Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity

A conservative finite-difference scheme is constructed for the problem of propagation of a light pulse in a one-dimensional nonlinear photonic crystal with combined nonlinearity. The invariants of the corresponding differential problem and their difference analogues are given. The scheme is compared with those based on the widespread splitting method. For combined cubic and quadratic nonlinearity in photonic crystal layers, it is shown that the classical splitting method is ineffective, since it requires time steps that are smaller by one or more orders of magnitude. The finite-difference scheme proposed conserves the propagation invariants, which cannot be achieved for splitting schemes even on considerably finer grids. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes as applied to the simulation of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The simulation is based on the approach proposed by the authors for the given class of problems.     

凝析气田压力曲线特征分析

本文采用一个带汇项的流动方程描述了凝析气井在压力大于最大凝析压力时的压力时间变化特征.根据Duhamel叠加原理建立了反映凝析作用的汇项;引入了描述这一汇项的两个新的物理参数:凝析强度R_D和凝析弛豫时间λ_D.由汇项在流动方程中的作用,给出了凝析作用影响井口压力的定量表述,阐明了凝析作用影响井口压力的机理.本文给出了这一流动方程外边界条件为无限大、内边界以定产量生产情况下的解析解.本文的结论可用于试井理论.     

On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification

A singularly perturbed initial–boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction–diffusion–advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated.

     

Quark and gluon condensates in nuclear matter with Brown-Rho scaling

Quark and gluon condensates in nuclear matter are investigated in a density-dependent relativistic mean-field theory. The in-medium quark condensate decreases rapidly as the density of nuclear matter increases, if the Brown-Rho scaling is included. The decrease in the in-medium quark condensate with the nuclear matter density is consistent with the result predicted by the partial chiral symmetry restoration. The gluon condensate and the influence of the strange quark contents on the gluon condensate in nuclear matter are discussed.     

Numerical analysis of the effect of small geometrical imperfections on photonic crystal wires

Imperfections in the geometry of photonic crystal wires (PCWs) are always a result of current manufacture techniques. The influence of such random defects on the propagating modes in PCWs is studied computationally by means of a full vectorial finite-element method using a perfectly matched layer (PML) as absorbing boundary condition, and the numerical results show a large sensitivity of the birefringence to the geometrical defects in the transversal section of the fibre. It has also been found that imperfections in PCWs have a greater effect on wave propagation than those in photonic crystal fibres (PCFs).     

Influence of the pseudoscalar condensate gradient on the cooling regime of compact stars

We consider the processes in compact stars that arise during the potential formation of a pseudoscalar condensate in finite volumes. We do not propose specific hypotheses about the nature of this condensate. Considering that in the regions with a changing pseudoscalar density, photon propagation can be described in the framework of Maxwell–Chern–Simons electrodynamics, we find the reflection/transmission coefficients for regions with different densities. We study the fermion spectrum in the presence of an axial field considering the pseudoscalar condensate gradient. We also study the influence of the modified photon and fermion spectra on the cooling process of compact stars.     

凝析油-气在存在裂缝的双渗介质中渗流的变产量数学模型及其应用

当凝析气藏压力低于露点压力时,有凝析油析出,致使井底附近阻力变大,影响凝析气的采出量,反凝析现象带来了一些特殊的经济问题.选择合理的开发方式,提高凝析气的采收率,成为了当前工作中迫切需要解决的难题.为了控制合理的井底流压常会引起产量的改变.主要针对凝析气在存在裂缝的双渗气藏中的渗流问题,建立气井变产量生产新模型并进行求解,同时选择相关合理参数绘制了试井理论图版,根据试井理论图版利用试井测试数据进行解释,可以得到相应动态参数为气田开发预案提供相应的理论依据.     

Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers

We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self-induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two-dimensional spatial optical solitons. We apply the matrix criterion for stability of these two-parameter solitons, and verify it by direct numerical simulations.     

Chaotic transport of a matter-wave soliton in a biperiodically driven optical superlattice

Under the effective particle approximation, we study the temporal ratchet effect for chaotic transport of a matter-wave soliton consisting of an attractive Bose–Einstein condensate held in a quasi-one-dimensional symmetric optical superlattice with biperiodic driving. It is known that chaos can substitute for disorder in Anderson’s scenario [Wimberger S, Krug A, Buchleitner A. Phys Rev Lett 2002;89:263601] and only a higher level of disorder can induce Anderson localization for some special systems [Schwartz T, Bartal G, Fishman S, Segev M. Nature 2007;46:52], and a matter-wave soliton can transit to chaos with high or low probability in a high- or low-chaoticity region [Zhu Q, Hai W, Rong S. Phys Rev E 2009;80:016203]. Here we demonstrate that varying the driving phase to break the time reversal symmetry of the system can increase the size of the high-chaoticity region for low- and moderate-frequency regions. Consequently, the parameter region of the exponential spatial localization increases to the same size, and the low-chaoticity and delocalization region, which includes subregions of the ratchet effect and its inverse effect, correspondingly decreases. The positive dependence of the localization on the driving frequency is also revealed. The results indicate that a high-chaoticity region could replace higher disorder and assists in Anderson localization. From the results we suggest a method for controlling directed motion of a matter-wave soliton by adjusting the driving frequency and amplitude to strengthen or suppress, or even reverse, the temporal ratchet effect.     

