The Nosé theorem of the extended-system method of the constant-temperature molecular dynamics is generalized by including the conservation of the total virtual momentum. It is proved that a canonical ensemble of an (N-1)-particle system is generated from an extended system of an N-particle system only if the total virtual momentum is zero. It is also shown that the resulting (N-1)-particle system has a slightly different mass spectrum than that of the original N-particle system. The consequences of this new mass spectrum are relevant in the calculation of dynamical properties and the relaxation times of the system, but irrelevant to thermodynamic averages. For practical considerations, numerical simulations are performed and tested against this theorem. The differences in application of the Nosé theorem and the generalized Nosé theorem are discussed.

The continued-fraction formalism demonstrates that the Laplace-transformed dynamical correlations can be expressed as infinite continued fractions (ICF’s). We propose a generalization of the dynamical convergence method (GDCM) of J. Hong and M. H. Lee [Phys. Rev. Lett. 55, 2375 (1985)] of perturbatively evaluating insoluble ICF’s when a closely related ICF is exactly soluble. The proposed method overcomes an existing limitation of the dynamical convergence method which involves accurate computing of ratios of small numbers. The limitations are surmounted by exploiting an ‘‘inversion’’ property of ICF’s. The GDCM allows computationally fast and simple perturbative evaluation of insoluble ICF’s with up to ${10}^{\xi }$, ξ≤6, levels of the insoluble ICF when a related ICF is soluble. The method appears to be appropriate for studies of asymptotic behavior of dynamical correlations described by slowly converging and nonconverging ICF’s, which are otherwise insoluble, when closely related soluble ICF’s exist. The desirable feature of the GDCM is that the computation times required to solve the ICF’s are unrelated to the details of the convergence properties. The method has been applied to recalculate the dynamical-spin pair correlation of a recently studied classical XX spin cluster. This application is described in this work.

We calculate the probability distributions of the largest local Lyapunov exponent for three Hamiltonian systems at different values of the energy E, for a set of increasing values of the length in which the trajectory is partitioned. The systems we study are the Hénon-Heiles model and the classical ${\mathrm{Ar}}_3$ and ${\mathrm{Ar}}_7$ clusters. We show that these distributions contain much information about the dynamics of the system and, in particular, can be used to study the evolution of ergodic properties as the internal energy of the system increases; therefore, even though the inequivalence of chaos and ergodicity does not allow one to consider Lyaponov exponents to be a direct measure of ergodicity, the sample distributions of short-term Lyapunov exponents can be used to evaluate the extent of ergodic behavior in the various situations.

A model-independent method is developed for the reconstruction of the scattering-length-density profile of a film on top of a known substrate or bulk from the measured reflectivity data. The method is first tested on simulated reflectivity data calculated from profiles resembling those used in real experiments. It is shown that the method is effective in faithfully reproducing the original profiles from the simulated data. The method is then tested on experimental data from four different surface films. It is found again that the method is capable of generating physically reasonable profiles whose calculated reflectivities agree to within ${\mathrm{\chi }}^2$=1 with the measured data. In the tests, detailed descriptions are also given for the implementation of the method. Finally, a discussion is given with regard to the application of the method and the precautions needed for using this method.

The growth kinetics of a system quenched into the ordered phase from high temperatures is considered for systems with power-law interactions of the form 1/${\mathit{r}}^{\mathit{d}+\mathrm{\sigma }}$, with 0<σ<2. For σ>1, the characteristic scale L(t), which describes the growth of order at late times, is predicted to obey the conventional Lifshitz-Slyozov and Lifshitz-Cahn-Allen laws, L(t)∼${\mathit{t}}^{1/3}$ and ${\mathit{t}}^{1/2}$ for conserved and nonconserved scalar order parameters, respectively. For σ<1, the results L(t)∼${\mathit{t}}^{1/(2+\mathrm{\sigma })}$ and ${\mathit{t}}^{1/(1+\mathrm{\sigma })}$, respectively, are obtained. For a vector order parameter, we find L(t)∼${\mathit{t}}^{1/(2+\mathrm{\sigma })}$ and ${\mathit{t}}^{1/\mathrm{\sigma }}$ for conserved and nonconserved fields, respectively, for all σ<2.

