A fully discrete evolving surface finite element method

In this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In earlier papers using a suitable variational formulation in time dependent Sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces [IMA J. Numer Anal., 25 (2007), pp. 385--407; Math. Comp., to appear]. Optimal order L2(Γ(t)) and H1(Γ(t)) error bounds were proved for linear finite elements. In this work we prove optimal order error bounds for a backward Euler time discretization

Use of mathematical derivatives (time-domain differentiation) on chromatographic data to enhance the detection and quantification of an unknown 'rider' peak

Two samples of an anticancer prodrug, AQ4N, were submitted for HPLC assay and showed an unidentified impurity that eluted as a 'rider' on the tail of the main peak. Mathematical derivatization of the chromatograms offered several advantages over conventional skimmed integration. A combination of the second derivative amplitude and simple linear regression gave a novel method for estimating the true peak area of the impurity peak. All the calculation steps were carried out using a widely available spreadsheet program. (C) 2003 Elsevier B.V. All rights reserved

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

The resistible effects of Coulomb interaction on nucleus-vapor phase coexistence

We explore the effects of Coulomb interaction upon the nuclear liquid vapor phase transition. Because large nuclei (A>60) are metastable objects, phases, phase coexistence, and phase transitions cannot be defined with any generality and the analogy to liquid vapor is ill-posed for these heavy systems. However, it is possible to account for the Coulomb interaction in the decay rates and obtain the coexistence phase diagram for the corresponding uncharged system.Comment: 5 pages, 5 figure

Optimal control of the propagation of a graph in inhomogeneous media

We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the $H^{-1}$-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results

Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid

The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to suggest the presence of one dominant length scale. However, the Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we show that, by stirring the mixture at a sufficiently large amplitude, we excite the diffusion and overwhelm the segregation to create a homogeneous liquid. At intermediate amplitudes we see regions of bubbles coexisting with regions of hyperdiffusive filaments. Thus, the problem possesses two dominant length scales, associated with the bubbles and filaments. For simplicity, we use use a chaotic flow that mimics turbulent stirring at large Prandtl number. We compare our results with the case of variable mobility, in which growth of bubble size is dominated by interfacial rather than bulk effects, and find qualitatively similar results.Comment: 20 pages, 27 figures. RevTeX

The ordered K-theory of a full extension

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9 is not correct as stated. See arXiv:1505.05951 for more details. Since Theorem 4.9 is an application to the main results of the paper, the main results of this paper are not affected by the error. Version III comments: Some typos and errors corrected. Some references adde

Flow of nitrogen-pressurized Halon 1301 in fire extinguishing systems

Halon 1301 which is a halocarbon fire extinguishing agent (CBrF3) used by the U.S. Army for vehicle fire suppression is discussed. Halon 1301 is discharged under nitrogen pressure, and the Halon-nitrogen mixture is a two phase, two component mixture that obeys compressible fluid laws and exhibits choking effects. A computer model was developed to analyze the discharge of Halon and nitrogen from a storage bottle through pipes and nozzles. The model agrees well with data from Halon 1301 discharge tests. The discharge time depends mainly on nozzle area and pipe volume, for given initial conditions. Graphs were developed for estimating discharge times. A nozzle employing multiple concentric converging/diverging nozzles was developed which gave hemispherical coverage

Compound nuclear decay and the liquid to vapor phase transition: a physical picture

Analyses of multifragmentation in terms of the Fisher droplet model (FDM) and the associated construction of a nuclear phase diagram bring forth the problem of the actual existence of the nuclear vapor phase and the meaning of its associated pressure. We present here a physical picture of fragment production from excited nuclei that solves this problem and establishes the relationship between the FDM and the standard compound nucleus decay rate for rare particles emitted in first-chance decay. The compound thermal emission picture is formally equivalent to a FDM-like equilibrium description and avoids the problem of the vapor while also explaining the observation of Boltzmann-like distribution of emission times. In this picture a simple Fermi gas thermometric relation is naturally justified and verified in the fragment yields and time scales. Low energy compound nucleus fragment yields scale according to the FDM and lead to an estimate of the infinite symmetric nuclear matter critical temperature between 18 and 27 MeV depending on the choice of the surface energy coefficient of nuclear matter.Comment: Five page two column pages, four figures, submitted to Phys. Rev.