Size segregation is a natural occurrence both in everyday life and in industrial processes. Understanding and research of the phenomenon has overwhelmingly been from a mechanistic point of view. This paper demonstrates through simulations that segregation can also be explained and trends predicted geometrically. The algorithm used in this study contains three simple elements: random walks combined with a rebounding probability to encourage particles to settle, plus the nonoverlap constraint. It is implemented digitally in a regular lattice grid, to make it easy to deal with arbitrary shapes. It does not explicitly consider any particle interaction forces, and it does not include any rules specifically designed to promote or suppress segregation. Yet particle movement, which occurs within a digitized cubic grid, leads to shaking-induced segregation comparable to that observed in physical tests. The paper details the comparison of shaking-induced particle segregation between a series of computer based simulations and those of physical experiments undertaken in the laboratory. A range of mixtures, comprising nonspherical, arbitrary shaped/sized particles are investigated, having been packed into pseudo-two-dimensional containers. The simulation results suggest that segregation can be adequately explained, from a geometrical point of view, as a result of the relative motion between particles of different sizes and shapes. The geometrical algorithm thus provides a fast and qualitative prediction as to how likely segregation is to occur for any given mixture of arbitrary shapes.

The nonequilibrium response of a colloidal liquid-crystalline nematic phase to an external aligning field, which rotates in a plane, is explored by dynamical fundamental measure density-functional theory. Depending on the drive frequency, different dynamical states are found, which are characterized by towing and overtaking of the nematic director by the field as well as by breathing and dynamical splitting of the orientational distribution peak. This complex response can be exploited for smart optical switching and mixing devices.

We have performed exhaustive multicanonical Monte Carlo simulations of elastinlike polypeptides with a chain including amino acids ${\left(\text{valine-proline-glycine-valine-glycine}\right)}_n$ or in short ${\left(VPGVG\right)}_n$, where $n$ changes from 1 to 4, in order to investigate the thermodynamic and structural properties. To predict the characteristic secondary structure motifs of the molecules, Ramachandran plots were prepared and analyzed as well. In these studies, we utilized a realistic model where the interactions between all types of atoms were taken into account. Effects of solvation were also simulated by using an implicit-solvent model with two commonly used solvation parameter sets and compared with the vacuum case.

We perform simulations of model proteins to study folding on rugged energy landscapes. We construct “first-passage” networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to basins and transitions between them in the energy landscape. We find power-law relations between the folding time and the number of nodes and bonds. We show that these scalings are determined by the fractal properties of first-passage networks. Thus, we have identified a possible mechanism—the small fractal dimension of first passage networks—which can give rise to reliable folding in proteins with rugged energy landscapes.

We analyze the behavior of a suspension of active polar particles under shear. In the absence of external forces, orientationally ordered active particles are known to exhibit a transition to a state of nonuniform polarization and spontaneous flow. Such a transition results from the interplay between elastic stresses, due to the liquid crystallinity of the suspension, and internal active stresses. In the presence of an external shear, we find an extremely rich variety of phenomena, including an effective reduction (increase) in the apparent viscosity depending on the nature of the active stresses and the flow-alignment property of the particles, as well as more exotic behaviors such as a nonmonotonic stress–strain-rate relation and yield stress for large activities.

An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform depth. The canonically conjugate variables are derived from the previously developed noncanonical conformal description of water waves over a strongly undulating bottom [V. P. Ruban, Phys. Rev. E 70, 066302 (2004)]. Also an alternative approach to the problem is discussed, which gives weakly nonlinear Hamiltonian models of different orders, both for free-surface waves and for interfacial waves.

Using three-dimensional computer simulations, we examine hovering aerodynamics of flexible planar wings oscillating at resonance. We model flexible wings as tilted elastic plates whose sinusoidal plunging motion is imposed at the plate root. Our simulations reveal that large-amplitude resonance oscillations of elastic wings drastically enhance aerodynamic lift and efficiency of low-Reynolds-number plunging. Driven by a simple sinusoidal stroke, flexible wings at resonance generate a hovering force comparable to that of small insects that employ a very efficient but much more complicated stroke kinematics. Our results indicate the feasibility of using flexible wings driven by a simple harmonic stroke for designing efficient microscale flying machines.

