Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of “nonlocal” electrostatics since their dielectric response is characterized by a scale-dependent dielectric function $\epsilon \left(q\right)$, where $q$ is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, “local” formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.

We study the classical and quantum dynamics of periodically kicked particles placed initially within an open double-barrier structure. This system does not obey the Kolmogorov-Arnold-Moser (KAM) theorem and displays chaotic dynamics. The phase-space features induced by non-KAM nature of the system lead to dynamical features such as the nonequilibrium steady state, classically induced saturation of energy growth and momentum filtering. We also comment on the experimental feasibility of this system as well as its relevance in the context of current interest in classically induced localization and chaotic ratchets.

Cytoskeletal filaments often interact laterally through cross-linking proteins, contributing to passive cellular viscoelasticity and, perhaps surprisingly, active force generation. We present a theory, based on the formation and rupture of cross-linker bonds, that relates molecular properties of those interactions to the macroscale mechanics of filament bundles. Computing the force-velocity relation for such a bundle, we demonstrate significant contractile forces in the absence of molecular motors. This theory provides insight into cytokinesis, cytoskeletal mechanics, and stress-fiber contraction.

We study random walks (RWs) on classical and dual Sierpinski gaskets (SG and DSG), naturally embedded in $d$-dimensional Euclidian spaces (ESs). For large $d$ the spectral dimension $d_{\text{s}}$ approaches 2, the marginal RW dimension. In contrast to RW over two-dimensional ES, RWs over SG and DSG show a very rich behavior. First, the time discrete scale invariance leads to logarithmic-periodic (log-periodic) oscillations in the RW properties monitored, which increase in amplitude with $d$. Second, the asymptotic approach to the theoretically predicted RW power laws is significantly altered depending on $d$ and on the variant of the fractal (SG or DSG) under study. In addition, we discuss the suitability of standard RW properties to determine $d_{\text{s}}$, a question of great practical relevance.

We present results from a detailed simulation of a quasi-two-dimensional dissipative granular gas, kept in a noncondensed steady state via vertical shaking over a rough substrate. This gas shows a weak power-law decay in the tails of its pair distribution functions, indicating clustering. This clustering depends monotonically on the dissipation coefficient and disappears when the sphere-sphere collisions are conservative. Clustering is also sensitive to the packing fraction. This gas also displays the standard nonequilibrium characteristics of similar systems, including non-Maxwellian velocity distributions. The diffusion coefficients are calculated over all the conditions of the simulations, and it is found that diluted gases are more diffusive for smaller restitution coefficients.

Solitonlike structures called “droplets” are found to exist within a paradigm reaction-diffusion model that can be used to describe patterning in a number of biological systems, for example, on the skin of various fish species. They have also been found in many other systems that can be modeled with a complex Ginzburg-Landau system. These droplets can be analyzed in the biological paradigm model because the system has two nonzero stable steady states that are symmetric; however, the asymmetric case is more challenging. We first review the properties of the paradigm system and then extend a recently developed perturbation technique [D. Gomila et al., J. Opt. B: Quantum Semiclassical Opt. 6, S265 (2004)] to investigate the weakly asymmetric case. We compare the results of our mathematical analysis with numerical simulations and show good agreement in the region where the assumptions hold.

Recently, Kawai, Parrondo, and Van den Broeck [Phys. Rev. Lett. 98, 080602 (2007)] have related dissipation to time-reversal asymmetry. We generalized the result by considering a protocol where the physical system is driven away from an initial thermal equilibrium state with temperature ${\beta }_0$ to a final thermal equilibrium state at a different temperature. We illustrate the result using a model with an exact solution, i.e., a particle in a moving one-dimensional harmonic well.

We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly the models with savings. For the model with uniform savings, agents perform simple random walks in the “wealth space.” On the other hand, we observe ballistic diffusion in the model with distributed savings. There is an associated skewness in the gain-loss distribution which explains the steady-state behavior in such models. We find that, in general, an agent gains while interacting with an agent with a larger saving propensity.

