A dynamical network (consisting of a time-evolving wiring of interactions among a group of random walkers) is introduced to model the spread of an infectious disease in a population of mobile individuals. We investigate the main properties of this model, and show that peculiar features arise when individuals are allowed to perform long-distance jumps. Such peculiarities are captured and conveniently quantified by a series of appropriate parameters able to highlight the structural differences emerging in the networks when long-distance jumps are combined with local random walk processes.

Thermoemission plasma—i.e., a system consisting of dust grains and electrons—is studied. In the proposed model, it is assumed that the major part of the electronic gas is uniformly distributed in space and the spatial inhomogeneities of electronic density exist only near the dust grains. The experimental data, well described by the proposed theory, are given.

A methodology is proposed that pushes the thermodynamic perturbation theory (TPT) from first order to higher order. The second-order correction is superior to a macroscopic compressibility (MC) approximation of Barker and Henderson. The present third-order TPT performs far better than the original first-order TPT and second-order TPT based on the MC approximation for many subfields in fluid statistical mechanics, such as predicting excess Helmholtz free energy, excess chemical potential, bulk pressure, gas-liquid coexistence, and solid-liquid equilibrium of very short-range potential fluids. A nonuniform version of the TPT is proposed; it is also shown that the nonuniform third-order TPT performs far better than the nonuniform first-order TPT in predicting density profile of fluids in critical region. The present report indicates that the TPT still can be a “universal” and accurate theoretical tool that has general applicability in fluid statistical mechanics, especially in soft-matter physics.

Mean squared displacements and velocity auto correlation functions are calculated using molecular dynamics for hard spheres under a range of conditions (i) for the equilibrium fluid below freezing; (ii) for the metastable fluid above freezing; and (iii) for the hard sphere crystal, both in the metastable region between freezing and melting, and in the stable region above melting. In addition, simulations are carried out for a metastable Lennard-Jones system. The results confirm recent studies that indicated the disappearance of the classical Alder long-time tail, and show that they apply to systems other than the metastable hard sphere fluid. The implications of these results for our understanding of crystallization and the glass transition are discussed.

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

In a rotating tumbler that is more than one-half filled with a granular material, a core of material forms that should ideally rotate with the tumbler. However, the core rotates slightly faster than the tumbler (precession) and decreases in size (erosion). The precession and erosion of the core provide a measure of the creeping granular motion that occurs beneath a continuously flowing flat surface layer. Since the effect of gravity on the subsurface flow has not been explored, experiments were performed in a 63% to 83% full granular tumbler mounted in a large centrifuge that can provide very high $g$-levels. Two colors of $0.5\mathrm{mm}$ glass beads were filled side by side to mark a vertical line in the $45\mathrm{mm}$ radius quasi-two-dimensional tumbler. The rotation of the core with respect to the tumbler (precession) and the decrease in the size of the core (erosion) were monitored over 250 tumbler revolutions at accelerations between $1g$ and $12g$. The flowing layer thickness is essentially independent of the $g$-level for identical Froude numbers, and the shear rate in the flowing layer increases with increasing $g$-level. The degree of core precession increases with the $g$-level, while the core erosion is essentially independent of the $g$-level. Based on a theory for core precession and erosion, the increased precession is likely a consequence of the higher shear rate. Core erosion, on the other hand, is related to the creep region decay constant, which is connected with slow diffusion in the bed and unaffected by gravity.

Random processes are generally described by Gaussian statistics as formulated by the central limit theorem. However, there exists a large number of exceptions to this rule that can be found in a variety of fields. Diffusion processes are often analyzed by the scaling law $⟨r^2⟩\sim t^{2\beta }$, where the second moment of the diffusion propagator or molecular mean square displacement, $⟨r^2⟩$, in the case of Gaussian diffusion is proportional to $t$, i.e., $\beta =1∕2$. A deviation from Gaussian behavior may be either superdiffusion $(\beta >1∕2)$ or subdiffusion $(\beta <1∕2)$. In this paper we demonstrate that all three diffusion regimes may be observed for the surfactant self-diffusion, on the length scale of ${10}^{-6}\mathrm{m}$ and the time scale of $0.02–0.8\mathrm{s}$. in a system of wormlike micelles, depending on small variations in the sample composition. The self-diffusion is followed by pulsed gradient NMR where one not only measures the second moment of the diffusion propagator, but actually measures the Fourier transform of the full diffusion propagator itself. A generalized diffusion equation in terms of fractional time derivatives provides a general description of all the different diffusion regimes, and where $1∕\beta$ can be interpreted as a dynamic fractal dimension. Experimentally, we find $\beta =1∕4$ and $3∕4$, in the regimes of sub- and superdiffusion, respectively. The physical interpretation of the subdiffusion behavior is that the dominating diffusion mechanism corresponds to a lateral diffusion along the contour of the wormlike micelles. Superdiffusion is obtained near the overlap concentration where the average micellar size is smaller so that the center of mass diffusion of the micelles contributes to the transport of surfactant molecules.

