Τμήμα Μαθηματικών και Εφαρμοσμένων Μαθηματικών - Department of Mathematics and Applied Mathematics

16 May 2016 Manolis Paspalakis (U. of Patras, Department of Materials Science)

Modeling the interaction of light and matter in nanostructures

12:15, A303 (Seminar Room - Mathematics Building)

Abstract:
In recent years there is increasing interest in the study of the
interaction of quantum emitters with metallic nanostructures. The main
reason for this is that the large fields and the strong light
confinement associated with the plasmonic resonances of the metallic
nanostructures enable strong interaction between light and the quantum
emitters. In this seminar, we present new theoretical results on the
controlled dynamics and the optical properties of quantum emitters near
metallic nanostructures, with emphasis to systems with applications in
nanophotonics and quantum computing. For the modeling of the
light-matter interaction, we combine the density matrix approach for
the quantum systems with classical electromagnetic calculations for the
metallic nanostructures.

13 Oct 2015 Enrico Scalas (University of Sussex, UK)

Exactly-solvable non-Markovian dynamic network

13:15, A303 (Seminar Room - Mathematics Building)

Abstract: Non-Markovian
processes are widespread in natural and human-made systems, yet
explicit modelling and analysis of such systems is underdeveloped. In
this talk we consider a dynamic network with random link activation and
deletion (RLAD) with non-exponential inter-event times. We study a
semi-Markov random process when the inter-event times are heavy tailed
Mittag-Leffler distributed, thus considerably slowing down the
corresponding Markovian dynamics and study the system far from
equilibrium. We derive an analytically and computationally tractable
system of forward equations utilizing the Caputo derivative for the
probability of having a given number of active links in the network.

Paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042801

Paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042801

10 Dec 2014 Peter J. Veerman (Portland State Univ. (Math.& Stat.), & QCN, Physics, UOC )

Synchronization of high dimensional coupled dynamical systems

12:15, A302 (Seminar Room - Mathematics Building)

Abstract: We
give some simple examples of identical linear dynamical systems coupled
along a so-called communication graph. We are interested in the the
dynamical behavior of these systems if the number of dynamical systems
(or ``agents") is large. In particular the questions we consider in
these examples are: What is the set of parameter values so that the
behavior is stable, that is: initial eventually die out. In the case
the system is stable, we also want to know exactly what the response to
a 'kick' is.

These questions can be completely or partially answered (depending on what system we consider) by making certain conjectures about these systems. We describe those conjectures, and the results they lead to.

In the applications we consider, it is desirable if the response to the 'kick' dies out as fast as possible. Hence the notion of synchronization.

These questions can be completely or partially answered (depending on what system we consider) by making certain conjectures about these systems. We describe those conjectures, and the results they lead to.

In the applications we consider, it is desirable if the response to the 'kick' dies out as fast as possible. Hence the notion of synchronization.

20 Nov 2014 K. Chrysafinos (National Technical University of Athens)

Error estimates for discontinuous time-stepping schemes for the velocity tracking problem

11:15, A302 (Seminar Room - Mathematics Building)

Abstract: (.pdf)

15 May 2014 A. Hadjidimos (U. of Crete)

On the choice of parameters in MAOR type splitting methods for the linear complementarity problem

13:05, A302 (Seminar Room - Mathematics Building)

Abstract: (.pdf)

30 Apr 2014 E. Georgoulis (U. of Leicester)

On multiscale discontinuous Galerkin methods for elliptic problems.

13:05, A302 (Seminar Room - Mathematics Building)

Abstract:
I will present an adaptive multiscale discontinuous Galerkin (dG)
method for elliptic problems, based on the variational multiscale
methods paradigm, driven by energy norm a posteriori bounds. Localized
fine scale constituent problems are solved on patches of the domain and
are used to obtain a modified coarse scale equation. The a posteriori
error estimate is used within an adaptive algorithm to tune the
critical parameters, i.e., the refinement level and the size of the
different patches on which the fine scale constituent problems are
solved. The fine scale computations are completely parallelizable,
since no communication between different processors is required for
solving the constituent fine scale problems. The convergence of the
method, the performance of the adaptive strategy and the computational
effort involved are investigated through a series of numerical
experiments. Moreover, some a priori bounds for the proposed method
will be presented.

If time permits, I will also briefly discuss two directions of related ongoing work. First, I will discuss the possibility of using polytopical meshes in the context of multiscale dG methods. Second, I will comment on the incorporation of the multiscale dG method above into a stochastic collocation framework for the case of elliptic problems with random diffusion and forcing coefficients. The stochastic collocation is based on a recent high dimensional approximation framework based on combinations of anisotropic kernels (radial basis functions).

If time permits, I will also briefly discuss two directions of related ongoing work. First, I will discuss the possibility of using polytopical meshes in the context of multiscale dG methods. Second, I will comment on the incorporation of the multiscale dG method above into a stochastic collocation framework for the case of elliptic problems with random diffusion and forcing coefficients. The stochastic collocation is based on a recent high dimensional approximation framework based on combinations of anisotropic kernels (radial basis functions).

10 Apr 2014 P. Chatzipantelidis (U. of Crete)

Error estimates bounded only by data of the finite volume element method for a parabolic problem.

13:05, A302 (Seminar Room - Mathematics Building)

Abstract: We
discretize in space a model parabolic problem by the finite volume
method on polygonal domains in $R^2$. This method can be formulated as
a Petrov-Galerkin method and analysed using techniques developed for
the finite element method. We derive error bounds of the error in $L_2$
norm that depend only on the data and compare the results with the
corresponding ones for the finite element method. In the case of the
homogeneous
parabolic problem with initial data only in $L_2$, special assumptions
on the mesh are required for optimal convergence rate.