q-Gaussians in the porous-medium equation: stability and time evolution

The stability of q-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index q_i, approaches asymptotically the final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for the kurtosis evolves in time according to a q-exponential, with a relaxation index q_rel ≡q_rel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (q_i ≥ 5/3) into a finite-variance one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.     

量子位Heisenberg XX开链中边界量子位之间的纠缠

Heisenberg 开链对研究量子态在自旋链上的传递有重要的意义.本文研究了五量子位Heisenberg XX 开链中边界量子位之间的纠缠，在该系统中引入了磁杂质和系统杂质且它们之间满足线性关系时，该系统可以精确求解，此时边界量子位之间存在纠缠.选择合适的杂质参数和磁场参数，该边界纠缠的最大值可达到0.5. 关键词： Heisenberg XX开链 边界纠缠 杂质     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Physical implication of two problems in transition prediction of boundary layers based on linear stability theory

Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.     

Combined wave and ray based room acoustic simulations of audio systems in car passenger compartments,Part I: Boundary and source data

The present series of papers summarizes the results of a three-year research project on the realistic simulation of car audio sound in car passenger compartments using a combined Finite Element (FE) and Geometrical Acoustics (GA) approach. The simulations are conducted for the whole audible frequency range with the loudspeakers of the car audio system as the sound sources. The challenges faced during the project relate to fundamental questions regarding the realistic sound field simulation in small enclosures with strong modal and diffraction effects.The paper denoted here as Part I focuses on boundary and source representations in the FE and GA domain and suggests guidelines for a best-possible acquisition of the required data. Since a straight-forward determination of the boundary and source characteristics is mostly hampered by the immense complexity and inhomogeneity of the materials and loudspeaker configurations inside a car compartment, different measurement and calculation methods have been applied to determine the required data and quantify the corresponding uncertainty. The paper clearly points out the strength and weaknesses of the applied methods depending on the considered frequency range and material characteristics. In order to keep the complexity of the FE simulations at a manageable level, all passive boundaries were considered as locally reacting with impedance conditions.Part II of the study applies the obtained data in combined FE-GA room acoustic simulations and compares the simulated room impulse responses (RIR) with corresponding measurement results. In a final step the observed differences in the RIRs are related to the uncertainty and inherent errors in the boundary and source representation.     

Rotation selectivity of random phase encoding in volume holograms

We present the study of angular selectivity for holographic multiplexing based on random phase encoding by a ground glass. The rotational selectivity of the volume hologram is calculated theoretically and coincides with the experimental measurement. By controlling the parameters including rotational center, effective numerical aperture of both volume hologram and the ground glass, we can obtain different rotational selectivity applied to random phase encoding in volume holographic storage.     

无限包层Bragg光纤的传输模式研究

分析得到了横向电场分量和磁场分量所满足的耦合方程,对于介质折射率的不连续处,采用严格的边界条件来处理。基于全矢量模型,使用有限差分法编写了复模式的求解器,并将其应用于Bragg光纤的模式求解和分析。绘制出了Bragg光纤模式谱图,分类分析了在无限包层情况下Bragg光纤模式的基本特性。     

One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

We study a simple microscopic model for the one-dimensional stochastic motion of a (non-)relativistic Brownian particle, embedded into a heat bath consisting of (non-)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic conservation laws for the microscopic collision processes, provided one additionally assumes probabilistic independence of the initial momenta. It is shown that, in the non-relativistic case, the integral criteria do correctly identify the Maxwellian momentum distributions as stationary (invariant) solutions. Subsequently, we apply the same criteria to the relativistic case. Surprisingly, we find here that the stationary momentum distributions differ slightly from the standard Jüttner distribution by an additional prefactor proportional to the inverse relativistic kinetic energy.