Numerical simulations of random sound waves

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of wave is always attenuated, driven sound waves can be either retarded or speeded up depending on their wavenumber and amplitude and on the strength of the random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.     

One-dimensional simulations of a compressional Z-pinch

One-dimensional numerical simulations of compressional Z-pinch show that the plasma radius after first compression is oscillating in time. Previous experiments with end-on diagnostics showed no evidence of such behavior but a recent series of experiments with side-on diagnostics on hydrogen plasma has shown that this is indeed the case     

One-dimensional random walk with self-interaction

A standard random walk on a one-dimensional integer lattice is considered where the probability ofk self-intersections of a path =(0, (1),..., (n) is proportional toe ^–k . It is proven that for <0,n ^–1/3(n) converges to a certain continuous random variable. For >0 the formulas are given for the asymptotic Westerwater velocity of a generic path and for the variance of the fluctuations about the asymptotic motion.     

One-dimensional numerical analysis of transistor lasers

We demonstrate one-dimensional numerical analysis of transistor lasers (TLs). The high frequency performances of TLs and laser diodes (LDs) are compared. The charging time definitions of the TL and LD are given. The TL has a larger bandwidth and a shorter rise time than the LD due to the shorter charging time in the former. We find that the bandwidth decreases and the eye diagram of 40?Gb/s is degraded with increasing base region width of the TL. Finally, compared with the TL, the bandwidth reduction of LDs at high injection currents is due to a narrower small-signal response for the virtual states carrier density to the modulation current ratio.     

磁化套筒惯性聚变一维集成化数值模拟

磁化套筒惯性聚变(magnetized liner inertial fusion,MagLIF)结合了传统磁约束聚变和惯性约束聚变的优点,理论上可以显著地降低聚变实现的难度,具有极大的应用潜力.以研究MagLIF中的关键问题为目标,建立能够综合考虑磁化、预加热、套筒内爆、聚变反应、端面效应、磁通压缩等多种复杂机制在内的集成化物理模型,特别是通过引入流体喷射模型,使得可以在一维计算条件下考虑具有二维特性的端面损失情况,并额外考虑Nernst扩散项对磁通损失的影响.在此基础上编写实现一维集成化MagLIF数值模拟程序MIST(magnetic implosion simulation tools),与FP-1装置(2 MA,7.2μs)上铝套筒内爆实验结果的对比验证了程序磁流体模块的正确性;将聚变模块纳入后与国外同类程序LASNEX和HYDRA计算结果进行整体比较,所得数值结果总体接近,主要差异体现在燃料温度的计算上,对可能影响的原因进行了简要分析.所建立的集成化模型与程序将为未来开展MagLIF聚变实验研究提供坚实的理论基础和重要工具.     

Dynamic response of linear structures to correlated random impulses

A systematic analysis of the dynamic response of linear continuous structures to randomly arriving impulses is presented. A counting (or point) process characterizing the considered stream of impulses is described by the product density functions of degree one and two. By making use of a normal mode approach and assuming specific forms for the product densities (characterizing the expected arrival rate of the impulses and their correlation) the formulae for the variances and cross-covariances of modal responses are derived. The variance of the plate response is obtained and discussed for different practical situations and the results are shown graphically.     

线谱声源随机运动和随机海洋信道引起的非相干散射

本文采用广义相干函数和广义散射函数的概念探讨线谱声源随机运动和随机海洋声信道引起的非相干散射,指出接收点的散射函数是线谱辐射过程时空过滤函数和随机海洋声信道散射函数的卷积。文中分别给出了声源随机运动和海洋信道随机时延引起的空间频率谱扩展。     

One-dimensional non-nearest-neighbor random walks in the presence of traps

A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

One-dimensional random field Ising model and discrete stochastic mappings

Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.Contribution to the symposium Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebo, CSSR, September 1–6, 1986.     

