² = λ_i (∂ W/∂λ_i), i = 1, 2. Under equal-biaxial pre-stretched condition, P₁ = P₂ = P, λ _p1 = λ _p2 = λ_p, C(λ₁, λ ₂) = C(λ). The parameter C(λ)= ε(Vλ²/t₀)²/(λ ²-λ ^-4-(λ _p-λ _p^-4)(λ/λ _p)) is obtained. Through analysing the test results of VHB4905 which contains a series of equal-biaxial pre-stretched tests, the data (λ, C(λ)) are obtained from the test data (λ, V). C(λ) =a + be^√I₁-3, (I₁ = λ ₁² + λ ₂² + λ ₃²) can be determined by data points (λ, C(λ)). By computing the integral of λ_i (∂ W/∂λ_i)= a + be^√I₁-3)(λ_i²-λ ₁^-2 λ ₂^-2), i = 1, 2, a new free energy function W = (a/2)(I₁-3) + b[e^√I₁-3(√I₁-3-1) + 1] (the new model) is achieved.
The test results of VHB4905 are fitted by Neo-Hookean, Gent model and the new model. Neo-Hookean model fits well only in small deformation. Gent model fits well only in small-middle deformation, and does not work well when stretch λ > 3.5. The new model fits well in small, middle and large deformation. It is better than Neo-Hookean and Gent model. The new model can give big support in the study of dielectric elastomer materials and structure property, and can be used in engineering practice effectively.

Two-dimensional (2D) electron gas with high-mobility is found in wurtzite ZnO/Zn(Mg)O heterostructure, which probably arises from the polarization discontinuity at the ZnO/Zn(Mg)O interface, and the 2D electron gas in the heterostructure is usually also regarded as resulting from polarization-induced charge. In order to explore both the formation mechanism and the origin of the 2D electron gas in ZnMgO/ZnO heterostructure, it is necessary to study the polarization properties of Zn_1-xMg_xO alloy and energy band alignment of ZnO/Zn_1-xMg_xO super-lattice.
In this paper, we study the polarization properties of Zn_1-xMg_xO alloy with different Mg compositions by using first-principles calculations with GGA+U method, and the polarization properties are calculated according to Berry-phase method. Owing to the excellent match between the in-plane lattice constants of ZnO and Zn_1-xMg_xO, the lattice constants of the ZnO and Zn_1-xMg_xO interface are similar, ZnO/Zn_1-xMg_xO super-lattice could be constructed easily.
The planar-averaged electrostatic potential for the Mg_0.25Zn_0.75O/ZnO super-lattice and the macroscopically averaged potential along Z(0001) direction are calculated. The large size of (5+3) Mg_0.25Zn_0.75O/ZnO super-lattice ensures the convergence of potential to its bulk value in the region of the ZnO layer and Mg_0.25Zn_0.75O layer far from ZnO/Zn_1-xMg_xO interface. Besides, the valence band offset at the Mg_0.25Zn_0.75O/ZnO interface is calculated to be 0.26~eV based on the macroscopically averaged potential mentioned above, and the ratio of conduction band offset (ΔE_C) to valence band offset (ΔE_V) is in a reasonable range, and this is in substantial agreement with the values reported in recent experimental results. Because strain induces additional piezoelectric polarization in Mg_xZn_1-xO, which is introduced by Mg dopant, the lack of inversion symmetry and the bulk ZnO induce its spontaneous polarization in the [0001] direction. The polarization discontinuity at the Mg_0.25Zn_0.75O/ZnO interface leads to the charge accumulation in the form of interface monopoles, giving rise to built-in electric fields in the super-lattice. In addition, energy alignment determination of the Mg_0.25Zn_0.75O/ZnO super-lattice is performed, which shows a type-I band alignment with ΔE_V=0.26 eV and ΔE_C=0.33 eV. The determination of the band alignment indicates that the Mg_0.25Zn_0.75O/ZnO super-lattice is competent to the confining of both electron and hole.
These findings will be useful for designing and optimizing the 2D electron gas at Mg_0.25Zn_0.75O/ZnO interface, which can be regarded as an important reference for studying the 2D electron gas at Mg_xZn_1-xO/ZnO super-lattices for electronics and optoelectronics applications.

At present, there are mainly two kinds of methods to prevent crack and reduce tensile stress of the silicon substrate GaN based light emitting diode (LED) epitaxial films: one is to use the patterned silicon substrate and the other is to grow a thick AlGaN buffer layer. The two kinds of methods have their own advantages and disadvantages. Although the patterned silicon substrate GaN based LED has industrialized and is gradually accepted by the market, there remain many scientific and technical problems, to be resolved, and a lot of research gaps worth studying deeply. Among these problems, to clearly investigate the different micro zone photoluminescence and the stress states in a single-patterned GaN based LED film grown on patterned silicon substrate. The studies of the stress interaction between the buffer layer and the quanturn well layer and the effect on the luminescent properties have important guiding significance for improving the quality and performance of the devices. Different micro zone photoluminescence (PL) properties in single-patterned GaN-based LED films grown on patterned silicon substrates, nondestructive free-standing LED thin film after removing away the silicon substrate, and the free-standing LED films after removing away the AlN buffer layer are studied. The variations of the bending degree of the free-standing LED thin films before and after removing away AlN buffer layer are inverstigated by using fluorescence microscopy and scanning electron microscopy. The results show as follows. 1) After removing away the silicon substrate, the free-standing LED film bends to the substrate direction in a cylindrical bending state. After removing away the AlN buffer layer, the LED film bends into flat. 2) For LED thin films on silicon substrates or off silicon substrates, their PL spectra have significant differences in different micro zones for the same pattern. When the AlN buffer layer is removed from the substrate its PL spectrum tends to be consistent in the different micro zones of the same pattern. When the patterned silicon substrate GaN-based LED thin film is removed from the silicon substrate, the PL spectrum is redshifted in each micro zone. After AlN buffer layer is removed from the substrate, the PL spectra present different degrees of blueshift in each micro zone. 3) The LED films before and after removing away the AlN buffer layer show some differences in droop effect.

