Biomedical subjects

PG Kevrekidis

Publications and source records attributed to PG Kevrekidis.

3 recordsLinked to original sources

PubMed2000

Statistical mechanics of a discrete nonlinear system

Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.

Journal Article↗

PubMed2000

Two-dimensional discrete breathers: construction, stability, and bifurcations

We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schrodinger equation on a square lattice reveals three different types of breathers. Considering an elementary plaquette, the most unstable mode is centered on the plaquette, the most stable mode is centered on its vertices, while the intermediate (but also unstable) mode is centered at the middle of one of the edges. Below the turning points of each branch in a frequency-power phase diagram, the construction methodology fails and a continuation method is used to obtain the unstable branches of the solutions until a triple point is reached. At this triple point, the branches meet and subsequently bifurcate into the final state of an extended phonon mode.

Journal Article↗

PubMed2000

Localized excitations and their thresholds

We propose a numerical method for identifying localized excitations in discrete nonlinear Schrodinger type models. This methodology, based on the application of a nonlinear iterative version of the Rayleigh-Ritz variational principle yields breather excitations in a very fast and efficient way in one or higher spatial dimensions. The typical convergence properties of the method are found to be super-linear. The usefulness of this technique is illustrated by studying the properties of the recently developed theoretical criteria for the excitation power thresholds for nonlinear modes.

Journal Article↗