Biomedical subjects

Stavros Theodorakis

Publications and source records attributed to Stavros Theodorakis.

3 recordsLinked to original sources

PubMed2003

Piecewise linear emulation of propagating fronts as a method for determining their speeds.

We use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations. The resulting analytic solution constitutes an excellent approximation to the exact propagating front, as is explicitly shown in the case of cubic and quintic nonlinearities, yielding also the correct value for the physically selected speed of the observable front. Such a piecewise linear emulation can be used for any nonlinearity, giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states, especially pushed fronts.

Journal Article↗

PubMed2003

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Journal Article↗

PubMed2002

Speed selection mechanism for propagating fronts in reaction-diffusion systems with multiple fields.

We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large finite intervals in the comoving frames of reference. The unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field, making thus the solution approximately translation invariant. The fronts for the various fields may propagate at different speeds, all of them being determined though through this mechanism. We present analytic results for the case of piecewise parabolic potentials, and numerical results for other cases.

Journal Article↗