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445 results on '"Mischaikow, Konstantin"'

159. The efficiency of a homology algorithm based on discrete morse theory and coreductions (extended abstract)

Author

Harker, Shaun, Mischaikow, Konstantin, Mrozek, Marian, Nanda, Vidit, Wagner, Hubert, Juda, Mateusz, and Dlotko, Pawel

Subjects
ComputingMethodologies_PATTERNRECOGNITION, Mathematics::K-Theory and Homology, Efficient homology algorithms, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, Coreductions, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Computer Science::Computational Geometry, Mathematics::Geometric Topology, Mathematics::Algebraic Topology, Mathematics::Symplectic Geometry, Discrete Morse theory
Abstract

Two implementations of a homology algorithm based on the Forman’s discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of homology algorithms.

Published
2010

162. Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

Author

Krishan, Kapilanjan, Kurtuldu, Huseyin, Schatz, Michael F., Gameiroc, Marcio, Mischaikow, Konstantin, and Sánchez Madruga, Santiago

Subjects
Physics::Fluid Dynamics, Física, Aeronáutica
Abstract

Algebraic topology (homology) is used to analyze the state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Bénard convection. The analysis reveals topological asymmetries that arise when non-Boussinesq effects are present. The asymmetries are found in different flow fields in the simulations and are robust to substantial alterations to flow visualization conditions in the experiment. However, the asymmetries are not observable using conventional statistical measures. These results suggest homology may provide a new and general approach for connecting spatiotemporal observations of chaotic or turbulent patterns to theoretical models.

Published
2007

163. Singular boundary value problems via the Conley index

Author

Gedeon, Tomáš and Mischaikow, Konstantin

Abstract

We use Conley index theory to solve the singular boundary value problem $\varepsilon^2D u_{xx} + f(u,\varepsilon u_x,x) = 0$ on an interval $[-1,1]$, where $u \in \mathbb R^n$ and $D$ is a diagonal matrix, with separated boundary conditions. Since we use topological methods the assumptions we need are weaker then the standard set of assumptions. The Conley index theory is used here not for detection of an invariant set, but for tracking certain cohomological information, which guarantees existence of a solution to the boundary value problem.

Published
2006

168. Conley{Morse Databases for the Angular Dynamics of Newton's Method on the Plane.

Author

Bush, Justin, Cowan, Wes, Harker, Shaun, and Mischaikow, Konstantin

Subjects
DATABASES, NEWTON-Raphson method, DYNAMICAL systems, PARAMETERIZATION, ITERATIVE methods (Mathematics), ANGULAR momentum (Mechanics)
Abstract

In this paper we showcase the technique of Conley-Morse databases for studying a parameterized family of dynamical systems. The dynamical system of interest arises from considering the limiting behavior of Newton's root-finding method applied to functions f : R² - R² when the iterates converge to the origin. Considering the progression of angular orientations gives rise to a self- map of the unit circle we call the angular dynamics map. We demonstrate how the technique of Conley{Morse dynamical databases allows us to quickly survey and prove theorems about the global dynamics of the parameterized family of angular dynamics maps. [ABSTRACT FROM AUTHOR]

Published
2016
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175. A Database Schema for the Analysis of Global Dynamics

Author

Arai, Zin, primary, Kalies, William, additional, Kokubu, Hiroshi, additional, Mischaikow, Konstantin, additional, Oka, Hiroe, additional, Pilarczyk, Pawel, additional, Simos, Theodore E., additional, Psihoyios, George, additional, and Tsitouras, Ch., additional

Published
2009
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195. PREFACE

Author

Mischaikow, Konstantin, primary and Yi, Yingfei, additional

Published
2000
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