Breathers in two-dimensional neural media

In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could arise from external stimuli or reflect changes in the excitability of local populations of neurons as a precursor for epileptiform activity. The resulting dynamical instability breaks the underlying radial symmetry of the stationary pulse, leading to the formation of a nonradially symmetric breather. The number of breathing lobes is consistent with the order of the dominant unstable Fourier mode associated with perturbations of the stationary pulse boundary.     

Optic-fiber communications: Nonlinear-transformation group

A new method for finding solutions of the nonlinear Schrödinger equation is proposed. A comutative multiplicative group of nonlinear transformations, which operate on stationary localized solutions, enables a consideration of fractal subspaces in the solution space, stability, and deterministic chaos. An increase of the transmission rate in the optic-fiber communications can be based on new forms of localized stationary solutions, without significant change of input power. The estimated transmission rate is 50 Gbit/s, for certain available soliton transmission systems.     

The Hopf bifurcation of twodimensional systems under the influence of one external noise source

The behaviour of the Hopf bifurcation under the influence of external noise is investigated by means of a twodimensional model which uses Gaussian white noise as input. The model includes the case of multiplicative and/or additive noise. Applying the Birkhoff transformation the model is transformed to the coordinates normally used to discuss the deterministic Hopf bifurcation. Then the stationary solution of the model is calculated as an expansion for weak noise: The Hopf bifurcation under the influence of noise exhibits a bifurcation interval with width and position depending on the noise power. Moreover, a class of the systems described by the model can perform noise driven bifurcations.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Solitons in collisionless cold plasma

The relativistic nonlinear self-consistent equations for a collisionless plasma with stationary ions are transformed into a form appropriate for finding exact analytic solutions. It is shown that for an axial system with planar geometry, the two-dimensional stationary equations for this system can be reduced to the sh-Gordon equation. The exact solution of this equation describing the charge-density equilibrium configuration is obtained, the solution having sharp transverse boundaries and a soliton form in longitudinal direction. The generalization to the nonstationary case is considered in an perturbative approach.     

A rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1xS2. It describes a rotating "black ring." This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.     

New exact solutions of Einstein's field equations: Gravitational force can also be repulsive!

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given.     

光孤子脉冲在增益色散和增益饱和非线性介质中的传播

本文获得了增益色散和增益饱和非线性介质中的光孤子脉冲的解析解。数值计算结果表明,在这类介质中光孤子脉冲传输是可能的,然而由于波传输的内禀特性,这种稳定传输被限制在较短的距离内。在高能量脉冲注入的情况下,光孤子脉冲将分裂为不同传输速度的多个光脉冲。     

A study of non-linear autoregressive processes: Differential theory

Summary It is shown how the general analytical expression of an autoregression, whose stationary solution has an arbitrary given form, can be obtained. The central-limit theorem is used to state a correspondence between autoregression and relevant diffusion equation which not only permits to give analytical form to the stationary distribution of a given autoregression, but also to obtain appropriate series expansions of its fundamental solution and the exact relaxation constants. The interest of the analysis in the context of Monte Carlo simulations of relaxation and steady-state processes is discussed. The procedure is illustrated by two examples of interest in the field of ionized gases.     

Symmetry breaking and self-oscillations in intracavity vectorial second-harmonic generation

We show that, in vectorial intracavity second-harmonic generation, symmetry breaking occurs if the input amplitude exceeds a critical value. The resulting asymmetric stationary solutions are characterized by a second harmonic that is independent of the input amplitude. The solutions can destabilize through Hopf bifurcations, leading to self-oscillations with pronounced antiphase dynamics. We demonstrate that symmetry breaking can be exploited for flip-flop operation.     

