A resistive model including additional dc currents and electrodes enables understanding and analysis of rf discharges in the low-frequency range (ω≪${\mathrm{\omega }}_{\mathit{p}\mathit{i}}$). A general and exact analysis based on asymptotic solutions results in analytic representations of relations between sheath voltages, bias, and rf voltage. For sinusoidal rf voltage an expansion of sheath voltages and discharge current into Fourier series, e.g., important for probe measurements, and a general relation between these series is presented. From the power balance a lower bound of a sinusoidal rf voltage is derived. The model is extended for different densities and electron temperatures along the sheath edges. Correction and error estimation show the asymptotic solution to be well suited.

The longitudinal and transverse collective modes in a nonrelativistic electron-positron plasma are studied in two cases: a static uniform magnetic field is present or absent. The dispersion relations for the longitudinal and transverse collective modes in the absence of a magnetic field and those for the longitudinal mode in the presence of a magnetic field (Bernstein mode) are found to be similar to those for the one-component electron plasma. The transverse modes in the presence of a magnetic field, on the other hand, are found to be quite different from the electron-ion plasma: The dispersion relations for the left- and right-circularly polarized waves propagating parallel to the magnetic field are found to be identical. In addition to the transverse plasma oscillations, the low-frequency Alfvén mode exists, while the whistler mode does not exist. For waves propagating perpendicular to the magnetic field, the extraordinary wave becomes a pure transverse mode. In the cold-plasma limit, there is only one resonance at the cyclotron frequency and one cutoff frequency for the extraordinary mode, in contrast to the electron-ion plasma, where there are two hybrid resonances and two cutoff frequencies.

We present a theoretical study and a numerical simulation of the formation and development of the cathode region (cathode-fall and negative-glow ones) in ${\mathrm{CO}}_2$ and ${\mathrm{N}}_2$ discharges from the inception of the discharge to its stationary state. The model is a self-consistent one: the distribution of the electric field is found from the charge carriers and the hydrodynamic moment equations (density, velocity, energy) are solved by a sophisticated flux-corrected transport method. The ionization and excitation source terms are calculated using an electron-energy distribution function which takes into account the electron-density gradient and the local electric field. The results show that this choice is more realistic in representing the spatiotemporal evolution of the cathode region. Our theoretical results are compared with the experimental ones obtained by other authors and a good agreement is observed concerning the current intensity and the spatial distribution of light in the cathode region in ${\mathrm{N}}_2$.

The state-specific drift velocity of ${\mathrm{Ca}}^{+}$ ions in the 3 ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{3/2}^{}{}_{}{}^{}$ metastable state and of ${\mathrm{Cd}}^{+}$ in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ highly excited state in a helium glow-discharge plasma have been precisely measured by using a tunable single-mode diode laser and the state-specific mobility of excited ions has been discussed. The results show that the mobility of ${\mathrm{Ca}}^{+}$ ions in the metastable state is determined by momentum-loss collisions and is almost identical with the value for ${\mathrm{Ca}}^{+}$ in the ground state. In the experiment with a thin cylindrical tube, the apparent value of the mobility is dependent on the diffusion in the radial direction. On the other hand, the apparent mobility of ${\mathrm{Cd}}^{+}$ ions in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ state is much smaller than the calculated result for ${\mathrm{Cd}}^{+}$ in the ground state, but the value increases significantly with Cd vapor density. This is explained by the fact that ${\mathrm{Cd}}^{+}$ ions in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ highly excited state decay quickly by the radiative process and the apparent mobility of the ${\mathrm{Cd}}^{+}$ ions in this state in the plasma is dependent not only on the radiative lifetime but also on the excitation mechanisms for the state.

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.