Slow relaxation in a-diffusional model for granular compaction

We introduce and perform numerical simulations of a lattice model for the compaction of a granular system based on the ideas of random sequential adsorption and diffusional relaxation. The lattice is composed by a given number of horizontal layers where nonoverlapping particles diffuse. Besides diffusion within its own layer a particle suffers a downfall to the layer below whenever there is enough space there. We restrict ourselves to the case of one-dimensional layers and particles that occupy k consecutive sites. We observe time algebraic decay in the density of particles with exponents that are in several cases distinct from mean-field values.

Second-order deconfining transition in SU(2) lattice gauge theory and the continuum limit

In granular matter, consisting of discrete particles, long‐range interactions imply that each of the particles is interacting with all others. For many charged granular materials with Coulomb repulsion or large‐scale gravitationally attractive systems, a Molecular Dynamics environment is developed. In granular systems with long‐range interaction forces and dissipative collisions, both effects can lead to large‐scale structure formation, whereas already dissipation alone leads to ever growing clusters. For our three‐dimensional mono‐charged dissipative homogeneous systems we present the effect of both repulsive and attractive mutual long‐range forces and make an attempt to predict the collision frequency and the temperature decay in the system by means of a modified pseudo‐Liouville operator formalism. The theoretical predictions are in perfect agreement with the simulations, but only in the limit of low density and for not too strong interaction potential enrgy.

An ideal gas is a particular molecular model system consisting of independent molecules without intermolecular forces and without volume. The molecules of an ideal gas are thus point particles, which are, when belonging to the same chemical compound, indistinguishable. Such a model system cannot exist in reality. However, in the limit of very low density the molecules of real a gas are, on the average, so far apart from each other that the forces between them and their volumes have no influence on some of the thermodynamic properties of the system. We may, therefore, expect that at least some aspects of thermodynamic behavior of real gases in the limit of low density are accurately described by the ideal gas model.

We obtain long series (28 terms or more) for the coverage (occupation fraction) $\theta$, in powers of time $t$ for two models of random sequential adsorption with diffusional relaxation using an efficient algorithm developed by the authors. Three different kinds of analyses of the series are performed for a wide range of $\gamma$, the rate of diffusion of the adsorbed particles, to investigate the power law approach of $\theta$ at large times. We find that the primitive series expansions in time $t$ for $\theta$ capture rich short and intermediate time kinetics of the systems very well. However, we see that the series are still not long enough to extract the kinetics at large times for general $\gamma$. We have performed extensive computer simulations employing an efficient event-driven algorithm to confirm the $t^{-1/2}$ saturation approach of $\theta$ at large times for both models, as well as to investigate the short and intermediate time behaviors of the systems.

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS–NO). The system considered exhibits interesting multicritical behaviour including tricritical points.

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach (VA), which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case shows that the system can exhibit not only the homogeneous phases—superconducting (SS) and non-ordered (NO)—but also the phase separated states (PS: SS–NO). Depending on the values of interaction parameters, the PS state can occur in higher fields than the SS phase (field induced PS). Some ground state results beyond the VA are also presented.

In the Yule-Simon process, creation and selection of words follows the preferential attachment mechanism, resulting in a power-law growth in the cumulative number of individual word occurrences as well as the power-law population distribution of the vocabulary. This is derived using mean-field approximation, assuming a continuum limit of both the time and number of word occurrences. However, time and word occurrences are inherently discrete in the process, and it is natural to assume that the cumulative number of word occurrences has a certain fluctuation around the average behavior predicted by the mean-field approximation. We derive the exact and approximate forms of the probability distribution of such fluctuation analytically, and confirm that those probability distributions are well supported by the numerical experiments.

Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator–prey systems. In the mean-field rate equation approximation, the classic Lotka–Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochastic two-species predator–prey reaction systems on regular lattices display complex spatio-temporal structures associated with persistent erratic population oscillations. The Doi–Peliti path integral representation of the master equation for stochastic particle interaction models is utilized to arrive at a field theory action for spatial Lotka–Volterra models in the continuum limit. In the species coexistence phase, a perturbation expansion with respect to the nonlinear predation rate is employed to demonstrate that spatial degrees of freedom and stochastic noise induce instabilities toward structure formation, and to compute the fluctuation corrections for the oscillation frequency and diffusion coefficient. The drastic downward renormalization of the frequency and the enhanced diffusivity are in excellent qualitative agreement with Monte Carlo simulation data.

