涡场中黏附性颗粒团聚体粒径分布的预测

黏附性颗粒团聚现象在自然界和工业界普遍存在,扰动流场中黏附性颗粒间的碰撞、摩擦和吸附等动力学行为,导致团聚体形态不断演化,准确预测黏附性颗粒团聚体的粒径分布是调控颗粒团聚过程的重要前提。本文通过二维泰勒格林涡场中黏附性颗粒团聚的数值模拟研究,明确了利用Monte Carlo模型预测团聚体粒径分布的可行性及其适用范围,发现当黏附性颗粒间内聚数小于3.5×10^?4时,Monte Carlo模型可较好的预测团聚体粒径分布,且相对误差小于±30%;而当内聚数大于3.5×10^?4后,Monte Carlo模型不再适用。     

Stability of Tangential Discontinuity for the Vortex Pancakes

JETP Letters - Within the incompressible three-dimensional Euler equations, we study the pancake-like high vorticity regions, which arise during the onset of developed hydrodynamic turbulence. We...     

Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States

Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the extended Clausius relation for NESS, where the heat in the original relation is replaced by its “renormalized” counterpart called the excess heat, and the Gibbs-Shannon expression for the entropy by a new symmetrized Gibbs-Shannon-like expression. Here we concentrate on Markov processes describing heat conducting systems, and develop a new method for deriving thermodynamic relations. We first present a new simpler derivation of the extended Clausius relation, and clarify its close relation with the linear response theory. We then derive a new improved extended Clausius relation with a “nonlinear nonequilibrium” contribution which is written as a correlation between work and heat. We argue that the “nonlinear nonequilibrium” contribution is unavoidable, and is determined uniquely once we accept the (very natural) definition of the excess heat. Moreover it turns out that to operationally determine the difference in the nonequilibrium entropy to the second order in the temperature difference, one may only use the previous Clausius relation without a nonlinear term or must use the new relation, depending on the operation (i.e., the path in the parameter space). This peculiar “twist” may be a clue to a better understanding of thermodynamics and statistical mechanics of NESS.     

The Stability of the Non-Equilibrium Steady States

We show that the non-equilibrium steady state (NESS) of the free lattice Fermion model far from equilibrium is macroscopically unstable. The problem is translated to that of the spectral analysis of the Liouville Operator. We use the method of positive commutators to investigate it. We construct a positive commutator on the lattice Fermion system, whose dispersion relation is (k)=cosk–.     

On the Stability of a Singular Vortex Dynamics

In this paper we address the question of the singular vortex dynamics exhibited in [15], which generates a corner in finite time. The purpose is to prove that under some appropriate small regular perturbation the corner still remains. Our approach uses the Hasimoto transform and deals with the long range scattering properties of a Gross-Pitaevski equation with time-variable coefficients.     

Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems

In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff problems $K_{σ,τ}$ is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for $K_{σ,0}$ are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.     

Nonlinear Stability of MKdV Breathers

Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H ² topology. Our proof introduces a new Lyapunov functional, at the H ² level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicity of the solution, as well as a direct control of the corresponding instability modes. In particular, degenerate directions are controlled using low-regularity conservation laws.     

具有尺寸限制的点接触结构自旋极化电流驱动下磁涡旋的稳态振荡

选取具有尺寸限制的点接触结构作为研究对象,采用Thiele方程对模型中磁涡旋在自旋极化电流作用下的动力学行为进行计算.计算表明磁涡旋可以在一定的电流密度范围内稳定旋转,该稳定旋转可以存在的电流密度范围与点接触区的大小和纳米点的尺寸有关.当磁涡旋核作稳态旋转时,其所处的轨道半径以及旋转频率都随电流密度的增加而增加,旋转频率可调节的范围随点接触尺寸的增加快速减小.     

利用高非线性光纤产生量子关联光子对的实验研究

光纤中基于三阶(克尔)非线性效应的自发四波混频是制备量子关联光子对的有效方法之一。若采用商售高非线性光纤作为产生光子对的非线性介质,则有利于减小所需光纤的长度,从而缩小实验装置体积并降低对于抽运源的要求。利用脉冲光抽运20m的高非线性光纤产生通讯波段的频率近简并关联光子对,研究了光纤的弱双折射特性对于光子对产生的影响。当抽运光沿高非线性光纤的偏振轴入射时,具有最大的光子对产生效率,且光子对绝大部分与抽运光偏振平行;抽运光沿与光纤偏振轴45°入射时,光子对的产生效率最小,约为最大值的80%。     

Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schrödinger Equations

We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.     

