Extremely short and quasi-monochromatic electromagnetic solitons in a two-component medium

The propagation of extremely short (without high-frequency filling) pulses and nonresonant envelope solitons in a two-component medium comprising two-level atoms with substantially different quantum transition frequencies was studied. The dynamics of a pulse whose reciprocal time scale lay between these frequencies was shown to be described by the Kosevich-Kovalev equation, the one-way variant of which was the Konno-Kameyama-Sanuki equation. If the transition dipole moments of medium components were equal, the one-way equation became integrable. Soliton and soliton-like solutions to these equations were used to analyze pulse propagation regimes at various two-component medium initial states. The stability of these localized wave formations was analyzed. The possible existence of stable soliton-like pulses propagating in a nonequilibrium medium at group velocities exceeding the velocity of light in vacuum was discussed.     

The design of metamaterial cloaks embedded in anisotropic medium

By using coordinate transformation method, this paper obtains an useful equation of designing meta-material cloaks embedded in anisotropic medium. This equation is the generalization of what was introduced early by Pendry et al (2006 \textit{Science} {312 1780) and can be more widely used. As an example of its applications, this paper deduces the material parameter equation for cylinder cloaks embedded in anisotropic medium, and then offers the numerical simulation. The results show that such a cylinder cloak has perfect cloaking performance and therefore verifies the method proposed in this paper.     

Nonlinear Airy Light Bullets in a 3D Self‐Defocusing Medium

The (3+1)‐dimensional [(3+1)D] nonlinear Schrödinger (NLS) equation is investigated, describing the propagation of nonlinear spatiotemporal wave packets in a self‐defocusing medium, and a new type of Airy spatiotemporal solutions is presented. By using the reductive perturbation method, the (3+1)D NLS equation is reduced to the spherical Kortewegde Vries (SKdV) equation. Based on the Hirota's bilinear method, the bilinear form of the SKdV equation is constructed and Airy light bullet (LB) solutions of different orders are obtained, which depend on the sets of two free constants associated with the amplitude and initial phase. The results show that these Airy LBs can exist in the self‐defocusing medium and their intensities can be controlled by selecting the suitable free parameters along the propagation distance. As examples, three types of low‐order approximate LB solutions are presented and their intensity profiles numerically discussed. The obtained results are helpful in exploring nonlinear phenomena in a self‐defocusing medium and providing a new approach for possible experimental verification of LBs.     

Stochastic functional analysis of propagation and localisation of cylindrical waves in a two-dimensional random medium

Propagation and localisation of cylindrical waves in a two-dimensional (2D) isotropic and homogeneous random medium is studied using the stochastic functional approach. By expanding the random permittivity fluctuation in the form of a Wiener integral equation, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved in the cylindrical coordinates system. An analytical expression of the cylindrical wave is derived and demonstrates the localisation phenomenon, as well as the wavenumber fluctuation in the random medium. Comparing with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effect owing to the medium randomness in both the amplitude and phase. Numerical simulations are presented to illustrate the functional dependence of the localisation phenomena.     

On a fourth-order wave equation for EM propagation in chiral media

A fourth-order wave equation is derived to study the propagation of an electromagnetic (EM) wave in a medium composed of chiral objects. This approximate wave equation does not reflect the handedness of the medium directly, which is more readily apparent, however, in a pair of two coupled second-order wave equations obtaineden route.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

Dispersion Laws,Nonlinear Solitary Waves,and Modeling of Kernels of Integro-Differential Equations Describing Perturbations in Hydrodynamic-Type Media With Strong Spatial Dispersion

Acoustical Physics - An integro-differential equation simulating a medium with strong spatial dispersion and hydrodynamic-type nonlinearities (the Whitham equation) is considered. A method is...     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Influence of then-n cross section on the observables in dynamical process of heavy ion collisions

The influence of then- n cross section on the observables in dynamical process of heavy ion collisions was investigated by means of the BUU (Boltzmann-Uehling-Uhlenbeck) equation. The influence of then-n cross section upon transverse momentum, flow angle and quadrupole moment of momentum distribution with increasing incident energy was successfully illustrated according to the variation law ofn-n cross section with and without the medium effects with increasing bombarding energy. This investigation also shows a close relationship between the medium effects of then- n cross section and the nuclear equation of state (EOS).     

