pinecone/core-2020-05-10-deduplication huggingface dataset:
Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control

This is the peer reviewed version of the following article: Kavallaris, N. I. (2018). Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control. Mathematical Methods in the Applied Sciences, 41(3), 1074-1082. doi:10.1002/mma.4176, which has been published in final form at DOI: 10.1002/mma.4176. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingIn the current paper, we consider a stochastic parabolic equation which actually serves as a mathematical model describing the operation of an electrostatic actuated micro-electro-mechanical system (MEMS). We first present the derivation of the mathematical model. Then after establishing the local well-posedeness of the problem we  investigate under which circumstances a {\it finite-time quenching}  for this SPDE, corresponding to the mechanical phenomenon of {\it touching down}, occurs. For that purpose the Kaplan's eigenfunction method adapted in the context of SPDES is employed
Epidemic transmission on SEIR stochastic models with nonlinear incidence rate

Our interest is to quantify the spread of an infective process with latency period and generic incidence rate that takes place in a Önite and homogeneous population. Within a stochastic framework, two random variables are deÖned to describe the variations of the number of secondary cases produced by an index case inside of a closed population. Computational algorithms are presented in order to characterize both random variables. Finally, theoretical and algorithmic results are illustrated by several numerical examples
Stability and Optimal Control of a Delayed HIV Model

We propose and investigate a delayed model that studies the relationship
between HIV and the immune system during the natural course of infection and in
the context of antiviral treatment regimes. Sufficient criteria for local
asymptotic stability of the infected and viral free equilibria are given. An
optimal control problem with time delays both in state variables (incubation
delay) and control (pharmacological delay) is then formulated and analyzed,
where the objective consists to find the optimal treatment strategy that
maximizes the number of uninfected $CD4^{+}$ T cells as well as CTL immune
response cells, keeping the drug therapy as low as possible.Comment: This is a preprint of a paper whose final and definite form is with
  'Mathematical Methods in the Applied Sciences', ISSN 0170-4214. Submitted
  05-July-2016; accepted 24-Sept-201
Solution Form of a Higher Order System of Difference Equation and
  Dynamical Behavior of Its Special Case

The solution form of the system of nonlinear difference equations
\begin{equation*} x_{n+1} = \frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\
y_{n+1} = \frac{y_{n-k+1}^{p}x_{n}}{\alpha x_{n-k}^{p}+\beta x_{n}}, \quad n, p
\in \mathbb{N}_{0},\ k\in \mathbb{N}, \end{equation*} where the coefficients
$a, b, \alpha, \beta$ and the initial values
$x_{-i},y_{-i},i\in\{0,1,\ldots,k\}$ are real numbers, is obtained.
Furthermore, the behavior of solutions of the above system when $p=1$ is
examined. Numerical examples are presented to illustrate the results exhibited
in the paper.Comment: A preprint of this manuscript, which is of 13 pages with 8 figures,
  is submitted for publicatio
Small Perturbations of an Interface for Elastostatic Problems

We consider solutions to the Lam\'e system in two dimensions. By using
systematic way, based on layer potential techniques and the field expansion
(FE) method (formal derivation), we establish a rigorous asymptotic expansion
for the perturbations of the displacement field caused by small perturbations
of the shape of an elastic inclusion with C2-boundary. We extend these
techniques to determine a relationship between traction-displacement
measurements and the shape of the object and derive an asymptotic expansion for
the perturbation in the elastic moments tensors (EMTs) due to the presence of
small changes in the interface of the inclusion.Comment: 42pages,0 figures. arXiv admin note: text overlap with
  arXiv:1601.0677
Uncertainty Principle for Measurable Sets and Signal Recovery in
  Quaternion Domains

The classical uncertainty principle of harmonic analysis states that a
nontrivial function and its Fourier transform cannot both be sharply localized.
It plays an important role in signal processing and physics. This paper
generalizes the uncertainty principle for measurable sets from complex domain
to hypercomplex domain using quaternion algebras, associated with the
Quaternion Fourier transform. The performance is then evaluated in signal
recovery problems where there is an interplay of missing and time-limiting
data.Comment: 10 pages, 3 figure
Homogenization of a Fully Coupled Thermoelasticity Problem for a Highly
  Heterogeneous Medium With a Priori Known Phase Transformations

