Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder

We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. We obtain rigorous limit theorems for the shape of the interface, the motion of a tagged particle, and the macroscopic density profile on the hydrodynamic scale. The theorems are valid under almost every realization of the disordered rates. Under suitable conditions on the distribution of jump rates the model displays a disorder-dominated low-density phase where spatial inhomogeneities develop below the hydrodynamic resolution. The macroscopic signature of the phase transition is a density discontinuity at the front of the rarefaction wave moving out of an initial step-function profile. Numerical simulations of the density fluctuations ahead of the front suggest slow convergence to the predictions of a deterministic particle model on the real line, which contains only random velocities but no temporal noise.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

Multiple Shocks in Bricklayers' Model

In bricklayers' model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schütz⁽⁴⁾ on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in Balázs,⁽²⁾ valak as seen from the random position of the second class particle.     

Spherical focusing of acoustic pulses in a liquid

Nonlinear processes accompanying the focusing of a microsecond acoustic pulse produced by an electromagnetic source shaped as a spherical segment are investigated. The processes are considered to be far from the boundaries of a liquid, in the absence of cavitation. Detailed measurements of the pressure field by a fiber-optic sensor and high-speed photography of the shock front are performed. The pressure field is found to be determined by the nonlinear effects that occur in the course of the propagation of the initial converging compression wave and an edge rarefaction wave. The peak pressure amplitudes at the focus are 75 and ?42 MPa for the compression and rarefaction waves, respectively, at the maximum voltage of the pulse generator in use. The measured length of the compression wave front is equal to the response time of the sensor (8 ns). The pressure amplitude is shown to be limited by the irregularity of the propagation of a shock wave in the form of Mach’s disk. At the focus, the pressure gradient across the radiator axis reaches 0.5 atm/μm, while the diameter of the focal spot is 2.5±0.2 mm. The focus of the edge rarefaction wave formed due to diffraction is located closer to the radiator than the focus of the compression wave, which may facilitate the study of the biological effect of cavitation independently of the shear motion of the medium.     

守恒律方程组的大时间步长叠波格式

大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.     

随机选取法和多波近似在一维浅水方程大时间步长格式中的应用

利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.     

Exact Connections between Current Fluctuations and the Second Class Particle in a Class of Deposition Models

We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers’ and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations. MSC: 60K35, 82C41     

Mechanism of laser-induced plasma shock wave evolution in air

A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.     

FeMnNi合金冲击相变与卸载逆相变历程研究

采用VISAR测试技术,将正向加载和逆向加载实验相结合,研究了不同加载压力下FeMnNi合金的冲击相变和卸载逆相变历程.结果表明:冲击加载压力与冲击相变阈值之差小于逆相变阈值时,即0＜σp-σt＜σn,FeMnNi合金发生α→ε相变,加载段呈现弹性波、塑性波和相变波三波结构,塑性波在自由面反射稀疏波使FeMnNi合金完...     

Superdiffusivity of Asymmetric Exclusion Process in Dimensions One and Two

We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as t ^1/4 in dimension d=1 and (logt)^1/2 in d=2. The method applies to nearest and non-nearest neighbor asymmetric exclusion processes.     

Nonself-similar regimes of isothermal collapse of protostellar clouds

We consider the development of inhomogeneity in the isothermal collapse of protostellar clouds. The initial and boundary conditions correspond to the classical statement of the problem on the contraction of a homogeneous cloud from a given volume. A centered rarefaction wave is shown to propagate from the outer boundary of the cloud toward its center at the first collapse stage. Analysis reveals two possible regimes of isothermal collapse, depending on the relationship between the rarefaction wave focusing time t^* and the cloud free-fall collapse time t_ff. For cold clouds, t^*=t _ff and the rarefaction wave is not reflected. In this case, as time elapses, the cloud collapse becomes self-similar with the characteristic density profile ρ～r^?2. In hot clouds, t*<t _ff and the focusing can take place before the formation of an opaque core. Since the velocities of the rarefaction wave along and across magnetic field lines in a magnetized cloud are different, its front assumes a shape elongated along magnetic field lines. Depending on the initial conditions, based on analytical estimates, we investigate various possible scenarios for the collapse of magnetic protostellar clouds.     

Transverse rarefaction of a layer behind the front of a longitudinal wave of nonlinear thermal conductivity and features of plasma formation inside the target cavity

A solution of the two-dimensional problem is presented for a transverse rarefaction wave of a plane layer behind a wavefront of nonlinear thermal conductivity produced by an instantaneous cylindrical energy source with its axis normal to the layer surface. The matter can rarefy through the free surfaces of the layer or through holes in the boundary walls, which are coaxial with the energy source axis. Analytic solutions are obtained describing the formation of the rear boundary in the heated zone due to transverse matter rarefaction. The energy fraction transferred to the energy of hydrodynamic motion is also determined. Models of plasma formation inside the inner target cavity under the action of pulsed energy sources are considered as applications of the approach suggested. Requirements on the source and target parameters are formulated for efficient matter heating with minimum energy losses caused by hydrodynamic rarefaction of the matter. Translated from Preprint No. 14 of the P. N. Lebedev Physical Institute, Moscow (1998).     