基于离散平稳小波变换的红外图像去噪

提出了一种基于离散平稳小波变换的红外图像去噪方法。在预先不知道噪声方差的前提下,只利用红外图像的输入数据就可以确定所要求的渐近最优阈值。对红外图像进行离散平稳小波变换后,分别对各个分解层的高频子带利用所提出的方法进行迭代去噪,使各个高频子带分别收敛于其最大信噪比。实验结果表明,所提出的方法在有效的去除红外图像噪声的同时,又能较好的保持红外图像的细节部分信息。算法在性能指标和视觉质量上均优于基于离散正交小波变换的阈值去噪方法和传统的中值滤波法。     

Using Asymptotic Analysis for Developing a One-Dimensional Substance Transport Model in the Case of Spatial Heterogeneity

We study a solution with an internal transition layer of a one-dimensional boundary value problem for the stationary reaction–advection–diffusion differential equation that arises in mathematical modeling of transport phenomena in the surface layer of the atmosphere in the case of non-uniform vegetation on the assumption of space isotropy along one of the horizontal axes and neutral atmospheric stratification. The parameters of the model at which a boundary value problem has a stable stationary solution with an internal transition layer localized near the boundary between different vegetation types are provided. The existence of such a solution and its local Lyapunov stability and uniqueness are proven. The results can be used for developing multidimensional substance transfer models in the case of a spatial heterogeneity.     

Quantum transport in one-dimensional systems via a master equation approach: Numerics and an exact solution

We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time-dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.     

Entanglement of movable mirror and cavity field enhanced by an optical parametric amplifier

A scheme to generate entanglement in a cavity optomechanical system filled with an optical parametric amplifier is proposed. With the help of the optical parametric amplifier, the stationary macroscopic entanglement between the movable mirror and the cavity field can be notably enhanced, and the entanglement increases when the parametric gain increases.Moreover, for a given parametric gain, the degree of entanglement of the cavity optomechanical system increases with increasing input laser power.     

Asymptotic stability of stationary states in the wave equation coupled to a nonrelativistic particle

We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition, which is a version of the “Fermi Golden Rule.” We prove that in the large time approximation, any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.     

On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation

A world is to be considered stationary in the sense of general relativity if the coefficients of its metric are independent of time in a coordinate system in which the masses are at rest on average. The remark on the system of coordinates is important because time itself is no invariant notion but is taken only in the sense of proper time. Our definition is unique, in the form given above. On the other hand it is also possible to have points where no matter is present. At such points we may place a test body of infinitesimally small mass and analyse whether it remains at rest in our coordinate system. A necessary and sufficient condition for this is that the time lines of our coordinate system are geodesics. Therefore the static solution given by de Sitter is not an example of a stationary world. The Schwarzschild line element which, from a cosmological point of view, is a world with a single central body can also not be considered a stationary solution. Indeed, there are no stationary solutions which are also spherically symmetric for the original field equations. The only such solution for the cosmological equations is Einstein's cylinder world. It is, to my knowledge, the only stationary world known so far. In that case the average matter density and the total mass of the world has to have a well defined value given by the cosmological constant which doubtless would be purely coincidental and is thus not a satisfactory assumption. In the following we shall discuss a new solution which is in accord with the original field equations without the need of an a priori relation between mass and cosmological constant. However, we shall find that its mass cannot be less than the mass of the cylinder world.     

On the stationary properties of an open system with internal coherent interactions

The asymptotic behaviour of an open system in which coherent and incoherent interactions interfere is discussed. It is shown that a stationary density operator exists which is diagonal with the coherent interaction, and that detailed balance is satisfied. A model-independent form for this density operator is given. A class of systems is identified for which the stationary solution can be constructed explicitly and in which some known models are contained.     

Universal properties of distorted Kerr–Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein–Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr–Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.     

核裂变扩散模型Kramers定态解的理论分析

在核裂变动力学扩散模型理论的框架内,严格求解Fokker-Planck方程.用所得到的结果对Kramers定态解进行了分析,指出其成功之处和存在的局限性.     

Variational analysis of evolution for magnetostatic envelope bright soliton with higher-order dispersion

The evolution characteristics of a magnetostatic envelope bright soliton in magnetic thin films with higher-order dispersion are investigated analytically by means of the variational approach. It is found that the envelope of the soliton is changed due to the effects of the higher-order dispersion; the evolution of the soliton does not depend on its phase; and a stationary soliton can be formed in an appropriate situation. It reveals the relation between the motion of the soliton and the initial input pulse area.