We present a Monte Carlo finite-size scaling analysis of the Pink model with the fitted parameters appropriate for dipalmitoyl phosphatidylcholine and disteroyl phosphatidylcholine lipid-bilayer systems. The numerical simulations were performed in conjunction with the extrapolation method of Ferrenberg and Swendsen [Phys. Rev. Lett. 61, 2635 (1988)] and the finite-size scaling method of Lee and Kosterlitz [Phys. Rev. Lett. 65, 137 (1990)]. In contrast to previous work, we found that there is no first-order phase transition and that the abrupt jump in the order parameter and the enhancement of the response functions found by previous numerical simulations are due to the presence of strong lateral density fluctuations which give rise to a large correlation length.

Conventional source-detection algorithms in high-energy astrophysics and other fields mostly use spherical or quadratic sliding windows of varying size on two-dimensionally binned representations of spatial event distributions in order to detect statistically significant event enhancements (sources) within a given field. While this is a reasonably reliable technique for nearly pointlike sources with good statistics, poor and extended sources are likely to be incorrectly assessed or even missed at all, as the calculations are governed by nonphysical parameters like the bin size and the window geometry rather than by the actual data. The approach presented here does not introduce any artificial bias but makes full use of the unbinned two-dimensional event distribution. A Voronoi tessellation on a finite plane surface yields individual densities, or fluxes, for every single event, the distribution of which allows the determination of the contribution from a random Poissonian background field (noise). The application of a nonparametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry. High-density fluctuations from the random background field will still be included in this tentative source list but can be easily eliminated, in most cases, by setting a lower threshold to the required number of events per source. Since no finite-size detection windows or the like have been used, this analysis yields automatically straightforward fluxes for every source finally accepted. The main disadvantage of this approach is the considerable CPU time required for the construction of the Voronoi tessellation—it is thus applicable only to either small fields or low-event density regions.

The long-time asymptotic properties of numerous dynamical lattice models are described by rich phase diagrams. A suggestive pattern is observed about the universality class of second-order phase transitions in such systems: if the transition occurs from (or into) a single absorbing state (where the order parameter is then zero) then it belongs to the same universality class as directed percolation and Reggeon field theory (RFT). This has been conjectured to be always true for one-component systems by Grassberger and also by Janssen. Grinstein, Lai, and Browne have argued for a possible generalization of this rule to multicomponent systems. I present an example of a one-component lattice model where the second-order transition about a single absorbing state is not in the RFT universality class, thus violating even the weaker conjecture of Grassberger and Janssen.

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

We formulate a method designed for lattice-gas problems that is analogous to the density-functional theory used to describe equilibrium properties of inhomogeneous classical liquids. After a discussion of the differences between the discrete and the continuous forms of the theory we present a quantitative test for a one-dimensional system. Possible applications of our approach to order-disorder transitions in lattice gases are pointed out.

The Hamiltonian H={${\mathit{p}}_{\mathit{x}}^2$+${\mathit{p}}_{\mathit{y}}^2$+[(${\mathit{y}}^2$-δ${\mathit{x}}^2$)/2${]}^2$}/2 is shown to exhibit large-scale chaos over a wide range of the parameter δ. Such Hamiltonians are physically interesting in plasma physics, deriving from the motion of a charged particle in a neutral-line magnetic field. We suggest that this physically realistic Hamiltonian may be a candidate for a fully chaotic system with no stable periodic orbits.

Himalayan avalanches are examined for agreement with power-law behavior between frequency of outfall and rock volume. The data support a scaling state beyond the size ranges in which corresponding sandpile experiments have suffered from finite-size effects. Large-scale data (12 orders of magnitude in rock volume) additionally suggest a possible role for the numerically predicted ‘‘snowball effects’’ of large rocks triggering more net dislodging events.

Jolicoeur and Le Guillou have recently proposed [Phys. Rev. A 40, 5815 (1989)] a very interesting derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy using functional techniques. In this paper we generalized their derivation to higher-form distributions in phase space. At the heart of our method there is a path integral for classical mechanics that we put forward some time ago. This path integral describes the dynamics not only of scalar distributions in phase space but also of p-form valued densities [E. Gozzi, M. Reuter, and W. D. Thacker, Phys. Rev. D 40, 3363 (1989)]. The distribution functions entering this infinite set of coupled integro-differential equations (BBGKY hierarchy) carry a double grading now: besides the level in the hierarchy, they are characterized by their degree as differential forms. The higher forms are related to the dynamics of the Jacobi fields and therefore contain information about the behavior of nearby trajectories. This kind of information could be used in the study of turbulence, for instance.

