Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M_t/M_t/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.     

吸积盘的X射线辐射对周围星际物质的离化研究

利用辐射流体力学程序对三倍频纳秒激光与靶物质相互作用进行了模拟研究，得到了可以产生黑体辐射谱分布的激光等离子体X射线辐射靶的最佳厚度；数值模拟研究了黑体谱分布的X射线辐射场对等离子体系统平均离化度分布的影响，它有助于深入理解天体物理中吸积盘对它周围星际物质的离化影响. 关键词： 辐射流体力学 激光等离子体 X射线辐射 吸积盘 离化     

年龄相关的非线性时变种群扩散系统最优分布控制的存在性

讨论了一类非线性时变种群扩散系统的最优分布控制问题,利用LionsJL的偏微控制理论和先验估计,证明了系统最优分布控制的存在性.所得结果可为非线性种群扩散系统中的最优控制问题的实际研究提供必要的理论基础.     

An efficient hydrodynamic cellular automata for simulating fluids with large viscosities

A hydrodynamic cellular automata (HDCA) for simulating two-dimensional fluids with large viscosities is proposed. The model is characterized by a mean free path which is of the same size as in the FHP-II model, but with a viscosity more than 10 times larger. This new model should make simulations of flows at low Reynolds number more efficient.     

A bi-virus competing model with time-varying susceptibility and repeated infection

This paper introduces a bi-virus model with time-varying susceptibility. The model describes the case that there coexist two viruses and the time-varying susceptibility due to repeated infections. For different parameters, we investigate the stability of various equilibriums. Under appropriate conditions the two viruses show competitive relationship, that is, one virus will eventually become a pandemic, and the other virus will eventually disappear. For this case, we further study the dynamical behavior of virus transmission. The model shows some new phenomena, that is, the outbreak of the virus will be delayed appropriately, giving people an illusion. Finally, we present a numerical example to illustrate the effectiveness of the theoretical results.     

Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients

In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.     

Influence of static and dynamical structural changes on ultrafast processes mediated by conical intersections

The technological needs imposed by the exponential miniaturization trend of conventional electronic devices has drawn attention towards the development of smaller and faster devices like ultrafast molecular switches. In recent years molecular switches emerge again in the focus of active and innovative research with state-of-the-art optical tools recording their dynamics in real time. Still many questions about the underlying microscopic mechanism are left open, including potential factors that effect the switching process in either way, improve or worsen it. Due to the complexity of such molecules it is difficult to obtain a global answer from experiment alone. On the other side molecular switches are generally too large for a complete quantum chemical and quantum dynamical calculation. In our group we therefore developed an ab initio based modular model to handle the laser induced quantum dynamics in molecular switches like fulgides. It enables us to study the effect of internal molecular coupling and of the molecular response to external fields. We can investigate the related wave packet dynamics, the switching efficiency and the controllability. Our results focus on the laser induced ring opening in fulgides, which equals one direction of the switching process. Presented are the influence of a conical intersection seam and of time-dependent potentials, mimicking the mean interaction with the environment. Furthermore the relation of controllability and the wave packet's momentum is studied and the influence of potential barriers on the switching dynamics is shown.     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.     

Three‐dimensional wave impact on a rigid structure using smoothed particle hydrodynamics

Navier–Stokes computations of a wave–structure interaction are performed with the aim of assessing the potential of smoothed particle hydrodynamics to accurately estimate impact loading time history. A three‐dimensional dam‐break flow with a rectangular column located downstream is considered. The net force and impulse exerted on the column is monitored throughout the simulation with the results correlating well with existing experimental data. Initial and boundary conditions and numerical parameters are varied and their effect on the column load investigated. The column load is found to be most sensitive to the choice of boundary treatment. Copyright © 2011 John Wiley & Sons, Ltd.