Random sequential adsorption (RSA) models have been studied due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated, in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case to the power law behavior in the continuum deposition. 2D lattice and continuum simulations rule out some "exact" conjectures for the jamming coverage. For the deposition of dimers on a 1D lattice with diffusional relaxation we find that the limiting coverage (100%) is approached according to the ~1/t**0.5 power-law preceded, for fast diffusion, by the mean-field crossover regime with the intermediate ~1/t behavior. In case of k-mer deposition (k>3) with diffusion the void fraction decreases according to the power-law t**[-1/(k-1)]. In the case of RSA of lattice hard squares in 2D with diffusional relaxation the approach to the full coverage is ~t**(-0.5).

String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. Using for concreteness the three-dimensional fundamental case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when deduced from the mean magnetic field inside a flat contour (the derivation of this field is also presented). Moreover, the obtained theory enables one to find also the coupling constants of terms in the expansion of the nonlocal string effective action, which are higher in the derivatives than the Nambu-Goto term (some of these terms vanish at the flat surface). In the four-dimensional case with the theta-term, the critical values of the theta-parameter, at which the problem of crumpling of large world sheets might be solved, are found in both the fundamental case and in the large-N limit of the adjoint case. These values are only accessible provided the electric coupling constant is larger than a certain value, in accordance with the known fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.

The normalized emission spectrum of the Li(2p−2s) resonance transition has been measured in the presence of 10–1000 Torr of noble gas. Fluorescence at 100–3000 Å from the atomic line, due to the A–X and B–X bands of Li–noble gas molecules, has been measured as a continuum with 1.5 nm resolution. The lithium is optically excited in a 670 °K cell. The lithium is optically thin (∼10−6 Torr) so that the continuum emission per excited lithium atom is obtained from the normalized emission. The attractive A-state potentials for Li–Ar, Kr, and Xe have been constructed by analysis of the A–X band spectra in the limit of high and low noble-gas densities. At high densities each spectrum is due to an equilibrated vibrational distribution of A-state molecules, whereas at low densities only free collision states contribute. The ratio of the two spectra thus depends on the excited state potential and has been used to determine this potential where it is attractive. Absorption and stimulated emission coefficients for Li–noble gas vapors are also deduced from the data.

A comprehensive characterisation of cold molecular beams from a cryogenic buffer-gas cell, providing insight into the physics of buffer-gas cooling, is presented. Cold molecular beams are extracted from a cryogenic cell by electrostatic guiding, which is also used to measure their velocity distribution. The rotational-state distribution of the molecules is probed by radio-frequency resonant depletion spectroscopy. With the help of complete trajectory simulations, yielding the guiding efficiency for all of the thermally populated states, it is possible to determine both the rotational and the translational temperature of the molecules at the output of the buffer-gas cell. This thermometry method is demonstrated for various regimes of buffer-gas cooling and beam formation as well as for molecular species of different sizes (CH3 F and CF3 CCH). Comparison of the rotational and translational temperatures provides evidence of faster rotational thermalisation for the CH3 F/He system in the limit of low He density. In addition, the relaxation rates for different rotational states appear to be different.

The anomalous dimension of the lattice London superconductor is determined from finite-size scaling of the susceptibility to be ηϕ = − 0.79(1). It is furthermore found that the vanishing of the vortex loop line tension in the 3D XY model, which should be related to that exponent, agrees reasonable well with this value of ηϕ. Deviations from this behavior are however also identified and it is suggested that they are an effect of the vortex loop intersections and therefore will vanish only in the limit of low vortex density.

This paper analyzes the effects of the catalyst layer porous structure on the performances of polymer electrolyte membrane fuel cells. Comparing the characteristic lengths of the porous structure with the characteristic lengths of the diffusion phenomena shows that the oxygen and hydrogen concentrations in the electrolyte phase change significantly at the pore scale level; therefore, the related diffusion phenomena need a nonhomogeneous description. These rapidly varying concentrations are coupled to the cell potentials through the reaction rate expression, i.e., the Butler-Volmer equation. Thus, to employ a macrohomogeneous description of the fuel cell without loss of accuracy, it is necessary to find an effective expression for the reaction rate which does not depend explicitly on the rapidly varying concentrations. This is done here through an analytical averaging procedure and results in an effective Butler-Volmer expression that includes implicitly the effects of nonhomogeneity of the porous structure. This expression is compared with the ordinary Butler-Volmer expression and with the agglomerate models in the literature. The former turns out to be valid only in the limit of low current densities, and the latter only in the high porosity limit. Finally, the effective Butler-Volmer expression is inserted in the framework of macrohomogeneous models. From the analysis of the model results, one can conclude that the effects of the porous structure on the cell performances are crucial for the correct description of the cell concentration polarization and the estimation of the effective Tafel slope at high current densities. © 2003 The Electrochemical Society. All rights reserved.