We establish the equivalence between a one-dimensional sandpile model recently introduced by Chhabra et al. [Phys. Rev. A (to be published)], and the diffusion-limited reaction A+A→0 with a point source. The equivalence is used to predict the power-law decay of the avalanche size distribution, P(s)∼${\mathit{s}}^{\mathrm{-}3}$, in agreement with numerical simulations. This result differs from the mean-field treatment of Chhabra et al., demonstrating the importance of fluctuations in this low-dimensional system.

In a recent paper [B. Tadić, U. Nowak, K. D. Usadel, R. Ramaswamy, and S. Padlewski, Phys. Rev. A 45, 8536 (1992)], the directed two-dimensional sandpile is modified to include a concentration p of randomly placed holes. For p>0, they observe a characteristic cutoff size for the duration (and mass) of avalanches. This breaks the formal power-law behavior that is a signature of self-organized criticality. The scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law, and the exponents are numerically determined. In this Brief Report, it is shown that a previously described mean-field approximation can account for the observed exponents.

A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.

The nonlinear quantum kinetic equation for the interaction of sound waves is solved via analytic and numerical techniques. In the classical regime energy cascades to higher frequency (ω) according to the steady-state power law ${\mathrm{\omega }}^{\mathrm{-}3/2}$. In the quantum limit, the system prefers a reverse cascade of energy which follows the power law ${\mathrm{\omega }}^{\mathrm{-}6}$. Above a critical flux, a new type of spectrum appears which is neither self-similar nor close to equilibrium. This state of nonlinear quantum wave turbulence represents a flow of energy directly from the classical source to the quantum degrees of freedom.

We expand an accurate, closed-form equation for the reflectivity in a power series around ${\mathit{q}}_2$=0, where ${\mathit{q}}_2$ is the z component of the wave-vector transfer in a film of constant composition. We examine, in particular, the case where ${\mathit{q}}_2$=0 at the critical edge. Such an example might be realized through a neutron-reflectivity experiment on a microemulsion that exhibits surface layering. We find the coefficients of this low-wave-vector expansion to be the moments of the scattering-length density profile. We demonstrate how the first moment of the profile can be obtained from an accurate reflectivity measurement.

The theroretical prediction of the existence of Clifford toroidal vesicles by Ou-Yang [Phys. Rev. A 41, 4517 (1990)] has been confirmed by the experiment of Mutz and Bensimon [Phys. Rev. A 43, 4525 (1991)]. However, the few nonaxisymmetric toroidal vesicles observed by Fourcade, Mutz, and Bensimon [Phys. Rev. Lett. 68, 2551 (1992)] raise the question of why the formation of nonaxisymmetric toroidal vesicles is so rare in comparison with that of axisymmetric ones. In this report we are going to show that for a solution of the shape equation of membranes, the spontaneous curvature ${\mathit{c}}_0$ of nonaxisymmetric Dupin cyclide has to be zero, while axisymmetric Clifford solution has no such restriction as shown by Ou-Yang [Phys. Rev. A 41, 4517 (1990)].

The Alfvén waves are shown to be linearly coupled with finite-frequency convective cell modes in a nonuniform cold dusty magnetoplasma. The dynamics of weakly interacting finite-amplitude electromagnetic oscillations is governed by a pair of nonlinear equations. The latter admit dipolar vortices as possible stationary solutions. The present results can have relevance to the nonlinear electromagnetic wave propagation in a space environment such as cometary tails or interstellar clouds.

Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch, and source processes, certain ‘‘bell-shaped’’ distributions may grow explosively in time while preserving the shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or, more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma.

The Stark broadening parameters of several Si ii lines have been measured in a pulsed discharge. Experimental results are compared with theoretical predictions and with other experiments.

We present exact results for the stress distribution for a pyramid-shaped hexagonally packed granular pile in two dimensions. In particular, we show that the load acting on each grain at the bottom layer is identical. The real granular pile, however, has voids inside and thus may show some deviation from the present results.

It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential ̭0). As a numerical apparatus, the theory relates to gauge-dependent errors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced.

We examine the signature of classical chaos on a generic quantum phenomenon, namely, quantum tunneling in a nonintegrable, conservative two-degree-of-freedom Hamiltonian system. We show that, as one passes from the regular to chaotic regime, the quantum tunneling probability versus coupling-constant curve exhibits a significant change of slope in the neighborhood of the critical chaotic threshold (beyond which classical chaos sets in). This shows that the presence of Kolmogorov-Arnold-Moser barriers of classical phase space manifests in quantum phenomena such as quantum tunneling.