We investigate a linear, fully coupled thermoelasticity problem for a highly
heterogeneous, two-phase medium. The medium in question consists of a connected
matrix with disconnected, initially periodically distributed inclusions
separated by a sharp interface undergoing an a priori known interface movement
due to phase transformations. After transforming the moving geometry to an
$\varepsilon$-periodic, fixed reference domain, we establish the well-posedness
of the model and derive a number of $\varepsilon$-independent a priori
estimates. Via a two-scale convergence argument, we then show that the
$\varepsilon$-dependent solutions converge to solutions of a corresponding
upscaled model with distributed time-dependent microstructures.Comment: 25 pages, 1 figur
A conformal group approach to the Dirac-K\"ahler system on the lattice

Starting from the representation of the $(n-1)+n-$dimensional Lorentz
pseudo-sphere on the projective space $\mathbb{P}\mathbb{R}^{n,n}$, we propose
a method to derive a class of solutions underlying to a Dirac-K\"ahler type
equation on the lattice. We make use of the Cayley transform $\varphi({\bf
w})=\dfrac{1+{\bf w}}{1-{\bf w}}$ to show that the resulting group
representation arise from the same mathematical framework as the conformal
group representation in terms of the {\it general linear group}
$GL\left(2,\Gamma(n-1,n-1)\cup\{ 0\}\right)$. That allows us to describe such
class of solutions as a commutative $n-$ary product, involving the
quasi-monomials $\varphi\left({\bf z}_j\right)^{-\frac{x_j}{h}}$ ($x_j \in
h\mathbb{Z}$) with membership in the paravector space $\mathbb{R}\oplus
\mathbb{R}{\bf e}_j{\bf e}_{n+j}$.Comment: 14 page
Modelling drinking with information.

In this article, we propose a mathematical model that describes the dynamics of a population divided into susceptible drinkers, moderate drinkers, and heavy drinkers subject to an external influence. The external influence is modelled using a supplementary dynamical variable that is not a group of individuals but that enters the equations affecting the choices of the population classes.\ud
\ud
The system we define can be investigated using two simplified systems (one of which is a real subsystem), which model the populations of susceptible and moderate drinkers or susceptible and heavy drinkers independently. The dynamics of these two subsystems can be described exhaustively. The full system is too rich in possible scenarios, but its qualitative behaviour is connected to that of the two simplified systems. We make a complete description only in one particular case by means of numerical simulations
Global well-posedness of 2D nonlinear Boussinesq equations with mixed
  partial viscosity and thermal diffusivity

In this paper, we discuss with the global well-posedness of 2D anisotropic
nonlinear Boussinesq equations with any two positive viscosities and one
positive thermal diffusivity. More precisely, for three kinds of viscous
combinations, we obtain the global well-posedness without any assumption on the
solution. For other three difficult cases, under the minimal regularity
assumption, we also derive the unique global solution. To the authors'
knowledge, our result is new even for the simplified model.Comment: 21 page
Attractors for the strongly damped wave equation with $p$-Laplacian

This paper is concerned with the initial boundary value problem for one
dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$,
we establish the existence of weak local attractors for this problem in
$W_{0}^{1,p}(0,1)\times L^{2}(0,1)$. Under restriction $2<p<4$, we prove that
the semigroup, generated by the considered problem, possesses a strong global
attractor in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$ and this attractor is a
bounded subset of $W^{1,\infty }(0,1)\times W^{1,\infty }(0,1)$
On mechanical waves and Doppler shifts from moving boundaries

