Showing papers by "David A. Kessler published in 1990"

Roughening phase transition in surface growth.

Abstract: We present first systematic numerical simulation results which show a strong indication of phase transitions, in {ital both} 2+1 and 3+1 dimensions, between weak-coupling and strong-coupling regimes in a surface-growth model. A modified ballistic deposition model is used to demonstrate the transitions and the roughness scaling exponent is measured. While the transition in 3+1 dimensions confirms the prediction of the renormalization-group analysis, the one in 2+1 dimensions had not been previously anticipated and exhibits a complex critical behavior.

Selection of the Viscous Finger in the 90° Geometry

Abstract: The theory of solvability is applied to the Saffman-Taylor experiment in the 90? geometry. We find that in the limit of zero surface tension the parameter ? which governs the width of the finger approaches 0.85 which agrees very well with the experimentally observed value. We also discuss the scaling of the parameter ?.

Stability of traveling waves in the Belousov-Zhabotinskii reaction.

Abstract: As we have seen in Dr. Muller’s talk, the Belousov-Zhabotinskii (BZ) reaction leads to a rich variety of non-equilibrium spatial structures and serves as a paradigm for pattern formation in excitable media1. In this talk, we will focus on the simplest such pattern, the planar travelling wave, in which regions of excited and quiescent reagents move uniformly through space (Fig. 1). Understanding this structure is a necessary first step towards a complete picture of more complex structures such as the target2, the rotating spiral3 or, in three dimensions, the scroll4. This is particularly true as these patterns far from their centers asymptotically approximate planar travelling waves.

Photoexcited quantum wells: Nonlinear screening, bistability, and negative differential capacitance.

Abstract: The dielectric response of an electron-hole plasma confined to a slab is calculated within the Hartree approximation for electric fields perpendicular to the slab walls. The results are used to infer the capacitance behavior of photoexcited quantum-well structures under different rate conditions. Case studies show that nonlinearities in the carrier-density dependence of the energy spectrum and scattering times can lead to bistability and negative differential capacitance.

Unbridled growth of spin-glass clusters.

Abstract: We investigate the application of the recent cluster-based acceleration methods of Wolff and of Kandel et al. to the problem of simulating spin glasses. We find the techniques offer no improvement as the clusters generated by these algorithms are infinitely large or interact infinitely strongly, respectively. We comment on the reasons for this failure.

Linear stability of directional solidification cells.

Abstract: We formulate the problem of finding the stability spectrum of the cellular pattern seen in directional solidification. This leads to a nonlinear eigenvalue problem for an integro-differential operator. We solve this problem numerically and compare our results to those obtained by linearizing the eigenvalue problem by employing the quasistatic approximation. Contrary to some recent claims, we find no evidence for a Hopf bifurcation to a dendritic pattern.

Comment on "Phase transition in a restricted solid-on-solid surface-growth model in 2+1 dimensions"

Abstract: Comment on "Phase Transition in a Restricted Solid-on-Solid Surface-Growth Model in 2 + 1 Dimensions" In a recent Letter, Amar and Family generalized a restricted solid-on-solid (RSOS) nonequilibrium growth model in 2+1 dimensions to include temperature and reported finding a rough-to-rough phase transition at *c«0.62 where the surface width £ scales with the system size L as (InL). It was later shown that the transition is due to the vanishing of the coefficient X of the nonlinear term in the Kardar, Parisi, and Zhang (KPZ) equation of interface growth. In this Comment, we present further systematic simulation results which suggest that at some finite X, this model exhibits behavior very similar to that observed in a modified ballistic deposition model. Furthermore, we describe the scaling behavior in the low-temperature regime based on a calculation in the limit of tc^> L. We performed our simulations on the model of Ref. 1 and measured the effective roughness exponent, aefr =ln[^(Ii)/^(L2)]/ln(Z0 for K > 0.62. Since the sign of X is irrelevant, one should expect a similar situation at some K > 0.62. There is indeed evidence of this sort shown in Fig. 1 at about K : « 1 . 1 . While the numerical results' suggest that there is a true phase transition at some finite X value, the possibility of a slow crossover, a situation somewhat more desirable on theoretical grounds, is not ruled out. We emphasize here, however, the striking similarity among different growth models in which X is tuned in different ways. In the low-temperature regime, the picture of a rough surface emerging from the simulations is puzzling, because one would imagine that the growth probability e~ will favor island growth and the surface will flatten out as the temperature gets lower. To investigate what is going on in this regime, we performed exact calculations on small systems and numerical simulations on large ones. We found that for a fixed L, when K is very large, island growth is favored and the surface width § scales as %-~Le ~, given Le ~<^\. The sharp contrast to the equilibrium case, where £ is independent of L, should be noted. The onset for this scaling to occur appears to be at K~-lnL. Thus for small systems, we should expect to see the crossover to this kind of scaling at some not-so-large K\ This crossover has shown up in 0.6

A Geometrical Model for Spirals: a Possible Paradigm for Belousov-Zhabotinskii

Abstract: We formulate and investigate a local, geometrical model for steady-state spiral motion in order to better understand the spiral pattern observed in Belousov-Zhabotinskii (BZ) reactions. In particular, we demonstrate that the surface tension (i.e. curvature dependent) term is responsible for velocity selection in the toy model. In this model, the selected velocity for small surface tension is the unique velocity for which the zero surface tension term is nonsingular. We conclude with speculations on the implications of our results for BZ spirals.