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27

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## Publications

Publications (27)

We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers , is to select a Riemannian metric on $\text{GL}_n$, and use its induced geodesic distance to measure the dis...

Under a proper assignment of a metric and a connection, the (classical) dynamical trajectories can be identified as geodesics of the underlying manifold. We show how these geometric structures can be derived; specifically, we construct them explicitly for configuration and phase spaces of Hamiltonian systems. We demonstrate how the correspondence b...

Fair allocation has been studied intensively in both economics and computer science. This subject has aroused renewed interest with the advent of virtualization and cloud computing. Prior work has typically focused on mechanisms for fair sharing of a single resource. We consider a variant where each user is entitled to a certain fraction of the sys...

Chemical reaction networks are commonly modeled by rate equations, which are systems of ordinary differential equations describing the evolution of species concentrations. Such models break down at low concentrations, where stochastic effects become dominant. Instead, one has to solve the master equation that governs the multidimensional probabilit...

We present a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order centraldifferencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the...

We present a theoretical analysis of intracellular calcium waves propagated by calcium feedback at the inositol 1,4,5-trisphosphate (IP3) receptor. The model includes essential features of calcium excitability, but is still analytically tractable. Formulas are derived for the wave speed, amplitude, and width. The calculations take into account cyto...

In this paper we present a numerical stability calculation for steadily rotating spirals in an excitable medium. While experiments, as well as numerical simulations of two-field reaction-diffusion models have shown the existence of a Hopf bifurcation from steady rotations to a meandering state, all the analytical approaches so far have failed to pr...

We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the int...

We study the propagation of compact superheated solid in the large undercooling limit using the phase-field model. Below a critical undercooling, the superheated solid decomposes into solid and liquid domains, either in the form of liquid droplets or in periodic structures of concentric rings. For the latter, a one-dimensional analysis provides an...

We study the propagation of compact superheated solid in the large undercooling limit using the phase-field model. Below a critical undercooling, the superheated solid decomposes into solid and liquid domains, either in the form of liquid droplets or in periodic structures of concentric rings. For the latter, a one-dimensional analysis provides an...

We report on the existence of tilted arrays of dendrites in solidification. It arises from a long-wavelength instability of the infinite array. The connection to the parity-broken dendrites recently discovered is pointed out. We show that the array is stable to short distance fluctuations explaining the existence of a stable envelope for solidifica...

We numerically solve the steady-state equation and the stability spectrum for solidification in a channel. For a large range of parameters stable symmetric and stable parity-broken solutions coexist. The branches of parity-broken solutions are found to originate from the; symmetric solutions through standard bifurcations.

We present a numerical study of asymptotic late-stage growth in a phase-field model. After a long transient time the patterns are independent of initial conditions, and have a well-defined shape-preserving envelope which propagates at constant velocity. To distinguish between implicit and explicit anisotropies, a model with explicit fourfold anisot...

„Konkurrenz belebt das Geschäft!“ Dies ist nicht nur ein Grundsatz unserer freien Marktwirtschaft; dieser Satz könnte auch das Motto einer allgemeinen Theorie der Musterbildung werden. Sobald es in einem System zum Wettstreit konkurrierender Kräften kommt, können daraus die vielfältigsten Muster erwachsen. In den Beiträgen dieses Buches haben wir b...

We consider the initiating energy for traveling normal domains in large composite superconductors. We perform numerical simulations of normal zone initiation using the effective circuit model. The initiating energy is obtained as a function of transport current and four dimensionless parameters characterizing the composite and cooling conditions. W...

The origination of propagating normal domains in large superconducting composites is studied numerically by means of an effective circuit model. The initial perturbation is considered to be a thermal pulse. The minimum energy required to form a propagating normal domain is calculated as a function of the dimensionless transport current, and three p...

Despite the major progress with the discovery of the microscopic solvability criterion [1, 2, 3, 4, 5, 6, 7, 8, 9], the problem of interfacial pattern formation is not yet solved [8, 10]. The new existence principle for dendritic growth predicts that, whenever anisotropy is present, a specific dendrite corresponding to the fastest-growing needle cr...

This paper considers the nucleation and propagation of a normal zone in large composite superconductors, considering the relatively long time of current redistribution in the stabilizer. A model is proposed for treating the composite as an effective electrical circuit, which yields two diffusion equations for the electric current and the temperatur...

We present a study of a phase-field model for diffusion-limited growth. A boundary-layer approximation is used to show that for sharp interface, the first approximation to the phase-field model is the free boundary model, which includes surface tension and a linear kinetic term. The velocity of propagation and the stability spectrum are calculated...

We present analytical and numerical studies of fluctuations about and transitions from the nonequi- librium dissipative steady state to the stable equilibrium state of a damped physical pendulum driven by constant torque and small white noise. We find the probability density function of the local flucutations about the nonequilibrium steady state a...

We study the nucleation and propagation of the normal zone in large composite superconductors, considering the relatively long time of current redistribution in the stabilizer. We propose a model treating the composite as an effective electrical circuit, which yields two diffusion equations for the electric current and temperature distributions alo...