Quantum size effects in the attractive hubbard model

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.     

Swelling of cross-linked polyelectrolyte gels

The European Physical Journal E - A model of a cross-linked polyelectrolyte gel has been examined using Monte Carlo simulations. The simple model contained a charged defect-free network represented...     

Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum

We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a real eigenvalue crosses the imaginary axis. For a model we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a pitchfork bifurcation of equilibria and the nonlinear stability of the bifurcating equilibria, again with respect to spatially localized perturbations.     

Dynamics of Multisection Semiconductor Lasers

We consider a mathematical model (the so-called traveling-wave system) which describes longitudinal dynamical effects in semiconductor lasers. This model consists of a linear hyperbolic system of PDEs, which is nonlinearly coupled with a slow subsystem of ODEs. We prove that a corresponding initial-boundary value problem is well posed and that it generates a smooth infinite-dimensional dynamical system. Exploiting the particular slow-fast structure, we derive conditions under which there exists a low-dimensional attracting invariant manifold. The flow on this invariant manifold is described by a system of ODEs. Mode approximations of that system are studied by means of bifurcation theory and numerical tools.     

Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.