Modeling of the vaporization front on a heater surface

The boiling-up of a metastable liquid with appearing vaporization fronts is theoretically considered. The boiling-up occurs usually on the surface of a heater. At the initial stage, growth of a spherical vapor bubble is observed. If the temperature of the liquid exceeds a threshold value, the vaporization fronts develop near the line of contact of a vapor bubble and the heater. The vaporization fronts extend along the heater with a constant speed. A model of steady propagation of the vaporization front is developed. The temperature and propagation velocity of the interface are determined from the balance equations of mass, momentum, and energy in the neighborhood of the vaporization front and from the stability condition of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The propagation velocity of the vaporization front also has the threshold value. The calculated velocity of interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid.     

Propagation of fronts in activator-inhibitor systems with a cutoff

We consider a two-component system of reaction-diffusion equations with a small cutoff in the reaction term. A semi-analytical solution of fronts and how the front velocities vary with the parameters are given for the case when the system has a piecewise linear nonlinearity. We find the existence of a nonequilibrium Ising-Bloch bifurcation for the front speed when the cutoff is present. Numerical results of solutions to these equations are also presented and they allow us to consider the collision between fronts, and the existence of different types of traveling waves emerging from random initial conditions.     

Photon acceleration in superluminous and accelerated ionizationfronts

The interaction of an electromagnetic wave packet with a superluminous ionization front is described here using the Hamiltonian theory of photon acceleration. We also describe the interaction with accelerated ionization fronts. The different qualitative photon trajectories are presented for both cases. The frequency up-shift is also derived. It is shown that a proper tailoring of the ionization front velocity can lead to higher frequency up-shifts than in constant velocity ionization fronts     

On the velocity of electromagnetic and gravitational wave fronts

It is shown that, in the space of the general theory of relativity, the velocity of an electromagnetic wave front in a non-inertial frame of reference, and of electromagnetic and gravitational wave fronts in a synchronous frame of reference, is constant and equal to the fundamental velocity. It is noted that the concept of a wave front is meaningful in synchronous frames of reference, of which inertial systems in a Minkowski world are a special case.     

Complex patterns in reaction-diffusion systems: A tale of two front instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatiotemporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.     

Effect of periodic corrugation,reinforcement, heterogeneity and initial stress on Love wave propagation

This paper investigates the impact of corrugated boundary surfaces, reinforcement on the propagation of Love-type wave in prestressed corrugated heterogeneous fiber-reinforced layer resting over a void pores half-space. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion equation in the complex form has been derived using method of separation of variables. The real and imaginary parts of the complex dispersion equation were separated and found in well agreement with the classical Love wave equation. Also, the attenuation of the Love waves has been discussed. The study reveals that such a medium transmits two fronts of Love waves. The first front depends upon the change in volume fraction of the pores and the second front depends upon the modulus of rigidity of the elastic matrix of the medium. The substantial influence of corrugation parameters, reinforcement, undulatory parameter, initial stress, heterogeneity parameter and position parameter on the phase velocity, and attenuation of Love-type wave have been observed and depicted by means of graph. It has been observed that the phase velocity decreases with the increase in initial stress parameters, heterogeneity, and reinforcement in upper layer.     

Bistable reaction-diffusion systems can have robust zero-velocity fronts

We show that for a class of bistable reaction-diffusion systems, zero-velocity fronts can be robust in the singular limit where one of the diffusion coefficients vanishes. In this case, stationary fronts can persist along variations of the system parameters. This property contrasts with the standard result that the front velocity v(&mgr;), expressed as a function of a control parameter &mgr;, is zero only at some isolated values &mgr;(0), and thus not giving robustness to zero-velocity fronts when &mgr; is varied. (c) 2000 American Institute of Physics.     

单相合金凝固过程时间相关的界面稳定性(I)理论分析

对定向凝固界面前沿非稳态溶质扩散场进行了系统的对比分析，发现无论在纯扩散还是存在对流的情况下，界面前沿的溶质扩散场通常满足指数分布的形式，可以采用一个统一的公式来描述界面前沿的瞬态溶质扩散场.进而在此基础上，对定向凝固界面形态稳定性进行了统一的时间相关的非稳态分析，发现界面临界稳定性条件的数学描述形式与Mullins和Seker ka理论给出的稳态解完全一致, 只是用时间相关的浓度梯度GtC、界面速度Vi、溶质扩散长度l代替了稳态生长中所得到的GC,V，DL/V.     

Exact and asymptotic solutions of the Cauchy–Poisson problem with localized initial conditions and a constant function of the bottom

In the paper, the asymptotic solutions for a problem of Cauchy–Poisson type with localized initial conditions are constructed. The bottom of the basin under consideration which was constant before the perturbation, is instantly perturbed at the initial time moment by a spatially localized function. Simplifications of the corresponding formulas are presented inside and outside the vicinity of the leading front, as well as in the case of a special choice of the initial condition. It is shown that, in the vicinity of the leading front, the asymptotic solution coincides with the asymptotic solution of the linear Boussinesq equation.     

