含强间断导热系数的三维扩散方程数值计算

针对惯性约束聚变领域需要求解的含强间断导热系数的扩散方程,借鉴各向异性导热的思想,给出了一种导热系数定义在网格节点的支撑算子改进格式。改进后的方法保留了支撑算子格式的算子相容性优点。数值算例表明,新方法可以很好地处理含强间断和强非线性的热扩散问题,计算结果保持较高的精度,适合于辐射流体力学问题的模拟。     

含强间断导热系数的三维扩散方程数值计算

针对惯性约束聚变领域需要求解的含强间断导热系数的扩散方程,借鉴各向异性导热的思想,给出了一种导热系数定义在网格节点的支撑算子改进格式。改进后的方法保留了支撑算子格式的算子相容性优点。数值算例表明,新方法可以很好地处理含强间断和强非线性的热扩散问题,计算结果保持较高的精度,适合于辐射流体力学问题的模拟。     

Long-range correlations in time series generated by time-fractional diffusion: A numerical study

Time series models showing power law tails in autocorrelation functions are common in econometrics. A special non-Markovian model for such kind of time series is provided by the random walk introduced by Gorenflo et al. as a discretization of time fractional diffusion. The time series so obtained are analyzed here from a numerical point of view in terms of autocorrelations and covariance matrices.     

Internal magnetic gradient fields in glass bead packs from numerical simulations and constant time diffusion spin echo measurements

Internal magnetic field gradients in water saturated glass bead packs were studied by numerical simulations and a constant time spin echo (CTSE) experiment. The CTSE is comprised of two spin echo refocusing periods where each of the two evolution periods, tau1 and tau2, is varied so that the total evolution, 2(tau1 + tau2), is held constant. The experiment is similar to that introduced by Norwood and Quilter and allows the effects of dephasing due to diffusion in a magnetic field gradient to be separated from other relaxation mechanisms. In our experiments, the magnetic susceptibility difference between the pore fluid and glass beads creates the internal field gradient. CTSE measurements were performed at 7 T (300 MHz 1H) for water saturated in 50 microm diameter glass bead pack. We find that the internal gradients in the center of the pore bodies, where free diffusion applies, is in the range of 10 to 100 G/cm. This fluid volume accounts for < or =10% of the total pore volume. From direct numerical simulations of the internal magnetic field based on a first principles calculation, we find that the major fraction, >90%, of the pore volume has internal gradients of order 500 to 5,000 G/cm. Signals from water in these large gradients is not observed in our CTSE measurements.     

CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: numerical simulation and application

Carr-Purcell-Meiboom-Gill (CPMG) measurements are the primary nuclear magnetic resonance (NMR) technique used for evaluating formation properties and reservoir fluid properties in the well logging industry and laboratory sample analysis. The estimation of bulk volume irreducible (BVI), permeability, and fluid type relies on the accurate interpretation of the spin-spin relaxation time (T(2)) distribution. The interpretation is complicated when spin's self-diffusion in an inhomogeneous field and restricted geometry becomes dominant. The combined effects of field gradient, diffusion, and a restricted geometry are not easily evaluated analytically. We used a numerical method to evaluate the dependence of the free and restricted diffusion on the system parameters in the absence of surface relaxation, which usually can be neglected for the non-wetting fluids (e.g., oil or gas). The parameter space that defines the relaxation process is reduced to two dimensionless groups: D* and tau*. Three relaxation regimes: free diffusion, localization, and motionally averaging regimes are identified in the (log(10)D*, log(10)tau*) domain. The hypothesis that the normalized magnetization, M*, relaxes as a single exponential with a constant dimensionless relaxation time T*(2) is justified for most regions of the parameter space. The numerical simulation results are compared with the analytical solutions from the contour plots of T*(2). The locations of the boundaries between different relaxation regimes, derived from equalizing length scales, are challenged by observed discrepancies between numerical and analytical solutions. After adjustment of boundaries by equalizing T*(2), numerical simulation result and analytical solution match each other for every relaxation regime. The parameters, fluid diffusivity and pore length, can be estimated from analytical solutions in the free diffusion and motionally averaging regimes, respectively. Estimation of the parameters near the boundaries of the regimes may require numerical simulation.     

Turbulent transport processes in a plasma as a diffusion process with random time

It is proposed to apply the statistical analysis of the increments of fluctuating particle fluxes to analyzing the probability characteristics of turbulent transport processes in plasma. Such an approach makes it possible to analyze the dynamic probability characteristics of the process under study. It is shown that, in the plasmas of the L-2M stellarator and the TAU-1 linear device, the increments of local fluctuating particle fluxes are of stochastic character and that their distributions are scale mixtures of Gaussians. In particular, for TAU-1, the increments have the Laplacian distribution (which is a scale mixture of Gaussians with an exponential mixing distribution). This implies that the rate of flux variations is a diffusion process with random time. It is shown that the characteristic growth (damping) time of fluctuations is one order of magnitude shorter than their characteristic correlation time. Physical mechanisms that may be responsible for the random character of the growth (damping) of fluctuations are discussed.     

