A singularly perturbed reaction diffusion problem forthe nonlinear boundary condition with two parameters

A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of differential inequalities, the existence and the asymptotic behaviour of the solution for the initial boundary value problem are studied. The obtained solution indicates that there are initial and boundary layers and the thickness of the boundary layer is less than the thickness of the initial layer.     

Study of reflection and transmission on the moving interface of medium

The laws of refection and transimission on a moving interface between two nonvacuum medium are studied and the new method, which can be used for handling reflection and transimission on the moving interfaces between the vacuum-nonvacuum media and between two nonvacuum medium is suggested. The formula of reflection and transmission coefficients that suitable for both cases are derived. The present paper not only enriches electrodynamical theory, but also laies the foundation of optical waveguide modulators and other similar device.     

Measurements of Absorption and Anisotropy Coefficients of the Fat Emulsion Intralipid-10%

We report measurements of absorption and anisotropy coefficients of the fat emulsion Intralipid-10%. An addingabsorber method is used for measurement of absorption and anisotropy coefficients of the Intralipid-10%. Using the diffusion theory which has been extended to include anisotropy scat geometry, we found that the standard deviations of multiple measurements for√μα/D are less than 0.6% and the residuals between the measured data and the fits have rms values of 0.1%, where μα is the absorbing coefficient of the solution in our experiment and D is the diffusion coefficient of the medium. The values of the standard deviations and the residuals demonstrate the high precision of the measurements.     

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.     

Hybrid diffusion approximation in highly absorbing media and its effects of source approximation

A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated. The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained. The effects of source approximation on the analytic solution are investigated, and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary. Monte Carlo simulation of recovering optical parameters from refiectant data is done with the use of this model. The errors of recovering μ＇s and μ＇s are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 mm.     

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo–Christov Heat Diffusion Theory

Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo–Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Further, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo–Christov heat diffusion model when matched with the profiles obtained for Fourier's theory of heat flux.     

Study on optical wave scattering from slightly Gaussian rough surface of layered medium

The optical wave scattering from the slightly rough surface of three-layer medium is studied.The formulaes of the scattering coefficients for different polarizations are derived using the small perturbation method. A Gaussian rough surface is presented for describing rough surface of layered medium,the influence of the permittivity of layered medium,the mean layer thickness of intermediate medium,the surface roughness parameters and the incident wavelength on the bistatic scattering coefficient of HH polarization are obtained and discussed by numerical implementation.     

Solutions for a Mode Ⅲ Growing Crack in a Piezoelectric Plane Under Two Kinds of Electric Boundary Conditions ＊

The solutions for a mode Ⅲ crack growing along an arbitrary propagation path in a piezoelectric plane are studied under the impermeable surface condition and the electrical contact surface condition respectively. According to the two kinds of electric boundary conditions, the Hilbert and Riemann boundary value problems in a half-plane including opening smooth arc are obtained from the theoretical analysis. Moreover, the equipollence of the solution formed under these two electric boundaries is proved, and unified solutions for the stress and electric displacement distribution in the crack-tipfield of the piezoelectric plane are achieved.     

Experimental Study of Effect of Medium Boundary on Light Distribution in Tissue Phantoms

An experimental method for investigating the effect of medium boundary on distributions of light in the biological tissue phantom intralipid is presented. Measurements of distributions of light in intralipid-10% suspensions at 633 nm are described, in which a narrow collimated beam is incident on the surface of the phantoms and into the different depths inside of the phantoms. The experimental results show that the effect of the boundary of the medium on the curves geometry of light distributions is trivial, but the effect on intensity of scattering light is obvious, the maximal relative change of the energy fluence reaches 53.8% and the position of the peak of the energy fluence curve has a shift of 1.1 mm in the reverse direction of incident light for the phantom with albedo a=0.998, and the effect of the boundary is decreased with the increase of the absorption coefficients of tissue phantoms. The experimental results were analysed by the diffusion theory. These studies will be helpful for further understandings of the relation between the boundary of biological tissue and the distribution of light in tissue.     

