Solution of a Variational inequality for charge transport DNA model with vibrational and rotational coupling motion

Milciades Cortez Gutiérrez M.; Oscar Cortez Gutiérrez H.; Jois Cortez Fuentes Rivera L.; Iara Cortez Fuentes Rivera G.; Ellyda Cortez Fuentes Rivera D.; Dario Mendoza Arias R. · Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology (2025) · DOI: 10.18687/laccei2025.1.1.1483

Resumen

We perform a numerical computation of eigenvalues of the statistical physics of DNA using a generalized Morse potential to obtain the mean displacement of nucleotides. Likewise, applying numerical methods, we solve the Peyrard-Bishop-Holdstein model to obtain the electronic distribution in DNA. We apply semigroup theory for charge transport DNA model with vibrational and rotational coupling motion . For that we use the theory of semigroup in its equivalent vector form, that is, (Formula presented) This system given by (2) stand for an initial value problem, which we show that, under suitable assumptions of the operator A and on the nonlinearity F the system supports a single global weak solution satisfying the given initial condition, for that one, we consider the Sobolev spaces which will solve the Cauchy problem. The ideas of Elena Díaz [4] have really been followed, who considers the Peyrard-Bishop-Holstein model, which introduces a description of polaronic effects for the transport of electrical charge in DNA. Consequently, a Schrödringer equation is added for electrical transport, whose indicator is the amplitude probability for an electric charge located in the nth nucleotide. Likewise, in the vibrational part, the Peyrard-Bishop model has been maintained in its continuous form, which has as its starting point the discrete form in the reference of [6].

Instituciones: Universidad Nacional de Trujillo; Universidad Nacional del Callao