An Isogeometric Error Estimate for Transport Equation in 2D

In this paper, an isogeometric error estimate for transport equation is obtained in 2D to prove the convergence of isogeometric method. The result that we have obtained, generalizes Ern result, got in finite elements method. For the time discretization, the two stage Heun scheme is used to prove this result. For a polynomial of degree k≥1, the order of convergence in space is 2 and in time is .

Noncommutative Phase Space and the Two Dimensional Quantum Dipole in Background Electric and Magnetic Fields

The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.

Reconstruction Method in <i>F(G)</i>Gravity: Stability Study and Inflationary Survey

The present paper is devoted to reconstruction and cosmological study in modified F(G) theory of gravity. Our reconstruction scheme is based on Friedmann metric induced equations in modified F(G) theory by supposing a power law form for the scale factor of Friedmann metric. Firstly, we deal with the stability study, the obtained model. This survey reveals that for appropriated choice of the reconstructed model parameter, this model is stable under two cosmological evolutions namely the de Sitter and the power law evolutions symbolized by the appropriated scale factor. Secondly, we investigate the inflationary survey by fitting the model with the inflation observables. These observables are determined and their comparison with Planck’s results leads to a special inflationary F(G) model. We prove that this model especially obtained for radiation domination evolution develops an instability, so can fall to ordinary matter domination era or dark energy domination era. This is the key of graceful exit from inflation.

Simple and Pseudo Quadratic Leibniz Superalgebras

Compactness of subspaces of a Z2-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds

It is well known that the representations over an arbitrary configuration space related to a physical system of the Heisenberg algebra allow to distinguish the simply and non simply-connected manifolds [arXiv:quant-ph/9908.014, arXiv:hep-th/0608.023]. In the light of this classification, the dynamics of a quantum particle on the line is studied in the framework of the conventional quantization scheme as well as that of the enhanced quantization recently introduced by J. R. Klauder [arXiv:quant-ph/1204.2870]. The quantum action functional restricted to the phase space coherent states is obtained from the enhanced quantization procedure, showing the coexistence of classical and quantum theories, a fundamental advantage offered by this new approach. The example of the one dimensional harmonic oscillator is given. Next, the spectrum of a free particle on the two-sphere is recognized from the covariant diffeomorphic representations of the momentum operator in the configuration space. Our results based on simple models also point out the already-known link between interaction and topology at quantum level.

Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics

Abstract: This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external sinusoidal excitation. The approximative solution to the first order of the modified Van der Pol-Duffing oscillator is found using the Lindstedt’s perturbation method. The harmonic balance method is used to find the amplitudes of the oscillatory states of the system under control. The effects of the constraint parameter and the control parameter of the model on the amplitude of oscillations are presented. The effects of the active control on the behaviors of the model are analyzed and it appears that with the appropriate selection of the coupling parameter, the chaotic behavior of the model has given way to periodic movements. Numerical simulations are used to validate and complete the analytical results obtained.

Modelling of sediment movement in the surf and swash zones

Under the action of marine currents,non-cohesive sediments evolve by bed-load,by saltation or suspension depending on their granulometry.Several authors have considered that the movement of sediment is bidimensional and modelized the effects of swell by a constant velocitynear the seabed.Here we have studied the velocity profile of fluctuating currents near the seabed and studied the movement of sediment in 3D.The results show that in the areas of study（surf and swash）the movement of sediment occurs in a volume,and the evolution of sediment varies from an areato another.The obtained theoretical profiles of the position and velocity vectors confirm the observations of several authors.

Study of Dissipating of Wave Energy in the Breakers Zone of the Gulf of Guinea: Case of Autonomous Port of Cotonou in Benin Coastal Zone

Rapid population growth and major trends of world economy growth have led to significant energy needs in our country. Benin, Gulf of Guinea country, although with a significant coastal network powered by potential energy from breaking waves, has experienced a deficit and a critical energy instability, marked by recurrent power cuts and disruption of the national economy. To ensure the integration of this source of renewable energy in the Benin energy mix and sustainably reduce the energy deficit in progress, this work has aimed to study the dissipation of wave energy at the bathymetric breaking in the breakers zone of Cotonou coast. Sea conditions and the statistics parameters of the breaking waves under perturbation effect of the seabed were evaluated to predict the beginning of the breaking. The modeling is based on the Navier-Stokes equation in which the viscosity and the interactions between the molecules of the oceanic fluid are neglected. The nonlinear wave dispersion relation is also used. The results obtained for this purpose showed that water particles have an almost parabolic motion during their fall;their velocity is higher than those of the early breaking. In this area, the waves dissipate about 80% of their energy: it generates turbulence which leads to a strong setting in motion of sediments.