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Adelina Georgescu

Publications and source records attributed to Adelina Georgescu.

6 recordsLinked to original sources
arXiv2013

Limit points and Hopf bifurcation points for a one - parameter dynamical system associated to the Luo - Rudy I model

A one - parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. An algorithm used to construct the equilibrium curve is presented. Some test functions are used in order to locate limit points and Hopf bifurcation points. Two extended systems allow to calculate these points. The numerical results are presented in a bifurcation diagram.

math.NA↗
arXiv2011

Approximation of pressure perturbations by FEM

In the mathematical problem of linear hydrodynamic stability for shear flows against Tollmien-Schlichting perturbations, the continuity equation for the perturbation of the velocity is replaced by a Poisson equation for the pressure perturbation. The resulting eigenvalue problem, an alternative form for the two-point eigenvalue problem for the Orr-Sommerfeld equation, is formulated in a variational form and this one is approximated by finite element method (FEM). Possible applications to concrete cases are revealed.

math.NA↗
arXiv2011

Limit cycles by FEM for a one-parameter dynamical system associated to the Luo-Rudy I model

An one-parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented.

math.NA↗
arXiv2006

Application of two spectral methods to a problem of convection with uniform internal heat source

Two methods based on Fourier series expansions (a Chandrasekhar functions-based method and a shifted Legendre polynomials -based method) are used to study analytically the eigenvalue problem governing the linear convection problem with an uniform internal heat source in a horizontal fluid layer bounded by two rigid walls. For each method some theoretical remarks are made. Numerical results are given and they are compared with some existing ones. Good agrement is found.

math-ph↗
arXiv2006

Stability bounds in a problem of convection with uniform internal heat source

Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due to the occurrence of variable coefficients in the nonlinear partial differential equations governing the evolution of the perturbations around the basic equilibrium, so far these phenomena were treated mostly numerically and experimentally. No rigorous study is known. In this paper we realize for the first time such a linear study for the eigenvalue problem associated with those equations for a convection problem with an uniform internal heat source in a horizontal fluid layer bounded by two rigid walls. Our method uses Fourier series expansions for the unknown functions. Numerical results and graphs are given showing a destabilizing effect of the presence of the heat source.

math-ph↗