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In this paper we present a new algorithm for computing the homology of regular CW-complexes. This algorithm is based on the coreduction algorithm due to Mrozek and Batko and consists essentially of a geometric preprocessing algorithm for the standard chain complex generated by a CW-complex. By employing the concept of S-complexes the original chain complex… (More)

We present an algorithm for computing the homology of inclusion maps which is based on the idea of coreductions and leads to significant speed improvements over current algorithms. It is shown that this algorithm can be extended to compute both persistent homology and an extension of the persistence concept to two-sided filtrations. In addition to… (More)

This paper gives theoretical results on spinodal decomposition for the Cahn-Hillard equation. We prove a mechanism which explains why most solutions for the Cahn-Hilliard equation which start near a homogeneous equilibrium within the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius R. Namely, most… (More)

Homology has long been accepted as an important computational tool for quantifying complex structures. In many applications these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study based on suitable discretizations. Such an approach immediately raises the question of how accurately the resulting… (More)

Cahn–Morral systems serve as models for several phase separation phenomena in multicomponent alloys. In this paper we study the dynamical aspects of nucleation in a stochastic version of these models using numerical simulations, concentrating on ternary, i.e., three-component, alloys on two-dimensional square domains. We perform numerical studies and give a… (More)

Isolated invariant sets and their associated Conley indices are valuable tools for studying dynamical systems and their global invariant structures. Through their design, they aim to capture invariant behavior which is robust under small perturbations, and this in turn makes them amenable to a computational treatment. Over the years, a number of algorithms… (More)

Topology is a natural mathematical tool for quantifying complex structures. In many applications, such as, for example, in the context of phase-field models in materials science, the structures of interest arise as sub-or superlevel sets of continuous functions, i.e., as nodal domains. From a computational point of view, any attempt at constructing a… (More)

Polarization decorrelation in single-mode fibers with randomly varying elliptical birefringence is studied. It is found that the effects of ellipticity on the polarization decorrelation length depend on the relative sizes of the beat length and the autocorrelation length of the birefringence fluctuations in the fiber. However, the evolution of the… (More)