This study carried out a direct numerical simulation of gas-solid swirling jet flow, focusing on the particle-vortex interaction and mechanisms of turbulence modulation. Two cases of flows with either a constant particle flow rate or a constant particle mass loading are simulated. The typical instantaneous particle-vortex interactions are illustrated and analyzed, as well as the spectrum representations and the projections of them. The results show that the small particles $\left(\text{St}<1\right)$ and light-mass loadings augment the vortices of the large-scale range in the power spectrum representation by shifting the peaks of wave numbers from small to large values as they pass through the large vortices and break them into smaller scales. The large particles and heavy-mass loadings suppress greatly the large scales of vortices, transferring the turbulent kinetic energy from large to relatively smaller scales of vortices, resulting in turbulence augmentation in the large wave numbers and turbulence attenuation in the range of small wave numbers. Moreover, by comparison between the two cases, it is found that the turbulence modulation is more highly sensitive to the effect of mass loadings rather than the dynamical response property of particles. The well-known knowledge on modulation of turbulence is true under the condition of the same mass loading. However, the situation becomes very complicated when the mass loading changes. Finally, these conclusions are verified by the analysis of energy spectrum and dissipation.

We propose a mechanism to alter the nature of the potential barriers when a biased Brownian particle undergoes a constrained motion in narrow periodic channel. By changing the angle of the external bias, the nature of the potential barriers changes from purely entropic to energetic, which in turn affects the diffusion process in the system. At an optimum angle of the bias, the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the enhancement of the scaled effective diffusion coefficient can be efficiently controlled by the angle of the bias. This mechanism enables the proper design of channel structures for transport of molecules and small particles. The approximate analytical predictions have been verified by precise Brownian dynamics simulations.

The motion of a ${\text{C}}_{60}$ molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a ${\text{C}}_{60}$ molecule near a graphene sheet is found to be diffusive in the lateral directions, while in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the ${\text{C}}_{60}$ molecule. We also examine the rotational diffusion of ${\text{C}}_{60}$ and show that its motion over the graphene sheet is not a rolling motion.

The dynamics of the discotic liquid-crystalline system, hexakis ($n$-hexyloxy) triphenylene (HAT6), is considered in the frame of the phenomenological model for rate processes proposed by Berlin. It describes the evolution of the system in the presence of the long-time scale correlations in the system, and we compare this with experimental quasielastic neutron scattering of the molecular assembly of HAT6 in the columnar phase. We interpret the parameters of this model in terms of nonextensive thermodynamics in which rare events in the local fast dynamics of some parts of the system control the slower dynamics of the larger molecular entity and lead to a fractional diffusion equation. The importance of these rare local events to the overall dynamics of the system is linked to the entropic index, this being obtained from the data within the model approach. Analysis of the waiting-time dependence from momentum transfer reveals a Lévy distribution of jump lengths, which allows us to construct the van Hove correlation function for discotic liquid-crystalline system.

We report on an x-ray scattering experiment of bulk poly[9,9-bis(2-ethylhexyl)fluorene] under quasihydrostatic pressure from 1 to 11 GPa at room temperature. The scattering pattern of high molecular weight (HMW) polyfluorene $\left(>10\text{kg}/\text{mol}\right)$ undergoes significant changes between 2 and 4 GPa in the bulk phase. The 110 reflection of the hexagonal unit cell disappears, indicating a change in equatorial intermolecular order. The intensity of the 00 21 reflection drops, with a sudden move toward higher scattering angles. Beyond these pressures, the diminished 00 21 reflection tends to return toward lower angles. These changes may be interpreted as a transition from crystalline hexagonal to glassy nematic phase (perceiving order only in one direction). This transition may be rationalized by density arguments and the underlying theory of phase behavior of hairy-rod polyfluorene. Also the possible alteration of the 21-helical main chain toward more planar main chain conformation is discussed. The scattering of low molecular weight polyfluorene $\left(<10\text{kg}/\text{mol}\right)$, which is glassy nematic in ambient pressure, is reminiscent with that of HMW polymer above 2–4 GPa.

We study the spatial organization and segregation of two self-avoiding polymers trapped inside a closed cylindrical pore. Using molecular-dynamics simulations, we show how confinement shapes the chains, especially their mutual (entropic) force, chain miscibility, and segregation dynamics. Under strong confinement, the chains are shown to repel more strongly and thus segregate better if they are shorter and the confining space is more asymmetric, in contrast to the spherically confined case, where nonlinear chain topology is required for chain partitioning in equilibrium. When applied to bacterial chromosomes, our results imply that chromosome miscibility depends on how they are compacted and structured inside the cell (by proteins and supercoiling). Finally, longitudinal confinement is shown to have nontrivial effects on segregation dynamics by randomizing and thus slowing down the segregation process, which would otherwise be assisted with entropic forces.

