A process of axisymmetric unlimited shock-free compression of a perfect gas

Using Sidorov's ideas and analytical methods for solving the problem of the shock-free compression of a gas acted upon by a piston, a new parameterc form of the solution of the equation for the self-similar velocity potential of a gas is proposed. This enables the problem of constructing the flow with an unlimited increase in the gas-dynamic parameters to be reduced to solving the Cauchy problem for a single ordinary differential equation with a bounded integration interval. The solution of the gas-dynamic equations thus obtained may be of interest in constructing the process of unlimited compression of a perfect gas, at rest at the initial instant of time inside a solid of revolution of the “plate” type, and its describes the gas flow in a certain part of the compressed volume. Asymptotic estimates of the gas-dynamic quantities are established analytically.     

Approximate analytical solutions for strong shocks with variable energy

Approximate analytical solutions are obtained for self-similar flows behind strong shocks with variable energy deposition or withdrawal at the wavefront in a perfect gas at rest with constant initial density. Numerical solutions are also obtained and the approximate solutions agree with these solutions. The effect of the adiabatic index on the solutions is investigated. The dependence of shock density ratio on the parameter characterizing the energy of the flow is studied. It is observed that the rate of deposition of energy at the wavefront decreases with increase of the parameter that specifies the total energy of the flow.     

Two-dimensional interaction of riemann compression waves

A class of solutions of the gas-dynamics equations containing a function arbitrariness is used for a qualitative and quantitative analysis of the gas flow which occurs as a result of the interaction between Riemann compression waves. Two types of flow are investigated matched flow, when the adiabatic exponent is matched in a special way with the initial geometry of the compressed volume, and the general case when there is no such matching. For matched interaction of non-self-similar Riemann waves, a phenomenon of partial collapse is established (only part of the initial mass of the gas is compressed to a point); here the asymptotic estimates for the velocity, density, internal energy and optical thickness are the same as for self-similar compression. It is proved that unmatched interaction of self-similar Riemann waves does not lead to unlimited unshocked compression of the gas; in this case a shock wave occurs when the maximum density of the gas is finite. The results obtained enable us to say that two-dimensional processes of unlimited compression are stable for a fairly wide range of perturbations.     

Spherical rarefaction flow in the neighbourhood of a reflection point of a “boundary” characteristic

The structure of the one-dimensional steady spherically symmetric rarefaction flow of an ideal (inviscid and non-heat-conducting) gas in the neighbourhood of a reflection point of a “boundary” C⁻-characteristic is investigated in principal order. The “boundary” C⁻-characteristic separates the gas at rest from the flow due to the outward motion of a piston which confines the gas. In the rt plane, where r is the distance from the centre of symmetry and t is the time, the reflection point, which coincides with the point of arrival on the t axis of the boundary characteristic, coincides with the origin of coordinates. The initial velocity of the piston may be zero (for positive acceleration) or finite. When two symmetrical plane pistons advance, the “derived” derivatives of all the flow parameters on the C⁻-characteristic at the origin of coordinates, which in this case lies on the plane of symmetry, are finite. When a cylindrical and spherical piston advance, the derived derivative of the pressure (velocity) of the gas on the C⁻-characteristic at the origin of coordinates becomes minus (plus)-infinity although without intersecting characteristics of the same family [1–4].     

Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces

We use particular fuzzy relation equations for compression/decompression of colour images in the RGB and YUV spaces, by comparing the results of the reconstructed images obtained in both cases. Our tests are made over well known images of 256×256 pixels (8 bits per pixel in each band) extracted from Corel Gallery. After the decomposition of each image in the three bands of the RGB and YUV colour spaces, the compression is performed using fuzzy relation equations of “min - →_t” type, where “t” is the Lukasiewicz t-norm and “→_t” is its residuum. Any image is subdivided in blocks and each block is compressed by optimizing a parameter inserted in the Gaussian membership functions of the fuzzy sets, used as coders in the fuzzy equations. The decompression process is realized via a fuzzy relation equation of max-t type. In both RGB and YUV spaces we evaluate and compare the root means square error (RMSE) and the consequentpeak signal to noise ratio (PSNR) on the decompressed images with respect to the original image under several compression rates.     

弱重力场中的平面活塞运动

本文分析了弱重力场中等速活塞运动驱动恒星大气的气体动力学过程.在活塞前面,气体被压缩.压缩气体利用其部分内能,以及有些情况下其动能,以克服外加重力.当逃逸速度与等离子体速度之比值为一小参数时,所有量可对小参数展开,基态解给出均匀流,如同没有重力场的气体动力学所讨论的那样.一阶关系给出外加引力场对流场的影响,即激波强度变化不大而气体内能不断耗散.对于强激波和活塞附近,近似得到的分析解有类似的特征.由于外加重力场在天体物理和大气物理过程中的重要性,这些结果对于恒星和行星大气中瞬变过程的机制会有启发.     

