On the theory of metastable states

It is shown that the stationary states of stochastic systems are stable. Therefore one cannot use the stationary probability distributions for describing the stochastic systems in metastable states. It is shown that the nonstationary stochastic processes can have sample paths with stationary parts. It is proposed to consider these stationary parts as the metastable states.     

Transient and Stationary Simulations for a Quantum Hydrodynamic Model

The transient and stationary characteristics of a one-dimensional quantum hydrodynamic model are comparatively studied for semiconductor charge transport in a resonant tunnelling diode. When the bias is not small, our numerical results show a deviation of the asymptotic transient solutions from the stationary ones. A dynamic instability accounts for such deviation. The stationary quantum hydrodynamic model is therefore unsuitable in general for simulating quantum devices.     

弯轨Čerenkov辐射计算中的稳相法

从介质中沿弯曲轨道运动的带电粒子辐射的频谱角分布公式出发, 分析了粒子速度大于介质中的光速时, 稳相点在?erenkov效应中所起的关键作用, 并给出了通过在稳相点附近做渐近展开来计算弯轨?erenkov辐射的稳相法. 运用稳相法, 计算了同步?erenkov辐射在粒子轨道平面附近以及在临界角附近的频谱角分布. 计算结果表明, 同步?erenkov辐射频谱的特征依赖于观测方向附近对应的稳相点性状, 特别是在较大的临界角附近的频谱与小角度近似时很不相同. 关键词： ?erenkov效应 稳相点 稳相法 同步?erenkov辐射     

Stochastic perturbation of a stable deterministic plasma system

A canonical model is proposed for a plasma system under the influence of stationary random fluctuations and its implication on the Liapunov stability of the stationary equilibria is studied.     

Stability analysis of a Morris-Thorne-Bronnikov-Ellis wormhole with pressure

The model of a spherical Morris-Thorne-Bronnikov-Ellis wormhole is analyzed for stability. The matter of this wormhole is composed of a radial monopole magnetic field and a quasi-perfect phantom fluid. In the stationary case, the energy density of this fluid is negative and equal in magnitude to twice the energy density of the magnetic field. There is no pressure of this fluid in the stationary case (phantom dust), while in the case where the fluid energy density deviates from its stationary value, the pressure is proportional to the deviation of the energy density from its stationary value. An example of a wormhole stable against radial perturbations has been obtained.     

Stationary Waves for the Discrete Boltzmann Equation in the Half Space with Reflective Boundaries

The present paper is concerned with stationary solutions for discrete velocity models of the Boltzmann equation with reflective boundary condition in the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of stationary solutions satisfying the reflective boundary condition as well as the spatially asymptotic condition given by a Maxwellian state. First, the sufficient condition is obtained for the linearized system. Then, this result is applied to prove the existence theorem for the nonlinear equation through the contraction mapping principle. Also, it is shown that the stationary solution approaches the asymptotic Maxwellian state exponentially as the spatial variable tends to infinity. Moreover, we show the time asymptotic stability of the stationary solutions. In the proof, we employ the standard energy method to obtain a priori estimates for nonstationary solutions. The exponential convergence at the spatial asymptotic state of the stationary solutions gives essential information to handle some error terms. Then we discuss some concrete models of the Boltzmann type as an application of our general theory. Received: 7 July 1999 / Accepted: 3 November 1999     

Entropy Production in Nonlinear,Thermally Driven Hamiltonian Systems

We consider a finite chain of nonlinear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system     

Flux Induced by Multiplicative Dichotomous Noise

The transport of particles induced by multiplicative dichotomous noise for a system is investigated. The stationary probability current is derived. It is shown that, for the system studied by us, the spatial asymmetry is the ingredient for the nonzero stationary current.     

