Partial Differential Equations Commons^™

Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones

Mathematical Sciences Technical Reports (MSTR)

Impedance imaging has received a lot of attention in the past two decades, as a means for non-destructively imaging the interior of a conductive object. One injects a known electrical current pattern into an object at the exterior boundary, then measures the induced potential (voltage) on some portion of the boundary. The goal is to recover information about the interior conductivity of the object, which (we hope) influences the voltages we measure. Of course one can also use multiple input currents and measured voltages. A variation on this problem is that of "boundary identification," in which some portion of the …

Soliton Perturbation Theory For The Modified Kawahara Equation, Anjan Biswas

Applications and Applied Mathematics: An International Journal (AAM)

The modified Kawahara equation is studied along with its perturbation terms. The adiabatic dynamics of the soliton amplitude and the velocity of the soliton are obtained by the aid of soliton perturbation theory.

On Existence And Uniqueness Theorem Concerning Time–Dependent Heat Transfer Model, Naji A. Qatanani, Qasem M. Heeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article we consider a physical model describing time-dependent heat transfer by conduction and radiation. This model contains two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-grey surfaces. The aim of this work is to present a reliable framework to prove the existence and the uniqueness of a weak solution for this problem. The existence of the solution can be proved by solving an auxiliary problem by the Galerkin-based approximation method and Moser-type arguments which implies the existence of solution to the original problem. The uniqueness of the solution will …

Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El- Doma (2006) and El-Doma (2008).

Remarks On The Stability Of Some Size-Structured Population Models Ii: Changes In Vital Rates Due To Size And Population Size, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003) and El-Doma (2006).

Oscillatory Behavior Of Second Order Neutral Differential Equations With Positive And Negative Coefficients, Jelena Manojlović, Yutaka Shoukaku, Tomoyuki Tanigawa, Norio Yoshida

Applications and Applied Mathematics: An International Journal (AAM)

Oscillation criteria are obtained for solutions of forced and unforced second order neutral differential equations with positive and negative coefficients. These criteria generalize those of Manojlović, Shoukaku, Tanigawa and Yoshida (2006).

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe

Theses Digitization Project

This thesis studied the existence, uniqueness, and quenching behavior of the solution to a degenerate equation subject to the initial condition and the second boundary conditions.

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Mikhail Khenner

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Stochastic Differential Equations With Jumps, Jose L. Menaldi

Mathematics Faculty Research Publications

Part I Stochastic Processes with Jumps Chapters: Probability Spaces, Semigroup Theory - Part II Stochastic Differential Equations with Jumps Chapters: Stochastic Calculus, Stochastic Differential Equations - Part III Reflected SDE with Jumps Chapters: Stochastic Differential Equations II, Stochastic Differential Equations III.

Comment: This is last version from 2014-01-07. *This Initial version 15/May/2008 was corrected and augmented to produce the others 5 volumes.

Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov

Articles

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

Optimising Design Parameters Of Enzyme-Channelling Biosensors, Dana Mackey, Tony Killard

Conference Papers

Two mathematical models for an electrochemical biosensor are proposed and compared with a view to determining the ratio of two immobilized enzymes which maximizes the amperometric signal amplitude.

On An Integrable Two-Component Camassa-Holm Shallow Water System, Adrian Constantin, Rossen Ivanov

Articles

The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a twocomponent integrable system of coupled equations. First we derive the system in the context of shallow water theory. Then we show that while small initial data develop into global solutions, for some initial data wave breaking occurs. We also discuss the solitary wave solutions. Finally, we present an explicit construction for the peakon solutions in the short wave limit of system.

Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov

Articles

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and H.1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left-invariant metric on SO(3). The CH and HS equations are integrable bi-hamiltonian equations and one of their Hamiltonian structures is associated to the …

Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades

Publications

Phototransduction is the process by which photons of light generate an electrical response in retinal rod and cone photoreceptors, thereby initiating vision. We compare the electrical response in salamander rods from increasingly more (spacialy) detailed models of phototransduction: 0-dimensional (bulk), 1-dimensional (longitudinal), 2-dimensional (axisymmetric), and 3-dimensional (with incisures). We discuss issues of finding physical parameters for simulation and validation of models, and also present some computational experiments for rods with geometry of mouse and human photoreceptors.