基于自适应小波变换和矢量量化的图像压缩编码

运用小波变换进行图像压缩的算法其核心都是小波变换的多分辨率分析以及对不同尺度的小波系数的量化和编码 .本文提出了一种基于能量的自适应小波变换和矢量量化相结合的压缩算法 .即在一定的能量准则下 ,根据子图像的能量大小决定是否进行小波分解 ,然后给出恰当的小波系数量化 .在量化过程中 ,采用一种改进的LBG算法进行码书的训练 .实验表明 ,本算法广泛适用于不同特征的数字图像 ,在取得较高峰值信噪比的同时可以获得较高的重建图像质量 .     

Spherical shock wave generated by a moving piston in mixture of a non-ideal gas and small solid particles under a gravitational field

Self-similar solutions are obtained for one-dimensional isothermal and adiabatic unsteady flows behind a strong spherical shock wave propagating in a dusty gas. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of a non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-conditions are maintained and variable energy input is continuously supplied by the piston. The medium is under the influence of the gravitational field due to a heavy nucleus at the origin (Roche model). The effects of an increase in the mass concentration of solid particles, the ratio of the density of the solid particles to the initial density of the gas, the gravitational parameter and the parameter of non-idealness of the gas in the mixture, are investigated. It is shown that due to presence of gravitational field the compressibility of the medium at any point in the flow-field behind the shock decreases and all other flow-variables and the shock strength increase. A comparison has also been made between the isothermal and adiabatic flows. It is investigated that the singularity in the density and compressibility distributions near the piston in the case of adiabatic flow are removed when the flow is isothermal.     

Approximate calculation method for one-dimensional gas flows induced by nonmonotonic motion of a piston : PMM vol. 40, n 6, 1976, pp. 1058–1064

The problem of one-dimensional piston which at the beginning moves with increasing velocity into a gas at rest, then is decelerated, and finally stops, is solved by means of special series. The gas flow field is constructed by a successive joining of three characteristic Cauchy problems in terms of their characteristic solutions. Generalized solution of the problem of instantaneous arrest of the piston is derived. Obtained equations are used for the approximate calculation of the motion of generated shock waves.Representation of solutions of certain boundary value problems for nonlinear equations of the hyperbolic kind in the form of special series was proposed in [1, 2], The problem of the piston moving into a gas at rest is solved there, and the obtained solution was used for an approximate determination of the generated shock wave. The piston velocity was assumed to be monotonically increasing. That problem is solved here with the use of similar series in the case when the piston velocity is nonmonotonous,Numerical methods make it possible at present to determine one-dimensional flows similar to that considered below, and multidimensional problems can be solved by the method proposed in [1, 2]. The use of the proposed scheme for solving the problem of the multidimensional piston, whose velocity is nonmonotonous, does not present theoretical difficulties, but except that the formulas are more cumbersome.     

On iterative and Monte Carlo solutions of the Boltzmann equation

The two most commonly used techniques for solving the Boltzmann equation, with given boundary conditions, are first iterative equations (typically the BGK equation) and Monte Carlo methods. The present work examines the accuracy of two different iterative solutions compared with that of an advanced Monte Carlo solution for a one-dimensional shock wave in a hard sphere gas. It is found that by comparison with the Monte Carlo solution the BGK model is not as satisfactory as the other first iterative solution (Holway's) and that the BGK solution may be improved by using directional temperatures rather than a mean temperature.     

Medium‐term horizon volatility forecasting: A comparative study

In this paper, volatility is estimated and then forecast using unobserved components‐realized volatility (UC‐RV) models as well as constant volatility and GARCH models. With the objective of forecasting medium‐term horizon volatility, various prediction methods are employed: multi‐period prediction, variable sampling intervals and scaling. The optimality of these methods is compared in terms of their forecasting performance. To this end, several UC‐RV models are presented and then calibrated using the Kalman filter. Validation is based on the standard errors on the parameter estimates and a comparison with other models employed in the literature such as constant volatility and GARCH models. Although we have volatility forecasting for the computation of Value‐at‐Risk in mind the methodology presented has wider applications. This investigation into practical volatility forecasting complements the substantial body of work on realized volatility‐based modelling in business. Copyright © 2007 John Wiley & Sons, Ltd.     