Partially Coherent Waves in Nonlinear Periodic Lattices

We study the propagation of partially coherent (random-phase) waves in nonlinear periodic lattices. The dynamics in these systems is governed by the threefold interplay between the nonlinearity, the lattice properties, and the statistical (coherence) properties of the waves. Such dynamic interplay is reflected in the characteristic properties of nonlinear wave phenomena (e.g., solitons) in these systems. While the propagation of partially coherent waves in nonlinear periodic systems is a universal problem, we analyze it in the context of nonlinear photonic lattices, where recent experiments have proven their existence.     

Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation.     

The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for tm waves propagating in a layer with arbitrary nonlinearity

The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue transmission problem for a system of two ordinary differential equations. A theorem on the existence and localization of at least one eigenvalue is proven. On the basis of this theorem, a method for finding approximate eigenvalues of the considered problem is proposed. Numerical results for Kerr and saturation nonlinearities are presented as examples.     

Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity

In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to establishing a similar result for a combined nonlinearity. Comparing to the result of wave equation without damping, one can say that the scattering damping has no influence.     

Asymptotic Stability of Large-amplitude Oscillations in Systems with Hysteresis

We study depending on a parameter periodic systems with the main linear part and a hysteresis nonlinearity; the linearized at infinity system has a one-dimensional subspace of periodic solutions for the critical parameter value. We prove theorems on a number, localization, and asymptotic stability of large-amplitude periodic solutions for the nonlinear system. Received March 1998     

On the optimal focusing of solitons and breathers in long‐wave models

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long‐wave models, the classic and the modified Korteweg–de Vries equations. The local solution for an isolated soliton or breather within the GE is obtained. The wave amplitude in the focal point is calculated exactly. It exhibits a linear superposition of partial amplitudes of the solitons and breathers. The crucial role of the choice of proper soliton polarities and breather phases on the cumulative wave amplitude in the focal point is demonstrated. Solitons are most synchronized when they have alternating polarities. The straightforward link to the problem of synchronization of envelope solitons and breathers in the focusing nonlinear Schrödinger equation is discussed (then breathers correspond to envelope solitons propagating above a condensate).     

Control for dynamics of two coupled Bose–Einstein condensate solitons by potential deviation

The control of the potential deviation for two coupled Bose–Einstein condensate solitons is investigated by the variational approach, and the effects of the potential deviation on dynamics of the two Bose–Einstein condensate solitons are discussed. The potential deviation resets the stationary state, affects the existence time, and changes the switching and self-trapping effect on the Bose–Einstein condensate solitons. The results are confirmed by the evolution of the atom population transferring ratio, and demonstrate a new way to guide the motion of the two Bose–Einstein condensate solitons.     

Application of the differential transformation method to the solution of a damped system with high nonlinearity

This paper employs the differential transformation method to investigate the response of a damped system with high nonlinearity. The accuracy and validity of the proposed method are demonstrated through its application to the solution of a dynamic system with various values of power-form nonlinearity. The numerical results indicate that the amplitude decays more rapidly at higher values of nonlinearity, particularly at higher values of the damping coefficient. It is shown that the current results are in excellent agreement with those provided by the Runge–Kutta method. Therefore, the method presented in this study provides an effective scheme for determining the solutions of a damped vibration problem with high nonlinearity.     

Modeling filmwise condensation of vapor on curvilinear fins with condensate suction from interfin grooves

The nonstationary process of filmwise condensation of vapor on curvilinear fins with condensate suction from interfin grooves is numerically simulated with account taken of surface tension and gravity. The problem is reduced to solving a nonlinear evolution equation for the thickness of the condensate film. We performed calculations of the ethanol vapor condensation at atmospheric pressure on the fins of constant curvature for various temperature differences between the fin surface and the vapor saturation and for various values of the rate of condensate suction from the interfin space. Numerical calculations show that the condensation process is stable in the device (i.e., in the condenser) with condensate suction. Filling the interfin space leads to diminishing the zone of intense condensation and reducing the condensate inflow; therefore, this yields stable equilibrium between the condensation and condensate suction. The changes of the condenser temperature at a constant condensate suction entail variation of the filling level of the interfin groove and establishment of a stationary process, provided that the fin temperature becomes constant.     

On Localization of Solutions of Elliptic Equations with Nonhomogeneous Anisotropic Degeneracy

The work deals with the Dirichlet problem for elliptic equations with nonhomogeneous anisotropic degeneracy in a possibly unbounded domain of multidimensional Euclidean space. The existence of weak solutions is proved. Some conditions are established connecting the character of nonlinearity of the equation and the geometric characteristics of the domain which guarantee the one-dimensional localization (vanishing) of weak solutions. The equation with anisotropic degeneracy is shown to admit localized solutions even in the absence of absorption.     

Mathematical analysis of the guided waves in photonic crystal fibers

The propagation of guided waves in photonic crystal fibers (PCFs) is studied. The structure of a PCF can be regarded as a perfect two-dimensional photonic crystal with a line defect along the invariant direction. This problem can be treated as an eigenvalue problem for a family of noncompact self-adjoint operators. We prove that line defects do not change the essential spectrum of the associated “background” medium. This result plays a key role for studying the influence of line defects on the “background” spectrum. A modified Combes-Thomas estimate is also formulated.