Visualization techniques in plasma numerical simulations

Numerical simulations of plasma processes usually yield a huge amount of raw numerical data. Information about electric and magnetic fields and particle positions and velocities can be typically obtained. There are two major ways of elaborating these data. First of them is calledplasma diagnostics. We can calculate average values, variances, correlations of variables, etc. These results may be directly comparable with experiments and serve as the typical quantitative output of plasma simulations. The second possibility is theplasma visualization. The results are qualitative only, but serve as vivid display of phenomena in the plasma followed-up. An experience with visualizing electric and magnetic fields via Line Integral Convolution method is described in the first part of the paper. The LIC method serves for visualization of vector fields in two dimensional section of the three dimensional plasma. The field values can be known only in grid points of three-dimensional grid. The second part of the paper is devoted to the visualization techniques of the charged particle motion. The colour tint can be used for particle’s temperature representation. The motion can be visualized by a trace fading away with the distance from the particle. In this manner the impressive animations of the particle motion can be achieved.     

One-dimensional strings, random fluctuations, and complex chaotic structures

The effect of random fluctuations on the set of equations resulting from coupling 200 points with one-dimensional maps is studied. This dynamical system exhibits a spatial exponential growth in fluctuations, resulting in a complex chaotic structure. The system suggests a closer look at stability in complex systems.     

Analysis of numerical limits in 2-D simulations of a ferromagnetic/antiferromagnetic interface using the random field Ising model

This paper explains the Random Field Ising Model simulations of a two-dimensional ferromagnetic/antiferromagnetic interface, influenced by the exchange-bias interaction. Exchange-biased shifts, coercivity fields, the number of unreversed spins as well as the numerical errors are provided. These were tested for different structure dimensions and boundary conditions in order to find limitations of the method. The algorithm developed is simple, very effective, and provides deeper insight into the nature of the exchange-bias phenomenon.     

Direct numerical simulations of electrophoresis of charged colloids

We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier-Stokes equations so that the electrohydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters; however, our simulation predicts notable deviations in the case of dense dispersions.     

A numerical study of sparse random matrices

A numerical study is presented for the eigensolution statistics of largeN×N real and symmetric sparse random matrices as a function of the mean numberp of nonzero elements per row. The model shows classical percolation and quantum localization transitions atp _c =1 andp _q >1, respectively. In the rigid limitp=N we demonstrate that the averaged density of states follows the Wigner semicircle law and the corresponding nearest energy-level-spacing distribution functionP(S) obeys the Wigner surmise. In the very sparse matrix limitpN, withp>p _q a singularity (E))1/¦E¦ is found as¦E¦ 0 and exponential tails develop in the high-¦E¦ regions, but theP(S) distribution remains consistent with level repulsion. The localization properties of the model are examined by studying both the eigenvector amplitude and the density fluctuations. The valuep _q 1.4 is roughly estimated, in agreement with previous studies of the Anderson transition in dilute Bethe lattices.     

Three-dimensional numerical simulations of cellular jet diffusion flames

Recent experimental investigations have demonstrated that the appearance of particular cellular states in circular non-premixed jet flames significantly depends on a number of parameters, including the initial mixture strength, reactant Lewis numbers, and proximity to the extinction limit (Damköhler number). For CO₂-diluted H₂/O₂ jet diffusion flames, these studies have shown that a variety of different cellular patterns or states can form. For given fuel and oxidizer compositions, several preferred states were found to co-exist, and the particular state realized was determined by the initial conditions. To elucidate the dynamics of cellular instabilities, circular non-premixed jet flames are modeled with a combination of three-dimensional numerical simulation and linear stability analysis (LSA). In both formulations, chemistry is described by a single-step, finite-rate reaction, and different reactant Lewis numbers and molecular weights are specified. The three-dimensional numerical simulations show that different cellular flames can be obtained close to extinction and that different states co-exist for the same parameter values. Similar to the experiments, the behavior of the cell structures is sensitive to (numerical) noise. During the transient blow-off process, the flame undergoes transitions to structures with different number of cells, while the flame edge close to the nozzle oscillates in the streamwise direction. For conditions similar to the experiments discussed, the LSA results reveal various cellular instabilities, typically with azimuthal wavenumber m = 1–6. Consistent with previous theoretical work, the propensity for the cellular instabilities is shown to increase with decreasing reactant Lewis number and Damköhler number.     

New proposal for numerical simulations of theta-vacuum-like systems

We propose a new approach to perform numerical simulations of theta-vacuum-like systems, test it in two analytically solvable models, and apply it to CP3. The main new ingredient in our approach is the method used to compute the probability distribution function of the topological charge at theta=0. We do not get unphysical phase transitions (flattening behavior of the free energy density) and reproduce the exact analytical results for the order parameter in the whole theta range within a few percent.