Statistical properties of type-I intermittency are investigated from the standpoint of the long-time description and time correlations of intermittent time series by utilizing the So-Ose-Mori mapping. It is shown that the two coexisting characteristics, laminar state and burst, can be singled out in a clear-cut way by introducing the ensemble processing with a parameter q. For q→-∞, the relevant statistical quantities describe the statistics of a purely laminar state and, for q→∞, they describe the statistics of a purely burst behavior. In particular the dynamical statistical characteristics (temporal correlations) turn out to exhibit clear-cut change at the so-called q-phase transition point ${\mathit{q}}_{\mathit{c}}$ in the limit of the intermittency transition of the control parameter. For q<${\mathit{q}}_{\mathit{c}}$, the spectral density takes a power-law form of the frequency, the exponent 2 being independent of q. On the other hand, for q>${\mathit{q}}_{\mathit{c}}$ it has a white-noise spectrum. These are characteristics of the pure laminar state and burst, respectively.

Fluctuations and noise are typical features of mesoscopic systems. Here we study the quantum-stochastic dynamics of an interacting network of local few-level subsystems. Controlled by the environment, this network is shown to exhibit a large repertoire of different behavioral patterns, including uncorrelated and correlated ‘‘quantum jumps’’: Such cooperation should be generic for certain networks and expected, e.g., also for various optically driven quasimolecular structures. When applied to a defect network controlling the current through a small tunnel junction, large-amplitude two-level current fluctuations appear, in agreement with experiment.

We propose a two-dimensional particle-cluster aggregation model which considers explicitly linear and angular momentum conservation. Each aggregate is grown from a seed of given mass and given initial angular velocity, to which particles of unitary mass and ballistic trajectories are added. The fractal dimensions of the resulting aggregates are calculated and Fourier transform analysis is performed. Very different features are found, as initial conditions are varied. Particularly, spiral structures are found for a seed of high mass and high initial angular velocity.

Aggregation kinetics are often described by the population balance (or Smoluchowski coagulation) equation. The population balance equation is a mean-field equation for an aggregation process. An upper critical dimension ${\mathit{d}}_{\mathit{c}}$ calculated for a given aggregation frequency has been used by other investigators to characterize the validity of this mean-field equation. It is shown that the upper critical dimension is also related to the singularity of the self-similar spectrum. This paper demonstrates that the usefulness of the upper critical dimension for determining the validity of the population balance equation is lost when the aggregation frequency is unknown. The validity of the equation can be inferred from the similarity or scaling distribution and the evolution of the average particle size in such cases.

We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.

The existence of a grooved phase in linear and nonlinear models of surface growth with horizontal diffusion is studied in d=2 and 3 dimensions. We show that the presence of a macroscopic groove, i.e., an instability towards the creation of large slopes and the existence of a diverging persistence length in the steady state, does not require higher-order nonlinearities but is a consequence of the fact that the roughness exponent α≥1 for these models. This implies anomalous behavior for the scaling of the height-difference correlation function G(x)=〈‖h(x)-h(0)${\mathrm{\Vert }}^2$〉 which is explicitly calculated for the linear diffusion equation with noise in d=2 and 3 dimensions. The results of numerical simulations of continuum equations and discrete models are also presented and compared with relevant models.

A molecular-dynamics simulation is carried out for particles (tracers) interacting with a screened Coulomb potential in three dimensions. A phase transition is observed from a liquid to an fcc solid on reducing the temperature at a fixed density, consistent with previous studies. In the liquid phase, the variation of the rms displacement ${\mathit{R}}_{\mathrm{tr}}$ of the charged particles with time seems to depend on the density and the temperature. In the short-time regime, the effective exponent k for the subdiffusive power-law behavior, i.e., ${\mathit{R}}_{\mathrm{tr}}$∼${\mathit{t}}^{\mathit{k}}$, decreases on increasing the density and lowering the temperature. A crossover from subdiffusive to a diffusive behavior is observed for a wide density regime in the liquid phase. At high temperatures and large densities, a single power law does not seem to describe the variation of ${\mathit{R}}_{\mathrm{tr}}$ with t.

