When a fluid is confined within a spatially periodic external field, the liquid-vapor transition is replaced by a different transition called laser-induced condensation (LIC) [Götze et al., Mol. Phys. 101, 1651 (2003)]. In $d=3$ dimensions, the periodic field induces an additional phase, characterized by large density modulations along the field direction. At the triple point, all three phases (modulated, vapor, and liquid) coexist. At temperatures slightly above the triple point and for low (high) values of the chemical potential, two-phase coexistence between the modulated phase and the vapor (liquid) is observed; by increasing the temperature further, both coexistence regions terminate in critical points. In this paper, we reconsider LIC using the Ising model to resolve a number of open issues. To be specific, we (1) determine the universality class of the LIC critical points and elucidate the nature of the correlations along the field direction, (2) present a mean-field analysis to show how the LIC phase diagram changes as a function of the field wavelength and amplitude, (3) develop a simulation method by which the extremely low tension of the interface between modulated and vapor or liquid phase can be measured, (4) present a finite-size scaling analysis to accurately extract the LIC triple point from finite-size simulation data, and (5) consider the fate of LIC in $d=2$ dimensions.

We obtain exact results for fractional equations of Fokker-Planck type using the evolution operator method. We employ exact forms of one-sided Lévy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the nonlinear continuum elasticity theory of columnar materials. We show that twisted textures of filament backbones necessarily introduce stresses into the cross-sectional packing of bundles and that these stresses are formally equivalent to the geometrically induced stresses generated in thin elastic sheets that are forced to adopt spherical curvature. As in the case of crystalline order on curved membranes, geometrically induced stresses couple elastically to the presence of topological defects in the in-plane order. We derive the effective theory of multiple disclination defects in the cross section of bundle with a fixed twist and show that above a critical degree of twist, one or more fivefold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multidisclination packings based on models of equilibrium and nonequilibrium cross-sectional order.

Twisted and ropelike assemblies of filamentous molecules are common and vital structural elements in cells and tissues of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross section and out-of-plane interfilament twist in bundles. Using nonlinear continuum elasticity theory of columnar materials, we study the favorable coupling of twist-induced stresses to the presence of edge dislocations in the lattice packing of bundles, which leads to a restructuring of the ground-state order of these materials at intermediate twist. The stability of dislocations increases as both the degree of twist and lateral bundle size grow. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist, giving rise to a rich class of “polycrystalline” packings.

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from the radius defined by the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analyzed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated and shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter $\sigma$. In these simulations, the magnitude of the excess equimolar radius is shown to be smaller than $\sigma /2$. This suggests that the surface tension of liquid drops at the nanometer length scale is much closer to that of the planar vapor-liquid interface than reported in studies based on the mechanical route.

We introduce an implicit solvent Molecular Dynamics approach for calculating ionic fluxes through narrow nanopores and transmembrane channels. The method relies on a dual-control-volume grand-canonical molecular dynamics (DCV-GCMD) simulation and the analytical solution for the electrostatic potential inside a cylindrical nanopore recently obtained by Levin [Europhys. Lett. 76, 163 (2006)]. The theory is used to calculate the ionic fluxes through an artificial transmembrane channel which mimics the antibacterial gramicidin A channel. Both current-voltage and current-concentration relations are calculated under various experimental conditions. We show that our results are comparable to the characteristics associated to the gramicidin A pore, especially the existence of two binding sites inside the pore and the observed saturation in the current-concentration profiles.

In this work we formulate a consistent Bayesian approach to modeling stochastic (random) dynamical systems by time series and implement it by means of artificial neural networks. The feasibility of this approach for both creating models adequately reproducing the observed stationary regime of system evolution, and predicting changes in qualitative behavior of a weakly nonautonomous stochastic system, is demonstrated on model examples. In particular, a successful prognosis of stochastic system behavior as compared to the observed one is illustrated on model examples, including discrete maps disturbed by non-Gaussian and nonuniform noise and a flow system with Langevin force.

The “liquid film motor,” a novel device with important implications for basic research and technology, is analyzed. It works perfectly with both direct current (dc) and alternating current (ac) fields. We develop a mathematical model describing electrohydrodynamical (EHD) motions induced by ac fields, which are more complex and have wider technological applications than those produced by dc fields. The main characteristics of these motions, derived in our paper and in full agreement with the experimental ones, are as follows: (i) Rotation of the film requires that the frequencies of the ac fields are exactly the same and their magnitudes surpass a threshold, which depends on their phase difference. (ii) Vibrations may be induced by fields with different frequencies. (iii) The EHD motions strongly depend on the polarization induced by the external electric field. However, these motions are little affected by the liquid's electrical conductivity, viscosity, dielectric constant, and density. Our model also predicts several features, which have yet to be experimentally verified.

The aim of this work is the description of the chain formation phenomena observed in colloidal suspensions of superparamagnetic nanoparticles under high magnetic fields. We introduce a methodology based on an on-the-fly coarse-grain (CG) model. Within this approach, the coarse-grain objects of the simulation and their dynamic behavior are not fixed a priori at the beginning of the simulation but rather redefined on the fly. The motion of the CG objects (single particles or aggregates) is described by an anisotropic diffusion model and the magnetic dipole-dipole interaction is replaced by an effective short-range interaction between CG objects. The methodology correctly reproduces previous results from detailed Langevin dynamics simulations of dispersions of superparamagnetic colloids under strong fields while requiring an amount of CPU time orders of magnitude smaller. This substantial improvement in the computational requirements allows the simulation of problems in which the relevant phenomena extend to time scales inaccessible with previous simulation techniques. A relevant example is the waiting time dependence of the relaxation time $T_2$ of water protons observed in magnetic resonance experiments containing dispersions of superparamagnetic colloids, which is correctly predicted by our simulations. Future applications may include other popular real-world applications of superparamagnetic colloids such as the magnetophoretic separation processes.

