arXiv subjects

Villevo Adanhounme

Publications and source records attributed to Villevo Adanhounme.

5 recordsLinked to original sources

arXiv2015

Solving Navier-Stokes equations coupled with a heat transfer equation using Bagarello's approach and the Hankel transform

In this paper, the dynamics of an incompressible fluid in a bounded connected domain, described by Navier-Stokes equations coupled with a heat transfer equation, is investigated by a method inspired from the non-commutative strategy developed by Bagarello, (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394).The solution of involved systems of partial differential equations is derived with the help of the unbounded self-adjoint densely defined Hamiltonian operator of the physical model and the Hankel transform.

math-ph↗

arXiv2015

Control of ordinary differential equations using Bagarello's operator approach : Case of forced harmonic oscillator systems

This work deals with the study of an optimal control of a system of nonlinear differential equations using the Bagarello's operator approach, recently introduced in a paper (Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394). The control problem is reduced by using the Pontryagin's maximum principle, to a system of ordinary differential equations with unknown state and adjoint variables. Its solution is then described in terms of a series expansion of commutators involving an unbounded self-adjoint, densely defined, system Hamiltonian operator H and initial position operators. Relevant simple applications are discussed.

math-ph↗

arXiv2015

Generalizing Bagarello's operator approach to solve a class of partial differential equations

The non-commutative strategy developed by Bagarello (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis of systems of ordinary differential equations (ODEs) is extended to a class of partial differential equations (PDEs), namely evolution equations and Navier-Stokes equations. Systems of PDEs are solved using an unbounded self-adjoint, densely defined, Hamiltonian operator and a recursion relation which provides a multiple commutator and a power series solution. Numerous examples are given in this work.

math-ph↗

arXiv2012

Hereditary kernel identification method of nonlinear polymeric viscoelastic materials

This paper deals with a polymeric matrix composite material. The matrix behaviour is described by the modified Rabotnov's nonlinear viscoelastic model assuming the material is nonlinear viscoelastic. The parameters of creep and stress-relaxation kernels of the model are determined. From the experimental data related to kernels approximated by spline functions and by means of the method of weighted residual, the formulas for the determination of viscoelastic parameters are derived.

math-ph↗

arXiv2010

Hamiltonian formulation of the Grosse-Wulkenhaar $ϕ^{4}_{\star D}$ model

A Hamiltonian formulation for the Grosse-Wulkenhaar $ϕ^{4}_{\star D}$ model is performed. The study is based on $D+1$ dimensional space-time formulation of $D$ dimensional non-local theories. The analysis of constraints shows that the secondary constraints describe the Euler-Lagrange equations of motion. Relevant tensors are computed and analyzed.

math-ph↗