A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the symmetries of the Bethe lattice. The properties of such embeddings are investigated and relations to Farey trees, devil’s staircases, and Apollonian tiling are pointed out.

We analyze, by means of the Melnikov method, the possibility of modifying the threshold of homoclinic chaos in general one-dimensional problems, by introducing small periodic resonant modulations. We indicate in particular a prescription in order to increase the threshold (i.e., to prevent chaos), and consider then its application to the bistable Duffing-Holmes potential. All results are confirmed both by numerical and by analog simulations, showing that small modulations can in fact sensibly influence the onset of chaos.

The two-dimensional wind-tree model with particles with four allowed velocities, which can scatter off obstacles with internal degrees of freedom, is solved exactly. Depending on initial conditions the distribution functions and entropy of obstacles can display a nonmonotonic time dependence with over- and underpopulations followed by transient relaxation.

Nonlinear evolution equations (NEE’s) are derived that describe weakly-two-dimensional motion of surface-gravity waves on a three-dimensional incompressible and inviscid fluid. When compared with the Kadomtsev-Petviashvili (KP) equation, the NEE’s presented here have the following two advantages: (a) they are applicable to wave phenomena on a fluid of arbitrary depth; and (b) they can deal with head-on collisions of various wave structures. A discussion is then made of NEE’s arising from the shallow- and deep-water limits. It is shown that the KP equation is a special case of our equations.

An explanation of the mechanism for the fingering instability at driven contact lines is presented. Semiquantitative predictions for the growth of the fingers as a function of time, the most unstable wavelength, and the initial growth rate are deduced. These predictions are consistent with recent experiments of de Bruyn [Phys. Rev. A 46, R4500 (1992)].

An alternative and general formalism for the frequency dependence of the spin-lattice relaxation time ${\mathit{T}}_1$ of polymer liquids is derived on the basis of memory functions of polymer theories. As examples the original Rouse model [J. Chem. Phys. 21, 1272 (1953)] and the renormalized Rouse model by Schweizer [J. Chem. Phys. 91, 5802 (1989)] are considered. The results fit well the experimental data obtained for polydimethylsiloxane (PDMS) melts and solutions by the field-cycling technique. The Rouse model fits solutions and low-molecular-weight melts. The renormalized Rouse model explains the peculiar ${\nu }^{0.25}$ dispersion of the spin-lattice relaxation time observed with PDMS melts at molecular weights ${\mathit{M}}_{\mathit{w}}$≫${\mathit{M}}_{\mathit{c}}$.

A heterogeneous network which is partially polymerized and partially fluid is studied by Monte Carlo simulation in two dimensions. Within statistical uncertainties, the compression modulus is found to be independent of polymer fraction, while the shear modulus vanishes below the connectivity percolation threshold. This behavior is different from networks without the fluid component, for which the rigidity percolation threshold is roughly double the connectivity percolation threshold.

We study the effect of fluctuations on the line tension τ at first-order and continuous wetting transitions. We consider thermal wandering, strong fluctuations as in random media, and weak fluctuations as in quasiperiodic systems. We obtain ${\mathrm{\alpha }}_{\mathit{l}}$=${\mathrm{\alpha }}_{\mathit{s}}$+${\nu }_{\mathrm{\parallel }}$, relating the exponent of τ, 2-${\mathrm{\alpha }}_{\mathit{l}}$, to the surface specific-heat exponent ${\mathrm{\alpha }}_{\mathit{s}}$, and the interfacial correlation-length exponent ${\nu }_{\mathrm{\parallel }}$. The singular behavior of τ at first-order wetting reveals that a critical phenomenon with a diverging correlation length, akin to complete wetting, is taking place.

The helical twisting power determines the pitch of the helical structure produced by introducing a given concentration of chiral dopant molecules to a nematic liquid-crystal phase. By using alternative, twisted, periodic boundary conditions, and measuring the relative chemical potentials of right- and left-handed dopants in a twisted nematic phase, we have succeeded in measuring this property by computer simulation of a simple molecular model. The technique should be generally applicable.

