526 research outputs found
Mathematical models for erosion and the optimal transportation of sediment
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment
Dynamic energy budget approach to evaluate antibiotic effects on biofilms
Quantifying the action of antibiotics on biofilms is essential to devise
therapies against chronic infections. Biofilms are bacterial communities
attached to moist surfaces, sheltered from external aggressions by a polymeric
matrix. Coupling a dynamic energy budget based description of cell metabolism
to surrounding concentration fields, we are able to approximate survival curves
measured for different antibiotics. We reproduce numerically stratified
distributions of cell types within the biofilm and introduce ways to
incorporate different resistance mechanisms. Qualitative predictions follow
that are in agreement with experimental observations, such as higher survival
rates of cells close to the substratum when employing antibiotics targeting
active cells or enhanced polymer production when antibiotics are administered.
The current computational model enables validation and hypothesis testing when
developing therapies.Comment: to appear in Communications in Nonlinear Science and Numerical
Simulatio
Asymptotic Behavior of 2-d Black Holes
We consider the solutions of the field equations for the large dilaton
gravity model in dimensions recently proposed by Callan, Giddings, Harvey
and Strominger (CGHS). We find time dependant solutions with finite mass and
vanishing flux in the weak coupling regime, as well as solutions which lie
entirely in the Liouville region.Comment: 10 page
A model for aperiodicity in earthquakes
International audienceConditions under which a single oscillator model coupled with Dieterich-Ruina's rate and state dependent friction exhibits chaotic dynamics is studied. Properties of spring-block models are discussed. The parameter values of the system are explored and the corresponding numerical solutions presented. Bifurcation analysis is performed to determine the bifurcations and stability of stationary solutions and we find that the system undergoes a Hopf bifurcation to a periodic orbit. This periodic orbit then undergoes a period doubling cascade into a strange attractor, recognized as broadband noise in the power spectrum. The implications for earthquakes are discussed
Religion and Coalition Politics
Cataloged from PDF version of article.The literature holds that coalition-building parties prefer the policy distance
of coalition partners to be as small as possible. In light of continued importance
of religion in electoral politics cross-nationally, the distance argument
is worrisome for minorities seeking political access because many minorities
are of different religion than the majority representatives forming coalitions.
The authors suggest plurality parties’ objectives to demonstrate inclusiveness
outweigh the concern over policy distance. They test their hypotheses
on a sample of all electorally active ethnic minorities in democracies from
1945 to 2004. The authors find support for their hypothesis that ethnic parties
representing minorities that diverge in religious family from the majority
are more likely to be included in governing coalitions than are ethnic minorities
at large. It is interesting, however, that they also find that minority parties
representing ethnic groups that differ in denomination from the majority are
less likely to be included in governing coalitions
The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis
The Paulsen problem is a basic open problem in operator theory: Given vectors
that are -nearly satisfying the
Parseval's condition and the equal norm condition, is it close to a set of
vectors that exactly satisfy the Parseval's
condition and the equal norm condition? Given , the squared
distance (to the set of exact solutions) is defined as where the infimum is over the set of exact solutions.
Previous results show that the squared distance of any -nearly
solution is at most and there are
-nearly solutions with squared distance at least .
The fundamental open question is whether the squared distance can be
independent of the number of vectors .
We answer this question affirmatively by proving that the squared distance of
any -nearly solution is . Our approach is based
on a continuous version of the operator scaling algorithm and consists of two
parts. First, we define a dynamical system based on operator scaling and use it
to prove that the squared distance of any -nearly solution is . Then, we show that by randomly perturbing the input vectors, the
dynamical system will converge faster and the squared distance of an
-nearly solution is when is large enough
and is small enough. To analyze the convergence of the dynamical
system, we develop some new techniques in lower bounding the operator capacity,
a concept introduced by Gurvits to analyze the operator scaling algorithm.Comment: Added Subsection 1.4; Incorporated comments and fixed typos; Minor
changes in various place
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