Biomedical subjects

Panayotis G Kevrekidis

Publications and source records attributed to Panayotis G Kevrekidis.

3 recordsLinked to original sources

PubMed2003

Using the finite domain remnant of the continuous spectrum to examine integrability: effect of boundary conditions.

The aim of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE), by examining it in a finite but large domain. For monoparametric families of PDE/DDE's, that are known to possess isolated integrable points, we find that very special features occur in the finite domain remnant of the continuous ("phonon") spectrum at these "singular" points. We identify these features in the case example of a PDE and a DDE (that sustain front and pulselike solutions, respectively) for different types of boundary conditions. The key finding of the work is that such spectral features are generic near the singular, integrable points and hence we propose to explore a given PDE/DDE in a finite but large domain for such traits, as a means of assessing its potential integrability.

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PubMed2003

Instabilities and bifurcations of nonlinear impurity modes.

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schrödinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity, and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.

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PubMed2003

Classical nucleation theory revisited.

A field-theoretic derivation of the correction to classical nucleation theory due to translational invariance of a nucleating droplet is proposed. The correction is derived from a functional integral representation of the classical partition function, where the two-body interaction potential is decomposed into a short-range repulsive part and a long-range attractive part. The functional integral is evaluated in the mean-field approximation, and the spatially nonuniform density solution of the Euler-Lagrange equation is approximated by a physically motivated hyperbolic tangent profile. Leading-order effects of the nonlocal attractive interaction are highlighted through a density-gradient expansion. The capillarity approximation to the droplet free energy of formation is obtained by performing a density resummation of the uniform state, low-density expansion of the Helmholtz free energy density, and by retaining the leading-order density-gradient term. The resulting translational-invariance correction modifies the droplet free energy by an additive mixing-entropy term. The additional contribution, which contains a logarithmic correction to the surface-energy term, defines a scaling volume that depends on the range of the coarse-grained attractive potential.

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