We present the experimental observation of multiple resonance transport of light waves, due to necklace states, in disordered one-dimensional systems. Transmission phase measurements allow us to identify these states unambiguously and investigate their statistical properties. A theoretical model is developed to describe the resonance statistics and the frequency dependance of the localization length.

A one-dimensional network on which there are long-range bonds at lattice distances $l>1$ with the probability $P\left(l\right)\propto l^{-\delta }$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbors apart from their nearest neighbors for $0⩽\delta <2$. It is observed that there is a finite temperature phase transition in the entire range. For $0⩽\delta <1$, finite-size scaling behavior of various quantities are consistent with mean-field exponents while for $1⩽\delta ⩽2$, the exponents depend on $\delta$. The results are discussed in the context of earlier observations on the topology of the underlying network.

In an earlier paper [Nichol et al., Phys. Rev. E, 70, 056307 (2004)] some of the present authors presented the results of an experimental study of the dynamics of a stretched grid driven into vibration at or near its resonant frequency in isotopically pure superfluid ${}^4\mathrm{He}$ over a range of pressures at a very low temperature, where the density of normal fluid is negligible. In this paper we present the results of a similar study, based on a different grid, but now including the temperature range where the normal fluid density is no longer insignificant. The new grid is very similar to the old one except for a small difference in the character of its surface roughness. In many respects the results at low temperature are similar to those for the old grid. At low amplitudes the results are somewhat history dependent, but in essence there is no damping greater than that in vacuo. At a critical amplitude corresponding to a velocity of about $50\mathrm{mm}{\mathrm{s}}^{-1}$ there is a sudden and large increase in damping, which can be attributed to the generation of new vortex lines. Strange shifts in the resonant frequency at intermediate amplitudes observed with the old grid are no longer seen, however they must therefore have been associated with the different surface roughness, or perhaps were due simply to some artifact of the old grid, the details of which we are currently unable to determine. With the new grid we have studied both the damping at low amplitudes due to excitations of the normal fluid, and the dependence of the supercritical damping on temperature. We present evidence that in helium at low amplitudes there may be some enhancement in the effective mass of the grid in addition to that associated with potential flow of the helium. In some circumstances small satellite resonances are seen near the main fundamental grid resonance, which are attributed to coupling to some other oscillatory system within the experimental cell.

We use optical interferometry to investigate ultrafast ionization induced by an intense, ultrashort laser pulse propagating in a helium gas. Besides standard phase shift information, our interferograms show a localized region of fringe visibility depletion (FVD) that moves along the laser propagation axis at luminal velocity. We find that such a loss of visibility can be quantitatively explained by the ultrafast change of refractive index due to the field ionization of the gas in the laser pulse width. We demonstrate that by combining the post facto phase shift distribution with the probe pulse transit effect in the ionizing region, the analysis of the observed FVD yields significant information on the ultrafast dynamics of propagation of the ionization front in the gas.

The flow of granular material in rotating tumblers is confined to a thin flowing layer at the free surface in which the particle velocity is primarily streamwise, perpendicular to the axis of rotation, with minimal axial motion. Particle tracking velocimetry was used to measure the surface velocity for 1 and $2\mathrm{mm}$ glass particles and sand in cylindrical tumblers of various diameters, lengths, and rotation rates for a flat continuously flowing surface. End-wall friction slows the streamwise surface velocity adjacent to the walls, yet material just inward from the end wall flows faster than the material in the center of a long tumbler. An axial velocity occurs near the end walls both upstream and downstream of the midlength of the flowing layer. Increasing the tumbler diameter and corresponding flowing layer length causes the magnitude of the axial and streamwise velocity components, as well as the axial thickness of the end-wall region, to increase. An increase of end-wall friction slows particles directly adjacent to the end wall, further enhancing the axial flow near the end wall. Increasing the rotation rate, while still maintaining a flat continuously flowing surface, causes a corresponding increase in both the streamwise and axial velocities in the tumbler. The boundary flow effects are localized to end walls when the axial length of the tumbler $\left(L\right)$ is greater than the diameter $\left(D\right)$, so that the flow in the center region of the tumbler is independent of the end walls and hence similar to the conditions at the center of an infinitely long tumbler. Decreasing the axial length of the tumbler so that $L∕D<1$ causes the axial velocity to decrease as the regions affected by the end walls merge. This also leads to a streamwise velocity in quasi-two-dimensional tumblers that can be more than twice that at the center of three-dimensional tumblers.

We use a combined phase-field–lattice-Boltzmann scheme [Medvedev and Kassner, Phys. Rev. E 72, 056703 (2005)] to simulate nonfaceted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Péclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Péclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane of undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favor of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.