Classical diffusion in random environments: A new numerical method

We present a numerical method for classical lattice diffusion processes in a random environment. The special merits of the presented procedure in comparison with Monte Carlo methods are in the economy of computer time and storage. As an example for the potential of the method we present results for excitation dynamics in disordered polymer chains.     

A necessary condition for the emergence of diffusion instability in media with nonclassical diffusion

A necessary condition is derived for the emergence of diffusion instability in media in which diffusion does not obey classical Fick laws. The equations derived by Yadav and Horsthemke [Phys. Rev. E 74, 066118 (2006)] using the continuous-time random walk model are employed as equations simulating reaction—diffusion processes. The waiting-time distribution function is represented by the sum of a finite number of exponents. It is shown that passage to the diffusion limit in the time variable is an incorrect operation if it is used to analyze diffusion instability in media with a distribution function that differs from the Poisson distribution function.     

A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure

In this work we present a pressure-correction scheme for the incompressible Navier–Stokes equations combining a discontinuous Galerkin approximation for the velocity and a standard continuous Galerkin approximation for the pressure. The main interest of pressure-correction algorithms is the reduced computational cost compared to monolithic strategies. In this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high Reynolds regimes. The proposed spatial velocity–pressure approximation is LBB stable for equal polynomial orders and it allows adaptive p-refinement for velocity and global p-refinement for pressure. The method is validated against a large set of classical two- and three-dimensional test cases covering a wide range of Reynolds numbers, in which it proves effective both in terms of accuracy and computational cost.     

Effects of diffusion in fluctuating media: A noise-induced phase transition

An example of a noise-induced phase transition in a chemical system with diffusion is studied. It is shown that effects of diffusion can radically change the classical results on extinction and coexistence in the models of Lotka-Volterra type. Fluctuation phenomena near the point of the noise-induced phase transition are discussed.     

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.     

Wave processes in elastic-viscoplastic media with dislocations

The mechanisms of plane harmonic wave propagation in homogeneous and interfaced elastic-viscoplastic media are considered using the field theory of defects with kinematic identities of a dislocation-containing elastic continuum and dynamic equations of the gauge theory of dislocations. The reflection and refraction coefficients were determined for displacement waves and defect field waves with the defect field characterized by the dislocation density tensor and flux density tensor. The dependence of the coefficients on the parameters of the interfaced media is analyzed.     

A fast chaos-based symmetric image cryptosystem with an improved diffusion scheme

In recent years, a number of chaos-based image cryptosystems have been proposed to meet the increasing demand for real-time secure image transmission. In this paper, an improved diffusion scheme named continuous diffusion strategy is proposed to promote the efficiency of the conventional permutation–diffusion type image cipher. The new scheme contains a supplementary diffusion procedure after the conventional diffusion process and the control parameters are altered by the cipher image after the first diffusion procedure. As a result, the difference can be introduced at the beginning and spread out to the whole image, and hence the same level of security can be achieved with fewer overall rounds. Moreover, to further enhance the confusion effect of the diffusion operation, an intensive diffusion approach is proposed, using stretched key stream elements to perform a cyclic shift to the cipher pixels. Extensive cryptanalysis has been performed using differential analysis, key space analysis, key sensitivity analysis and various statistical analyses. Experiment results demonstrate that the new scheme has a high level of security and fast encryption speed for practical image encryption.     

Generalized Langevin equation driven by Lévy processes: A probabilistic, numerical and time series based approach

Lévy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Lévy processes play an important role in the study of the Generalized Langevin Equation (GLE). The solution to the GLE is proposed using stochastic integration in the sense of convergence in probability. Properties of the solution processes are obtained and numerical methods for stochastic integration are developed and applied to examples. Time series methods are applied to obtain estimation formulas for parameters related to the solution process. A Monte Carlo simulation study shows the estimation of the memory function parameter. We also estimate the stability index parameter when the noise is a Lévy process.     

Importance of polarization processes near the electrodes in measurements of the dielectric constant of conducting media

We attempt in the present work to analyze from a unified viewpoint the complicated laws which are observed in experiments when the dielectric constant of media with rather high positive conductivity is measured. The proposed method allows the calculation of the basic parameters of a measuring cell and of the dielectric constant of media.     

A global IBA calculation with constant parameters and theN p N n scheme

It is shown that the principal features of theN _p N_n scheme can be reproduced with an IBA-2 Hamiltonian with constant parameters.