Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France.
Published: December 2013
AI Article Synopsis
Article Abstract
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amount to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: The convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: The propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.
We present a sequential growth scheme based on pulsed laser deposition, which yields dense arrays of ultrathin, match-shaped Au/CoNi nanopillars, vertically embedded in SrTiOthin films. Analysis of the magnetic properties of these nanocomposites reveals a pronounced out-of-plane anisotropy. We show that the latter not only results from the peculiar nanoarchitecture of the hybrid films but is further enhanced by strong magneto-structural coupling of the wires to the surrounding matrix.
Committed Mathematics Team, Research Unit in Mathematics and Applications, Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67 Dschang, Cameroon.
This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change. The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment. Firstly, we provide a theoretical study of the nonlinear differential equations model obtained.
A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace, and determining the coefficients of the linear combination. New schemes were developed to form the basis of the local approximation subspace, which were derived by approximating only the k 2 u term of the Helmholtz equation. The construction of a basis of the local approximation subspace allows the new approach to be able to represent any finite difference scheme that belongs to this subspace.
We propose a numerical approach to solve a long-standing challenge which is the applicability of the artificial compressibility (AC) formulation for solving the incompressible Navier-Stokes equations at very-low Reynolds numbers. A wide range of engineering applications involves very-low Reynolds number flows in Micro-ElectroMechanical Systems (MEMS) and in the fields of chemical-, agricultural- and biomedical engineering. It is known that the already existing numerical methods using the AC approach fail to provide physically correct results at very-low Reynolds numbers ( ≤ 1).
Variable viscosity, activation energy and microgravity effects on Darcy nanofluid for the thermal performance improvement in thermal energy storage systems through stretching flat plate solar collector is the focus of this research. Thermal energy storage (TES) can be improved though solar collectors, phase change materials and photovoltaic cells using nanofluid in the base liquid. To increase the reaction rate in nanoparticles, the activation energy and solar radiations are used for the efficiency of TES.
