Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Brigham Young University

Discipline
Keyword
Publication Year
Publication
Publication Type

Articles 241 - 255 of 255

Full-Text Articles in Mathematics

Numerical Aspects Of Discrete And Continuum Hybrid Models In Cell Biology, J. C. Dallon Feb 2000

Numerical Aspects Of Discrete And Continuum Hybrid Models In Cell Biology, J. C. Dallon

Faculty Publications

In this paper we introduce a method of modeling which mixes continuum and discrete variables, and explain two models in cell biology that use this method. The first application deals with wound healing, more specifically the collagen alignment in scar tissue formation and the second models early aggregation in the cellular slime mold Dictyostelium discoideum. We solve these models using numerical techniques similar to the particle-in-cell method which requires that the discrete and continuum variables are interpolated one to the other. The implementational and numerical details are discussed in an informal and practical manner with particular attention given to the …

Go to article

An Extension Of Zermelo's Model For Ranking By Paired Comparisons, Christopher P. Grant, Gregory R. Conner Jan 2000

An Extension Of Zermelo's Model For Ranking By Paired Comparisons, Christopher P. Grant, Gregory R. Conner

Faculty Publications

In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyse a natural extension of Zermelo's model resulting from a singular perturbation. We show that this extension produces a ranking for arbitrary (nonnegative) outcome matrices and retains several of the desirable properties of the original model. In addition, we discuss computational techniques and provide examples of their use.

Go to article

A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt Jan 2000

A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt

Faculty Publications

Orientation of extracellular matrix fibers in the skin is a key ingredient of tissue appearance and function, and differences in fiber alignment are one of the main distinctions between scar tissue and normal skin. In this paper, the authors develop a mathematical model for alignment of collagen fibers and the fibroblast cells that remodel them; the model extends previous work in which spatial variation was excluded. Numerical simulations of the model are presented, which show spatial variations in alignment over long transients, but with spatially uniform behavior in the long term. This is investigated further via asymptotic analysis, using the …

Go to article

Mathematical Modelling Of Extracellular Matrix Dynamics Using Discrete Cells: Fiber Orientation And Tissue Regeneration, J. C. Dallon, J. A. Sherratt, P. K. Maini Aug 1999

Mathematical Modelling Of Extracellular Matrix Dynamics Using Discrete Cells: Fiber Orientation And Tissue Regeneration, J. C. Dallon, J. A. Sherratt, P. K. Maini

Faculty Publications

Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modeled as a continuum. Using numerical simulations, we investigate the effect on alignment of changing cell properties and of varying cell interactions with collagen and fibrin.

Go to article

Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant Nov 1998

Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant

Faculty Publications

This paper addresses the qualitative behavior of a nonlinear convection-diffusion equation on a smooth bounded domain in Rn, in which the strength of the convection grows superlinearly as the density increases. While the initial-boundary value problem is guaranteed to have a local-in-time solution for smooth initial data, it is possible for this solution to be extinguished in nite time. We demonstrate that the way this may occur is through nite-time "blow up," i.e., the unboundedness of the solution in arbitrarily small neighborhoods of one or more points in the closure of the spatial domain. In special circumstances, such as the …

Go to article

A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer Oct 1998

A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer

Faculty Publications

We develop a mathematical model of cell-to-cell-signalling in Dictyostelium discoideum that predicts the cAMP signal seen by individual cells in early aggregation. The model employs two cells on a plane and is designed to predict the space-time characteristics of both the extracellular cAMP signal seen by one cell when a nearby cell relays, and the intracellular cAMP response produced by the stimulus in the receiving cell. The effect of membrane bound phosphodiesterase is studied and it is shown that cells can orient effectively even in its absence. Our results give a detailed picture of how the spatio-temporal characteristics of the …

Go to article

Recognizing Constant Curvature Discrete Groups In Dimension 3, J. W. Cannon, E. L. Swenson Feb 1998

Recognizing Constant Curvature Discrete Groups In Dimension 3, J. W. Cannon, E. L. Swenson

Faculty Publications

We characterize those discrete groups Gwhich can act properly discontinuously, isometrically, and cocompactly on hyperbolic 3-space H^3 in terms of the combinatorics of the action of G on its space at infinity. The major ingredients in the proof are the properties of groups that are negatively curved (in the large) (that is, Gromov hyperbolic), the combinatorial Riemann mapping theorem, and the Sullivan-Tukia theorem on groups which act uniformly quasiconformally on the 2-sphere.

