Area-preserving dynamics of a long slender finger by curvature: a test case for the globally conserved phase ordering

A long and slender finger can serve as a simple ``test bed'' for different phase ordering models. In this work, the globally-conserved, interface-controlled dynamics of a long finger is investigated, analytically and numerically, in two dimensions. An important limit is considered when the finger dynamics are reducible to the area-preserving motion by curvature. A free boundary problem for the finger shape is formulated. An asymptotic perturbation theory is developed that uses the finger aspect ratio as a small parameter. The leading-order approximation is a modification of ``the Mullins finger" (a well-known analytic solution) which width is allowed to slowly vary with time. This time dependence is described, in the leading order, by an exponential law with the characteristic time proportional to the (constant) finger area. The subleading terms of the asymptotic theory are also calculated. Finally, the finger dynamics is investigated numerically, employing the Ginzburg-Landau equation with a global conservation law. The theory is in a very good agreement with the numerical solution.Comment: 8 pages, 4 figures, Latex; corrected typo

Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters

Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formulated that can follow the whole dynamics of a diffusion controlled growth, coarsening, fragmentation and approach to equilibrium in a system with conserved order parameter.Comment: 4 pages, 4 figures, RevTex, submitted to PR

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Anomalous Dynamic Scaling in Locally-Conserved Coarsening of Fractal Clusters

We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as functions of time. Analyzing the correlation function dynamics, we identify two different time-dependent length scales that exhibit power laws in time. The exponents of these power laws are independent of D, one of them is apparently the classic exponent 1/3. The solute mass versus time exhibits dynamic scaling with a D-dependent exponent, in agreement with a simple scaling theory.Comment: 5 pages, 4 figure

Instability driven fragmentation of nanoscale fractal islands

Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by the deposition conditions and cluster composition. Sharing common features with other materials' breakup phenomena, the fragmentation instability is governed by the length-to-width ratio of the fractal arms.Comment: 5 pages, 3 figures, Physical Review Letters in pres

N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras

We present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincare and Euclidean superalgebras. We consider in detail new family of four supertwists of N=1 Poincare superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D=4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the N=1/2 SUSY Seiberg's star product deformation scheme.Comment: 17 pages, LaTeX, new (re-worked) revised and extended versio

Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction

[EN] Ischaemic heart disease is considered as the single most frequent cause of death, provoking more than 7 000 000 deaths every year worldwide. A high percentage of patients experience sudden cardiac death, caused in most cases by tachyarrhythmic mechanisms associated to myocardial ischaemia and infarction. These diseases are difficult to study using solely experimental means due to their complex dynamics and unstable nature. In the past decades, integrative computational simulation techniques have become a powerful tool to complement experimental and clinical research when trying to elucidate the intimate mechanisms of ischaemic electrophysiological processes and to aid the clinician in the improvement and optimization of therapeutic procedures. The purpose of this paper is to briefly review some of the multiscale computational models of myocardial ischaemia and infarction developed in the past 20 years, ranging from the cellular level to whole-heart simulations.This work was partially supported by the 'VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica' from the Ministerio de Economia y Competitividad of Spain (grant number TIN2012-37546-C03-01) and the European Commission (European Regional Development Funds-ERDF-FEDER), and by the Direccion General de Politica Cientifica de la Generalitat Valenciana (grant number GV/2013/119).Ferrero De Loma-Osorio, JM.; Trénor Gomis, BA.; Romero Pérez, L. (2014). Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction. EP-Europace. 16(3):405-415. https://doi.org/10.1093/europace/eut405S40541516