Letter: Self-Similar Bianchi Type VIII and IX Models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admits a four dimensional group of homotheties is given.     

A Grain of Dust Falling Through a Sierpinski Gasket

In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket G, where at each layer either absorption or delays are considered. In the case of motion with absorption the explicit distribution of the position of the descending particle in the pre-gasket Gn is obtained and the limiting case of the Sierpinski gasket discussed. For the delayed downward motion we derive a representation of the random time needed to arrive at the base of Gn in terms of independent binomial random variables （containing the contribution of delays at different layers with different geometrical structures）.     

Identifying the Anisotropical Function of a <Emphasis Type="Italic">d</Emphasis>-Dimensional Gaussian Self-similar Process with Stationary Increments

We perform the estimation of the anisotropical function of a Gaussian self-similar process with stationary increments. Article note: In final form 31 May 2005     

Small and Large Scale Behavior of the Poissonized Telecom Process

The stable Telecom process has infinite variance and appears as a limit of renormalized renewal reward processes. We study its Poissonized version where the infinite variance stable measure is replaced by a Poisson point measure. We show that this Poissonized version converges to the stable Telecom process at small scales and to the Gaussian fractional Brownian motion at large scales. This process is therefore locally as well as asymptotically self-similar. The value of the self-similarity parameter at large scales, namely the self-similarity parameter of the limit fractional Brownian motion, depends on the form the Poissonized Telecom process. The Poissonized Telecom process is a Poissonized mixed moving average. We investigate more general Poissonized mixed moving averages as well.     

Self-similarity of nonlinear screening in asymmetric complex plasmas

In this paper, two-component electroneutral systems of finite-sized macroions and oppositely charged point-like microions in the average spherical electroneutral Wigner–Seitz cell with a central macroion are studied. We investigate the self-similarity of nonlinear screening of highly charged macroions by microions in a classical asymmetrically charged complex plasma. This work is devoted to the problem of the relationship between the effective (‘visible’) charge of the macroion Z^* and its initial charge Z taking into account the effect of the nonlinear screening. It is analysed how the form of the dependence Z^*(Z) changes. The self-similarity of this dependence has been demonstrated for various characteristic system temperatures, macroion concentrations, and macroion sizes.     

Oblique entry of a wedge into an ideal incompressible fluid

A new approach to the solution of the self-similar problem of the entry of a wedge into an ideal fluid at an arbitrary angle to the free surface is proposed. The method is based on the construction of the expressions for the complex velocity and the derivative of the complex potential in a parametric variable domain. An integral and an integro-differential equation are obtained for determining the absolute magnitude and the angle of the velocity vector at the free boundary. The calculated results for the free surface shape, the angles of contact between the free surface and the wedge, and the coefficients of the hydrodynamic forces are presented.     

Time Fractional Diffusion: A Discrete Random Walk Approach

The time fractional diffusion equation is obtained from the standarddiffusion equation by replacing the first-order time derivative with afractional derivative of order (0, 1). From a physicalview-point this generalized diffusion equation is obtained from afractional Fick law which describes transport processes with longmemory. The fundamental solution for the Cauchy problem is interpretedas a probability density of a self-similar non-Markovian stochasticprocess related to a phenomenon of slow anomalous diffusion. By adoptinga suitable finite-difference scheme of solution, we generate discretemodels of random walk suitable for simulating random variables whosespatial probability density evolves in time according to this fractionaldiffusion equation.     

Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.     

The near wake structure of a square cylinder

The near wake structure of a square cross section cylinder in flow perpendicular to its length was investigated experimentally over a Reynolds number (based on cylinder width) range of 6700–43,000. The wake structure and the characteristics of the instability wave, scaling on θ at separation, were strongly dependent on the incidence angle () of the freestream velocity. The nondimensional frequency (St_θ) of the instability wave varied within the range predicted for laminar instability frequencies for flat plate wakes, jets and shear layers. For = 22.5°, the freestream velocity was accelerated over the side walls and the deflection of the streamlines (from both sides of the cylinder) towards the center line was higher compared to the streamlines for = 0°. This caused the vortices from both sides of the cylinder to merge by x/d 2, giving the mean velocity distribution typical of a wake profile. For = 0°, the vortices shed from both sides of the cylinder did not merge until x/d 4.5. The separation boundary layer for all cases was either transitional or turbulent, yet the results showed good qualitative, and for some cases even quantitative, agreement with linearized stability results for small amplitude disturbances waves in laminar separation layers.     

双电极对脉冲放电时间间隔τ=0s时的能量增强效应

In this paper we it is presented a self-similar image model based on Fractional Brown Motion (FBM), in which the various structure functions and scale dependent Hurst parameters can be choosed to simulate the scale-dependent textures. The method is quite efficient for generation of realistic nature textures and synthesis of digital holograms. The synthesized digital holograms can be used in laser anti-counterfeiting field.