Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients

We propose a new second-order finite volume scheme for non-homogeneous and anisotropic diffusion problems based on cell to vertex reconstructions involving minimization of functionals to provide the coefficients of the cell to vertex mapping. The method handles complex situations such as large preconditioning number diffusion matrices and very distorted meshes. Numerical examples are provided to show the effectiveness of the method

Discrete hilbert transform \ue0 la gundy-Varopoulos

We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic processes considered have jump components. The stochastic representation of the function and that of its Hilbert transform are under differential subordination and orthogonality relation with respect to the sharp bracket of quadratic covariation. This illustrates the Cauchy-Riemann relations of analytic functions in this setting. This result is inspired by the seminal work of Gundy and Varopoulos on stochastic representation of the Hilbert transform in the continuous setting

Evaluation of genetic variability in four Nigerian locally-adapted chicken populations using major histocompatibility complex-linked LEI0258 microsatellite marker

Major Histocompatibility Complex (MHC) is a group of genes that generally influence immune response in vertebrates, and it has been explored among different animal species in various countries. However, there is a paucity of information on its application in Nigerian locally-adapted chickens (NLAC). This research investigated genetic polymorphism, allele variability, and genetic relationships using LEI0258 major histocompatibility complex-linked microsatellite marker among four NLAC populations: Fulani × Yoruba ecotypes, FUNNAB Alpha × Noiler breeds. Blood samples were randomly collected from 50 mature birds in each population and DNA was extracted and subsequently subjected to PCR, Sanger sequencing, and bioinformatic analysis. There were two variable numbers of tandem repeats (VNTRs), with 90% of the alleles containing only one R13 and varying numbers of the R12 motifs that ranged from 1 to 19. Additional polymorphism was revealed by the presence of five SNPs and three indels in the upstream and downstream regions of LEI0258. A total of 48 alleles were observed with sizes ranging from 188 to 530 base pairs while the allele frequencies within the populations ranged from 1.9 to 29.2%. However, only 17 out of the 48 alleles had corresponding MHC-B haplotypes. Haplotypes B2, B12, and B21 found in this study had been reported to confer resistance to infectious poultry diseases especially avian influenza in locally adapted chickens. There were high allelic variability and genetic polymorphisms observed via the atypical LEI0258 microsatellite in describing the MHC-B region

An Efficient Implementation of a 3D CeVeFE DDFV Scheme on Cartesian Grids and an Application in Image Processing

International audienceIn this work we describe the implementation of a 3D Center-Vertex-Face/Edge Discrete Duality Finite Volume (CeVeFE DDFV) scheme using only the degrees of freedom (DOF) disposed on a Cartesian grid. These DOF are organised in a three-mesh structure proper to the CeVeFE DDFV setting. Reposing on a diamond structure, the approach presented here greatly simplifies the implementation, also in the case of grids topologically equivalent to the uniform Cartesian one. The numerical scheme is then applied to a problem in image processing, where uniform Cartesian structure of the DOF is naturally imposed by the pixel/voxel structure. A semi-implicit DDFV scheme is used for solving a nonlinear advection-diffusion equation, the subjective surfaces equation, in order to reconstruct the volume of a tumour from noisy 3D SPECT images with signal intensity on the tumour boundary. The matrix of the linear system has a band structure and the method is fast and able to successfully reconstruct the tumour volume

An Asymptotic-Preserving Scheme for Systems of Conservation Laws with Source Terms on 2D Unstructured Meshes

In this paper, finite volumes numerical schemes are developed for hyperbolic systems of conservation laws with source terms. The systems under consideration degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving ı.e. that they degenerate accordingly. Here, an asymptotic-preserving numerical scheme is proposed for any system within the aforementioned class on 2D unstructured meshes. This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometrical property on the mesh. Finally, numerical examples are given to illustrate its behavior

Global Classical Solutions Close to Equilibrium to the Vlasov Euler-Fokker-Planck System

International audienceWe are concerned with the global well-posedness of a two-phase flow system arising in the modelling of fluid-particle interactions. This system consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the incompressible Euler equations for a dense phase (fluid) through the friction forcing. Global existence of classical solutions to the Cauchy problem in the whole space is established when initial data is a small smooth perturbation of a constant equilibrium state, and moreover an algebraic rate of convergence of solutions toward equilibrium is obtained under additional conditions on initial data. The proof is based on the macro-micro decomposition and Kawashima's hyperbolic-parabolic dissipation argument. This result is generalized to the periodic case, when particles are in the torus, improving the rate of convergence to exponential