ISSN 1556-6757


SJI 

 

 




 
 
 
Volume 1, Issue 1, 2007
 
 

Pattern Formation Induced by an Electric Field in Thin Liquid Films
Emily Tian

Abstract
This paper addresses some nonlinear problems arising from thin film pattern formation induced by an electric field. The physical setup is a thin liquid film confined between two electrodes and separated by an air gap from the top mask electrode. The objective is to study the dependence of the interfacial morphology on certain parameters. The mathematical model consists of a lubrication equation including the effects of surface tension describing the thin film thickness and Maxwell's equations describing the electric field strengths. In the long wavelength limit, a single interfacial evolution equation is derived. A weakly nonlinear stability analysis of the planar interface solution to this equation shows that the thickness ratio of the air gap to the liquid plays a critical role in the pattern formation process. Full Article


Some remarks concerning the representation of certain subnormal derivations and their Hilbert-Schmidt norm estimate   Vasile Lauric

Abstract
In this note we extend a result of D. Jocic concerning the representation of some derivations. Precisely, we prove that if A and are subnormal operators on a Hilbert space H and X 2 L(H) is such that AX ¡ XB 2 C2(H); then f(A)X ¡ Xf(B) and f(A)¤X ¡ Xf(B)¤belong to C2(H) and each of these expressions has a certain integral representation when the function f belongs to the class Lip (§) \ R(§); where § = ¾(A) [ ¾(B): Furthermore, Hilbert-Schmidt norm estimates of f(A)X ¡ Xf(B) and f(A)¤X ¡ Xf(B)¤ are given.  Full Article



On the relationship between the Hausdorff dimension and the integration order
Leon C. Hardy
 

Abstract
We use the Gr¨unwald definition for the integration of the function f : [0, 1] R to

construct an iterated function system on the interval [0, 1]. Then we show that this iterated

function system satisfies the open set condition. Using this construction, we further

show that the Hausdorff dimension is intimately related to the order of the fractional

integration process for any real order q > 0.  Full Article



Visualization of Algorithms from Computational Geometry using QuickTime® Movies
Jay Martin Anderson

Abstract
QuickTime movies provide students of computational geometry with a useful pedagogical tool that helps them to follow, implement and analyze algorithms. QuickTime movies can include explanatory text to support the visualization, breakpoints to stop the visualization for student interaction, and the ability to rewind, fast-forward and move step-by-step through the visualization. QuickTime Virtual Reality movies provide an additional element of interactivity. We introduce here a suite of visualizations spanning many algorithms for many topics in computational geometry, offering thereby to stimulate discussion and debate on the pedagogical merits of this technique. Full Article


 

The Inverse Boundary Value Problem for the Two-Dimensional Elliptic Equation in Anisotropic Media    Borislava Gutarts
 

Abstract

In this article we consider the inverse boundary value problem for the elliptic equation r ¢ (°(x)ru) = 0 in R2. We use Fadeev’s fundamental solution and a method previously employed by Sylvester, which consists of reducing the anisotropic conductivity °, to an isotropic one. This results, after a change of dependent variables, in a Schr¨odinger equation with the potential q(x). Then using Nachman and the @-equation, we give a different proof of his result, that

the Dirichlet-to-Neumann map ¤ determines the coefficients ° of the equation uniquely, up to a change of coordinates  Full Article


 

Using Geographic Information Systems and Spatial Statistics to Examine the Spatial Dimension of Animal Social Behavior: A Baboon Example
Vicki K. Bentley-Condit, Timothy S. Hare

Abstract
Geographic Information Systems (GIS) mapping technology and its associated inferential spatial statistics are used to examine the spatial dimension of animal social behavior – in this case, adult captive female olive baboons (Papio anubis).  Seventeen lactating females were observed and mapped over a two-month period at the Southwest Foundation for Biomedical Research, San Antonio, Texas (n=593 mapped focals).  All except one of the females were found to significantly differ from one another in the area(s) of the habitat preferred and used.  Different areas were preferred and utilized by differently ranked females (i.e., high, mid, and low-ranked) and use of space also varied by age (i.e., young, middle, and old-aged) – although the latter pattern was not as strong.  Many of the animals’ social behaviors correlated with areas contiguous to preferred feeding areas.  Our data demonstrate the importance that relative spatial arrangement can have on animal interactions.  GIS and its associated inferential spatial statistics offer the means by which this spatial context can be most rigorously examined.
Full Article




Visualization of Algorithms from Computational Geometry using QuickTime® Movies

Jay Martin Anderson

Abstract
QuickTime®1 movies provide students of computational geometry with a useful pedagogical tool that helps them to follow, implement and analyze algorithms. QuickTime movies can include explanatory text to support the visualization, breakpoints to stop the visualization for student interaction, and the ability to rewind, fast-forward and move step-by-step through the visualization. QuickTime Virtual Reality movies provide an additional element of interactivity. We introduce here a suite of visualizations spanning many algorithms for many topics in computational geometry, offering thereby to stimulate discussion and debate on the pedagogical merits of this technique. Full Article



 

Optimal designs for linear mixed-effects models
Lei Nie
 

Abstract

Optimal design theories of mixed-e®ects models are not well established, mainly because

there are some substantial di®erences between them and ¯xed-e®ects models. The di®er-

ences are \local optimality", lack of orthogonality and independence, and two layout design

structure. Despite all of these di®erences, optimal designs for mixed-e®ects models could be

surprisingly similar to optimal designs for relevant ¯xed-e®ects models. These circumstances

include some mixed-e®ects models for stability research for drug development, which initially

motivated this research project. We construct optimal designs for many mixed-e®ects mod-

els. These optimal designs do not depend on unknown parameters and the optimality of

these designs may extend to variance components estimation. Full Article



A Two-dimensional Cell Motility Model
Ravi K Vuta, Roger Lui, Gretar Tryggvason
 

Abstract

A simple two-dimensional continuum model of a cell crawling on a surface is introduced. The model resulted in a moving boundary problem (MBP) involving b the length density of certain protein ¯laments inside the cell. This MBP may be solved numerically by a level set method and we show by examples that under certain assumptions on the protrusion rate, solutions of the MBP converge to the traveling domain solution as time goes to in¯nity. Biologically, this means that under the assumptions of the model, all cells, regardless of their initial shapes and sizes,

will eventually become identical and move in a particular direction at the same speed. Extensions of this model are also discussed. Full Article


 

Mathematical Determination of Competitive Feedback Inhibition Rates in Branched Metabolic Pathways       Luis Jimenez,Christopher Pickens, Weijiu Liu
 

Abstract

In this paper, we consider the problem of mathematically determining the feedback inhibition rates in multi-branched metabolic pathways. To solve the problem, we model the system with a series of nonlinear ordinary di®erential equations by using the law of mass action without the usual quasi-steady state assumptions.Through an equilibrium analysis, we develop formulas to calculate the feedback inhibition rates in terms of the concentrations of end-products and regulatory enzymes at equilibrium. We then prove that the linearized system of the nonlinear system at its equilibrium is exponentially stable by applying Routh's stability criterion, thus the equilibrium of the nonlinear system is locally exponentially stable. This local stability proves that the feedback inhibition rates determined by our formulas are e®ective in regulating the end-products. This feasibility of these feedback inhibition rates is further tested numerically using both randomly generated data and biological data. Full Article