We investigate the propagation of infinitesimal harmonic mechanical waves
emitted from a boundary with variable velocity and arriving at a stationary
observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the
location of the source with constant velocity $v$. In the present work,
however, we consider a source co-located with a moving boundary
$x=X_\mathrm{s}(t)$, where $X_\mathrm{s}(t)$ can have an arbitrary functional
form. For "slowly moving" boundaries (\textit{i.e.}, ones for which the
timescale set by the mechanical motion is large in comparison to the inverse of
the frequency of the emitted wave), we present a multiple-scale asymptotic
analysis of the moving-boundary problem for the linear wave equation. We obtain
a closed-form leading-order (with respect to the latter small parameter)
solution and show that the variable velocity of the boundary results not only
in frequency modulation but also in amplitude modulation of the received
signal. Consequently, our results extending the applicability of two basic
tenets of the theory of a moving source on a stationary domain, specifically
that (a) $\dot X_\mathrm{s}$ for non-uniform boundary motion can be inserted in
place of the constant velocity $v$ in the classical Doppler formula and (b)
that the non-uniform boundary motion introduces variability in the amplitude of
the wave. The specific examples of decelerating and oscillatory boundary motion
are worked out and illustrated.Comment: 14 pages, 4 figures, Wiley journal style; accepted for publication in
  Mathematical Methods in the Applied Sciences; v2 corrects typographical
  error
Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that
arise in various applications such as in motor control, biometrics and optimal
transport theory. We provide qualitative properties, explicit analytical
formulas and computational algorithms for the cost functions. We also perform
numerical simulations to illustrate the analytical results. In addition, as a
by-product of our analysis, we obtain an explicit formula for the inverse of a
Wronskian matrix that is of independent interest in linear algebra and
differential equations theory.Comment: 28 page
A nonhomogeneous boundary value problem for the Kuramoto-Sivashinsky
  equation in a quarter plane

We study the initial boundary value problem for one-dimensional
Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through
the analysis of the boundary integral operator, and applying the known results
on the Cauchy problem, we obtain both the local well-posedness and the global
well-posedness for the nonhomogeneous initial boundary value problem. It is
shown that the Kuramoto-Sivashinsky equation is well-posed in Sobolev space
$C([0,T]; H^s (R^+)) \bigcap L^2(0,T; H^{s+2}(R^+))$ for $s>-2$
Numerical and asymptotic study of non-axisymmetric magnetohydrodynamic boundary layer stagnation-point flows

Both numerical and asymptotic analyses are performed to study the similarity solutions of three-dimensional boundary-layer viscous stagnation point flow in the presence of a uniform magnetic field. The three-dimensional boundary-layer is analyzed in a non-axisymmetric stagnation point flow, in which the flow is developed because of influence of both applied magnetic field and external mainstream flow. Two approaches for the governing equations are employed: the Keller-box numerical simulations solving full nonlinear coupled system and a corresponding linearized system that is obtained under a far-field behavior and in the limit of large shear-to-strain-rate parameter (Î»). From these two approaches, the flow phenomena reveals a rich structure of new family of solutions for various values of the magnetic number and Î». The various results for the wall stresses and the displacement thicknesses are presented along with some velocity profiles in both directions. The analysis discovered that the flow separation occurs in the secondary flow direction in the absence of magnetic field, and the flow separation disappears when the applied magnetic field is increased. The flow field is divided into a near-field (due to viscous forces) and far-field (due to mainstream flows), and the velocity profiles form because of an interaction between two regions. The magnetic field plays an important role in reducing the thickness of the boundary-layer. A physical explanation for all observed phenomena is discussed. Copyright Â© 2017 John Wiley & Sons, Ltd. Copyright Â© 2017 John Wiley & Sons, Ltd
Vanishing Viscosity Limit For the 3D Nonhomogeneous Incompressible
  Navier-Stokes Equations With a Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for the 3D
nonhomogeneous incompressible Navier-Stokes equations with a slip boundary
condition. We establish the local well-posedness of the strong solutions for
initial boundary value problems for such systems. Furthermore, the vanishing
viscosity limit process is established and a strong rate of convergence is
obtained as the boundary of the domain is flat. In addition, it is needed to
add some additional condition for density to match well the boundary condition.Comment: 14 page
Damping Functions correct over-dissipation of the Smagorinsky Model

