The influence of a stationary shear flow on the crystallization in a glassy system is studied by means of molecular dynamics simulations and subsequent cluster analysis. The results reveal two opposite effects of the shear flow on the processes of topological ordering in the system. Shear promotes the formation of separated crystallites and suppresses the appearance of the large clusters. The shear-induced ordering proceeds in two stages, where the first stage is related mainly to the growth of crystallites and the second stage is due to an adjustment of the created clusters and a progressive alignment of their lattice directions. The influence of strain and shear rate on the crystallization is also investigated. In particular, we find two plausible phenomenological relations between the shear rate and the characteristic time scale needed for ordering of the amorphous system under shear.

Liquid-crystal anchoring at a polymer surface arises from interactions at several different length scales. At the molecular level, a liquid-crystal molecule may tend to align with the substrate polymer chain, while at the nanometer length scale grooves can exist that arise from the periodic repeat structure of a polymer chain or from nanometer-scale undulations due to surface stresses. On a still longer scale there is the secondary effect of grooves or surface inhomogeneities. We have performed a total of more than 900 ns of atomistic molecular dynamics simulations in order to study the relative importance of the molecular-level interaction and the topography of the polymer surface in liquid-crystal anchoring. Substrates were constructed in which grooves were induced along a direction perpendicular to the constituent molecular chains. In the results presented for the case of 32 5CB molecules on a poly(vinyl alcohol) substrate, the liquid-crystal director orientation appeared to be determined principally by the substrate chain orientation. Only for the deepest grooves did the director align along the grooves and perpendicular to the substrate molecular chain direction.

A large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion?

In the framework of nonextensive statistical mechanics, the equilibrium structures of astrophysical self-gravitating systems are stellar polytropes, parametrized by the polytropic index $n$. By careful comparison to the structures of simulated dark-matter halos we find that the density profiles, as well as other fundamental properties, of stellar polytropes are inconsistent with simulations for any value of $n$. This result suggests the need to reconsider the applicability of nonextensive statistical mechanics (in its simplest form) to equilibrium self-gravitating systems.

The present study proposes a unified Lagrangian transport template for topological description of advective fluid transport and advective-diffusive scalar transport in laminar flows. The key to this unified description is the expression of scalar transport as purely advective transport by the total scalar flux. This admits generalization of the concept of transport topologies known from laminar mixing studies to scalar transport. The study is restricted to two-dimensional systems and the fluid and scalar transport topologies, as a consequence, prove to be Hamiltonian. The unified Lagrangian transport template is demonstrated and investigated for a heat-transfer problem with nonadiabatic boundaries, representing generic scalar transport with permeable boundaries. The fluid and thermal transport topologies under steady conditions both accommodate islands (constituting isolated flow and thermal regions) that undergo Hamiltonian disintegration into chaotic seas upon introducing time periodicity. The thermal transport topology invariably comprises transport conduits that connect the nonadiabatic boundaries and facilitate wall-wall and wall-fluid heat transfer. For steady conditions these transport conduits are regular; for time-periodic conditions these conduits may, depending on degree of diffusion, be regular or chaotic. Regular conduits connect nonadiabatic walls only with specific flow regions; chaotic heat conduits establish connection (and thus heat exchange) of the nonadiabatic walls with the entire flow domain.

Thermogravitational separation has, until now, been used in differentially heated vertical cells, called thermogravitational columns (TGCs). The cell can be either a slit or an annular cavity whose two isothermal faces are maintained at different temperatures $T_1$ and $T_2$. In this study, we show contrary to what has been done until now, that it is possible to carry out the separation of the species of a binary mixture in the classical configuration of Rayleigh-Bénard (horizontal cell heated from below with the separation ratio $\psi >{\psi }_{\mathrm{mono}}>0$ or from above with $\psi <0$); we obtain a monocellular flow for $\psi >{\psi }_{\mathrm{mono}}$ at the onset of convection. The species separation, in a horizontal cell, is obtained without fear of the remixing observed in vertical thermogravitational cells for fluids with negative Soret coefficients. In this situation, the heaviest component concentrates in the upper part of the cell creating an unstable physical situation. We improve the efficiency of separation for the development of an industrial process of separation. We study the thermogravitational separation of the components of a binary fluid mixture saturating a horizontal porous layer, in the presence of the Soret effect. The horizontal walls of the cavity are impermeable and maintained at constant and different temperatures. The system of equations governing the problem has an equilibrium solution with a vertical stratification of temperature and concentration. This solution loses its stability via a stationary bifurcation for values of the separation ratio $\psi >{\psi }_0$ while, for $\psi <{\psi }_0$, stability is lost via a Hopf bifurcation. For a cavity heated from below, the flow resulting from the stationary bifurcation becomes monocellular beyond a certain value of $\psi >{\psi }_{\mathrm{mono}}>0$ and leads to a separation of the species between the two ends of the cell. We propose to determine whether the monocellular flow remains stable until the optimum of separation and if we can obtain high separation in the case of a horizontal cavity. We verify that the critical Rayleigh number ${\mathrm{Ra}}_{c_2}$, associated with the transition between monocellular flow and multicellular flow, is higher than the optimum Rayleigh number leading to maximum separation of species. Thus this study reveals that it is possible to obtain optimal separation before the monocellular flow loses its stability. We show also that the separation inside the horizontal cell in a Rayleigh-Bénard configuration permits us to produce the same degree of separation but with a greater quantity of each species compared to a thermogravitational vertical column.