The laws of establishing stationary composition in a droplet condensing in a binary vapor-gas environment

It is shown that the mole fractions of components within a droplet growing in an atmosphere of two condensing gases and a carrier gas approach their stationary values with a power-law behavior in time on a large scale and with exponential behavior on a small scale for both diffusion-controlled and free-molecular regimes of isothermal condensation. The parameters of the power and the exponential laws are specified for each regime of binary condensation and are linked to the thermodynamic and kinetic characteristics of condensing vapors and to the stationary mole fractions of the components in a growing binary droplet. The stationary composition of the solution within the droplet is shown to be established at a comparatively small relative increase of the droplet radius. A relaxation equation for the droplet composition at arbitrary initial deviations of mole fractions from their stationary values has been solved, and the limitations on the initial deviations allowing monotonic establishment of stationary composition in solution within a growing droplet have been considered.     

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.     

Necessary stationary condition for polarized radiation in scattering media

The stationary condition is derived taking into account the polarization of radiation in the general case of a scattering inhomogeneous medium in an arbitrary-shape emitter. The necessary stationary condition for an emitter in which radiation is emitted and extinguished simultaneously is complete extinction of the entire emitted radiation. Radiation extinction as a result of absorption by the medium and the emergence of radiation from the emitter is analyzed. The stationary condition is an analytical form of writing that extinction of radiation is a sure event whose probability is equal to unity. The passage of radiation through the medium is described on the basis of the linear transport theory with the help of the matrices of the Green functions. The stationary condition includes the characteristics of polarized radiation extinction of which is analyzed, the absorption coefficients of the medium, and the elements of the matrices of the Green functions, which are determined by optical and geometrical parameters of the emitter. The stationary condition obtained is used for deriving the relations between the components of scalar intensity observed in an arbitrary region of the emitter. These relations include, in addition to the absorption coefficients and the matrix elements of the Green functions, the powers of the primary radiation. Possible applications of the stationary condition and the relations between intensity components in computations and experimental studies are considered.     

动态广义球对称含荷黑洞的统计熵

利用改进了的brickwall膜模型,计算了动态广义球对称含荷黑洞的熵,研究结果表明,对于动态黑洞,将黑洞熵表示为与视界面积成正比时,则比例系数总与动态黑洞的视界速度有关 关键词： 广义球对称黑洞 黑洞熵 brick-wall膜模型 WKB近似     

一维定态薛定谔方程的宏观模拟解法

将实验模拟法引入量子力学.设计了一个弦振动系统,这个系统的定态方程与定态薛定谔方程数学形式一样,为定态薛定谔方程的模拟解法提供了理论和实验途径.宏观模拟的结果为理解薛定谔方程提供了宏观类比. 关键词： 薛定谔方程 宏观模拟解法     

Nonlinear Standing Langmuir Waves

The structure of stationary nonlinear standing Langmuir waves is examined in a self-consistent manner. A singularity for the stationary wave function is found which may cause the Langmuir waves to collapse, or expand indefinitely.     

一般稳态时空视界的确定

本文给出在一般稳态时空中确定是否存在事件视界并决定其位置的普遍适用的解析方法。 关键词：     

Gap solitons in waveguide arrays

Bright and dark spatial gap solitons are demonstrated in waveguide arrays. These gap solitons travel across the array at zero transverse velocity, in complete analogy with stationary (immobile) temporal gap solitons. Furthermore, the launching configuration for observing these stationary gap solitons is shown to be the analog of an "ideal experiment" for observing stationary temporal gap solitons, never observed so far. A clear distinction is established between the family of Floquet-Bloch solitons in general and discrete solitons in particular, and the limiting case of gap solitons.     

化学反应中非平衡定常态下的细致平衡问题

研究了化学反应中远离平衡的定常态的形成机制,证明了双变量化学系统的非平衡定态可能有细致平衡存在,但这种定态是不稳定的。 关键词：     

Stationary Worldline Power Distributions

A worldline with a time-independent spectrum is called stationary. Such worldlines are arguably the most simple motions in physics. Barring the trivially static motion, the non-trivial worldlines are uniformly accelerated. As such, a point charge moving along a stationary worldline will emit constant radiative power. The angular distribution, maximum angle scaling and Thomas precession of this power is found for all stationary worldlines including those with torsion and hypertorsion.

     

Stationary state of a heated granular gas: Fate of the usual H-functional

We consider the characterization of the nonequilibrium stationary state of a randomly driven granular gas in terms of an entropy-production-based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the nonequilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.