This paper studies the time-averaged energy dissipation rate $\langle
\varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and
damping function. The Smagorinsky model is well known to over-damp. One common
correction is to include damping functions that reduce the effects of model
viscosity near walls. Mathematical analysis is given here that allows
evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function.
Moreover, the analysis motivates a modified van Driest damping. It is proven
that the combination of the Smagorinsky with this modified damping function
does not over dissipate and is also consistent with Kolmogorov phenomenology.Comment: 14 pages, 5 figures, Mathematical Methods in the Applied Sciences,
  ISSN 1099-1476 201
Asymptotical stability of almost periodic solution for an impulsive
  multispecies competition-predation system with time delays on time scales

In this paper, we consider the almost periodic dynamics of an impulsive
multispecies Lotka-Volterra competition system with time delays on time scales.
By establishing some comparison theorems of dynamic equations with impulses and
delays on time scales, a permanence result for the model is obtained.
Furthermore, based on the permanence result, by studying the Lyapunov stability
theory of impulsive dynamic equations on time scales, we establish a criterion
for the existence and uniformly asymptotic stability of a unique positive
almost periodic solution of the system. Finally, we give an example to show the
feasibility of our main results and our example also shows that the continuous
time system and its corresponding discrete time system have the same dynamics.
Our results of this paper are completely new even if for both the case of the
time scale $\mathbb{T}=\mathbb{R}$ and the case of $\mathbb{Z}$.Comment: 4
Tangential Fluid flow within 3D narrow fissures: Conservative velocity
  fields on associated triangulations and transport processes

For a fissured medium with uncertainty in the knowledge of fractures'
geometry, a conservative tangential flow field is constructed, which is
consistent with the physics of stationary fluid flow in porous media and an
interpolated geometry of the cracks. The flow field permits computing
preferential fluid flow directions of the medium, rates of mechanical energy
dissipations and a stochastic matrix modeling stream lines and fluid mass
transportation, for the analysis of solute/contaminant mass advection-diffusion
as well as drainage times.Comment: 17 pages, 15 figure
General phase transition models for vehicular traffic with point
  constraints on the flow

We generalize the phase transition model studied in [R. Colombo. Hyperbolic
phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002],
that describes the evolution of vehicular traffic along a one-lane road. Two
different phases are taken into account, according to whether the traffic is
low or heavy. The model is given by a scalar conservation law in the
\emph{free-flow} phase and by a system of two conservation laws in the
\emph{congested} phase. In particular, we study the resulting Riemann problems
in the case a local point constraint on the flux of the solutions is enforced
Shape recovery from sparse tomographic X-ray data

A two-dimensional tomographic problem is studied. The target is assumed to be
a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis
Splines (NURBS) curve is used as computational representation of the boundary.
This approach conveniently provides the result in a format readily compatible
with computer-aided design (CAD) software. However, the linear tomography task
becomes a nonlinear inverse problem due to the NURBS-based parameterization.
Therefore, Bayesian inversion with Markov chain Monte Carlo (MCMC) sampling is
used for calculating an estimate of the NURBS control points. The
reconstruction method is tested with both simulated data and measured X-ray
projection data. The proposed method recovers the shape and the attenuation
coefficient significantly better than the baseline algorithm (optimally
thresholded total variation regularization), but at the cost of heavier
computation
Convergence Analysis for Second Order Accurate Convex Splitting Schemes
  for the Periodic Nonlocal Allen-Cahn and Cahn-Hilliard Equations

In this paper we provide a detailed convergence analysis for fully discrete
second order (in both time and space) numerical schemes for nonlocal Allen-Cahn
(nAC) and nonlocal Cahn-Hilliard (nCH) equations. The unconditional unique
solvability and energy stability ensures $\ell^4$ stability. The convergence
analysis for the nAC equation follows the standard procedure of consistency and
stability estimate for the numerical error function. For the nCH equation, due
to the complicated form of the nonlinear term, a careful expansion of its
discrete gradient is undertaken and an $H^{-1}$ inner product estimate of this
nonlinear numerical error is derived to establish convergence. In addition, an
a-priori $W^{1,\infty}$ bound of the numerical solution at the discrete level
is needed in the error estimate. Such a bound can be obtained by performing a
higher order consistency analysis by using asymptotic expansions for the
numerical solution. Following the technique originally proposed by Strang
(e.g., 1964), instead of the standard comparison between the exact and
numerical solutions, an error estimate between the numerical solution and the
constructed approximate solution yields an $O( s^3 + h^4)$ convergence in
$\ell^\infty (0, T; \ell^2)$ norm, which leads to the necessary bound under a
standard constraint $s \le C h$. Here, we also prove convergence of the scheme
in the maximum norm under the same constraint
Quantized Mechanics of Affinely-Rigid Bodies