A generalized model for the behavior of the stress tensor in non-Newtonian fluids is investigated for spatially homogeneous plane Couette flow, showing a variety of nonlinear responses and deterministic chaos. Mapping of chaotic solutions is achieved through the largest Lyapunov exponent for the two main parameters: The shear rate and the temperature and/or density. Bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found. Suggested mechanisms for stability loss in these complex fluids include Hopf, saddle-node, and period-doubling bifurcations.

We develop a three-dimensional (3D) lattice Boltzmann model that recovers in the continuous limit the two-fluids theory for plasmas, and consequently includes the generalized Ohm’s law. The model reproduces the magnetic reconnection process just by giving the right initial equilibrium conditions in the magnetotail, without any assumption on the resistivity in the diffusive region. In this model, the plasma is handled similar to two fluids with an interaction term, each one with distribution functions associated to a cubic lattice with 19 velocities (D3Q19). The electromagnetic fields are considered as a third fluid with an external force on a cubic lattice with 13 velocities (D3Q13). The model can simulate either viscous fluids in the incompressible limit or nonviscous compressible fluids, and successfully reproduces both the Hartmann flow and the magnetic reconnection in the magnetotail. The reconnection rate in the magnetotail obtained with this model lies between $R=0.062$ and $R=0.073$, in good agreement with the observations.

The paper presents the dynamic compound wavelet method (dCWM) for modeling the time evolution of multiscale and/or multiphysics systems via an “active” coupling of different simulation methods applied at their characteristic spatial and temporal scales. Key to this “predictive” approach is the dynamic updating of information from the different methods in order to adaptively and accurately capture the temporal behavior of the modeled system with higher efficiency than the (nondynamic) “corrective” compound wavelet matrix method (CWM), upon which the proposed method is based. The system is simulated by a sequence of temporal increments where the CWM solution on each increment is used as the initial conditions for the next. The numerous advantages of the dCWM method such as increased accuracy and computational efficiency in addition to a less-constrained and a significantly better exploration of phase space are demonstrated through an application to a multiscale and multiphysics reaction-diffusion process in a one-dimensional system modeled using stochastic and deterministic methods addressing microscopic and macroscopic scales, respectively.

We discuss the application of wavelet transforms to a critical interface model which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of the surface tension), the effective interface roughness exponent $\zeta$ is $\simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.

We study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices. These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function. (These exact renormalizations on diamond lattices can also be considered as approximate Migdal-Kadanoff renormalizations for hypercubic lattices.) In terms of the rescaled partition function $z=Z/Z_{\text{typ}}$, we find that the critical point corresponds to a fixed point distribution with a power-law tail $P_c\left(z\right)\sim \Phi \left(\text{ln}z\right)/z^{1+\mu }$ as $z\to +\infty$ [up to some subleading logarithmic correction $\Phi \left(\text{ln}z\right)$], so that all moments $z^n$ with $n>\mu$ diverge. For the wetting transition, the first moment diverges $\overline{z}=+\infty$ (case $0<\mu <1$), and the critical temperature is strictly below the annealed temperature $T_c<T_{\text{ann}}$. For the directed polymer case, the second moment diverges $\overline{z^2}=+\infty$ (case $1<\mu <2$), and the critical temperature is strictly below the exactly known transition temperature $T_2$ of the second moment. We then consider the correlation length exponent $\nu$: the linearized renormalization around the fixed point distribution coincides with the transfer matrix describing a directed polymer on the Cayley tree, but the random weights determined by the fixed point distribution $P_c\left(z\right)$ are broadly distributed. This induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions.

Granular media are reversible and elastic if the stress increments are small enough. An elastic stress-strain relation, employed previously to determine static stress distributions, in this paper is compared to experiments by Kuwano and Jardine [Geotechnique 52, 727 (2002)] on incremental stress-strain relations, and shown to yield satisfactory agreement. In addition, the yield condition is given a firmer footing.

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon et al., Phys. Rev. E 75, 050301(R) (2007); I. Fouxon et al.,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter $\mathcal{L}$ that describes the relative role of the inelastic energy loss and heat diffusion. At $\mathcal{L}⪢1$ the intermediate cooling dynamics proceeds as a competition between “holes”: low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the “hole ripening” statistics exhibits a simple dynamic scaling behavior.