The Infrared Ray Transport in an N-Layered Matched Skin

Infrared ray (IR) has great potential in medical diagnosis and therapy. In order to detect tumor in skin, we set up the steady-state and time domain IR diffusion model of an n-layered matched medium with an infinitely thick. We utilize the diffuse equation to solve a five-layered infinite matched medium and obtain the accurate solution of a matched medium of the steady state and time domain in tissue. We compare the steady-state spatially resolved reflectance calculated with Monte-Carlo simulations. The Monte-Carlo simulation shows that the solution is valid. Our equation can be used to obtain the tumor information in medical diagnosis and therapy.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

Mass transfer in nonuniform media

The lattice model was used to derive equations describing diffusion in a nonuniform medium in the absence of local equilibrium at nonzero temperature gradients. Equations are obtained that extend a diffusion equation with fractional derivative in time and a nonlinear diffusion equation, which was previously obtained within the framework of a generalized thermodynamic approach, to cover diffusion in a medium with a nonuniform temperature field.     

Radiative transfer in one-dimensional hollow sphere with anisotropic scattering and variable medium properties

The effects of variable medium properties on radiation transfer in participating and anisotropically scattering one-dimensional spherical medium were investigated by Tsai et al. (JQSRT 42(3) (1989) 187). The discrete ordinates method solutions they provided for hollow spherical medium cases are incorrect. The correct DOM S₈ and the integral transfer equation solutions are provided.     

Open quantum system approach for heavy quark thermalization

We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schr?dinger equation (SSE) from the full Schr?dinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.     

Nonstationary contrasting structures for the generalized Kolmogorov-Petrovskiy-Piskunov equation

The solution to the generalized Kolmogorov-Petrovskiy-Piskunov (GKPP) equation is shown to have a contrasting structure. Contrasting structures (CSs) are characterized by the existence of wide areas with a small field gradient separated by narrow internal transition layers (ITLs) with a large field gradient. The ITLs in an inhomogeneous medium are shown to drift and the drift velocity is determined. The CS drift velocity for the GKPP equation is compared with a simpler model of the reaction-advection-diffusion equation.     

Propagation of shock waves in a medium with the Rayleigh energy release mechanism

The effect of the familiar Rayleigh mechanism of energy release in an elastic medium (which plays an important role, in particular, in gas discharge plasma) on the structure of a running shock wave (SW) is considered in the general case in the 1D approximation. The equation describing the propagation of the SW in this case is derived. An analytic solution to this equation is obtained for small values of the parameter characterizing the properties of the medium. The type of the solution for different signs of this parameter and for its values modulo equal to unity is analyzed. It is found that, for positive values of this parameter, a SW in the form of a step is suppressed in such a medium and degenerated into a perturbation in the form of a hump. On the contrary, for negative values of the parameter, the SW is enhanced. It is found that a stationary solution exists in the system of coordinates associated with the SW propagation in a medium with the Rayleigh energy release mechanism only if the boundary of the medium lies downstream from the shock layer. The position of this boundary corresponds to the so-called critical energy supply and the local Mach number is equal to unity at this point. For a positive value of the parameter of the medium with the Rayleigh energy release mechanism, the equation of propagation has no stationary solution for any position of the boundary of the medium upstream from the shock layer when the value of the parameter exceeds a certain limiting value. The results make it possible to analyze the features of SW propagation in a weakly ionized gas discharge plasma.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the 'wings' of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Angular spectrum approach to electromagnetic wave propagation in inhomogeneous media

The angular spectrum representation of the electromagnetic wave field is employed to solve the wave propagation in a weakly inhomogeneous medium. Taking the two-dimensional spatial Fourier transform of the radiation field as well as of the dielectric constant, the angular amplitude is shown to satisfy an integro-differential equation. A similar equation is also applicable for the propagation of radiation in a non-linear medium. This integro-differential equation is solved for two specific cases of interest, namely that of a stratified medium and of a square-law medium.     

Anomalous Dimension in the Solution of the Modified Porous Medium Equation

A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.     

双折射吸收非线性介质薄膜中倍频的产生

从二次谐波电场满足的波动方程出发，考虑到介质对二次谐波的吸收以及把完全边界条件应用于基频波和二次谐波在介质的入射面和出射面之间的反射效应，推导出了单光轴非线性薄膜介质中的二次谐波输出功率的计算式.结果表明：当采用复折射率的概念时，可以把非线性无吸收介质的二次谐波输出功率计算式应用到非线性吸收介质二次谐波输出功率计算式中去.