A hyperbolic model of chemotaxis on a network: a numerical study

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation

A new approach in the use of SIT in determining the dependence on ionic strength of activity coefficients. Application to some chloride salts of interest in the speciation of natural fluids

AbstractThis paper describes a modified version of the SIT (Specific ion Interaction Theory) method and its use in determining the dependence on ionic strength of activity coefficients. In the new approach the interaction coefficients (e) are not constant but depend on ionic strength (I /mol kg-1) according to the simple relationship:e = e∞+ (e0 - e∞) / (l + 1)where e0 and are true constants for I→ 0 and l→ ∞, respectively. To check the two parameter SIT equation, we calculated e0 and for the activity coefficients of HCl, LiCl, NaCl, KCl, MgCl2, CaCl2 and SrCl2, in a wide ionic strength range (0.1 ≤ l/mol kg-1 ≤ 4.5, for KCl; 0.1 ≤ l/mol kg-1 ≤ 6, for HCl, LiCl, NaCl; 0.3 ≤ l/mol kg-1 ≤ 12, for SrCl2; 0.3 ≤ l/mol kg-1 ≤ 15, for MgCl2; 0.3 ≤ l/mol kg-1 ≤ 18, for CaCl2). Results show that the γ values calculated using this approach fit quite well over the whole I-range for all the electrolytes considered. Comparison is made with the analogous one parameter SIT equation. The temperature coefficients of inter..

On Quadrature Rules Associated with Appell Polynomials

A quadrature rule using Appell polynomials and generalizing both the Euler-MacLaurin quadrature formula and a similar quadrature rule, obtained in Bretti et al [15], which makes use of Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the extrema of the considered interval, is derived. An expression of the remainder term and a numerical example are also enclosed

Bernoulli type polynomials on Umbral Algebra

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we provide to deriving identities for these polynomials

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201