We study the optical absorbance from a magnetically arranged colloidal structure, and investigate the possibility of creating a magnetically controlled optical sensor using this system. The colloids form chains when exposed to an external magnetic field, which tend to collapse and form a more random particle arrangement when the field is removed. We show that a small magnetic field is able to change the sensor’s reflection coefficient by more than 30%, and investigate in detail the relaxation mechanism when the field is turned off.

We report measurements of the x-ray scattering intensity as mesoporous silica glasses are filled with neon. The intensity of the first peak in the liquidlike diffraction pattern increases nonlinearly with mass adsorbed. We outline a simple model assuming that the major coherent contribution to the first peak in the scattering function $S\left(Q\right)$ is due to interference from nearest-neighbor scatterers. This allows us to demonstrate an approach for surface area determination which does not rely on thermodynamic models—and is therefore complementary to existing methods. We also suggest that the overestimation of surface area by the traditional Brunauer-Emmett-Teller method may be resolved by using the capillary, and not the bulk, condensation pressure as the reference pressure $p_0$. Furthermore, the alternative analysis offers an insight into the atomic structure of monatomic sorption, which may be of use for further studies on materials with different surface properties.

We present a high-resolution x-ray study of the effects of disorder induced by random cross-linking side-chain smectic elastomers. The influence of variation of the concentration and stiffness of the cross-link units on the disruption of the one-dimensional translational order is reported in detail. Precise analysis of the line shape of the quasi-Bragg peaks associated with the smectic layering indicates a transition from algebraic decaying ordering to disorder. The smectic line shapes can be described by the Caillé correlation function convoluted with a finite-size factor represented by a stretched Gaussian (compressed exponential). The transition to disorder is signaled by a change in the exponent of the stretched Gaussian from 1 (simple Gaussian describing finite-size domains) via 0.5 (Lorentzian describing exponentially decaying short-range correlations) to $<0.5$ (stretched exponential correlations). For a flexible cross linker the changeover occurs for concentration between 0.15 and 0.20, for a stiff cross linker below about 0.10. Broadening of the higher harmonics of the x-ray peak indicates strong nonuniform strain within finite-size domains and local deformations induced by randomly distributed dislocations.

In the first part of the paper, the stochastic dynamics of the Peyrard-Bishop-Dauxois (PBD) DNA model is studied. A one-dimensional averaged Itô stochastic differential equation governing the total energy of the system and the associated Fokker-Planck equation governing the transition probability density function of the total energy are derived from the Langevin equations for the base-pair (bp) separation of the PBD DNA model by using the stochastic averaging method for quasinonintegrable Hamiltonian systems. The stationary probability density function of the average energy and the mean square of the bp separation are obtained by solving the reduced Fokker-Planck equation. In the second part of the paper, the local denaturation of the thermalized PBD DNA model is studied as a first-passage-time problem in the energy. A backward Kolmogorov equation and a Pontryagin equation are derived from the averaged Itô equation and solved to yield the waiting-time distribution and the mean bp opening time. All the analytical results are confirmed with those from Monte Carlo simulation. It is pointed out that the proposed method may yield a reasonable mean bp opening time if the friction coefficient is fixed using experimental results.

One aim of synthetic biology is to exert systematic control over cellular behavior, either for medical purposes or to “program” microorganisms. An engineering approach to the design of biological controllers demands a quantitative understanding of the dynamics of both the system to be controlled and the controllers themselves. Here we focus on a widely used method of exerting control in bacterial cells: plasmid vectors bearing gene-promoter pairs. We study two variants of the simplest such element, an unregulated promoter constitutively expressing its gene, against the varying genomic background of four Escherichia coli cell strains. Absolute protein numbers and rates of expression vary with both cell strain and plasmid type, as does the variability of expression across the population. Total variability is most strongly coupled to the cell division process, and after cell size is scaled away, plasmid copy number regulation emerges as a significant effect. We present simple models that capture the main features of the system behavior. Our results confirm that complex interactions between plasmids and their hosts can have significant effects on both expression and variability, even in deliberately simplified systems.

The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods. The approach is based on the general characteristic-based algorithm for off-lattice Boltzmann simulations that preserves all appealing properties of the standard lattice Boltzmann method while extending the method to unstructured grids. We show that the use of multispeed models indeed gives rise to major improvements in accuracy. The suggested approach thus renders truly large-scale off-lattice Boltzmann computations practical.

Starting from the minimal model for the electrically interacting densities of electrons and ions in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. Solutions of the moving boundary model have already been discussed, but the derivation of the model was postponed to the present paper. The key ingredient of the model is the boundary condition on the moving front. It is found to be of kinetic undercooling type, and the relation to other moving boundary models is discussed. Furthermore, the model is compared to two-dimensional simulations of the underlying density model. The results suggest that our moving boundary approximation adequately represents the essential dynamics of negative streamer fronts.