Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes

We consider the following repulsive-productive chemotaxis model: Let $p\in (1,2)$, find $u \geq 0$, the cell density, and $v \geq 0$, the chemical concentration, satisfying \begin{equation}\label{C5:Am} \left\{ \begin{array} [c]{lll} \partial_t u - \Delta u - \nabla\cdot (u\nabla v)=0 \ \ \mbox{in}\ \Omega,\ t>0,\\ \partial_t v - \Delta v + v = u^p \ \ \mbox{in}\ \Omega,\ t>0, \end{array} \right. \end{equation} in a bounded domain $\Omega\subseteq \mathbb{R}^d$, $d=2,3$. By using a regularization technique, we prove the existence of solutions of this problem. Moreover, we propose three fully discrete Finite Element (FE) nonlinear approximations, where the first one is defined in the variables $(u,v)$, and the second and third ones by introducing ${\boldsymbol\sigma}=\nabla v$ as an auxiliary variable. We prove some unconditional properties such as mass-conservation, energy-stability and solvability of the schemes. Finally, we compare the behavior of the schemes throughout several numerical simulations and give some conclusions.Comment: arXiv admin note: substantial text overlap with arXiv:1807.0111

Comparison of two finite element schemes for a chemo-repulsion system with quadratic production

In this paper we propose two fully discrete Finite Elements (FE) schemes for a repulsive chemotaxis model with quadratic production term. The first one (called scheme UV) corresponds to the backward Euler in time with FE in space approximation; while the second one (called scheme US$_\varepsilon$) is obtained as a modification of the scheme US proposed by [Guill\'en-Gonz\'alez et al.], by applying a regularization procedure. We prove that the schemes UV and US$_\varepsilon$ have better properties than the FE scheme US. Specifically, we prove that, unlike the scheme US, the scheme UV is energy-stable in the primitive variables of the model, under a "compatibility" condition on the FE spaces. On the other hand, the scheme US$_\varepsilon$ is energy-stable with respect to the same modified energy of the scheme US, and an "approximated positivity" property holds (which is not possible to prove for the schemes US and UV). Additionally, we study the well-posedness of the schemes and the long time behaviour obtaining exponential convergence to constant states. Finally, we compare the numerical schemes throughout several numerical simulations

A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes

We consider the following repulsive-productive chemotaxis model: find 0, the cell density, and 0, the chemical concentration, satisfying 0 in 0 in 0 (1) with 1 2 , a bounded domain ( 1 2 3), endowed with non-flux boundary conditions. By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for 1 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables under structured meshes, and the second one by using the auxiliary variable and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions

Unconditionally energy stable fully discrete schemes for a chemo-repulsion model

This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, such that ∂tu − Δu −∇· (u∇v) = 0 in Ω, t> 0, ∂tv − Δv + v = u in Ω, t> 0, in a bounded domain Ω ⊆ Rd, d = 2, 3. By using a regularization technique, we propose three fully discrete Finite Element (FE) approximations. The first one is a nonlinear approximation in the variables (u, v); the second one is another nonlinear approximation obtained by introducing σ = ∇v as an auxiliary variable; and the third one is a linear approximation constructed by mixing the regularization procedure with the energy quadratization technique, in which other auxiliary variables are introduced. In addition, we study the well-posedness of the numerical schemes, proving unconditional existence of solution, but conditional uniqueness (for the nonlinear schemes). Finally, we compare the behavior of such schemes throughout several numerical simulations and provide some conclusions.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Vicerrectoría de Investigación y Extensión (Universidad Industrial de Santander

Numerical analysis for a chemotaxis-navier-stokes system

In this paper we develop a numerical scheme for approximating a d-dimensional chemotaxis- Navier–Stokes system, d= 2, 3, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases where the chemical signal is consumed with a rate proportional to the amount of organisms. We construct numerical approximations based on the Finite Element method and analyze optimal error estimates and convergence towards regular solutions. In order to construct the numerical scheme, we use a splitting technique to deal with the chemo-attraction term in the cell-density equation, leading to introduce a new variable given by the gradient of the chemical concentration. Having the equivalent model, we consider a fully discrete Finite Element approximation which is well-posed and mass-conservative. We obtain uniform estimates and analyze the convergence of the scheme. Finally, we present some numerical simulations to verify the good behavior of our scheme, as well as to check numerically the optimal error estimates proved in our theoretical analysis

Data Communication Magazine

Los multiplexores son herramientas importantes en la comunicación de datos, debido a que se permiten en envío de diferentes señales a través de un solo medio. En la actualidad, son aplicados en diversas áreas entres las que se encuentran seguridad, redes telefónicas, redes internas, entre otras.Desarrollo e implementación de un multiplexor y demultiplexor por división de timepo para la transmisión de señales digitales, triangualres y análogas. -- Proyecto de simulación de la trasformada de fourier discreta es sus aplicaciones físicas (transmisión de datos). -- Medición de pérdida de potencia. -- Opnet: modelado de infiniband(iba). -- Construcción de un escenario para la transmisión de datos mediante el uso de telefonía ip. -- Simulación de algoritmos de programación. -- Conmutación de paquetes. -- Simulación de computacional. -- Descripción de procedimientos para el muestreo y reconstrucción de señales. -- Planeación, diseño y desarrollo de un software didáctico. -- Descripción de los principales puertos usados en la comunicación de datos. -- Esquemas de codificación.Multiplexers are important tools in data communication because they allow different signals to be sent through a single medium. Currently, they are applied in various areas, including security, telephone networks, internal networks, among others

EDUCACIÓN AMBIENTAL Y SOCIEDAD. SABERES LOCALES PARA EL DESARROLLO Y LA SUSTENTABILIDAD

Este texto contribuye al análisis científico de varias áreas del conocimiento como la filosofía social, la patología, la educación para el cuidado del medio ambiente y la sustentabilidad que inciden en diversas unidades de aprendizaje de la Licenciatura en Educación para la Salud y de la Maestría en Sociología de la SaludLas comunidades indígenas de la sierra norte de Oaxaca México, habitan un territorio extenso de biodiversidad. Sin que sea una área protegida y sustentable, la propia naturaleza de la región ofrece a sus visitantes la riqueza de la vegetación caracterizada por sus especies endémicas que componen un paisaje de suma belleza