More attention should be paid to the neural system, which is a quantitative system. There are few reports about the quantitative research on neural system. It will hinder the quantitative studies on animal binaural sound localization. The existing physiological experiments have found that there is a monotonic increase/decrease relationship between the input sound levels and the output spike frequencies of auditory neurons, so the variations of input sound level can be simplified into the change of output spike frequency of auditory neurons. In this paper, based on the theory of circle map and symbolic dynamics, a quantitative model of auditory neural circuitry is presented. In this neural circuit model, the neurons of ipsilateral input circuit propagate the action potentials as excitatory inputs, the neurons of heterolateral input one propagate the action potentials as inhibitory inputs. We also use a chemical neuronal model, which shows that the neurotransmitters released from pre-synapse vesicles have characteristics of quantitative release. The strength of the coupling between two neurons is represented by a coupling coefficient. The relationship between the input/output spike sequences of neural circuitry is simulated by using an Hodgkin-Huxley equation. In the range of simulating parameters, there is a monotonic increase/decrease phenomenon between input and output spike frequency. For the neuron with a single input and output structure, it is symbolized according to the method of symbolic dynamics; for the neurons with multi-input and single output structure, the output spike time will be used to detect the input spike frequency variations which are caused by the changes of interaural level difference (ILD), and the binaural level differences from those spike sequences are analyzed to locate the source of the sounds. With the increase of output spikes, the length of symbolic sequence increases, the symbolic sequence is sensitive to the variation of input signal. The simulation results show that the quantitative model proposed in this paper is able to detect the ILD signals by neural spike sequences.

We report the development of an incoherent broadband cavity enhanced absorption spectroscopy (IBBCEAS) based on an ultraviolet light emitting diode (UV-LED), and the IBBCEAS instrument is used for simultaneously measuring of the atmospheric HONO and NO₂. The cavity-enhanced method is characterized by high sensitivity and spatial resolution. The incoherent broadband light is focused into a high-finesse optical cavity, two highly reflecting mirrors form the ends of the cavity, and the light is then trapped between the two highly reflecting mirrors, resulting in long photon residence time and long optical path length. The effects of the Rayleigh scattering of the gases in the cavity and stability of the UV-LED light source were discussed in this paper. The reflectivity of the highly reflecting mirror was calibrated by the difference of Rayleigh scattering of He and N₂, and the optimum averaging time of the IBBCEAS instrument was confirmed to be 320 s by the Allan variance analysis. Detection limits (1σ) of 0.22 ppb for HONO and 0.45 ppb for NO₂ were achieved with an optimum acquisition time of 320 s. In order to test the accuracy of measured results by the IBBCEAS instrument, concentrations of HONO and NO₂ were recorded during about continuous three days by the IBBCEAS instrument and compared with the results obtained by a different optical absorption spectroscopy (DOAS) instrument. The results of HONO show a linear correction factor (R²) of 0.917, in a slope of 0.897 with an offset of 0.13 ppb; NO₂ concentration measured by the IBBCEAS instrument accords well with the result obtained by the DOAS instrument, with a linear correlation of R² = 0.937, in a slope of 0.914 with an offset of-0.17 ppb.

In this paper, we numerically study the efficiencies of high-order harmonic generation (HHG) from CO₂ molecule exposed to strong laser fields with different laser wavelengths and different orientation angles. Through calculating the HHG spectra in the directions parallel and perpendicular to the laser polarization, we show that the efficiency of perpendicular harmonics can be higher than or comparable to the parallel ones at the relatively small and intermediate orientation angles in some wavelength cases. At larger angles, the efficiency of perpendicular harmonics is generally lower than the parallel one. Further analyses show that the structure of the CO₂ molecule plays an important role in the HHG efficiency and this role is also related to the laser wavelength.
Specifically, we show that the relative yields of perpendicular harmonic versus parallel harmonic are closely associated with the parallel and perpendicular dipoles of the molecule. Due to the effect of two-center interference, the parallel or perpendicular dipoles of the molecule show some deep hollows in some energy regions, which depend on the molecular orientation, and so do the corresponding parallel and perpendicular harmonics. As the parallel harmonics are suppressed due to the interference effect strongly in some energy regions, the yields of the perpendicular harmonics, which are not subjected to the interference effect in the corresponding energy regions, can be higher than the parallel one. As a result, the integrated harmonic yield (i.e., the harmonic efficiency) in the perpendicular case can be higher than the parallel one, especially for the cases with short laser wavelengths and small orientation angles. In these cases, the interference effect induces the suppression of parallel harmonics in the whole HHG plateau. We therefore expect that the interference effect plays an important role in the HHG efficiency in these cases. For the case of long laser wavelength, the HHG plateau extends to high energy region and the main contributions to the integrated HHG yield can come from harmonics out of the interference-effect-dominating region. As a result, the interference effect plays a smaller role in determining the HHG efficiencies of parallel and perpendicular harmonics, in comparison with the case of short laser wavelength. For large orientation angles, the value of the perpendicular dipole is smaller than the parallel one in a wide energy region, and accordingly, the perpendicular harmonics are weaker than the parallel ones on the whole. As a rule, the parallel efficiency is usually higher than the perpendicular one.
As the perpendicular harmonic can contribute importantly to the harmonic emission in some cases, our results suggest that for the complicated molecule, the perpendicular harmonics should be considered in the molecular orbital tomography experiments.