冲击加载下FeMnNi合金相变和层裂特性实验研究(英文)

采用激光速度干涉仪(VISAR)、X射线衍射(XRD)和扫描电镜(SEM)联合测试技术,利用等厚对称加载和逆向加载实验,研究了Fe MnNi合金的冲击相变和层裂行为。结果发现:加载压力大于6.5 GPa时,Fe MnNi合金样品发生α→ε相变;中心稀疏波的卸载作用使内压力降至4~5 GPa时,Fe MnNi合金样品发生ε→α逆相变,并伴有卸载稀疏冲击波形成。分析Fe MnNi合金样品中塑性波、相变波、稀疏波和稀疏冲击波的传播作用过程,发现加载压力大于其相变应力时,等厚对称加载下Fe MnNi合金存在产生层裂行为的物理机制。     

Pulsed volume discharge with preionization in two-dimensional gasdynamic flow

The interaction between a pulsed volume discharge with preionization by ultraviolet radiation from plasma sheets and a gasdynamic flow with a known density distribution is studied experimentally. The complex quasi-two-dimensional flow that emerges after the diffraction of a plane shock wave by rectangular obstacles in the channel is experimentally studied and numerically simulated. The glow intensity fields for an unsteady gasdynamic flow are imaged for the first time when recording the plasma radiation from a pulsed discharge in the flow. Since the ionization duration is short (150–200 ns), the gas-flow structure does not change and the flow does not heat up in the glow time of the discharge plasma in the flow. Our images are compared with the reciprocal-density fields of the corresponding two-dimensional gas flow. The effects of gasdynamic structures on the discharge plasma redistribution in the flow are analyzed. The energy contribution is localized into low-density zones (vortices, rarefaction waves) and into regions of density jumps and significant density gradients. The discharge current from adjacent regions with low E/N is redistributed into these zones. Breakdown channels are formed along rarefaction waves, vortices, and discontinuity surfaces between high-electron-density regions.     

A simple nonlinear element model

We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.     

Burgers方程的声速点故障问题

研究了在Burgers方程跨声速稀疏波计算中遇到的sonic point glitch问题,对它产生的原因及其与数值格式熵条件的关系进行了分析.对若干著名格式,按照是否满足熵条件进行了分类.为了消除sonic point glitch现象,提出了一种新的两步分裂方法,并用这种方法改进了一系列典型格式.数值试验表明这是一种很好的消除sonic point glitch的方法.     

Possible localized transport induced by a wave propagating along a vacuum–matter interface

Macroscopic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum–matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the matter-freezed or zero-volume-flow-rate states for specific Reynolds numbers and wave numbers which might be linked to the evolution of the Universe.     

Death and Resurrection of a Current by Disorder,Interaction or Periodic Driving

We present several models of biased transport on (random) comb-like structures and on percolating backbones, that allow full mathematical control. We show how power-law corrections in the distribution of trap sizes may lead to a discontinuity in the current-field characteristic: the current jumps to zero when the driving exceeds a threshold. The current may resurrect when the field is modulated in time, also discontinuously: a little shaking enables the current to jump up. Finally, exclusion between particles postpones or even prevents the current from dying, while attraction such as modeled in zero range processes may expedite it.     

On the Asymmetric Zero-Range in the Rarefaction Fan

We consider one-dimensional asymmetric zero-range processes starting from a step decreasing profile leading, in the hydrodynamic limit, to the rarefaction fan of the associated hydrodynamic equation. Under that initial condition, and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps, we derive the Law of Large Numbers for a second class particle, under the initial configuration in which all positive sites are empty, all negative sites are occupied with infinitely many first class particles and there is a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle it picks randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation, through some sort of renormalization function. By coupling the constant-rate totally asymmetric zero-range with the totally asymmetric simple exclusion, we derive limiting laws for more general initial conditions.     

An analysis of 1D finite-volume methods for geophysical problems on refined grids

This paper examines high-order unstaggered symmetric and upwind finite-volume discretizations of the advection equation in the presence of an abrupt discontinuity in grid resolution. An approach for characterizing the initial amplitude of a parasitic mode as well as its decay rate away from a grid resolution discontinuity is presented. Using a combination of numerical analysis and empirical studies it is shown that spurious parasitic modes, which are artificially generated by the resolution discontinuity, are mostly undamped by symmetric finite-volume schemes but are quickly removed by upwind and semi-Lagrangian integrated mass (SLIM) schemes. Slope/curvature limiting is insufficient to completely remove these modes, especially at low forcing frequencies where the incident wave can act as a carrier of the parasitic mode. Increasing the order of accuracy of the reconstruction at the grid interface is effective at removing noise from the lowest-frequency incident modes, but insufficient at high frequencies. It is shown that this analysis can be extended to the 1D linear shallow-water equations via Riemann invariants.