Null transmission ellipsometry has been employed to study the molecular arrangements in freestanding films of two no-layer-shrinkage liquid crystal homologous compounds above the bulk smectic $A$–smectic $C^{*}$ (Sm $C^{*}$) transition temperature. An unusual nonplanar-parallel or nonplanar-antiparallel-parallel transition has been observed in both compounds under a proper electric field. With the addition of one ${\mathrm{CH}}_2$ group, while the $\mathrm{Sm}{C}^{*}$ phase is more stable thermally, the magnitude of the critical field needed to induce a parallel-antiparallel transition decreases dramatically.

Numerical simulations of the recently derived fully nonlinear equations of motion for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)] with quasirandom initial conditions are reported, which show the spontaneous formation of a single extreme wave on deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.

An elementary hydrodynamic and Brownian motion model of the thermal diffusivity $D_T$ of a restricted class of binary liquid mixtures, previously proposed by the author, is given a more transparent derivation than originally, exposing thereby the strictly kinematic-hydrodynamic nature of an important class of thermodiffusion separation phenomena. Moreover, it is argued that the solvent’s thermometric diffusivity $\alpha$ appearing in that theory as one of the two fundamental parameters governing $D_T$ should be replaced by the solvent’s (isothermal) self-diffusivity $D_S$. In addition, a corrective multiplier of $O\left(1\right)$ is inserted to reflect the general physicochemical noninertness of the solute relative to the solvent, thus enhancing the applicability of the resulting formula $D_T=\lambda D_S\beta$ to “nonideal” solutions. Here, $\beta$ is the solvent’s thermal expansivity and $\lambda$ is a term of $O\left(1\right)$, insensitive to the physicochemical nature of the solute (thus rendering $D_T$ primarily dependent upon only the properties of the solvent). This formula is, on the basis of its derivation, presumably valid only under certain idealized, albeit well-defined, circumstances. This occurs when the solute molecules are: (i) large compared with those of the solvent; and (ii) present only in small proportions relative to those of the solvent. When the solute is physicochemically inert, it is expected that $\lambda =1$. When these conditions are met, the resulting thermal diffusivity of the mixture is, in theory, independent of any and all properties of the solute. Moreover, because $\beta$ is algebraically signed, the thermal diffusivity can either by positive or negative, according as the solvent expands or contracts upon being heated. This formula for $D_T$ is compared with available experimental data for selected binary liquid mixtures. Reasonable agreement is found in almost all circumstances with $\lambda$ near unity, the more so the higher the temperature, especially when the solute-solvent mixture properties closely approximate those where agreement would be expected and conversely. Finally, it is pointed out that for the restricted circumstances described, the formula $D_T=\lambda D_S\beta$ is equally credible for gases. Here, based on gas-kinetic theory, it is possible to furnish the theoretical value of $\lambda$. Overall, while spanning a range of about five orders of magnitude, the $D_T$ values given by this elementary formula are shown to apply with reasonable accuracy to: (i) liquids (including circumstances for which $D_T$ is negative) as well as gases; (ii) all combinations of solvents and solutes tested (the latter including, for example, polymer molecules and metallic colloidal particles); and (iii) all sizes of solute molecules, from angstroms to submicron.

A class of symplectic algorithms is introduced to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an advanced gradientlike decomposition approach. Its main advantage over the standard gradient scheme is the avoidance of time-consuming evaluations of force gradients by force extrapolation without any loss of precision. As a result, the efficiency of the integration improves significantly. The algorithms obtained are analyzed and optimized using an error-function theory. The best among them are tested in actual molecular dynamics and celestial mechanics simulations for comparison with well-known nongradient and gradient algorithms such as the Störmer-Verlet, Runge-Kutta, Cowell-Numerov, Forest-Ruth, Suzuki-Chin, and others. It is demonstrated that for moderate and high accuracy, the extrapolated algorithms should be considered as the most efficient for the integration of motion in molecular dynamics simulations.

We propose a simulation method which can be used to readily parallelize simulations on systems with a large spatial extent. We simulate small parts of the system with independent molecular dynamics simulations, and only occasionally pass information between them through a constitutive model free continuum approach. We illustrate the power of this method in the case of a polymeric fluid undergoing rapid one-dimensional shear flow. Since we show that this flow problem cannot be modeled by using a steady-state constitutive model, this method offers the unique capability for accessing the nonlinear viscoelasticity of complex fluids.

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $\gamma$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for $\gamma <3$. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for $\gamma >3$. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

Bulk dissipation of a sandpile on a square lattice with the periodic boundary condition is investigated through a dissipating probability $f$ during each toppling process. We find that the power-law behavior is broken for $f>{10}^{-1}$ and not evident for ${10}^{-1}>f>{10}^{-2}$. In the range ${10}^{-2}\ge f\ge {10}^{-5}$, numerical simulations for the toppling size exponents of all, dissipative, and last waves have been studied. Two kinds of definitions for exponents are considered: the exponents obtained from the direct fitting of data and the exponents defined by the simple scaling. Our result shows that the exponents from these two definitions may be different. Furthermore, we propose analytic expressions of the exponents for the direct fitting, and it is consistent with the numerical result. Finally, we point out that small dissipation drives the behavior of this model toward the simple scaling.