Molecular Dynamics Study of a Thermal Expansion Coefficient： Ti Bulk with an Elastic Minimum image Method

Linear thermal expansion coefficient （TEC） of Ti bulk is investigated by means of molecular dynamics simulation. The elastic minimum image convention of periodic boundary conditions is introduced to allow the bulk to adjust its size according to the new fixed temperature. The TEC and the specific heat of Ti are compared to the available theoretical and experimental data.     

Research of NO2 vertical profiles with look-up table method based on MAX-DOAS

Obtaining the vertical distribution profile of trace gas is of great significance for studying the diffusion procedure of air pollution.In this article,a look-up table method based on multi-axis differential optical absorption spectroscopy(MAX-DOAS)technology is established for retrieving the tropospheric NO₂ vertical distribution profiles.This method retrieves the aerosol extinction profiles with minimum cost function.Then,the aerosol extinction profiles and the atmospheric radiation transfer model(RTM)are employed to establish the look-up table for retrieving the NO₂ vertical column densities(VCDs)and profiles.The measured NO₂ differential slant column densities(DSCDs)are compared with the NO₂ DSCDs simulated by the atmospheric RTM,and the NO₂ VCDs,the weight factor of NO₂ in the boundary layer,and the boundary layer height are obtained by the minimization process.The look-up table is established to retrieve NO₂ VCDs based on MAX-DOAS measurements in Huaibei area,and the results are compared with the data from Copernicus Atmospheric Monitoring Service(CAMS)model.It is found that there are nearly consistent and the correlation coefficient R2 is more than 0.86.The results show that this technology provides a more convenient and accurate retrieval method for the stereoscopic monitoring of atmospheric environment.     

Measurement of Diffusion Coefficient of Liquids by Using an Asymmetric Liquid-Core Cylindrical Lens： Observing the Diffusion Process Directly

We report a method for measuring diffusion coefficient D of liquids by using an aplanatic and asymmetric cylinder lens with a liquid core, which is designed as both a diffusion pool and the main imaging element. The precision is better than 10-4 RIU in measuring refractive index. The D values of ethylene glycol （EG） in water are measured for various EG concentrations at 25℃, and Dinf = 1.043 × 10^-5 cm^2/s under the condition of infinite dilution is obtained. The method is characterized by observing the diffusion process directly, faster measurement and obtaining the D value under the condition of infinite dilution.     

Electronic structure and optical properties of Al and Mg co-doped GaN

The electronic structure and optical properties of Al and Mg co-doped GaN are calculated from first principles using density function theory with the plane-wave ultrasoft pseudopotential method.The results show that the optimal form of p-type GaN is obtained with an appropriate Al:Mg co-doping ratio rather than with only Mg doping.Al doping weakens the interaction between Ga and N,resulting in the Ga 4s states moving to a high energy region and the system band gap widening.The optical properties of the co-doped system are calculated and compared with those of undoped GaN.The dielectric function of the co-doped system is anisotropic in the low energy region.The static refractive index and reflectivity increase,and absorption coefficient decreases.This provides the theoretical foundation for the design and application of Al–Mg co-doped GaN photoelectric materials.     

Intersubband absorption with difference-frequency generation in GaAs asymmetric quantum wells

An asymmetric quantum well(AQW) is designed to emit terahertz(THz) waves by using difference frequency generation(DFG) with the structure of GaAs/Al 0.2 Ga 0.8 As/Al 0.5 Ga 0.5 As.The characteristics of absorption coefficients are analysed under the parabolic and non-parabolic energy-band conditions in detail.We find that the absorption coefficients vary with the two pump optical intensities,and they reach the maxima when the pump wavelengths are given as λ p1 = 9.70 μm and λ p2 = 10.64 μm,respectively.Compared with non-parabolic conditions,the total absorption coefficient under parabolic conditions shows a blue shift,which is due to the increase in the energy difference between the ground and excited states.By adjusting the two pump optical intensities,the wave vector phase-matching condition inside the AQW is satisfied.     

