16,616 research outputs found
An hp-Local Discontinuous Galerkin method for Parabolic\ud Integro-Differential Equations
In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains
Interaction of Ising-Bloch fronts with Dirichlet Boundaries
We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg
Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of
spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen
that the interaction of fronts with boundaries is similar in both systems,
establishing the generality of the Ising-Bloch bifurcation. We derive reduced
dynamical equations for the FN model that explain front dynamics close to the
boundary. We find that front dynamics in a highly non-adiabatic (slow front)
limit is controlled by fixed points of the reduced dynamical equations, that
occur close to the boundary.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
An extended Falicov-Kimball model on a triangular lattice
The combined effect of frustration and correlation in electrons is a matter
of considerable interest of late. In this context a Falicov-Kimball model on a
triangular lattice with two localized states, relevant for certain correlated
systems, is considered. Making use of the local symmetries of the model, our
numerical study reveals a number of orbital ordered ground states, tuned by the
small changes in parameters while quantum fluctuations between the localized
and extended states produce homogeneous mixed valence. The inversion symmetry
of the Hamiltonian is broken by most of these ordered states leading to
orbitally driven ferroelectricity. We demonstrate that there is no spontaneous
symmetry breaking when the ground state is inhomogeneous. The study could be
relevant for frustrated systems like , (in its low temperature
C2/m phase) where two Mott localized states couple to a conduction band.Comment: 6 pages, 8 figure
Polyelectrolyte multilayer assembly bearing ketoprofen for transdermal delivery
A novel microencapsulation technology based on layer-by-layer assembly has been extensively studied and used for controlled delivery of drug microcrystal having poor aqueous solubility and low bioavailability. A non-steroidal anti-inflammatory drug ketoprofen (KF)was selected for encapsulation using biodegradable and biocompatible polyions and synergistically the fabricated system was embedded in gel matrix for topical application. Topical application of the drugs at the pathological sites offer potential advantages of delivering the drug directly to the site of action and thus producing high tissue concentrations of the drug
Self-Synchronization in Duty-cycled Internet of Things (IoT) Applications
In recent years, the networks of low-power devices have gained popularity.
Typically these devices are wireless and interact to form large networks such
as the Machine to Machine (M2M) networks, Internet of Things (IoT), Wearable
Computing, and Wireless Sensor Networks. The collaboration among these devices
is a key to achieving the full potential of these networks. A major problem in
this field is to guarantee robust communication between elements while keeping
the whole network energy efficient. In this paper, we introduce an extended and
improved emergent broadcast slot (EBS) scheme, which facilitates collaboration
for robust communication and is energy efficient. In the EBS, nodes
communication unit remains in sleeping mode and are awake just to communicate.
The EBS scheme is fully decentralized, that is, nodes coordinate their wake-up
window in partially overlapped manner within each duty-cycle to avoid message
collisions. We show the theoretical convergence behavior of the scheme, which
is confirmed through real test-bed experimentation.Comment: 12 Pages, 11 Figures, Journa
Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data
In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result
Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data
In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2
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