A careful analysis of the well-known Kanai-Caldirola Hamiltonian yields rather surprising results concerning its physical origin. Recourse to the maximum entropy principle sheds some light regarding the meaning of the equivalence between different Lagrangians and/or Hamiltonians.

We study the properties of an isotropic lattice model by low-temperature expansion. In particular, the interface between ferromagnetic phases for the case when a third modulated phase is in thermodynamic equilibrium is considered. Throughout the three-phase coexistence region the interfacial tension between all three phases is very low and actually vanishes at zero temperature. This reflects the fact that the surface of the finite-temperature three-phase equilibria arises from a curve of zero-temperature multiphase points. We show that throughout the three-phase region and in the limit of low temperature, the modulated phase never wets the interface between the ferromagnetic phases.

Starting from the equation for advection in laminar flows, known to generate chaotic trajectories, three Schrödinger-type equations are constructed. The first two manifestly conserve characteristics of classical chaotic behavior, the reason for this being a dynamical decoupling between position and its conjugate variable. The third model is a quantized version of the advection equation; it leads to a time-dependent Harper’s equation and is ideally suited to study the subtle differences between classical and quantum behavior.

We present a numerical study of the onset of turbulence in a discretized version of the complex Ginzburg-Landau equation. The transition point is determined by computing Lyapunov exponents, which show a first-order transition at a parameter value ${\mathrm{\alpha }}_1$ below the linear stability threshold for the uniform state. On further decreasing the parameter, the finite-time Lyapunov exponent remains positive only up to a characteristic transient time, after which the vortices get entangled and the asymptotic Lyapunov exponents become zero. The finite-time exponent goes to zero at ${\mathrm{\alpha }}_{\mathit{c}}$<${\mathrm{\alpha }}_1$ as a power law.

We study both experimentally and theoretically the behavior of a freely suspended ferroelectric smectic-${\mathit{C}}^{\mathrm{*}}$ liquid-crystal film in the presence of an ac electric field. The field drives the system periodically between two ordered phases with opposite polarization. We find several different regimes of dynamical behavior depending on the strength of the field. These results are explained in terms of a phenomenological free energy.

We have studied the delay of onset of the scattering of light by the microbubbles at the solid-liquid interface of succinonitrile during growth as a function of the growth velocity and the initial dissolved gas concentration. We have also attempted to identify the dissolved gas by infrared spectroscopy.

A problem with the quasistatic mean-field equations for branchless diffusion-limited aggregation, which were given and solved by Cates [Phys. Rev. A 34, 5007 (1986)], is pointed out and resolved. In particular, it is shown that the exponent γ describing the time dependence of the growing aggregate (which was set infinite by Cates) equals 1/2 on the mean-field level. An approximate analytical solution to the full mean-field equations is presented and compared with its numerically exact counterpart. Properties of the aggregate boundary as described by the exact solution are derived analytically. It is shown that scaling of the aggregate density at all times implies that the random-walker density cannot satisfy simple constant (nonzero) density or flux boundary conditions at infinity.

Nan-xian Chen [Phys. Rev. Lett. 64, 1193 (1990)] has generalized a formula of classical algebraic number theory to continuous variables and noted some useful consequences of the generalization. We present an alternative view of this analysis, based on the Mellin transformation and Riemann’s ζ function.

The effects of quantum fluctuation on the classical dynamical structure are investigated by using the semiquantal dynamics derived from the effective action. A pulsed-spin system is studied as an example, which shows that global chaos is suppressed by quantum fluctuation. The quantum-classical correspondence is explicitly examined for low-spin cases.

The heat flux (Nusselt number) as a function of Rayleigh number, ${\mathit{N}}_{\mathrm{Nu}}$≊0.3${\mathit{N}}_{\mathrm{Ra}}^{2/7}$, is deduced from the presence of a mean flow and the nesting of the thermal boundary layer within the viscous one. The numerical coefficients are obtained from those known empirically for turbulent boundary layers. The consistency of our assumptions as a function of Prandtl number limits this regime to (${10}^7$–${10}^8$)${\mathit{N}}_{\mathrm{Pr}}^{5/3}$≲${\mathit{N}}_{\mathrm{Ra}}$≲ (${10}^{13}$–${10}^{15}$)${\mathit{N}}_{\mathrm{Pr}}^4$. The Bolgiano-Obukhov ${\mathit{k}}^{\mathrm{-}7/5}$ spectrum for the temperature fluctuations is inconsistent with a simple scaling treatment of the equations.

We discuss the small-scale energy spectrum E(k) of two-dimensional fully developed turbulence. As its scaling exponent is related to the fractal dimension of isovorticity lines, we suggest that it could be nonuniversal with a dependence on the particular class of initial conditions considered. This should explain the different values obtained in numerical experiments for decaying turbulence and for statistically stationary forced turbulence with particular kinds of forcing. Finally, the scaling E(k)∼${\mathit{k}}^{\mathrm{-}3}$ is related to the most random situation where the vorticity can be considered as a scalar passively advected by the velocity field.

We consider the relaxation kinetics for folding intermediate structures in random uncorrelated RNA chains. Folding patterns correspond to intrachain secondary structures. We make use of a Monte Carlo simulation that mimics a Markov process to study the refolding dynamics. This is done to obtain the time-dependent behavior of the activation energies. We conclude that the mechanism of relaxation to the equilibrium secondary structure is compatible with the random-energy model as the thermodynamic limit is approached.

We have used optical second-harmonic generation and infrared-visible sum-frequency generation to study liquid-crystal monolayers on clean glass and on surfactant-treated glass. The results provide insight into the competing effects of polar adsorption sites and surfactant alkyl chains in aligning the bulk liquid crystal.

We propose a theoretical interpretation of observed anomalous rheological behavior of diblock copolymers quenched into microphase-separated states having locally lamellar morphology with disorder. The proposed mechanism of the anomaly is associated with the second-sound modes occurring in a locally lamellar structure that are overdamped in a wide wave-vector region due to large shear viscosity. The resulting complex shear modulus is proportional to (iω${)}^{1/2}$, which contains no adjustable parameter and is consistent with the experimental result by Bates et al. [J. Chem. Phys. 92, 6255 (1990)].

We present dielectric measurements extended over the frequency range from ${10}^6$ to ${10}^9$ Hz on a pure ferroelectric liquid crystal. In clear contrast to the generally attributed origin of the ferroelectricity in liquid crystals arising from a slowing down of the molecular rotation around the long molecular axis, we find by direct observation the corresponding dielectric relaxation unchanged at the smectic-A to smectic-${\mathit{C}}^{\mathrm{*}}$ transition. This result requires a new interpretation of a recently published degenerate four-wave-mixing experiment by Lalanne et al. [Phys. Rev. Lett. 62, 3046 (1989)].

The formation of cracks in brittle materials is investigated for arbitrary dependence of the crack growth on the stresses at its boundary. It is shown that, despite the possible complexity of the growth law, the shape of the crack for large sizes and long times is determined by the high-stress limit of the growth law, provided only that the probability of cracking increases with stress. This result may help to explain the appearance of long and straight cracks in many fracture processes. Other pattern-formation models are expected to show the same features.

New experimental evidence of the plasma structure has been presented in the rf glow discharge in ${\mathrm{SiH}}_4$ at 13.56 MHz by spatiotemporal emission spectroscopy. Theoretical estimation by the relaxation continuum model strongly supports the accumulative effect of the negative ion, ${\mathrm{SiH}}_{\mathit{n}}^{\mathrm{-}}$, by the electron attachment in the bulk plasma due to the potential barriers in the positive-ion sheath on the discharge structure.