Universal Scaling Law for Atomic Diffusion and Viscosity in Liquid Metals

The recently proposed scaling law relating the diffusion coefficient and the excess entropy of liquid [Samanta A et al. 2004 Phys. Reu. Lett. 92 145901; Dzugutov M 1996 Nature 381 137], and a quasi-universal relationship between the transport coefficients and excess entropy of dense fluids [Rosenfeld Y 1977 Phys. Rev. A 15 2545],are tested for diverse liquid metals using molecular dynamics simulations. Interatomic potentials derived from the glue potential and second-moment approximation of tight-binding scheme are used to study liquid metals.Our simulation results give sound support to the above-mentioned universal scaling laws. Following Dzugutov,we have also reached a new universal scaling relationship between the viscosity coefficient and excess entropy.The simulation results suggest that the reduced transport coefficients can be expressed approximately in terms of the corresponding packing density.     

Efficient loading of ultracold sodium atoms in an optical dipole trap from a high power fiber laser

We report on a research of the loading of ultracold sodium atoms in an optical dipole trap,generated by two beams from a high power fiber laser.The effects of optical trap light power on atomic number,temperature and phase space density are experimentally investigated.A simple theory is proposed and it is in good accordance with the experimental results of the loaded atomic numbers.In a general estimation,an optimal value for each beam with a power of 9 W from the fiber laser is achieved.Our results provide a further understanding of the loading process of optical dipole trap and laid the foundation for generation of a sodium Bose–Einstein condensation with an optical dipole trap.     

Effect of Low Diffusion Coefficient on Eutectic Instability of Al-25wt%Sm Alloy

Diffusion coefficient decides the solute diffusion length and is a critical parameter in the selection of microstructare scales and in governing microstructure transitions. Al-25 wt%Sm alloy is selected to reveal the impact of low diffusion coefficient on the eutectic instability, and the results are compared with those of Al-Cu alloys. Laser remelting experiments are performed and the transition growth velocity from euteetic to α-Al dendrite is examined. Compared with Al-Cu alloys, the eutectic instability takes place at a velocity more than one order of magnitude smaller. The theoretical calculation by the Trivedi-Magnin-Kurz （TMK） model also predicts that the eutectic will become instable at smaller growth velocity for Al-Sm alloy than Al-Cu alloy, which is ascribed to the low diffusion coefficient.     

Acoustic scattering from multiple spheres by using a kind of addition formulae for the spherical wave functions

A kind of addition formulae for the spherical wave functions is generated by using the bicentric expansion of Green function in spherical coordinates. For an acoustical system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the multiple scattering easily. The two-sphere acoustical system with different boundary conditions is considered and the field scattered by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by a plane wave at arbitrary angles of incidence are calculated and the addition formulae presented are validated by comparing the corresponding numerical results with those of the existing literature.     

Solution of the Energy Level of Hydrogen－Like Atom for the Debye Shidlding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms under the condition of Debye shielding potential are achieved by means of the Rayleigh-Schroedinger perturbation theory.meanwhile,the corresponding recurrence relations are obtained from the use of the solution of power series,Based on the above solutions and with the use of energy consistent method the equivalent value of second-order reversion under the condition of Debye shielding potential is produced as well and the esult is compared with the data obtained by the numerical method.Besides,the critical bond-state and corresponding cut-off conditions are discussed.     

Comparative study of Mo_2Ga_2C with superconducting MAX phase Mo_2GaC: First-principles calculations

The structural, electronic, optical and thermodynamic properties of Mo_2Ga_2C are investigated using density functional theory(DFT) within the generalized gradient approximation(GGA). The optimized crystal structure is obtained and the lattice parameters are compared with available experimental data. The electronic density of states(DOS) is calculated and analyzed. The metallic behavior for the compound is confirmed and the value of DOS at Fermi level is 4.2 states per unit cell per e V. Technologically important optical parameters(e.g., dielectric function, refractive index, absorption coefficient, photo conductivity, reflectivity, and loss function) are calculated for the first time. The study of dielectric constant(ε1) indicates the Drude-like behavior. The absorption and conductivity spectra suggest that the compound is metallic.The reflectance spectrum shows that this compound has the potential to be used as a solar reflector. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient of Mo_2Ga_2C MAX phase are derived from the quasi-harmonic Debye model with phononic effect also for the first time. Analysis of T c expression using available parameter values(DOS, Debye temperature, atomic mass,etc.) suggests that the compound is less likely to be superconductor.