Graphical simulation of bushfire spread

Four methods for the computer simulation of bushfires are compared. Three of these are grid models, based on work by Kourtz and O'Regan, Frandsen and Andrews, and Green. A fourth contour-based “Huygens” method is due to Anderson et al. Green's method is found to be the most general but to require very much more computation. The grid methods of Kourtz and O'Regan and Frandsen and Andrews execute quickly but produce severe distortion of fire shapes. The Huygens method executes quickly and produces little distortion, but has problems coping with nonhomogeneous conditions.     

A flow of a heat-conducting gas analogous to a centred Riemann wave

A flow of a heat-conducting non-viscous gas, analogous to a centred Riemann wave and transmitting an intense compression of one-dimensional layers of gas is described using a special infinite converging series, taking a number of physical effects into account.     

Multidimensional stability of traveling fronts in monostable reaction-difusion equations with complex perturbations

This paper studies the multidimensional stability of traveling fronts in monostable reaction-difusion equations,including Ginzburg-Landau equations and Fisher-KPP equations.Eckmann and Wayne(1994)showed a one-dimensional stability result of traveling fronts with speeds c c(the critical speed)under complex perturbations.In the present work,we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions(n=2,3),employing weighted energy methods.     

Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems

For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on “parallelism across the problem”, on “parallelism across the method” and on “parallelism across the steps”. The first type of parallelism does not require special integration methods and can be exploited within any available IVP solver. The method-parallelism approach received much attention, particularly within the class of explicit Runge-Kutta methods originating from fixed point iteration of implicit Runge-Kutta methods of Gaussian type. The construction and implementation on a parallel machine of such methods is extremely simple. Since the computational work per processor is modest with respect to the number of data to be exchanged between the various processors, this type of parallelism is most suitable for shared memory systems. The required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor 2. The third type of parallelism (step-parallelism) can be achieved in any IVP solver based on predictor-corrector iteration and requires the processors to communicate after each full iteration. If the iterations have sufficient computational volume, then the step-parallel approach may be suitable for implementation on distributed memory systems. Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The dynamic step-parallel iteration process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to achieve speed-up factors up to 15.     

The uniform saturation property for a singularly perturbed reaction-diffusion equation

Although adaptive finite element methods for solving elliptic problems often work well in practice, they are usually not proven to converge. For Poisson like problems, an exception is given by the method of Dörfler ([8]), that was later improved by Morin, Nochetto and Siebert ([11]). In this paper we extend these methods by constructing an adaptive finite element method for a singularly perturbed reaction-diffusion equation that, in energy norm, converges uniformly in the size of the reaction term. Moreover, in this algorithm the arising Galerkin systems are solved only inexactly, so that, generally, the number of arithmetic operations is equivalent to the number of triangles in the final partition.This work was supported by the Netherlands Organization for Scientific Research and by the EU-IHP project “Breaking Complexity.”     

Lattice-Boltzmann Models for heat transfer

A multispeed heat transfer lattice Boltzmann model is presented. The model possesses the perfect gas state equation with arbitrary special heat ratio. The macroscopic conservation equations are derived by the Chapman-Enskog method. The one dimensional simulation for the sinusoidal energy distributions are compared with the theoretical results, showing good agreement. The theoretical conductivity in the energy equation is in accordance with the simulations.     

Mass,momentum and energy conservation laws in zero-pressure gas dynamics and δ-shocks: II

We study δ-shocks in a one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers (see References) this system is considered in the form of mass, momentum and energy conservation laws. In order to define such singular solutions, special integral identities are introduced which extend the concept of classical weak solutions. Using these integral identities, the Rankine–Hugoniot conditions for δ-shocks are obtained. It is proved that the mass, momentum and energy transport processes between the area outside the of one-dimensional δ-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving δ-shock wave front are going on. At the same time the total kinetic energy transforms into total internal energy.     

Singular perturbations in one-dimensional unsteady motion of a real gas : PMM vol. 39, n 6, 1975, pp. 1051–1059

Navier-Stokes equations for one-dimensional motion of gas are reduced to a special dimensionless form convenient for investigations involving a perturbation front. In new variables the transition from limit conditions of motion of an inviscid non-heat-conducting gas to the case of small but finite coefficients of viscosity and thermal conductivity, which is simulated by a perfect gas with singular perturbations induced by the indicated dissipative factors. We establish the inevitability of existence of two regions of singular perturbations, the neighborhood of the perturbation front and that of the point (line, surface) where the investigated motion is generated. The derivation of equations for both boundary layers, which is valid for a fairly general statement of problems of this kind, is presented and conditions of merging with the external (adiabatic) flow are formulated. Examples of computation of motion in boundary layers in problems of piston and point explosion are presented.