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ISSN 1556-6757 |
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| Volume
1, Issue 1, 2007 |
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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
B¤
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
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
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
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
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