Possible Scenarios of a Phase Transition from Isotropic Liquid to a Hexatic Phase in the Theory of Melting in Two-Dimensional Systems

Theoretical and Mathematical Physics - A two-stage process consisting of two continuous Berezinskii-Kosterlitz-Thouless-type transitions with an intermediate anisotropic liquid, a hexatic phase, is...     

Dependence of the Superfluidity Criterion on the Capillary Radius

We replace the conditions on the capillary boundary with the Born-Karman periodic conditions, i. e., we consider a two-dimensional torus of radius L ₂. If the velocity of a superfluid liquid exceeds 8πℏ /(mL ₂), then it brakes because of the friction against the eddy formed by pairs (similar to the pairs in the Andreev reflection).__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 3, pp. 307–327, June, 2005.     

Tensor Invariants of Geodesic,Potential, and Dissipative Systems on Tangent Bundles of Two-Dimensional Manifolds

Doklady Mathematics - Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles of smooth two-dimensional manifolds are presented. The connection between the...     

Dependence of the Phase Transition Temperature on the Domain Size

Dependence of the phase transition temperature on the domain size is investigated for a double-well quadratic potential. It is shown that for a domain whose boundary is subjected to a hydrostatical pressure, the temperature of phase transitions is independent of the domain and the surface tension coefficient and depends exclusively on the properties of the elastic media. If the displacement field vanishes on the boundary, then for sufficiently small domains, the temperature also does not depend on the surface tension and domain size and is determined by properties of the elastic media only. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 98–113.     

相关系的子相关系

在相关系概念的基础上,建立了相关系的子相关系,并进行了初步探究,得到了子相关系的若干性质.     

State-Space Stability of Two-Dimensional Systems

State-space stability of two-dimensional systems is considered.The stability criterion is simple: it consists of two one-dimensionalstability tests and the requirement that a single polynomialis devoid of roots on [—1, 1]. Along the same lines, wepropose a general relative-stability test and stability-margincomputation.     

On the Transition from Two-Dimensional to Three-Dimensional Water Waves

There are essentially two types of three-dimensional water waves: waves that bifurcate from the state of rest (these waves are commonly called short-crested waves or forced waves), and waves that bifurcate from a two-dimensional wave of finite amplitude (these waves are sometimes called spontaneous waves). This paper deals with spontaneously generated three-dimensional waves. To understand this phenomenon better from a mathematical point of view, it is helpful to work on model equations rather than on the full equations. Such an attempt was made formally by Martin in 1982 on the nonlinear Schrödinger equation, but it is shown here that it is hard to justify his results mathematically because of the hyperbolicity of the nonlinear Schrödinger equation for gravity waves. On the other hand, in some parameter regimes, the nonlinear Schrödinger equation becomes elliptic. In that case, the appearance of spontaneous three-dimensional waves can be shown rigorously by using a dynamical systems approach. The results are extended to the Benney–Roskes–Davey–Stewartson equations when they are both elliptic. Various types of three-dimensional waves bifurcating from a two-dimensional periodic wave are obtained.     

Quasiperiodic Perturbations of Two-Dimensional Hamiltonian Systems

Quasiperiodic nonconservative perturbations of two-dimensional Hamiltonian systems are studied. The behavior of solutions in a neighborhood of resonance and nonresonance levels is considered. Conditions for the existence of resonant quasiperiodic solutions (m-dimensional resonance tori) are found, and the global behavior of solutions in domains separated from the unperturbed separatrices is discussed. The results are illustrated by the example of the Duffing equation with the homoclinic figure eight of a saddle.     

Dynamical Systems Related to Fractional Hamiltonians on the Two-Dimensional Sphere

We consider a class of fractional Hamiltonian systems generalizing the classical problem of motion in a central field. Our analysis is based on transforming an integrable Hamiltonian system with two degrees of freedom on the plane into a dynamical system that is defined on the sphere and inherits the integrals of motion of the original system. We show that in the four-dimensional space of structural parameters, there exists a one-dimensional manifold (containing the case of the planar Kepler problem) along which the closedness of the orbits of all finite motions and the third Kepler law are preserved. Similarly, there exists a one-dimensional manifold (containing the case of the two-dimensional isotropic harmonic oscillator) along which the closedness of the orbits and the isochronism of oscillations are preserved. Any deformation of orbits on these manifolds does not violate the hidden symmetry typical of the two-dimensional isotropic oscillator and the planar Kepler problem. We also consider two-dimensional manifolds on which all systems are characterized by the same rotation number for the orbits of all finite motions.Deceased     

A Bound on the Real Stability Radius of Continuous-Time Linear Infinite-Dimensional Systems

The article examines bounds on disturbance norms under which a linear infinite-dimensional dynamical system remains stable.     

关于相关系间的同构映射

建立了相关系间的同构映射,给出了相关系间同构映射的一些等价条件,并通过具体的同构映射揭示出相关系的一些内在本质.     

Stochastic Two-Dimensional Hydrodynamical Systems: Wong-Zakai Approximation and Support Theorem

We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier–Stokes equations, 2D MHD models and 2D magnetic Bénard problems as well as some shell models of turbulence. Our main result describes the support of the distribution of solutions. Both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process.     

The Spatial Dependence of Supercritical Reacting Systems

We consider models for chemical reactions taking place withina solid. For one-dimensional systems for which the maximum temperaturerise of the solid is not small compared with the absolute temperaturewe find that as the temperature approaches its maximum, thereis a point in space near which the temperature rise is muchgreater than elsewhere.     

Asymptotic Behaviour of Solutions of Two-Dimensional Neutral Differential Systems

We study asymptotic properties of solutions of the system of differential equations of neutral type.     

Transition Manifolds of Complex Metastable Systems

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.     

一类二维系统的极限环的个数

本文利用Dulac函数方法讨论一类二维系统在环城上的包围多个奇点的极限环的唯一性及在n连城上极限环的唯n-1性，并给出了两个多项式的例子，讨论了极限环的唯一性和唯二性．     

基于完备剩余格的双标号转换系统

为了对不相容或不完备信息的系统进行形式化描述和满足对系统进行量化验证的需要,根据经典的双标号转换系统,提出基于完备剩余格的双标号转换系统作为此类系统的一般模型。在该模型框架下,将传统的互模拟关系推广到格值情形,来度量系统之间的接近程度。通过引入格值Hennessy-Milner逻辑的概念,给出格值互模拟关系的逻辑刻画。