The behavior of biopolymer networks comprised of clickable polysaccharide chains that can undergo force-induced conformational transitions was investigated during straining using a simulation technique. The simulation was carried out both using an affine deformation field and alternatively using Lees-Edwards boundary conditions as an example of a nonaffine case. In the affine situation the simulated stress-strain curves were found to be consistent with results obtained by evaluating the molecular force-extension curve at a single average extension and calculating the bulk modulus as an average over all possible orientations with respect to the deformation. While in all cases examined the macroscopic mechanical responses of networks of randomly oriented chains, consisting either of simple extensible wormlike chains or their clickable analogs, were found to be indistinguishable, the simulation additionally allowed the number of chains containing sugar rings in different conformational states to be monitored, and this was found to change significantly during straining. This supports the hypothesis that in networks of randomly oriented clickable polysaccharide chains, such conformational transitions could have biological significance as stress switches in signaling processes but that they are unlikely to affect the bulk rheological properties of tissue.

We investigated changes in the shape of tubular ternary vesicles induced by phase separation into liquid-ordered and liquid-disordered phases. Tubular vesicles transform into two types of periodically modulated vesicles depending on the area fraction of the liquid-ordered phase. One type is a necklace of oblate subunits with two circular domains of the liquid-order phase, and the other is a periodically modulated tube with stripes of the liquid-order phase. The transition between the circular and striped domains is governed by the domain boundary energy, whereas the periodicity of modulated vesicles is determined geometrically based on the fixed volume and area constraints. The observed multidomain vesicles are kinetically trapped in metastable states, and all domains show budding to reduce the boundary energy.

Hundred twenty years after the fundamental work of Poincaré, the statistics of Poincaré recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime, where the measure of stability islands is significant, the decay of recurrences is characterized by a power law at asymptotically large times. The exponent of this decay is found to be $\beta \approx 1.3$. This value is smaller compared to the average exponent $\beta \approx 1.5$ found previously for two-dimensional symplectic maps with divided phase space. On the basis of previous and present results a conjecture is put forward that, in a generic case with a finite measure of stability islands, the Poincaré exponent has a universal average value $\beta \approx 1.3$ being independent of number of degrees of freedom and chaos parameter. The detailed mechanisms of this slow algebraic decay are still to be determined. Poincaré recurrences in DNA are also discussed.

Embeddings are diffeomorphisms between some dynamical phase space and a reconstructed image. Different embeddings may or may not be equivalent under isotopy. We regard embeddings as representations of the dynamical phase space. We determine the topological labels required to distinguish inequivalent representations of three-dimensional dissipative dynamical systems when the embeddings are into ${\mathbb{R}}^k$, $k=3,4,5,\dots$. Three representation labels are required for embeddings into ${\mathbb{R}}^3$, and only one is required in ${\mathbb{R}}^4$. In ${\mathbb{R}}^5$ there is a single “universal” representation.

The equations of state and the structural, thermodynamic, and transport properties of the two- and three-dimensional nonideal dissipative systems consisting of particles interacting with different isotropic pair potentials are studied in a wide range of parameters typical for laboratory dusty plasma. Simple semiempirical expression for the energy density in liquid systems is considered. Comparison of the theoretical and numerical results is presented.

Minkowski operators (dilation and erosion of sets in vector spaces) have been extensively used in computer graphics, image processing to analyze the structure of materials, and more recently in molecular dynamics. Here, we apply those mathematical concepts to extend the discrete element method to simulate granular materials with complex-shaped particles. The Voronoi-Minkowski diagrams are introduced to generate random packings of complex-shaped particles with tunable particle roundness. Contact forces and potentials are calculated in terms of distances instead of overlaps. By using the Verlet method to detect neighborhood, we achieve CPU times that grow linearly with the body’s number of sides. Simulations of dissipative granular materials under shear demonstrate that the method maintains conservation of energy in accord with the first law of thermodynamics. A series of simulations for biaxial test, shear band formation, hysteretic behavior, and ratcheting show that the model can reproduce the main features of real granular-soil behavior.