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Harmandaris V.A.,University of Crete | Harmandaris V.A.,Institute of Applied and Computational Mathematics
Korea Australia Rheology Journal | Year: 2014

Study of complex macromolecular systems through molecular simulations is a very intense research area. Here we present an overview concerning the development and application of hierarchical particle coarsegraining molecular dynamics simulations on the quantitative prediction of the dynamics and the rheology of polymers. Through a systematic time mapping approach that involves data from detailed atomistic dynamic simulations the coarse-grained polymer model can be used to quantitatively predict the dynamics and the rheology of the polymeric chains in a very broad range of characteristic length and time scales. Data from the application of these approaches on the dynamics of polystyrene melts under equilibrium and under shear flow conditions are presented. © 2014 The Korean Society of Rheology and Springer. Source

Antonopoulos D.C.,National and Kapodistrian University of Athens | Dougalis V.A.,National and Kapodistrian University of Athens | Dougalis V.A.,Institute of Applied and Computational Mathematics
Mathematics and Computers in Simulation | Year: 2012

We consider the 'classical' Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog.) We discretize the initial-boundary-value problem for these systems, corresponding to homogeneous Dirichlet boundary conditions on the velocity variable at the endpoints of a finite interval, using fully discrete Galerkin-finite element methods of high accuracy. We use the numerical schemes as exploratory tools to study the propagation and interactions of solitary-wave solutions of these systems, as well as other properties of their solutions. © 2010 IMACS. Published by Elsevier B.V. All rights reserved. Source

Taroudakis M.I.,University of Crete | Taroudakis M.I.,Institute of Applied and Computational Mathematics | Smaragdakis C.,University of Crete
Journal of the Acoustical Society of America | Year: 2013

The paper presents an application of a method for the characterization of underwater acoustic signals based on the statistics of the wavelet transform sub-band coefficients in range-dependent environments. As it was illustrated in previous work, this statistical characterization scheme is a very efficient tool for obtaining observables to be exploited in problems of ocean acoustic tomography and geoacoustic inversion, when range-independent environments are considered. Now the scheme is applied in range-dependent environments for the estimation of range-dependent features in shallow water. A simple denoising strategy, also presented in the paper, is shown to enhance the quality of the inversion results as it helps to keep the signal characterization to the energy a significant part of it. The results presented for typical test cases are encouraging and indicative of the potential of the method for the treatment of inverse problems in acoustical oceanography. © 2013 Acoustical Society of America. Source

Antonopoulou D.,University of Crete | Karali G.,Institute of Applied and Computational Mathematics
Networks and Heterogeneous Media | Year: 2013

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this flow, to observe that they become convex very fast. ©American Institute of Mathematical Sciences. Source

Makridakis C.,University of Crete | Makridakis C.,Institute of Applied and Computational Mathematics | Suli E.,University of Oxford
Archive for Rational Mechanics and Analysis | Year: 2013

This paper is devoted to a new finite element consistency analysis of Cauchy-Born approximations to atomistic models of crystalline materials in two and three space dimensions. Through this approach new "atomistic Cauchy-Born" models are introduced and analyzed. These intermediate models can be seen as first level atomistic/quasicontinuum approximations in the sense that they involve only short-range interactions. The analysis and the models developed herein are expected to be useful in the design of coupled atomistic/continuum methods in more than one dimension. Taking full advantage of the symmetries of the atomistic lattice, we show that the consistency error of the models considered both in energies and in dual W1,p type norms is O(ε2), where ε denotes the interatomic distance in the lattice. © 2012 Springer-Verlag Berlin Heidelberg. Source

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