Global Stability of Vortex Solutions of the Two-Dimensional Navier-Stokes Equation

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-Stokes equation whose initial vorticity distribution is integrable converges to an explicit self-similar solution called Oseens vortex. This implies that the Oseen vortices are dynamically stable for all values of the circulation Reynolds number, and our approach also shows that these vortices are the only solutions of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. Finally, under slightly stronger assumptions on the vorticity distribution, we give precise estimates on the rate of convergence toward the vortex.Acknowledgement The first author is indebted to J. Dolbeault and, especially, to C. Villani for suggesting the beautiful idea of using the Boltzmann entropy functional in the context of the two-dimensional Navier-Stokes equation. The research of C.E.W. is supported in part by the NSF under grant DMS-0103915.     

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption

In this paper, by solving a complex nonlinear Schr¨odinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain.Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.     

基于非线性涡格法的快速静气动弹性数值模拟技术

基于2.5D RANS数据和VLM耦合的方式,发展了一种考虑非线性流动效应的混合型涡格法HVLM.采用矩形直/后掠机翼两个外形的跨声速算例,通过与VLM、三维CFD计算数据的比较,对HVLM的气动力预测精度进行了分析与评估.对比结果表明,HVLM在大幅降低时间成本的前提下可以获得和三维CFD方法预测值十分接近的计算数据,对线化VLM方法的修正效果显著.然后,HVLM与悬臂梁有限元求解耦合,实现了一种面向三维机翼的快速静气动弹性数值模拟技术,并通过矩形直机翼算例进行了验证.耦合算例的时间分析数据表明,HVLM/Beam耦合的方式能够在10 s以内完成1次三维机翼静气动弹性分析,在气动/结构耦合分析、优化设计方面展示出了良好的应用前景.      

Nonlinear Instability of Inhomogeneous Steady States Solutions to the HMF Model

Journal of Statistical Physics - In this work we prove the nonlinear instability of inhomogeneous steady states solutions to the Hamiltonian mean field (HMF) model. We first study the linear...     

Evolved Algorithm and Vibration Stability for Nonlinear Disturbed Security Systems

In this paper, a method sustaining system stability after decomposition is proposed. Based on the stability criterion derived from the energy function, a set of intelligent controllers is synthesized which is used to maintain the stability of the system. The sustainable stability problem can be reformulated as a Linear Matrix Inequalities (LMI) problem. The key to guaranteeing the stability of the system as a whole is to find a common symmetrically positive definite matrix for all subsystems. Furthermore, the Evolved Bat Algorithm (EBA) is employed to replace the pole assignment method and the conventional mathematical methods for solving the LMI. The EBA is utilized to find feasible solutions in terms of the energy equation. The experimental results show that the EBA is capable of providing proper solutions, which satisfy the sustainability and stability criteria, after a short period of recursive computing.     

空气中紫外波长局域涡旋光孤子的解及其稳定性

根据紫外波长光束在空气中传输时的非线性效应得到包含氧分子三光子电离等非线性效应的薛定谔方程。由该非线性薛定谔方程出发,研究了紫外波长光束在空气中传输时局域涡旋光孤子的形成。将涡旋孤子的形成和粒子在势阱中的运动联系起来,讨论了光束在空气中形成局域涡旋光孤子的初始条件。数值求解了柱坐标下的涡旋孤子解,随着初始幅值的变化,方程出现单环、双环等孤子解;分析了孤子解光强分布随着传播常数的变化情况,并得出光束尺度和脉冲能量对应初始幅值的变化关系。同时分析了孤子解的扰动稳定性,验证了Skarka所推导的一般性判据。     

Higher-Order Rogue Wave Pairs in the Coupled Cubic-Quintic Nonlinear Schrödinger Equations

We study some novel patterns of rogue wave in the coupled cubic-quintic nonlinear Schrödinger equations. Utilizing the generalized Darboux transformation, the higher-order rogue wave pairs of the coupled system are generated. Especially, the first-and second-order rogue wave pairs are discussed in detail. It demonstrates that two classical fundamental rogue waves can be emerged from the first-order case and four or six classical fundamental rogue waves from the second-order case. In the second-order rogue wave solution, the distribution structures can be in triangle, quadrilateral and ring shapes by fixing appropriate values of the free parameters. In contrast to single-component systems, there are always more abundant rogue wave structures in multi-component ones. It is shown that the two higher-order nonlinear coefficients ρ₁ and ρ₂ make some skews of the rogue waves.