Nonlinear dynamics of the evolution of thermomagnetic perturbations in composite superconductors

Nonlinear dynamics of the thermal and electromagnetic perturbations in composite superconductors is studied.     

Rare events and scale-invariant dynamics of perturbations in delayed chaotic systems

We study the dynamics of perturbations in time-delay dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be described by the linear Zhang surface growth model [J. Phys. (France) 51, 2129 (1990)]], which is known to describe surface roughening driven by power-law distributed noise. As a consequence, Lyapunov vector dynamics is dominated by rare random events that lead to non-Gaussian fluctuations and multiscaling properties.     

Quantum dynamics in a thin film,I. Propagation of localized perturbations

In the one-particle approximation, the quantum behavior of a (quasi-)particle is studied in a thin waveguide having the form of a thin curvilinear film (in three-dimensional space) placed in external magnetic and electric fields. Objects of this type arise in the actively developing physics of nano-structures and, in particular, in the theory of ballistic transport of electrons. The corresponding quantum-mechanical equation is a Pauli-type equation with nonrelativistic Rashba spin-orbital interaction for a two-dimensional vector function. Asymptotic solutions of the Cauchy problem with special localized initial data and those of the spectral problem are obtained. The construction of asymptotic solutions is carried out in two stages. At the first stage, in the framework of the adiabatic approximation, using the “operator separation of variables” (the “generalized adiabatic principle”) for a rather broad class of quantum states, the original three-dimensional equation is reduced to a two-dimensional surface (the limit film), and then diverse solutions of this reduced equation are constructed. The first part of the paper is devoted to the reduction and the solutions of the Cauchy problem. Spectral problems will be treated in the second part. Dedicated to the memory of V. A. Geyler Supported by the RFBR grant no. 05-01-00968 and by the DFG-RAS project DFG 436 RUS 113/785.     

Bounded perturbations of the P(ϕ)2 theory

As a perturbation to the P(?)₂ theory we consider interaction densities of the form V(?(x)), where ?(x) is a scalar hermitian boson field and V(α) is a bounded real continuous function. It is proved that the asymptotic fields exist and are equal to the asymptotic fields of the P(?)₂ theory. The connection with non-polynomial theories of rational type is indicated. Furthermore the consequences of a bounded perturbation for the S-matrix and the spectral properties are discussed.     

Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy E_a, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.     

Bounded Bose Fields

Examples for bounded Bose fields in two dimensions are presented.     

Discontinuous perturbations

Perturbations of quantum systems ranging from oscillators to fields can be either continuous or discontinuous functions of the coupling. The system under consideration is the familiar harmonic oscillator in one degree of freedom. Previous studies have shown that when the harmonic oscillator is subjected to a perturbation with a power law singularity, a permanent change in the system characteristics is observed for a specific range of power law values. The introduction of a logarithmic singularity into the power law potential fine tunes the singularity power.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Bounded rational driver models

This paper introduces a car following model where the driving scheme takes into account the deficiencies of human decision making in a general way. Additionally, it improves certain shortcomings of most of the models currently in use: it is stochastic but has a continuous acceleration. This is achieved at the cost of formulating the model in terms of the time derivative of the acceleration, making it non-Newtonian. However, the recipe for construction of bounded rational driver models proposed in this paper seems to be very general and can be applied to most, if not all of the traditional car-following models. Received 18 November 2002 / Received in final form 6 February 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: ialub@fpl.gpi.ru RID="b" ID="b"e-mail: peter.wagner@dlr.de RID="c" ID="c"e-mail: reinhard.mahnke@physik.uni-rostock.de     

Bounded Subquotients of Pseudodifferential Operator Modules

Recently there have been several papers on the action of the Virasoro Lie algebra on the projective decompositions of the modules of pseudodifferential operators on the circle. We use their results to prove that a wide class of the uniserial (completely indecomposable) bounded modules of the Virasoro Lie algebra may be realized as subquotients of such modules of pseudodifferential operators. This gives easy proofs of the existence of many previously known uniserial modules, and moreover yields some hitherto undiscovered.Partially supported by NSA grant MDA 904-03-1-0004.     

Bounded confidence and social networks

In the so-called bounded confidence model proposed by Deffuant et al, agents can influence each others opinion provided that the opinions are already sufficiently close enough. We discuss here the influence of possible social network topologies on the dynamics of this model.Received: 9 January 2004, Published online: 14 May 2004PACS: 89.65.-s Social and economic systems - 89.75.Fb Structures and organization in complex systems     

Diffraction Fields of Fractally Bounded Apertures

Experimental study is performed of optical diffractions by two-dimensional, self-similar mass and surface fractal apertures as well as mass fractal apertures bounded by surface fractals. Self-similar intensity distributions are observed in the Fraunhofer diffraction fields from surface and mass fractal apertures. Power law decays in average intensities of the diffraction patterns are also investigated for the mass, surface and combined fractal apertures in connection with the fractal dimensions of the objects.     

Classicality of the primordial perturbations

We show that during inflation, a quantum fluctuation becomes classical at all orders if it becomes classical at first order. Implications are discussed.     

On local perturbations of waveguides

The paper deals with an arbitrary sufficiently small localized perturbation of waveguides with different types of boundary conditions. We study both the qualitative structure of the spectrum of the perturbed operator and conditions for the occurrence of eigenvalues from the continuous spectrum. For the case in which eigenvalues occur, their asymptotic behavior is obtained.     

Evolution of nonlinear cosmological perturbations

We define fully nonperturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our nonlinear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first- and second-order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.     

Singular perturbations of discrete spectrum

Even solutions of the Schrödinger equation with retaining potential x² are constructed for singular perturbation potentials |x|^–. It is shown that the perturbation automatically entails an induced point potential, taking account of which the perturbation matrix elements and Rayleigh-Schrödinger series may be constructed when 1 < < 3/2. In the opposite case (3/2 2), although the solutions are analytic with respect to , not even diverging series can be obtained for the energy solutions without solution of the Schrödinger equation. The analogy with quantum field theory is explored.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 58–64, March, 1988.     

Linear perturbations of gauge fields

It is shown that under certain weak conditions (the vanishing of the field strength along a family of self-dual or anti-self-dual geodesic two-surfaces), in a curved or flat space-time, the linear perturbations of a given gauge field configuration can be expressed in terms of the solutions of a single second-order linear partial differential equation for a matrix potential. The particular case of the self-dual gauge fields is treated in some detail.