We propose a Ginzburg-Landau-type model to describe the kinetics of mixtures undergoing a sol-gel transition (nonconserved order parameter) simultaneously with phase separation (conserved order parameter). We compute the temporal development of the structure factor and determine the wave vector ${\mathit{q}}_{\max }$ at which the structure factor is maximal. We find that after a certain time ${\mathit{t}}_{\mathit{f}}$, ${\mathit{q}}_{\max }$ saturates at a final value ${\mathit{q}}_{\mathit{f}}$, and we calculate the temperature dependence of both ${\mathit{t}}_{\mathit{f}}$ and ${\mathit{q}}_{\mathit{f}}$. The predictions of this zeroth-order model agree remarkably well with recent kinetic measurements in gelatin-water-methanol mixtures.

An analysis is performed of the perturbation theory dealing with particle interactions in the exact linearized collision integral (CI) for a plasma in an electric field. It is shown that for a fully ionized plasma the usual results of kinetic theory correspond to a high-frequency expansion of the CI, whereas the static limit of the exact CI in a weak-interaction approximation is in disagreement with the usual kinetic theory.

We consider a p-polarized electromagnetic wave incident on a semi-infinite plasma covered by a dielectric layer. The plasma density is supposed to vary periodically along the plasma surface. The coefficients for specular as well as backward reflection are calculated. We show that, for certain parameter values, the specular reflection vanishes completely because all the energy is reflected in the backward direction due to the excitation of leaking surface waves.

A relativistic electron beam passing through a plasma excites the microwave with phase velocity ${\mathit{scrv}}_{\mathrm{ph}}$<${\mathit{scrv}}_0$, where ${\mathit{scrv}}_0$ is the velocity of the relativistic electrons. At moderately high amplitude this microwave couples to a fast free-electron-laser mode (with ${\mathit{scrv}}_{\mathrm{ph}}$>c) via a negative-energy beam mode, and this process leads to the explosive growth of all the three waves at the expense of the energy of the beam. The explosion time can be decreased as long as reasonable parameters are chosen.

The inhibition of the chaotic behavior of the Duffing-Holmes oscillator by means of a small parametric perturbation of suitable frequency, as shown by Lima and Pettini [Phys. Rev. A 41, 726 (1990)], is here reconsidered. The discrepancies noted in that article between the analytical (Melnikov method) and numerical (Lyapunov exponents) results are shown to be basically due to an error in the calculation of the Melnikov distance rather than simply to the method’s perturbative nature.

The preceding Comment [Cuadros and Chacón, Phys. Rev. E 47, 4628 (1993)] on the paper by Lima and Pettini [Phys. Rev. A 41, 726 (1990)] contains a correct premise; however, erroneous consequences are drawn from it. In this Reply we explain why.

The q-fold web map is extended to a volume-preserving map in q dimensions. The qth iterate of this map is invariant under translations by 2π in any of the coordinate directions. As a consequence, well-behaved invariant sets that are periodic in ${\mathit{openR}}^{\mathit{q}}$ produce quasiperiodic sets when restricted to a two-dimensional, irrationally placed subspace identified with the original phase space. A quasilattice of fixed points is constructed in this manner. It is conjectured that the stochastic web, considered as the restriction of a q-dimensional periodic set, is itself quasiperiodic.

A systematic and simple method to find the correlation function of the Abelian sandpile model up to any finite order is developed. In addition, an algorithm for evaluating the distribution function of the avalanche size P(s) exactly is also discovered along the same line. This method is, in general, more efficient (and accurate) than the numerical simulation that is currently used in obtaining P(s).

Davydov’s model of solitons in α-helix protein chains is shown to display features of self-organized criticality (SOC), i.e., power-law behavior of correlations in space and 1/f noise, as a consequence of considering random peptide group displacements from their (periodic) equilibrium positions along a chain. This may shed light on a basic mechanism leading to obtaining flicker noise in α-helix protein chains and to predicting a SOC regime in biomolecular structures from first principles. We believe our treatment of 1/f noise to be of some relevance to recent findings due to Voss on DNA [Phys. Rev. Lett. 68, 3805 (1992)].

In this paper, we examine the level-spacing distribution P(S) of the rectangular billiard with a single pointlike scatterer, which is known as almost integrable. It is shown that the observed P(S) is a new type, which is quite different from the previous conclusion. Even in the strong-coupling limit, the Poisson-like behavior rather than Wigner-like behavior is seen for S≳1, although the level repulsion still remains in the small-S region. The difference from the previous works is analyzed in detail.