Domainlike temperature distributions (solitary structures) are studied, which may arise in the half space with the surface heated by the external heat flux depending in a nonlinear way on the local surface temperature. Solutions describing stationary axisymmetric structures for some model dependencies of the external heat flux density on the surface temperature are found analytically or numerically. The stability of stationary axisymmetric structures is analyzed. When applied to an analysis of spots on electrodes in arc discharges, for given characteristics of the near-electrode plasma layer such an approach results in the complete description of the stationary spots on smooth surfaces, including the spot radius and the integral current. An evaluation for cathode spots in vacuum arcs is given; the results are inside the usual range of characteristics of macrospots.

We have developed an effective description of surface-wave propagation along the boundary between vacuum and a dense plasma or a low-density and high-density plasma in the case when the high-density plasma can be characterized by a nonlocal asymmetric conductivity tensor. This last condition leads to a different dispersion relation from the well-known one for surface waves. The asymmetric conductivity significantly affects the phase velocity and attenuation of the surface wave and makes the conditions for its excitation simpler. The effects of energy dissipation in the dense plasma on the evanescent and surface waves are taken into consideration. It is shown that damping of the surface wave in the propagation direction is low, if the surface impedance is small (‖ξ‖≪1). We also discuss the possibilities of excitation surface waves in different geometries.

Space-charge effects are explored theoretically as an intense (beam current density ≳1 mA/${\mathrm{cm}}^2$), positively charged ion beam emerges from an aperture displaying a well-defined aspect ratio and enters into an electron-free region of space. In the absence of space-charge neutralization, the beam diverges under the influence of the mutual Coulomb repulsion of the ions. Under the assumption of a collisionless beam, the mass, the energy, and the phase-space density are conserved to generate a single, three-dimensional partial differential equation. This equation is then combined with Poisson’s equation and solved analytically to provide the beam ion density and potential at any point in space. Applying the resulting expression to beams of varying energies and current densities, it is found that irrespective of the initial aspect ratio, intense beams of all energies and currents continuously diverge and ultimately relax into near-Gaussian profiles.

Normal-form methods for solving nonlinear differential equations are reviewed and the comparative merits of three methods are evaluated. The method of minimal normal forms is then extended to apply to the evaluation of discrete maps of an accelerator or storage ring. Such an extension, as suggested in this paper, is more suited for accelerator-based applications than a formulation utilizing continuous differential equations. A computer code has been generated to implement systematically various normal-form formulations for maps in two-dimensional phase space. Specific examples of quadratic and cubic nonlinear fields were used and solved by the method developed. The minimal normal-form method shown here gives good results using relatively-low-order expansions.

A field-theoretical derivation is given for the Čerenkov radiation off a charged particle moving in an isotropic permeable medium trapped in a hollow cylinder with a perfectly conducting neutral surface. An exact expression is derived for the power spectrum and the explicit allowed discrete frequencies are obtained. A Čerenkov counter and the observation of the resulting spectrum would not only provide information on the presence of a charged particle, in the conventional sense, but would also indicate the presence of an enveloping surface to the medium and provide information on the ‘‘geometry’’ of the surface.

Kink dynamics in the spatially modulated ${\mathrm{\phi }}^4$ model is studied analytically with the Born approximation and a collective-coordinate approach, and numerically. Four types of kink behavior can be distinguished: (i) radiation at high velocity, (ii) strong resonant beating in the kink velocity, (iii) propagation of the kink with almost periodic velocity oscillations, and (iv) trapping at low velocity. Although some of these regimes exist also in the sine-Gordon (SG) case, the ${\mathrm{\phi }}^4$ model exhibits a much richer dynamics due to the existence of a localized internal mode of the kink, which can exchange energy with the translational mode. The propagation in a modulated substrate is very sensitive to this effect, and in this respect the ${\mathrm{\phi }}^4$ model could be more representative of real systems which may not have the peculiar properties of the integrable SG model.

Mixed vector-dyadic equations derived earlier [V. Twersky, J. Math. Phys. 16, 633 (1975)] for multiple scattering of elastic waves are applied to a doubly periodic planar array of elastic obstacles. Different approximations for the multiple-scattering wave and amplitudes are given. Three groups of four energy theorems are discussed. Results for identical rigid elastic scatterers are derived.

We discuss different aspects of one-soliton and multisoliton dynamics governed by the lattice equation iψ${\mathrm{̇}}_{\mathit{n}}$+(${\mathrm{\psi }}_{\mathit{n}\mathrm{-}1}$+${\mathrm{\psi }}_{\mathit{n}+1\mathrm{}}$)(1+‖${\mathrm{\psi }}_{\mathit{n}}$${\mathrm{\Vert }}^2$)-2γ(t)n ${\mathrm{\psi }}_{\mathit{n}}$=0. We propose reduction of this equation, drastically simplifying its treatment by means of the inverse scattering technique.

The transport of radiation in the bulk of multiply scattering media is well understood within the diffusion approximation. Such a description does not hold in the skin layers, where the transport mechanism crosses over from free propagation to diffusive propagation, or vice versa. In this work, we examine the effects of the skin layers of optically thick slabs on various quantities, including the angularly resolved diffuse reflection and transmission and the shape of the enhanced backscattering cone. This study is based on the ladder approximation to the multiple-scattering expansion. It does not rely on the diffusion approximation and incorporates a systematic treatment of the internal reflections which take place when the random-scattering medium and the outside have two different optical indices, in an arbitrary ratio m. Many exact results are recovered in the absence of internal reflections (m=1). A systematic approach describes accurately the large-index-mismatch regime (m→0 or ∞), where the improved diffusion approximation is shown to become exact asymptotically. The analytic predictions of the large-index-mismatch approach are compared in a detailed way with numerical results and with the outcomes of previous works.