By analysis of the thermally driven oscillation of an atomic force microscope (AFM) cantilever, we have measured both the damping and static forces acting on a sphere near a flat plate immersed in gas. By varying the proximity of the sphere to the plate, we can continuously vary the Knudsen number (Kn) at constant pressure, thereby accessing the slip flow, transition, and molecular regimes at a single pressure. We use measurements in the slip-flow regime to determine the combined slip length (on both sphere and plate) and the tangential momentum accommodation coefficient, $\sigma$. For ambient air at 1 atm between two methylated glass solids, the inverse damping is linear with separation and the combined slip length on both surfaces is $250\text{nm}\pm 100\text{nm}$, which corresponds to $\sigma =0.77\pm 0.24$. At small separations $\left(\text{Kn}>0.4\right)$ the measured inverse damping is no longer linear with separation, and is observed to exhibit reasonable agreement with the Vinogradova formula.

Using nonequilibrium molecular dynamics simulations on simple Lennard-Jones binary mixtures, we have studied the behavior of planar fluid-fluid interfaces undergoing shear flow. When the miscibility is low enough, a slip together with a partial depletion have been noticed at the interface between the two fluid phases. The slip length can reach a value equal to some molecular diameters and the corresponding interfacial viscosity can be two times smaller than the value in the bulk. It is shown how the omission of this slip may lead to flow-rate misevaluation when dealing with a multiphase flow in a nanoporous medium even for non polymer fluids. In addition, using the simulation results, a simple relation between interfacial tension and interfacial viscosity is proposed for the monoatomic systems studied in this work. Finally, it is shown that the interfacial viscosity cannot be fully accounted for by estimating the local viscosity deduced from the local thermodynamic properties of the interface.

The lattice Boltzmann (LB) method has proven to be a promising method for simulating fluid dynamics in porous media. When fluid flow in pores is the only concern, a standard LB implementation, which stores one or two sets of particle distribution functions (PDFs) for both pore and solid cells, wastes a large amount of memory, especially for low-porosity media. This paper proposes a LB implementation scheme that stores a single set of PDFs for pore cells only and therefore makes it possible to simulate flow through larger and more-realistic porous models. A unique feature of this scheme is that it decomposes all PDFs into a set of 1D arrays in such a way that each array corresponds to a set of pore cells that connect one another along a pair of opposite LB velocity directions. This allows LB propagation and a standard bounce-back rule to be realized together as one or two circular shifting operations on every array. For this reason, this scheme is called SHIFT. Although PDFs are not stored in an efficient way for LB collision operation, it is shown that the incurred overhead could be reduced by properly arranging PDF arrays according to the pore structures. A D3Q15 LB implementation of SHIFT using the lattice Bhatnagar-Gross-Krook model is applied to simulate the Stokes flow through models of four natural and synthetic rock samples with porosities ranging from about 10% to 38%. Results show that SHIFT requires 36–82 % less memory than a comparable D3Q15 LB does, which stores a single set of PDF for both pore and solid cells. SHIFT achieves minimum performances of over 11 and 3.8 mega-lattice-updates-per-second (MLUPS) for the combined propagation and bounce-back operation and the collision operation, respectively, and therefore a minimum of 2.8 MLUPS in total on a computer with one AMD Opteron 2218. The performance of the collision operation is significantly improved for all cases when a simple $K$-mean clustering technique is employed to rearrange PDF arrays. It is argued and shown that the number of PDF arrays per pore cell and the length frequency of PDF arrays are useful measurements on the geometry and topology of the pore structures and these characteristics are able to explain SHIFT performance variations.

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential shear profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then resegregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we map the local concentration (from the model) to changes in packing fraction; this provides a way to make a semiquantitative comparison with the measured global dilation. We observe that the resulting model successfully captures the presence of a fast mixing process and relatively slower resegregation process, but the model predicts a finite resegregation time, while in the experiment resegregation occurs only exponentially in time.

We extend the microscopic Poisson-Nernst-Planck theory of the effects of mobile charge carriers, completely blocked at the electrodes, on the properties of dielectric materials by incorporating a finite speed of response propagation. The usual microscopic theory is based on the assumption that the diffusion current is given by Fick’s law, relating the current density with the gradient of concentration at the same time. On the contrary we assume that the flux of diffusing particles is delayed with respect to the concentration gradient, as suggested by extended thermodynamics formulations. We show that, in the hyperbolic diffusion regime approximation, new trends for the real and imaginary parts of the small-signal electrical impedance of a dielectric containing ions versus the frequency of the applied voltage are expected when the delay time is comparable with the Debye relaxation time. In particular, at sufficiently high frequencies the real part of the conductivity, normally independent of frequency, decreases toward zero because of the finite, rather than the infinite propagation speed present in the hyperbolic diffusion regime model.

