Laila Taourirte

Bio: Laila Taourirte is an academic researcher from Cadi Ayyad University. The author has contributed to research in topics: Similarity (geometry) & Statistical physics. The author has an hindex of 2, co-authored 4 publications receiving 6 citations.

Periodic parabolic equation involving singular nonlinearity with variable exponent

Abstract: In this work we are interested in the periodic solutions of the singular problem involving variable exponent with a homogeneous Dirichlet boundary conditions modeled as $$\begin{aligned} {\partial _t u}-\varDelta u =\displaystyle \frac{f}{u^{\gamma (t,x)}}\text { in }]0,T[\times \varOmega \end{aligned}$$ Where $$\varOmega $$ is an open regular bounded subset of $${\mathbb {R}}^{N}$$ , $$T>0$$ is the period, $$\gamma (t,x)$$ is a nonnegative periodic function belonging in $${\mathcal {C}}(\overline{Q_{T}})$$ and f is a nonnegative measurable function periodic in time with period T and belonging to a certain Lebesgue space. Under suitable assumptions on $$\gamma $$ and f, we prove an existence result of a nonnegative weak time periodic solution to the considered problem.

Improved GWO algorithm for the determination of the critical wrinkle length of graphene

Abstract: Graphene, one of the most important discoveries in the field of materials, is an interesting two-dimensional flexible membrane which has been highly studied by physicians in the last decade as it has shown tremendous utility in fundamental studies, industrial and electronic applications, ranging from nanoelectronics to biology, thanks to its notable electronic, mechanical and chemical properties. Graphene in its natural state is non-flat and tends to crumple. The wrinkles are usually considered to be a result of stretching and bending forces, and are viewed as local minimizers of a suitable elastic energy. In this paper we focus on the study of the wrinkling shape of graphene. A detailed geometric model provided by Yamamoto et al. describing the shape of the wrinkles in terms of a deflection profile, is numerically analysed. The Euler Lagrange equation associated to this problem is formulated in the context of a constrained optimization problem and numerical simulations are carried out to compute the optimal profile using the Grey Wolf Optimizer (GWO), leading to good results in comparison with the ones found in the litterature.

On the existence of global weak solutions to a generalized Keller Segel model with arbitrary growth and nonlinear signal production

Abstract: In this work we present the mathematical analysis of a system able to describe the biological chemotaxis phenomena. The proposed model is a modification of the classical Keller Segel model and its subsequent developments, which, in many cases, have been developed to obtain models that prevent the non-physical blow up of solutions.

Scaling properties of a class of interfacial singular equations

Abstract: This paper can be considered as an introductory review of scale invariance theories illustrated by the study of the equation ∂th=−∂x∂xh1−2ν+∂xxxh, where ν>1/2. The d−dimensionals version of this equation is proposed for ν≥1 to discuss the coarsening of growing interfaces that induce a mound-type structure without slope selection (Golubović, 1997). Firstly, the above equation is investigated in detail by using a dynamic scaling approach, thus allowing for obtaining a wide range of dynamic scaling functions (or pseudosimilarity solutions) which lend themselves to similarity properties. In addition, it is shown that these similarity solutions are spatial periodic solutions for any ν>1/2, confirming that the interfacial equation undergoes a perpetual coarsening process. The exponents β and α describing, respectively, the growth laws of the interfacial width and the mound lateral size are found to be exactly β=(1+ν)/4ν and α=1/4, for any ν>12. Our analytical contribution examines the scaling analysis in detail and exhibits the geometrical properties of the profile or scaling functions. Our finding coincides with the result previously presented by Golubović for 0<ν≤3/2.

Intrinsic ripples in graphene

Abstract: The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Nonnegative weak solution for a periodic parabolic equation with bounded Radon measure

Abstract: The purpose of this work is to study a class of periodic parabolic equations having a critical growth nonlinearity with respect to the gradient and bounded Radon measure. By the main of the sub- and super-solution method, we employ some new technics to prove the existence of a nonnegative weak periodic solution to the studied problems.

Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

Abstract: The aim of this paper is to investigate a class of nonlinear periodic systems involving general differential operators with variable exponents. We assume that the reactions contain strong nonlinearities with p(x)-growth conditions on the gradients of the solutions. By using Leray Schauder’s topological degree combined with the sub- and super-solutions method, we prove the existence of weak periodic solutions to the considered systems.