A model is presented that is intended to provide a realistic physical picture of the energy-transfer mechanism in cell microtubules. A classical ${\mathrm{\phi }}^4$ model in the presence of a constant electric field is used as a conceptual basis. It is demonstrated that kinklike excitations arise as a result of the guanosine 5’-triphosphate (GTP) hydrolysis and that an intrinsic electrical force may cause them to propagate along a microtubule. A discussion is given on the possible effects of these excitations on the dynamics of microtubules.

We present a simulation of the growth of a two-dimensional biological cellular system in which the cells experience mitosis whenever the area-to-perimeter ratio reaches a critical value. The model also includes the effect of interfacial energy and temperature. A stationary state with a constant average area is attained. We calculate the distribution of cells as a function of area, perimeter, and number of sides and also the two-cell correlation function. The results depend on temperature and are in agreement with experimental data, simulations, and theoretical models.

Poisson’s ratio, which was obtained by measuring swelling curves of free and radially constrained gels, has been investigated as a function of temperature and ionic strength for N-isopropylacrylamide (NIPA) gels and as a function of acetone concentration for polyacrylamide gels. It was found that the Poisson ratio exhibits a negative dip near the transition temperature for both neutral and ionic NIPA gels. The dip becomes deeper and shifts to a higher temperature as the ionic strength increases. The negative Poisson ratio of NIPA gels suggests that the bulk modulus is much smaller than the shear modulus as gels undergo the phase transition. The Poisson ratio of acrylamide gel, however, was found to be positive throughout the measured region.

A Caldeira-Leggett-type system-bath Hamiltonian is used to construct a new class of local stochastic equations on a lattice and to determine the conditions under which the lattice field evolves to thermal equilibrium. Both scalar and two-dimensional vector fields driven by multiplicative noise are considered. The latter model is developed to describe magnetization dynamics with spatial dispersion of relaxation. A systematic method of constructing stochastic field equations from a complex dispersion relation is proposed. The corresponding lattice Fokker-Planck equation is written down and it is shown that thermal equilibrium is its stationary state.

The dynamical pair approximation was modified to study the stationary states in a two-dimensional repulsive-lattice-gas model driven far from equilibrium by the application of an external field. This approximation distinguishes between the forward, backward, and transverse directions with respect to the electric field. In the present driven system, the forward-backward symmetry is broken at the level of the pair approximation. The difference between the forward and backward directions is confirmed by Monte Carlo simulations.

We investigate site percolation on lattices with directed bonds. Numerical simulations in which the lattice coordination number of the percolation lattices is systematically varied show that the inverse of the percolation threshold depends approximately linearly on the lattice coordination number. We show that this linear relationship is due to a similarity of percolation clusters in lattices for different coordination numbers. We compare this relationship to results obtained by Flory [Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953), Chap. IX] in the study of gelation processes and discuss its general applicability for related percolation models.

It is shown that the free-energy model for the inhomogeneous hard-sphere fluid introduced by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)], which contains both vector and scalar contributions, and the fully scalar expression proposed subsequently by Kierlik and Rosinberg [Phys. Rev. A 42, 3382 (1990)] represent two equivalent forms of the same functional. This unexpected result was partly obscured by a sign error in the original derivation of the vector part.

In situ observation technique is employed to study the fractal growth in a thin isothermal aqueous-solution film of Ba(${\mathrm{NO}}_3$${)}_2$. The micromorphology and the growing process of the fractals have been investigated. The experimental findings provide direct evidence that the fractals are formed by random successive nucleation. A nucleation-limited-aggregation (NLA) model is proposed to describe the fractal growth in our system. A computer simulation using the NLA model is also presented.

The in-plane projection of the director in smectic-C liquid crystals and the hexatic order parameter in hexatic smectic liquid crystals are both analogous to the magnetization in an XY ferromagnet. Recent experimental results and theoretical arguments suggest that two-dimensional XY ferromagnets have a universal finite-size-induced effective magnetization exponent β≊0.23 [S. T. Bramwell and P. C. W. Holdsworth, J. Phys. Condens. Matter 5, L53 (1993)]. From these results, we predict that XY-like order parameters in thin free-standing smectic liquid-crystal films should behave as ∝(${\mathit{T}}_{\mathit{C}}$-T${)}^{\mathrm{\beta }}$ in an intermediate temperature range below the relevant transition temperature ${\mathit{T}}_{\mathit{C}}$ if they exhibit a Kosterlitz-Thouless transition of a single XY-like order parameter.

The influence of ac electric field on the shape and thermal fluctuations of giant vesicles is theoretically investigated. The experiments show that at high frequencies (dielectric regime) vesicles deform into oblate ellipsoids with the symmetry axis parallel to the applied electric field, while at low frequencies (conductive regime) they deform into prolate ones. Depending on the medium conductivity, the transition frequency between both regimes may be as low as a few kilohertz.

The tunneling of particles is in direct analogy with the transmission of evanescent electromagnetic waveguide modes as has been shown quite recently. We compare experimental data of an electromagnetic wave packet traversing an evanescent waveguide region with theoretical values derived for particle tunneling through a rectangular potential barrier. The transmission time was deduced by transformation of the experimental frequency data to the time domain. The data are in agreement and reveal superluminal wave-packet velocities for opaque evanescent regions.