5,906 research outputs found
Optimal Control of Convective FitzHugh-Nagumo Equation
We investigate smooth and sparse optimal control problems for convective
FitzHugh-Nagumo equation with travelling wave solutions in moving excitable
media. The cost function includes distributed space-time and terminal
observations or targets. The state and adjoint equations are discretized in
space by symmetric interior point Galerkin (SIPG) method and by backward Euler
method in time. Several numerical results are presented for the control of the
travelling waves. We also show numerically the validity of the second order
optimality conditions for the local solutions of the sparse optimal control
problem for vanishing Tikhonov regularization parameter. Further, we estimate
the distance between the discrete control and associated local optima
numerically by the help of the perturbation method and the smallest eigenvalue
of the reduced Hessian
Nonmonotone hybrid tabu search for Inequalities and equalities: an experimental study
The main goal of this paper is to analyze the behavior of nonmonotone hybrid tabu search approaches when solving systems of nonlinear inequalities and equalities through the global optimization of an appropriate
merit function. The algorithm combines global and local searches and uses a nonmonotone reduction of the merit function to choose the
local search. Relaxing the condition aims to call the local search more often and reduces the overall computational effort. Two variants of a perturbed pattern search method are implemented as local search. An
experimental study involving a variety of problems available in the literature
is presented.Fundação para a Ciência e a Tecnologia (FCT
Pattern formation in a diffusion-ODE model with hysteresis
Coupling diffusion process of signaling molecules with nonlinear interactions
of intracellular processes and cellular growth/transformation leads to a system
of reaction-diffusion equations coupled with ordinary differential equations
(diffusion-ODE models), which differ from the usual reaction-diffusion systems.
One of the mechanisms of pattern formation in such systems is based on the
existence of multiple steady states and hysteresis in the ODE subsystem.
Diffusion tries to average different states and is the cause of spatio-temporal
patterns. In this paper we provide a systematic description of stationary
solutions of such systems, having the form of transition or boundary layers.
The solutions are discontinuous in the case of non-diffusing variables whose
quasi-stationary dynamics exhibit hysteresis. The considered model is motivated
by biological applications and elucidates a possible mechanism of formation of
patterns with sharp transitions.Comment: 32 pages, 8 picture
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