We analyze a deterministic, one-dimensional solid-on-solid model for sputter deposition where the local growth rate is a function V(θ) of the exposure angle θ. For long times an algebraic height distribution N(h)∼${\mathit{h}}^{\mathrm{-}(1+\mathit{p})}$ develops, where the exponent p depends on the behavior of V(θ) close to θ=π and the extremal statistics of the substrate roughness. Analytic predictions for p, based on scaling arguments, are verified by large-scale simulations using a hierarchical algorithm.

It is demonstrated that a recent finite-barrier expansion for jump rates accounts quantitatively for the observed discrepancy between numerically determined exact rates and the Kramers estimates of these rates.

We model a shock wave in an ideal gas by solving a modified version of the compressible Navier-Stokes equations of hydrodynamics, where, following an earlier conjecture by Holian [Phys. Rev. A 37, 2562 (1988)], we use the temperature in the direction of shock propagation ${\mathit{T}}_{\mathit{x}\mathit{x}}$, rather than the average temperature T=(${\mathit{T}}_{\mathit{x}\mathit{x}}$+${\mathit{T}}_{\mathit{y}\mathit{y}}$+${\mathit{T}}_{\mathit{z}\mathit{z}}$)/3, in the evaluation of the linear transport coefficients. The results are found to agree much better with the molecular-dynamics simulations of Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] than standard Navier-Stokes theory.

In a turbulent flow, diluted polymers are shown to inhibit the formation of coherent high-vorticity filaments and to reduce correspondingly the rate of formation of large eddies. This effect demonstrates that in a three-dimensional turbulent flow, some nondissipative small-scale structures, the vorticity filaments, are nuclei of formation of large-scale structures. The reduction of the energy dissipation rate also suggests that this breakdown of the vorticity filaments into eddies is important for the formation of the dissipative structures.

We investigate the adsorption of a polymer on a planar, random surface. For this we use a generalization of de Gennes’s boundary condition to a random one, and path-integral methods. For weak randomness, the chain size is reduced slightly from its value in the absence of randomness. But as one increases the randomness or chain length, the chain size becomes ∼R, where R is the correlation length of the potential. If the length or the randomness exceeds a certain critical value, the chain is found to collapse in the direction perpendicular to the surface, to a thickness zero, so that it becomes a two-dimensional object.

We study spinodal decomposition after a critical quench to finite temperature for a three-dimensional Langevin fluid model which includes full couplings between the order parameter and the currents. Our results agree with the expectation based on phenomenological considerations, namely, that the asymptotic growth exponent for this model is n=1, and, when compared to two-dimensional results for the same model, indicate that the dimensionality may be relevant in this problem.

We study the properties of the reaction front formed in a reversible reaction-diffusion process, A+B${\mathrm{?}}_{\mathit{g}}^{\mathit{k}}$C, with initially separated reagents. It is shown that the dynamics of the front can be described in terms of a crossover between ‘‘irreversible’’ scaling at short times (t≪${\mathit{g}}^{\mathrm{-}1}$) and ‘‘reversible’’ scaling at long times (t≫${\mathit{g}}^{\mathrm{-}1}$). The reversible regime is dominated by diffusion and the critical exponents characterizing the properties of the front are independent of dimension.

We present a nonlinear dynamical model for DNA denaturation which includes cooperativity effects through anharmonic nearest-neighbor stacking interactions. Transfer-integral calculations show that this one-dimensional model, without including long-range interactions, exhibits a sharp denaturation reminiscent of a first-order transition at a temperature lower than a similar model with harmonic coupling. Self-consistent phonon calculations point out the essential role of nonlinear effects in the mechanism.

I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality.

We compute the asymptotic structure factor S(k,t) of the O(n) model for n≤d, where d and n are the dimensions of space and of the order parameter, respectively. Topological defects in the field lead to the power-law tail S(k,t)=A(n,d)ρ(t)${\mathit{k}}^{\mathrm{-}(\mathit{d}+\mathit{n})}$, where ρ is the defect density. The amplitude A(n,d) is calculated exactly using purely geometrical arguments based on the defect field.