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Katsaounis T.,King Abdullah University of Science and Technology | Katsaounis T.,University of Crete | Lee M.-G.,King Abdullah University of Science and Technology | Tzavaras A.,King Abdullah University of Science and Technology | Tzavaras A.,Institute of Applied and Computational Mathematics
Journal of the Mechanics and Physics of Solids | Year: 2017

Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions. © 2016 Elsevier Ltd

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.

Kontzialis K.,University of Patras | Kontzialis K.,Institute of Applied and Computational Mathematics | Ekaterinaris J.A.,University of Patras | Ekaterinaris J.A.,Institute of Applied and Computational Mathematics
Computers and Fluids | Year: 2013

Accurate predictions of skin friction and thermal loads of high speed complex flows in both simple and nontrivial geometries, require high resolution computations. High order discontinuous Galerkin (DG) discretizations possess features that make them very attractive for computation of complex flows with strong shocks. The key ingredient that would make the DG method suitable for these computations, is application of p-adaptive procedures that ensure accurate capturing of discontinuities with low order approximations and resolution of smooth complex features, such as vortices and shear layers, with higher order accuracy. A limiting procedure of DG discretizations capable of computing high speed flows with strong shocks around complex geometries using a p-adaptive procedure on mixed type meshes is used and positivity is enforced on pressure and density for flows with large expansions. The unified slope limiting combined with the positivity limiters are applied for a number of inviscid flows with strong shocks to demonstrate the potential of the method. © 2012 Elsevier Ltd.

Antonopoulou D.C.,Institute of Applied and Computational Mathematics | Antonopoulou D.C.,University of Chester | Kamvissis S.,University of Crete | Kamvissis S.,Institute of Applied and Computational Mathematics
Nonlinearity | Year: 2015

Initial-boundary value problems for one-dimensional 'completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data suffices to make the problem well-posed but the Fokas method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the 'Fokas transform'. In this paper, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also sufficiently decaying and that, hence, the Fokas method can be applied. © 2015 IOP Publishing Ltd & London Mathematical Society.

Taroudakis M.I.,University of Crete | Smaragdakis C.,Institute of Applied and Computational Mathematics
Proceedings of Forum Acusticum | Year: 2014

A hybrid approach for problems of ocean acoustic tomography is presented, based on the statistical characterization (SC) of the acoustic signal followed by a mode identification and linear inversion. The statistical characterization is used for the estimation of a reference solution to the inverse problem of estimating the sound speed profile in the water column. This non-linear inversion problem is solved using a Genetic Algorithm. By applying first order perturbation approach, variations of the sound speed profile are associated with modal travel time variations. This relationship provides the framework for the development of an iterative linear inversion scheme which converges when the reference environment is close to the actual one and provides a fine tuning of the results obtained by the non-linear inversions. The performance of the method is demonstrated by means of a simulated experiment in range-dependent environment representing a cold eddy.

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.

Okal E.A.,Northwestern University | Synolakis C.E.,University of Southern California | Synolakis C.E.,Technical University of Crete | Synolakis C.E.,Institute of Applied and Computational Mathematics | And 2 more authors.
Pure and Applied Geophysics | Year: 2011

We present 14 scenarios of potential tsunamis in the South China Sea and its adjoining basins, the Sulu and Sulawezi Seas. The sources consist of earthquake dislocations inspired by the the study of historical events, either recorded (since 1900) or described in historical documents going back to 1604. We consider worst-case scenarios, where the size of the earthquake is not limited by the largest known event, but merely by the dimension of the basin over which a coherent fault may propagate. While such scenarios are arguably improbable, they may not be impossible, and as such must be examined. For each scenario, we present a simulation of the tsunami's propagation in the marine basin, exclusive of its interaction with the coastline. Our results show that the South China, Sulu and Sulawezi Seas make up three largely independent basins where tsunamis generated in one basin do not leak into another. Similarly, the Sunda arc provides an efficient barrier to tsunamis originating in the Indian Ocean. Furthermore, the shallow continental shelves in the Java Sea, the Gulf of Thailand and the western part of the South China Sea significantly dampen the amplitude of the waves. The eastern shores of the Malay Peninsula are threatened only by the greatest-and most improbable-of our sources, a mega-earthquake rupturing all of the Luzon Trench. We also consider two models of underwater landslides (which can be triggered by smaller events, even in an intraplate setting). These sources, for which there is both historical and geological evidence, could pose a significant threat to all shorelines in the region, including the Malay Peninsula. © 2010 Springer Basel AG.

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.

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.

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.

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