The multifractal structure of flow distribution is investigated in the river-network model of Scheidegger [Bull. IASH 12, 15 (1967)]. It is shown that the partition function Z(q)==${\mathit{tsum}}_{\mathit{i}}$${\mathit{I}}_{\mathit{i}}^{\mathit{q}}$ scales as Z(q)≊${\mathit{L}}^{\mathrm{\zeta }\left(\mathit{q}\right)}$ where ${\mathit{I}}_{\mathit{i}}$ is the flow of water passing over the bond i within the river network, the summation ranges over all bonds, and L is the size of the river network. In the limit of a sufficiently large q, ζ(q)/q gives the exponent of the drainage basin of a river. The exponent also equals to the fractal dimension ${\mathit{d}}_{\mathit{f}}$ of a single river. The f-α spectrum of the normalized flow distribution is calculated. It is found that the fractal dimension ${\mathit{d}}_{\mathit{f}}$ of a river is exactly given by ${\mathit{d}}_{\mathit{f}}$=2-α(∞). The flow distribution shows a characteristic multifractal structure for the river network. The river-width distribution also shows the multifractality if the width w of a river scales as w≊${\mathit{I}}^{\mathrm{\beta }}$.

The influence of an applied electric field on the impact ionization and on the mass-action law of a nonideal hydrogen plasma is discussed. The coupling of field and many-body effects leads to a minimum behavior of the impact-ionization coefficient as a function of the plasma density.

A diagrammatic technique has been worked out in the framework of nonequilibrium statistical mechanics as developed by Prigogine and co-workers to tackle the problem of radiation emission from a relativistic electron in an ambient plasma embedding an axial-wiggler magnetic field. The theory is exact in that the diagrams contributing towards the self-consistent-field approximation have been summed up exactly and one obtains a time-dependent response function. The kinetic regime has been obtained by eliminating the memory by taking an asymptotic limit in time. Explicit calculations have been affected to obtain functions like the Čerenkov angle and the refractive index as well as the power emitted by the system. It has been shown that the radiation emitted has very peculiar polarization features.

We have derived expressions for the longitudinal and transverse resistive wall coupling impedances for a beam pipe of arbitrary cross section in the ultrarelativistic limit. These expressions involve the integral of the square of the tangential magnetic fields along the wall, which can be obtained from the solution of the two-dimensional Poisson equations with a monopole and dipole singularity, respectively. Explicit results are given for beam pipes of elliptical and rectangular cross sections, including the limiting cases of a circle and a pair of parallel plates.

An electromagnetic wave theory of bounded homogeneous anisotropic media is developed by using the method of angular spectrum expansion. The series and integral representations of the circular cylindrical wave functions and the spherical wave functions of the first, second, third, and fourth kind for homogeneous anisotropic media are obtained. Each coefficient of the Fourier series of a circular cylindrical wave function is a one-dimensional finite range of integration and every coefficient of the spherical-harmonic-function series is a two-dimensional finite range of integration. The addition theorem of wave functions for anisotropic media can be derived from that of wave functions for isotropic media. Weyl’s method of deriving the scalar Green’s function in isotropic media is generalized to the study of the dyadic Green’s function in anisotropic media. The cold homogeneous magnetoplasma is considered as an illustrative example. For a cold homogeneous magnetoplasma, simplified series representations of wave functions and dyadic Green’s functions are given. The distributional singular behavior of the dyadic Green’s functions in the source region is investigated and taken into account by solving the static problem and the boundary integral equation is derived.

Exciton dephasing in crystals due to the phonon scattering is studied within the framework of the stochastic Haken-Strobl model. The model corresponds to the extremely fast-modulation limit and is applicable to triplet excitons in molecular crystals. The model describes the crossover from the coherent (band) short-time exciton dynamics to incoherent diffusive motion on the long time scale. An efficient method for the determination of the moments of the exciton displacement is developed. Analytic expressions for the mean-square displacement tensor and for the fourth-order moment of exciton displacement on a three-dimensional lattice with inversion symmetry are derived. Solution of the model for arbitrary initial conditions is obtained. The equilibrium state of the system corresponds to the uniform population of the states in the exciton band. The equilibration time scale coincides with the time scale on which the crossover between coherent and diffusive motion occurs. It is given approximately by the inverse amplitude of the second-order correlation function of the stochastic modulation. Physical assumptions underlying the model and the range of its applicability are discussed.

The transverse stability of the planar solitons described by the fifth-order Korteweg–de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative. This is in agreement with the dynamics of the two-dimensional Kawahara solitons.

Brillouin spectra have been measured from wet-spun films of Li and Na hyaluronate (NaHA) between 0% and 93% relative humidity (RH). The speed of sound is very high (about 5 km/s) in both Li and NaHA films at low values of RH. The Brillouin spectra show substantial coupling between the longitudinal-acoustic phonons and a relaxation mode of the water of hydration. A coupled-modes model is used to interpret these data. This analysis shows that the relaxation time of the water of hydration (about 50 ps) is constant over the range of hydration. The microscopic coupling constant also appears to be independent of hydration. Between 84% and 88% RH, the uncoupled phonon frequency for both Li and NaHA is found to drop by ∼40%, and ∼25% for phonons propagating in the parallel and perpendicular directions, respectively, indicative of a phase transition.

We present a model for the dynamical structure of DNA that can be considered as an extension of the usual Ising-like statistical approach to the melting curves. The model uses the stretching of the hydrogen bonds in a base pair as its main variable. Numerical simulations at constrained temperature show that it provides a good qualitative description of the collective motions of the base pairs, including their large-amplitude fluctuational openings and the emergence of the denaturation bubbles from the thermal fluctuations. The results are in good agreement with a statistical-mechanics analysis of the denaturation and specific-heat curves, performed with the transfer-integral method, provided that discreteness effects are treated exactly by a numerical solution of the transfer-integral operator. Second-order self-consistent phonon theory agrees with the exact transfer-integral results in the low- and intermediate-temperature ranges and explains the phonon softening observed in the molecular-dynamics simulations. When the temperature approaches the denaturation temperature, the second-order self-consistent phonon results deviate significantly from the exact ones, pointing to the fundamental role of nonlinear processes in DNA denaturation.

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.