Vibrationally mediated negative differential resistance in a single molecule

Negative ion density fronts have been shown to occur in electronegative steady-state plasmas with hot electrons. In this Letter, we report theoretical and numerical results on the spatiotemporal evolution of negative ion density fronts during plasma ignition and extinction (afterglow). During plasma ignition, the negative ion fronts are analogous to hydrodynamic shocks. This is not the case during plasma extinction where, although negative ions diffuse freely in the plasma core, the negative ion front propagates towards the chamber walls with a nearly constant velocity.     

Transient effects in pulsed laser irradiation

Theoretical analysis of the influence of the temporal profile (rectangular, triangular, Gaussian) of the laser pulse on heating/cooling and phase transition velocities and quantity of ablated material was performed on the basis of a multifront Stephan problem. Modeling showed that material removal under stationary conditions (that correspond to long pulses) is entirely controlled by specific heat and material density, while in the case of transient regimes (short pulses) thermal conductivity and heat capacity play a predominant role. Interaction of the melting and evaporation fronts characterized by an evaporation front velocity far exceeding the melting front one is one of the examples of the transient nature of the phenomena influenced by the laser pulse parameters.     

激光脉冲在气体中产生的离化波前的演化及其对光脉冲传播的影响

利用带离化子程序的一维粒子模拟程序，对光脉冲与离化波前的相互作用进行了模拟研究，讨论了在原子多度电离的情况下光脉冲与离化波前的相互作用关系.研究表明，由于原子各级离化势的不连续性使得离化波前在空间上出现平台区；离化过程导致激光频率发生蓝移，这个蓝移又对脉冲形状产生调制，使脉冲前沿呈阶跃型增长；阶跃型的光脉冲包络使离化波前的平台区变短，直至整个离化波前分为几个不同梯度的区域.还讨论了不同元素和不同密度的气体中产生的离化波前的特点.同时分析了光脉冲频率随传播距离的关系，指出由于光脉冲宽度的增加，将导致出射的光 关键词： 激光等离子体 光电离 离化波前 激光频率上转换     

Parameters of an erosion carbon plasma in the channel of a railgun

The working current dependences of the thermodynamic and electrophysical parameters of a free plasma piston moving with a near-maximal velocity in the channel of an electromagnetic rail launcher with graphite electrodes are obtained. The composition and weight of the plasma depend on the degree of electrode erosion due to discharge current passage (i = 40–80 kA). It is shown that the mean temperature of the plasma piston only slightly depends on the plasma mean pressure and plasma piston weight and increases with current by a near-power law. The measured values of the maximal velocity of the plasma piston front are compared with the calculated value of the sound velocity inside the piston. With the working current and cross-sectional area of the channel fixed, the initial gas density in the channel is found to influence the ratio of the piston maximal velocity to the sound velocity in the plasma. If the initial gas density is low (lower than some critical value), the maximal velocity of the plasma piston front exceeds the sound velocity in the plasma.     

Persistence of zero velocity fronts in reaction diffusion systems

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.     

One-dimensional dynamics for traveling fronts in coupled map lattices

Multistable coupled map lattices typically support traveling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one-dimensional circle homeomorphism, whose rotation number gives the propagation velocity. The mode locking of the velocity with respect to the system parameters then typically follows. We study the behavior of fronts near the boundary of parametric stability, and we explain how the mode locking tends to disappear as we approach the continuum limit of an infinite density of sites.     

Poiseuille advection of chemical reaction fronts

Poiseuille flow between parallel plates alters the shapes and velocities of chemical reaction fronts. In the narrow-gap limit, the cubic reaction-diffusion-advection equation predicts a front-velocity correction equal to the gap-averaged fluid velocity epsilon. In the singular wide-gap limit, the correction equals the midgap fluid velocity 3epsilon/2 when the flow is in the direction of propagation of the reaction front, and equals zero for adverse flow of any amplitude for which the front has a midgap cusp. Stationary fronts are possible only for adverse flow and finite gaps. Experiments are suggested.     

Front formation in an active scalar equation

We study the formation of thermal fronts in an active scalar equation that is similar to the Euler equation. For a particular initial condition, an earlier candidate for finite-time blowup, the front forms in a generalized self-similar way with constant hyperbolicity at the center. The behavior belongs to a class of scenarios for which finite-time blowup is impossible. A systematic exploration of many different initial conditions reveals no evidence of singular solutions.     

Shock waves and formation of carbon dioxide hydrate at an increased pressure in the gas-liquid medium

The processes of breaking, solution, and formation of hydrates behind a shock wave of moderate amplitude were studied experimentally in water with carbon dioxide bubbles under different initial static pressures. It is shown that an increase in the static pressure in a gas-liquid medium leads to reduction of critical relative amplitude of the shock wave, corresponding to starting development of Kelvin — Helmholtz instability and bubble splitting into small gas inclusions behind the shock wave front. It is shown that the rates of carbon dioxide solution and hydrate formation behind the shock wave front are close by the value; their dependences on medium and wave parameters are determined. Calculations by the model of gas hydration behind the shock wave are presented. The work was financially supported by the Russian Foundation for Basic Research (grants Nos. 06-01-00142 and 06-08-00657).