In this report we present an elegant method to build and maintain an antiphase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The antiphase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration. This example provides a proof of principle that open-loop control can be used to create desired synchronization patterns for nonlinear oscillators, when feedback is expensive or impossible to obtain.

We study the temperature dependence of the structure and orientation of the first hydration layers of the protein lysozyme and compare it with the situation for a model homogeneous hydrophobic surface, a graphene sheet. We show that in both cases these layers are significantly better structured than bulk water. The geometrical constraint of the interface makes the water molecules adjacent to the surface lose one water-water hydrogen bond and expel the fourth neighbors away from the surface, lowering local density. We show that a decrease in temperature improves the ordering of the hydration water molecules, preserving such a geometrical effect. For the case of graphene, this favors an ice Ih-like local structuring, similar to the water-air interface but in the opposite way along the $c$ axis of the basal plane (while the vicinal water molecules of the air interface orient a hydrogen atom toward the surface, the oxygens of the water molecules close to the graphene plane orient a lone pair in such a direction). In turn, the case of the first hydration layers of the lysozyme molecule is shown to be more complicated, but still displaying signs of both kinds of behavior, together with a tendency of the proximal water molecules to hydrogen bond to the protein both as donors and as acceptors. Additionally, we make evident the existence of signatures of a liquid-liquid transition (Widom line crossing) in different structural parameters at the temperature corresponding to the dynamic transition incorrectly referred to as “the protein glass transition.”

We investigate cage breaking in dense hard-disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free-energy landscape containing two energy minima separated by an energy barrier. The exact free-energy landscape can be calculated as a function of system size by a direct enumeration of states. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of using a one-dimensional representation to understand dynamics through a multidimensional space, such as diffusion acquiring spatial dependence and discontinuities in spatial derivatives of free energy.

Nematic liquid crystal phase diagrams in temperature-biaxiality space are usually complex. We construct a Landau theory based on the analogous molecular-field theory for orthorhombic biaxial nematic fluids. A formal procedure yields coefficients (some of which, unusually, can be tensorial) in this Landau expansion, correctly predicts the complete set of invariants formed from the ordering tensors, and avoids ad hoc parametrization of the molecular biaxiality. By regularizing the Landau expansion to avoid unwanted order parameter divergences at low temperatures, we predict phase behavior over the whole range of biaxiality. The resulting phase diagrams have the same topology as those of molecular-field theory.

We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular, we take constraints on the membrane area and the volume of fluid that it encapsulates into account when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the nonthermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane, a curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active transport of fluid through the membrane. For the direct force and curvature force cases, we compare our results to existing experiments on active membranes.

Based on numerical simulations of a stochastic three-phase traffic flow model, we reveal the physics of the fundamental hypothesis of three-phase theory that, in contrast with a fundamental diagram of classical traffic flow theories, postulates the existence of a two-dimensional (2D) region of steady states of synchronized flow where a driver makes an arbitrary choice of a space gap (time headway) to the preceding vehicle. We find that macroscopic and microscopic spatiotemporal effects of the entire complexity of traffic congestion observed up to now in real measured traffic data can be explained by simulations of traffic flow consisting of identical drivers and vehicles, if a microscopic model used in these simulations incorporates the fundamental hypothesis of three-phase theory. It is shown that the driver's choice of space gaps within the 2D region of synchronized flow associated with the fundamental hypothesis of three-phase theory can qualitatively change types of congested patterns that can emerge at a highway bottleneck. In particular, if drivers choose long enough spaces gaps associated with the fundamental hypothesis, then general patterns, which consist of synchronized flow and wide moving jams, do not emerge independent of the flow rates and bottleneck characteristics: Even at a heavy bottleneck leading to a very low speed within congested patterns, only synchronized flow patterns occur in which no wide moving jams emerge spontaneously.

We propose a route to spatiotemporal chaos, in which the system is assumed to have spatial reflection antisymmetry and field-translation symmetry. The lowest-order nonlinear equation that satisfies these symmetries is explored with the weak nonlinear analysis around the bifurcation point. We conclude that the nonlinear term ${\partial }_x^{2}u{\partial }_x^{3}u$ is important to make a nontrivial dynamics, and show that the nonlinear dynamical equation having this term produces a turbulent dynamics.

We study the effect of weak vibrations on the imbibition of water in granular media. In our experiments, we have observed that as soon as the vibration is applied, an initially pinned wetting front advances in the direction of imbibition. We found that the front motion is governed by the avalanches of localized intermittent advances directed at 45${}^{\circ }$ to the imbibition direction. When the rescaled gravitational acceleration of vertical vibrations is in the range of $0.81⩽G⩽0.95$, we observed an almost steady motion of wetting front with a constant velocity $v_{cr}\left(G\right)\propto \exp \left(-1/G\right)$ during more than 20 min, whereas at lower accelerations ($0.5⩽G⩽0.8$) the front velocity decreases in time as $v\propto t^{-\delta }$. We suggest that the steady motion of an imbibition front in a weakly vibrated granular medium can be treated as a creep motion associated with nonthermal temporal fluctuations of packing density in a weakly vibrated granular medium.

Weak Alfvénic turbulence in a periodic domain is considered as a mixed state of Alfvén waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed, and, indeed, none is found. If the 2D modes are not directly forced, $k^{-2}$ and $k^{-1}$ spectra are found for the Alfvén waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar, and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagating Alfvén waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved.