The linear stability of cylindrical Couette flow of an electrically conducting fluid in the presence of an axial magnetic field is examined, where the magnetic field has a small oscillatory component imposed on a steady value. The effect of the field modulation on the threshold of instability is studied for different values of gap width, Chandrasekhar number, magnetic Prandtl number, and oscillation frequency. Modulation is found to have a stabilizing effect for low values of the Chandrasekhar number, a destabilizing effect for intermediate values, and again a stabilizing effect for still higher values of the Chandrasekhar number. The effect of modulation is found to be almost independent of the magnetic Prandtl number and the modulation frequency.

Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system and find excellent agreement with our analytic results.

The quasistatic behavior of a simple two-dimensional model of a cohesive powder under isotropic loads is investigated by discrete element simulations. We ignore contact plasticity and focus on the effect of geometry and collective rearrangements on the material behavior. The loose packing states, as assembled and characterized in a previous numerical study [Gilabert, Roux, and Castellanos, Phys. Rev. E 75, 011303 (2007)], are observed, under growing confining pressure $P$, to undergo important structural changes, while solid fraction $\Phi$ irreversibly increases (typically, from 0.4–0.5 to 0.75–0.8). The system state goes through three stages, with different forms of the plastic consolidation curve, i.e., $\Phi$ as a function of the growing reduced pressure $P^{*}=Pa∕F_0$, defined with adhesion force $F_0$ and grain diameter $a$. In the low-confinement regime (I), the system undergoes negligible plastic compaction, and its structure is influenced by the assembling process. In regime II the material state is independent of initial conditions, and the void ratio varies linearly with $\ln P$ [i.e., $\Delta (1∕\Phi )=\lambda \Delta \left(\ln P^{*}\right)$], as described in the engineering literature. Plasticity index $\lambda$ is reduced in the presence of a small rolling resistance (RR). In the last stage of compaction (III), $\Phi$ approaches an asymptotic, maximum solid fraction ${\Phi }_{\max }$, as a power law ${\Phi }_{\max }-\Phi \propto {\left(P^{*}\right)}^{-\alpha }$, with $\alpha \simeq 1$, and properties of cohesionless granular packs are gradually retrieved. Under consolidation, while the range $\xi$ of fractal density correlations decreases, force patterns reorganize from self-balanced clusters to force chains, with correlative evolutions of force distributions, and elastic moduli increase by a large amount. Plastic deformation events correspond to very small changes in the network topology, while the denser regions tend to move like rigid bodies. Elastic properties are dominated by the bending of thin junctions in loose systems. For growing RR those tend to form particle chains, the folding of which, rather than tensile ruptures, controls plastic compaction.

Changes in the resonant frequency $\Delta f$ and the dissipation factor $\Delta D$ of a quartz crystal microbalance due to adsorption of molecules onto the electrode surface in solutions at different concentrations have been numerically analyzed. It has been found that the contribution from the solution due to the variation of the concentration can mask the overall behaviors of the $\Delta f$ and $\Delta D$ isotherms. However, if the solution is sufficiently dilute or the contribution of the solution can be characterized accurately, the corrected $\Delta f$ and $\Delta D$, as a function of the solution concentration, will reveal characteristic features of the adsorption processes for the adsorbed films. Specifically, steplike behaviors will be displayed in $\Delta f$ isotherms, which correspond to layer formation and layer-by-layer growth of the films, but the onsets of the steps usually do not coincide with the layer completion. Oscillatory behaviors will be revealed in $\Delta D$ isotherms if the adsorbed molecular layer is soft at low concentration and becomes rigid near layer completion.

We study the statistical properties of the total work associated with the Langevin equation for an electrically charged Brownian particle in a two-dimensional harmonic trap and in the presence of a uniform magnetic field. The calculations are performed under the overdamped approximation. The center of the harmonic trap is dragged in an arbitrary time-dependent way. As a result we have found the relation of the averaged work and the variance in the work distribution in the presence of the magnetic field. In addition, the Jarzynski equality (JE) is considered when the potential associated with the working force contains a time-dependent term, giving a way to calculate the change in the free energy. The particular cases in Jayannavar and Sahoo’s work [Phys. Rev. E 75, 032102 (2007)] and their use of the JE are also discussed.

This study revisits the problem of advective transfer and spectra of a diffusive scalar field in large-scale incompressible flows in the presence of a (large-scale) source. By “large scale” it is meant that the spectral support of the flows is confined to the wave-number region $k<k_d$, where $k_d$ is relatively small compared with the diffusion wave number $k_{\kappa }$. Such flows mediate couplings between neighboring wave numbers within $k_d$ of each other only. It is found that the spectral rate of transport (flux) of scalar variance across a high wave number $k>k_d$ is bounded from above by $U{k}_{d}k\Theta (k,t)$, where $U$ denotes the maximum fluid velocity and $\Theta (k,t)$ is the spectrum of the scalar variance, defined as its average over the shell $(k-k_d,k+k_d)$. For a given flux, say $\vartheta >0$, across $k>k_d$, this bound requires $\Theta (k,t)⩾(\vartheta ∕U{k}_d)k^{-1}$. This is consistent with recent numerical studies and with Batchelor’s theory that predicts a $k^{-1}$ spectrum (with a slightly different proportionality constant) for the viscous-convective range, which could be identified with $(k_d,k_{\kappa })$. Thus, Batchelor’s formula for the variance spectrum is recovered by the present method in the form of a critical lower bound. The present result applies to a broad range of large-scale advection problems in space dimensions $⩾2$, including some filter models of turbulence, for which the turbulent velocity field is advected by a smoothed version of itself. For this case, $\Theta (k,t)$ and $\vartheta$ are the kinetic energy spectrum and flux, respectively.

We describe the motion of an asymmetric dimer across a horizontal surface when exposed to an oscillatory fluid flow. The dimer consists of two spheres of distinct sizes, rigidly attached to each other. The dimer is found to move in a direction perpendicular to the fluid flow, with the smaller sphere foremost. We have determined how the speed depends upon the vibratory conditions, on the fluid viscosity, and on the dimer size and aspect ratio. Computer simulations are used to give an insight into the mechanism responsible for the motion. We use a scaling argument based on the asymmetry of the streaming flow to predict the approximate dependence of the migration speed on the system parameters.

We investigate the dynamics of a thin liquid film on an inclined planar substrate in the presence of an insoluble surfactant on its free surface. We consider both the linear and nonlinear regimes. The linear regime is examined through the Orr-Sommerfeld eigenvalue problem of the full Navier-Stokes and concentration equations and wall and free-surface boundary conditions. The nonlinear regime is investigated through two different models. The first one is obtained from the classical long-wave expansion and the second one through an integral-boundary-layer approximation combined with a simple Galerkin projection. Although accurate close to the instability threshold, the first model fails to describe the dynamics of the system far from criticality. On the other hand, the second model not only captures accurately the behavior close to the instability threshold, but is also valid far from criticality. Analytical and numerical results on the role of the surfactant on the free-surface dynamics are presented. In the linear regime, the Marangoni stresses induced by the surfactant reduce the domain of instability for the base flow. In the nonlinear regime, the system evolves into solitary pulses for both the free surface and surfactant concentration. The amplitude and velocity of these pulses decrease as the Marangoni effect becomes stronger.

We perform a direct numerical simulation (DNS) of forced homogeneous isotropic turbulence with a passive scalar that is forced by mean gradient. The DNS data are used to study the properties of subgrid-scale flux of a passive scalar in the framework of large eddy simulation (LES), such as alignment trends between the flux, resolved, and subgrid-scale flow structures. It is shown that the direction of the flux is strongly coupled with the subgrid-scale stress axes rather than the resolved flow quantities such as strain, vorticity, or scalar gradient. We derive an approximate transport equation for the subgrid-scale flux of a scalar and look at the relative importance of the terms in the transport equation. A particular form of LES tensor-viscosity model for the scalar flux is investigated, which includes the subgrid-scale stress. Effect of different models for the subgrid-scale stress on the model for the subgrid-scale flux is studied.

We present a general and unifying framework for deriving Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework yields uniform sampling rules for thermodynamic states given by the mechanically extensive variables appearing in the Hamiltonian. Likewise, Monte Carlo schemes which uniformly sample the thermodynamic fields that are conjugate to the mechanical variables can be derived within this framework. We apply these different, yet equivalent sampling schemes to the extended Hubbard model in the atomic limit with explicit electron spin. Results for the full density-of-states, the charge-order parameter distribution, and phase diagrams for different ratios of the on-site Hubbard repulsion and the intersite interaction are presented. A tricritical point at half-filling of the lattice is located using finite-size scaling techniques.

We carry out a theoretical investigation of the evolution of a wetting film formed by pressing a bubble against a solid substrate. Our model incorporates the effects of capillarity and Derjaguin-Landau-Verwey-Overbeek (DLVO) (van der Waals and electrostatic) components of the disjoining pressure. Rapid changes in the relative position of the bubble and the substrate are shown to result in surprisingly rich dynamics of wetting film deformations. Even for stable films, we find transient rippled deformations with several points of local maximum of wetting film thickness and discuss how their evolution depends on changes in the meniscus position relative to the substrate and the disjoining pressure parameters. A connection is made to the recently reported experimental observations of one such rippled deformation, the so-called wimple, characterized by a local minimum of the thickness in the center, surrounded by a ring of greater film thickness and bounded at the outer edge by the barrier rim. Guidelines are provided for experimental detection of more complex rippled deformations in stable wetting films. Development of instability is studied in a situation when the electrostatic component of disjoining pressure is destabilizing, with particular emphasis on the nonlinear evolution and rupture of the film. Potential applications of our findings to small-scale mixing and deposition of nanoparticles are discussed.

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

The environment inside a living cell is dramatically different from that found in in vitro models, presenting a problem for computational models of biochemistry that are only beginning to capture these differences. This deviation between idealized in vitro models and more realistic intracellular conditions is particularly problematic for models of molecular self-assembly, but also specifically hard to address because the large sizes and long assembly times of biological self-assembly systems force the use of highly simplified models. We have developed a prototype of a molecular self-assembly simulator based on the Green’s function reaction dynamics (GFRD) model to achieve more realistic models of assembly in the crowded conditions of the cell without unduly sacrificing tractability. We tested the model on a simple representation of dimer assembly in a two-dimensional space. Our simulations verify that the model is computationally efficient, provides a realistic quantitative model of reaction kinetics in uncrowded conditions, and exhibits expected excluded volume effects under conditions of high crowding. This work confirms the effectiveness of the GFRD technique for more realistic coarse-grained modeling of self-assembly in crowded conditions and helps lay the groundwork for exploring the effects of in vivo crowding on more complex assembly systems.

We demonstrate experimental evidence of noise-induced attractor hopping in a multistable fiber laser. Multistate hopping dynamics displays complex statistical properties characterized by nontrivial scalings. When hopping is encountered between two states, the dynamics of the system is characterized by the $-3∕2$ power law for the probability distribution of periodic windows versus their length, just as in the case of two-state on-off intermittency. A surprising noise saturation effect is found: average output noise in the hopping regime is almost independent of input noise. Such robustness of the system against external noise may be beneficial for some applications: for example, for communications with multistable systems or for designing noise-insensitive detectors.

Localized states in out of equilibrium one-dimensional systems are described by the homoclinic snaking associated with the infinite sequence of multibump localized solutions of the corresponding time reversible dynamical system. We show that when the pattern undergoes a saddle-node bifurcation the homoclinic snaking bifurcation diagram becomes slanted and a finite set of localized states continue to exist outside the region of bistability. This generic behavior offers a local theory resolution of the discrepancy between models and experiments.

We study the chaotic properties of steady-state traveling-wave solutions of the particle number density of a Bose-Einstein condensate with an attractive interatomic interaction loaded into a traveling optical lattice of variable shape. We demonstrate theoretically and numerically that chaotic traveling steady states can be reliably suppressed by small changes of the traveling optical lattice shape while keeping the remaining parameters constant. We find that the regularization route as the optical lattice shape is continuously varied is fairly rich, including crisis phenomena and period-doubling bifurcations. The conditions for a possible experimental realization of the control method are discussed.

An interesting question in turbulent convection is how the heat transport depends on the strength of thermal forcing in the limit of very large thermal forcing. Kraichnan predicted [Phys. Fluids 5, 1374 (1962)] that for fluids with low Prandtl number (Pr), the heat transport measured by the Nusselt number (Nu) would depend on the strength of thermal forcing measured by the Rayleigh number (Ra) as $\mathrm{Nu}\sim {\mathrm{Ra}}^{1∕2}$ with logarithmic corrections at very high Ra. According to Kraichnan, the shear boundary layers play a crucial role in giving rise to this so-called ultimate-state scaling. A similar scaling result is predicted by the Grossmann-Lohse theory [J. Fluid Mech. 407, 27 (2000)], but with the assumption that the ultimate state is a bulk-dominated state in which both the average kinetic and thermal dissipation rates are dominated by contributions from the bulk of the flow with the boundary layers either broken down or playing no role in the heat transport. In this paper, we study the dependence of Nu and the Reynolds number (Re) measuring the root-mean-squared velocity fluctuations on Ra and Pr, for low Pr, using a shell model for homogeneous turbulent convection where buoyancy is acting directly on most of the scales. We find that $\mathrm{Nu}\sim {\mathrm{Ra}}^{1∕2}{\mathrm{Pr}}^{1∕2}$ and $\mathrm{Re}\sim {\mathrm{Ra}}^{1∕2}{\mathrm{Pr}}^{-1∕2}$, which resemble the ultimate-state scaling behavior for fluids with low Pr, and show that the presence of a drag acting on the large scales is crucial in giving rise to such scaling. As a large-scale drag cannot exist by itself in the bulk of turbulent thermal convection, our results indicate that if buoyancy acts on most of the scales in the bulk of turbulent convection at very high Ra, then the ultimate state cannot be bulk dominated.

A comprehensive study is made of the energy relaxation rates between ions and electrons in a dense hydrogen plasma. Results of classical molecular dynamics (MD) simulations are compared with quantal calculations using the Fermi golden rule and using dimensional continuation. The rates from the molecular dynamics simulations employing a screened potential are found to be in reasonable agreement with the Landau-Spitzer relaxation rates, and are around 30% higher than the Fermi golden rule rates. By inverting the classical MD relaxation rate vs the quantal result, a semiclassical value for the screening length is suggested. We present energy relaxation rates relevant for radiation-hydrodynamic simulations of inertial confinement fusion devices.

We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability $p$; namely, at any instance of time, with probability $p$ a regular link is switched to a random one. In a range of weak coupling, where spatiotemporal chaos exists for regular lattices (i.e., for $p=0$), we find that $p>0$ yields synchronized periodic orbits. Further, we observe that this regularity occurs over a window of $p$ values, beyond which the basin of attraction of the synchronized cycle shrinks to zero. Thus we have evidence of an optimal range of randomness in coupling connections, where spatiotemporal regularity is efficiently obtained. This is in contrast to the commonly observed monotonic increase of synchronization with increasing $p$, as seen, for instance, in the strong-coupling regime of the very same system.