Transport properties of binary mixtures of diatomic gases in vibrational nonequilibrium are analyzed and the corresponding terms are established. In order to solve the Boltzmann equation, a generalized Chapman-Enskog method is used, valid whatever the degree of nonequilibrium, contrarily to previous analyses in which only the extreme regimes were considered, at weak or strong nonequilibrium, and generally for pure gases only. The transport coefficients, first written in terms of collision integrals, are finally expressed as functions of macroscopic quantities, known or experimentally attainable, following Mason and Monchick type approximations and with the harmonic-oscillator model. Finally, examples of calculations are given for ${\mathrm{N}}_{2\mathrm{-}}$${\mathrm{H}}_2$ and ${\mathrm{O}}_{2\mathrm{-}}$${\mathrm{N}}_2$ mixtures. Results are in good agreement with available experimental data. Comparisons with approximate formulas, extensively used in the literature, show also that, at least for the investigated mixtures, the use of these formulas seems roughly justified.

We show by computer simulation that a one-dimensional closed system of hard spheres with different masses exhibits equipartition. This is true even when the system contains as few as two particles or is nonergodic. Use of periodic boundary conditions gives very different results from the fixed boundaries. For more than two particles, it is shown that, for most mass ratios, the probability of an exact return to the initial state is vanishingly small. The density of states in momentum space accessible by a particular particle corresponds to a uniform density of states in the region allowed by conservation laws. There are special mass ratios for which ergodicity fails and recurrence occurs. Even for these nonergodic cases, equipartition is obtained. The free volume available to each particle is independent of its mass. These results are in contrast with numerous studies of systems using soft, anharmonic interactions and have implications regarding equipartition in molecular-dynamic simulations.

A binary mixture of hard-sphere polyions and monovalent point counterions is studied using the virial expansion (VEX) of the Ornstein-Zernike equation. The zero-order VEX term, which coincides with the symmetrized Poisson-Boltzmann equation (SPB), exhibits an attraction among polyions at sufficiently high temperatures and densities where the VEX convergence is fast. The linear VEX term intensifies this effect that may be explained using the suggestion that polyions interact via a screened potential of Jukawa type. A general solution of the linearized SPB (LSPB) is not represented by a single Debye-Hückel exponent and also exhibits an attraction. Within the SPB applicability region the LSPB and SPB provide similar results.

By means of computer simulations we investigate the dynamical behavior of a binary lattice-gas mixture with short-range interactions in order to provide a stringent test of mode-coupling theory (MCT). The dynamics of the particles is given by Monte Carlo–like moves that change the positions of the particles and binary collisions that change the velocities. By monitoring the self part of the van Hove correlation function we find the low-temperature dynamics to be glasslike. In accordance with MCT the imaginary part of the dynamic susceptibility χ’’ shows a well-defined α peak whose high-frequency wing follows a von Schweidler law with an exponent that is independent of temperature. The low-frequency wing of the peak follows a different power-law dependence that corresponds to a power law of the form -P+A/${\mathit{t}}^{\mathrm{\delta }}$ (A,P,δ>0) in the self part of the intermediate scattering function ${\mathit{F}}_{\mathit{s}1}$(k,t). In agreement with MCT we find that the diffusion constant for one of the two types of particles, the relaxation times of ${\mathit{F}}_{\mathit{s}1}$(k,t), the location of the α peak in the susceptibility, and the prefactor of the von Schweidler law all have a power-law dependence on temperature, (T-${\mathit{T}}_{\mathit{c}}$${)}^{\gamma }$, for T>${\mathit{T}}_{\mathit{c}}$ at constant density. As predicted by the theory the critical temperatures ${\mathit{T}}_{\mathit{c}}$ for the different quantities are the same within the statistical error. However, in contradiction to MCT, the critical exponents γ vary from one quantity to another.