The effect of the electric-field inhomogeneity has been experimentally studied by polarizing microscopy in a homeotropic nematic liquid crystal in confined electrode geometries which may be relevant in display applications. Defects related to tilt inversion have been detected by monitoring the transmitted intensity profile as a function of the applied voltage. The position of the defects could be controlled by an additional magnetic field breaking the symmetry of the original arrangement. The phenomenon has been interpreted via numerical calculation of the director distribution using the continuum theory of nematics. The influence of oblique light incidence and of weak anchoring has also been analyzed. Simulations have provided good qualitative agreement with the observations. The method has turned out to be a sensitive tool to detect small misalignment angles between the magnetic field and the cell plane.

Messenger RNA translation is often studied by means of statistical-mechanical models based on the asymmetric simple exclusion process (ASEP), which considers hopping particles (the ribosomes) on a lattice (the polynucleotide chain). In this work we extend this class of models and consider the two fundamental steps of the ribosome’s biochemical cycle following a coarse-grained perspective. In order to achieve a better understanding of the underlying biological processes and compare the theoretical predictions with experimental results, we provide a description lying between the minimal ASEP-like models and the more detailed models, which are analytically hard to treat. We use a mean-field approach to study the dynamics of particles associated with an internal stepping cycle. In this framework it is possible to characterize analytically different phases of the system (high density, low density or maximal current phase). Crucially, we show that the transitions between these different phases occur at different parameter values than the equivalent transitions in a standard ASEP, indicating the importance of including the two fundamental steps of the ribosome’s biochemical cycle into the model.

We studied how lateral connections affect the accuracy of a population code by using a model of orientation selectivity in the primary visual cortex. Investigating the effects of lateral connections on population coding is a complex problem because these connections simultaneously change the shape of tuning curves and correlations between neurons. Both of these changes caused by lateral connections have to be taken into consideration to correctly evaluate their effects. We propose a theoretical framework for analytically computing the Fisher information, which measures the accuracy of a population code, in stochastic spiking neuron models with refractory periods. Within our framework, we accurately evaluated both the changes in tuning curves and correlations caused by lateral connections and their effects on the Fisher information. We found that their effects conflicted with each other and the answer to whether or not the lateral connections increased the Fisher information strongly depended on the intrinsic properties of the model neuron. By systematically changing the coupling strengths of excitations and inhibitions, we found the parameter regions of lateral connectivities where sharpening of tuning curves through Mexican-hat connectivities led to an increase in information, which is in contrast to some previous findings.

A nonuniform ${\text{SF}}_6$ gas flow initial condition has been actualized in the context of shock tube experiment for the Richtmyer-Meshkov instability study. Two kinds of amplitude have been used to design the membrane supports which initially materialize the gaseous interface. The visualizations of $\text{air}/{\text{SF}}_6$ sinusoidal interfaces and shock wave propagations in the nonuniform field were obtained by Schlieren photography. Experiments are in very good agreement with simulations for the $\text{air}/{\text{SF}}_6$ case, but due to the initial nonuniform effects, Sadot model and Zhang-Sohn theory are far beyond the experimental and calculation results.

The Kirchhoff equations for flexible rods are extended to be able to describe size effects. Thus, the extended equations are applicable not only for macroscopic rods but also for ultrathin rods whose thickness is close to the material length. It is found that extensional size effects exist in flexible rods, namely, the external forces exerted on both ends of rods will increase as the rods are getting thinner if an identical deformation is remained.

Complex group velocity is common in absorbing and active media, yet its precise physical meaning is unclear. While in the case of a nondissipative medium the group velocity of propagating waves $C_g=d\omega /dk$ is exactly equal to the observable energy velocity (defined as the ratio between the energy flux and the total energy density) $C_g=\overline{F}/\overline{E}$, in a dissipative medium $C_g=d\omega /dk$ is in general a complex quantity which cannot be associated with the velocity of energy transport. Nevertheless, we find that the complex group velocity may contain information about the energy transport as well as the energy dissipated in the medium. The presented analysis is intended to expound the connection between the complex group velocity and energy transport characteristics for a class of hyperbolic dissipative dynamical systems. Dissipation mechanisms considered herein include viscous and viscoelastic types of damping. Both cases of spatial and temporal decay are discussed. The presented approach stems from the Lagrangian formulation and is illustrated with identities that relate the complex group velocity and energy transport characteristics for the damped Klein-Gordon equation; Maxwell’s equations, governing electromagnetic waves in partially conducting media; and Biot’s theory, governing acoustic wave propagation in porous solids.

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.