Go to article

Some Harmonic N-Slit Mappings, Michael Dorff Feb 1998

Some Harmonic N-Slit Mappings, Michael Dorff

Faculty Publications

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h+g where h(z) = (see PDF), g(z) = (see PDF) . SOH will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SOH. Finally we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius.

Go to article

A Mathematical Model For Fibroblast And Collagen Orientation, J. C. Dallon, J. A. Sherratt Jan 1998

A Mathematical Model For Fibroblast And Collagen Orientation, J. C. Dallon, J. A. Sherratt

Faculty Publications

Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integro-differential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum …

Go to article

On The Dynamic Behaviour Of A Thermoviscoelastic Body In Frictional Contact With A Rigid Obstacle, Kenneth Kuttler, K. T. Andrews, M. Shillor Jan 1997

On The Dynamic Behaviour Of A Thermoviscoelastic Body In Frictional Contact With A Rigid Obstacle, Kenneth Kuttler, K. T. Andrews, M. Shillor

Faculty Publications

We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive relation is assumed to be of Kelvin-Voigt type and the frictional heat generation on the contact surface is taken into account. In this setting we establish the existence of a solution to a weak version of the energy-elasticity system which consists of a parabolic equation coupled …

Go to article

Slow Motion In One-Dimensional Cahn-Morral Systems, Christopher P. Grant Jan 1995

Slow Motion In One-Dimensional Cahn-Morral Systems, Christopher P. Grant

Faculty Publications

In this paper we study one-dimensional Cahn-Morral systems, which are the multicomponent analogues of the Cahn-Hilliard model for phase separation and coarsening in binary mixtures. In particular, we examine solutions that start with initial data close to the preferred phases except at finitely many transition points where the data has sharp transition layers, and we show that such solutions may evolve exponentially slowly; i.e., if ε is the interaction length then there exists a constant C such that in exp(C/ε) units of time the change in such a solution is o(1). This corresponds to extremely slow coarsening of a multicomponent …

Go to article

Precision Spectroscopy Using The Lamb Dip In A Pure Ion Plasma, P. N. Barnes, Grant W. Hart Feb 1993

Precision Spectroscopy Using The Lamb Dip In A Pure Ion Plasma, P. N. Barnes, Grant W. Hart

Faculty Publications

The use of the Lamb dip as a technique for precision spectroscopy in a non-neutral plasma is explored through computer modeling. Using singly ionized magnesium as the ion and under typical pure ion plasma conditions, the measurement appears to be feasible. Under the conditions calculated here, the Lamb dip is only 4% wider than the natural linewidth of the transition.

Go to article

The Analysis Of A Model For Wave Motion In A Liquid Semiconductor: Boundary Interaction And Variable Conductivity, William V. Smith Mar 1991

The Analysis Of A Model For Wave Motion In A Liquid Semiconductor: Boundary Interaction And Variable Conductivity, William V. Smith

Faculty Publications

The theory of conducting fluids in relative motion with small conductivity is studied with a model including the Maxwell displacement current. The model is linearized, and the interaction of waves with a plane boundary in three space is studied for two orientations of the external magnetic field. It is found that two families of boundary conditions preserve energy in one orientation (external field orthogonal to the boundary), while in the other (external field parallel to the boundary) only one condition exists which preserves energy. It is shown that generalized Fourier transforms exist, generated from the generalized eigenfunction expansions. Further, it …

Go to article

Eigenvalue Problems Of Ginzburg–Landau Operator In Bounded Domains, Kening Lu, Xing-Bin Pan Jun 1990

Eigenvalue Problems Of Ginzburg–Landau Operator In Bounded Domains, Kening Lu, Xing-Bin Pan

Faculty Publications

In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in [openface R]2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.

Go to article

Quasilinear Evolution Equations In Nonclassical Diffusion, Kenneth Kuttler, Elias Aifantis Jan 1988

Quasilinear Evolution Equations In Nonclassical Diffusion, Kenneth Kuttler, Elias Aifantis

Faculty Publications

After describing the motivation leading to some nonclassical diffusion equations, we formulate a general abstract nonlinear evolution equation and establish existence of solutions. Then we return to the original equation and discuss particular initial-boundary value problems.

Go to article

First Prev