The value of the Lamb-Mössbauer factor shows qualitatively the wave-vector dependence predicted by MCT. The self part of a second kind of correlation function exhibits the two power laws predicted by MCT for the high- and low-frequency wings of the β relaxation. We show that in the vicinity of the minimum of the susceptibility the scaling behavior predicted by MCT holds. However, the location of this minimum at a given temperature depends on the quantity investigated, contrary to the predictions of MCT. Moreover, the value of χ’’ at this minimum exhibits a power-law dependence on temperature with an exponent that is significantly larger than the one predicted by MCT. We also find that the height of the α peak as well as the total energy per particle have a power-law dependence on temperature and that the corresponding critical temperatures are close to those obtained for the other quantities.

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

We develop a theory that is nonperturbative and free of uncontrolled approximations to understand scaling behavior in turbulence. The main tool is a connection between the dimension of the graphs of the hydrodynamic fields and the scaling exponents of their structure functions. The connection is developed in some generality for both scalar and vector fields, in terms of the geometric invariants of the gradient tensor. We show that fluid mechanics is consistent with fractal graphs for both the scalar and the vector fields, and explain how this leads to the scaling behavior of the structure functions. We derive scaling relations between various scaling exponents, and show that in the case of ‘‘strong scaling’’ (which is defined below) the Kolmogorov solution is unique. Our theory allows additional solutions in which a weaker version of scaling results in a spectrum of scaling exponents. In particular, we identify the dimensionless (but Reynolds-number-dependent) contributions which can lead to deviations from the Kolmogorov exponents (which are derived using dimensional analysis). Results for the dimensions of fractal level sets in hydrodynamic turbulence which are measured in experiments and simulations follow immediately from this theory.

Experimental results on the evolution of induced patterns in Bénard-Marangoni convection are reported. These patterns are initially forced by means of a thermal technique which allows the formation of a regular hexagonal pattern with a chosen wavelength. Several series of measurements have been performed in square vessels with different aspect ratios Γ. For fixed Γ, after inducing a pattern with a wavelength different from the optimal one, an evolution is observed that leads to an evolving mean wavelength. The main mechanism for this evolution is the generation of defects which increase the disorder in the pattern. This disorder is mainly due to nucleation of new cells when the forced ones are too large, or by fusion of cells when the original ones are too small. Another interesting phenomenon occurs when the forced wavelength λ is close to the optimal one. In large-aspect-ratio vessels the disorder rises initially at the center of the pattern, leading to a relaxation of the mean wavelength. However, in small-aspect-ratio vessels, the behavior can be nonmonotonous. Under well-chosen conditions (the initial pattern has a mean wavelength slightly smaller than the optimal one), λ increases initially as a consequence of sidewall effects; then it decreases due to the rising and propagation of a dislocation line in the pattern. This evolution has a form similar to the creep function in a viscoelastic material. This effect seems to provide an effective wavelength selection mechanism. Using a Ginzburg-Landau model adapted to the hexagonal lattice, the relative importance of local wavelength variations, disalignment of polygon lines, defects, and sidewalls have been determined.

The initial bifurcations in rotating Rayleigh-Bénard convection are studied in the range of dimensionless rotation rate 0<Ω<2150 for a cylindrical cell with an aspect ratio of 2.5. We used simultaneous optical-shadowgraph, heat-transport, and local-temperature measurements to determine the stability and characteristics of the azimuthally periodic wall convection state. We also show that the second transition corresponds to the onset of bulk convection. Our results for critical Rayleigh numbers, precession frequencies, and critical mode numbers agree well with theoretical results. The dynamics of the wall convection state can be described by a complex Ginzburg-Landau amplitude equation.