In this paper we develope the main ideas of the quantized version of
affinely-rigid (homogeneously deformable) motion. We base our consideration on
the usual Schr\"odinger formulation of quantum mechanics in the configuration
manifold which is given, in our case, by the affine group or equivalently by
the semi-direct product of the linear group ${\rm GL}(n,\mathbb{R})$ and the
space of translations $\mathbb{R}^{n}$, where $n$ equals the dimension of the
"physical space". In particular, we discuss the problem of dynamical invariance
of the kinetic energy under the action of the whole affine group, not only
under the isometry subgroup. Technically, the treatment is based on the
two-polar decomposition of the matrix of the internal configuration and on the
Peter-Weyl theory of generalized Fourier series on Lie groups. One can hope
that our results may be applied in quantum problems of nuclear dynamics or even
in apparently exotic phenomena in vibrating neutron stars. And, of course, some
more prosaic applications in macroscopic elasticity, structured continua,
molecular dynamics, dynamics of inclusions, suspensions, and bubbles are also
possible.Comment: 27 page
Aveiro Method in Reproducing Kernel Hilbert Spaces Under Complete
  Dictionary

Aveiro Method is a sparse representation method in reproducing kernel Hilbert
spaces (RKHS) that gives orthogonal projections in linear combinations of
reproducing kernels over uniqueness sets. It, however, suffers from
determination of uniqueness sets in the underlying RKHS. In fact, in general
spaces, uniqueness sets are not easy to be identified, let alone the
convergence speed aspect with Aveiro Method. To avoid those difficulties we
propose an anew Aveiro Method based on a dictionary and the matching pursuit
idea. What we do, in fact, are more: The new Aveiro method will be in relation
to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA)
involving completion of a given dictionary. The new method is called Aveiro
Method Under Complete Dictionary (AMUCD). The complete dictionary consists of
all directional derivatives of the underlying reproducing kernels. We show
that, under the boundary vanishing condition, bring available for the classical
Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient
expansion of any given element in the Hilbert space. The proposed method
reveals new and advanced aspects in both the Aveiro Method and the greedy
algorithm
Mehler's formulas for the univariate complex Hermite polynomials and
  applications

We give two widest Mehler's formulas for the univariate complex Hermite
polynomials $H_{m,n}^\nu$, by performing double summations involving the
products $u^m H_{m,n}^\nu (z,\overline{z}) \overline{H_{m,n}^\nu
(w,\overline{w})}$ and $u^m v^n H_{m,n}^\nu (z,\overline{z})
\overline{H_{m,n}^{\nu'} (w,\overline{w})}$. They can be seen as the complex
analogues of the classical Mehler's formula for the real Hermite polynomials.
The proof of the first one is based on a generating function giving rise to the
reproducing kernel of the generalized Bargmann space of level $m$. The second
Mehler's formula generalizes the one appearing as a particular case of the
so-called Kibble-Slepian formula. The proofs, we present here are direct and
more simpler. Moreover, direct applications are given and remarkable identities
are derived.Comment: 5 pages. To appear in Math. Methods Appl. Sc
Uniform Regularity and Vanishing Viscosity limit for the
  chemotaxis-Navier-Stokes system in a 3D bounded domain

We investigate the uniform regularity and vanishing viscosity limit for the
incompressible chemotaxis-Navier-Stokes system in a smooth bounded domain
$\Omega\subset\mathbb{R}^3$. It is shown that there exists a unique strong
solution of the incompressible chemotaxis-Navier-Stokes system in a finite time
interval which is independent of the viscosity coefficient. Moreover, the
solution is uniformly bounded in a conormal Sobolev space, which allows us to
take the vanishing viscosity limit to obtain the incompressible inviscid
chemotaxis-Navier-Stokes system.Comment: 42pages. arXiv admin note: text overlap with arXiv:1607.05920 by
  other author