We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%.

Rapid prototyping by combining evolutionary computation with simulations is becoming a powerful tool for solving complex design problems in materials science. This method of optimization operates in a virtual design space that simulates potential material behaviors and after completion needs to be validated by experiment. However, in principle an evolutionary optimizer can also operate on an actual physical structure or laboratory experiment directly, provided the relevant material parameters can be accessed by the optimizer and information about the material's performance can be updated by direct measurements. Here we provide a proof of concept of such direct, physical optimization by showing how a reconfigurable, highly nonlinear material can be tuned to respond to impact. We report on an entirely computer controlled laboratory experiment in which a $6\times 6$ grid of electromagnets creates a magnetic field pattern that tunes the local rigidity of a concentrated suspension of ferrofluid and iron filings. A genetic algorithm is implemented and tasked to find field patterns that minimize the force transmitted through the suspension. Searching within a space of roughly ${10}^{10}$ possible configurations, after testing only 1500 independent trials the algorithm identifies an optimized configuration of layered rigid and compliant regions.

We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius $R$ separated by a distance $H$ that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density-functional theory, and finite-size scaling theory, we study the location and order of the bridging transition and also the stability of the liquid bridges, which determines spinodal lines. The location of the bridging transitions is similar for cylinders and spheres, so that at bulk coexistence, for example, the distance $H_b$ at which a transition between bridged and unbridged configurations occurs is proportional to the colloid radius $R$. However, all other aspects, particularly the stability of liquid bridges, are very different in the two systems. Thus, for cylinders the bridging transition is typically strongly first-order, while for spheres it may be first-order, critical, or rounded as determined by a critical radius $R_c$. The influence of thick wetting films and fluctuation effects beyond mean field are also discussed in depth.

Phase-separation dynamics of weakly charged polyacid solutions under a constant gradient of base concentration is studied both theoretically and numerically. The time-evolution equation of polymer volume fraction is derived by assuming that the chemical equilibrium of the dissociation reaction is locally established. Numerical simulations of the system in contact with two reservoirs in which the base concentrations differ are performed. The numerical results show that the polymer volume fraction can be transported by the concentration gradient of the base, which leads to the dynamic behavior of mesophase domain structures.

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic $\left[\mathcal{O}\left(\sqrt{N}\right)\right]$ noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems—age-size relationships and species extinction time—in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of “zero mean” environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics, and discuss their relevance to realistic models of community dynamics.

We study isolation as a means to control epidemic outbreaks in complex networks, focusing on the consequences of delays in isolating infected nodes. Our analysis uncovers a tipping point: if infected nodes are isolated before a critical day $d_c$, the disease is effectively controlled, whereas for longer delays the number of infected nodes climbs steeply. We show that $d_c$ can be estimated explicitly in terms of network properties and disease parameters, connecting lowered values of $d_c$ explicitly to heterogeneity in degree distribution. Our results reveal also that initial delays in the implementation of isolation protocols can have catastrophic consequences in heterogeneous networks. As our study is carried out in a general framework, it has the potential to offer insight and suggest proactive strategies for containing outbreaks of a range of serious infectious diseases.

We study the phenomena of oscillation quenching in a system of limit cycle oscillators which are coupled indirectly via a dynamic environment. The dynamics of the environment is assumed to decay exponentially with some decay parameter. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). The critical curves for the regions of oscillation quenching as a function of coupling strength and decay parameter of the environment are obtained analytically using linear stability analysis and are found to be consistent with the numerics.

The impact of droplets on an inclined falling liquid film is studied experimentally using high-speed imaging. The falling film is created on a flat substrate with controllable thicknesses and flow rates. Droplets with different sizes and speeds are used to study the impact process under various Ohnesorge and Weber numbers, and film Reynolds numbers. A number of phenomena associated with droplet impact are identified and analyzed, such as bouncing, partial coalescence, total coalescence, and splashing. The effects of droplet size, speed, as well the film flow rate are studied culminating in the generation of an impact regime map. The analysis of the lubrication force acted on the droplet via the gas layer shows that a higher flow rate in the liquid film produces a larger lubrication force, slows down the drainage process, and increases the probability of droplet bouncing. Our results demonstrate that the flowing film has a profound effect on the droplet impact process and associated phenomena, which are markedly more complex than those accompanying impact on initially quiescent films.

The self-consistent laser evolution of an intense, short-pulse laser exciting a plasma wave and propagating in a preformed plasma channel is investigated, including the effects of pulse steepening and energy depletion. In the weakly relativistic laser intensity regime, analytical expressions for the laser energy depletion, pulse self-steepening rate, laser intensity centroid velocity, and phase velocity of the plasma wave are derived and validated numerically.

An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).

We investigate transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics.

The validity of the transient work fluctuation theorem for a charged Brownian harmonic oscillator embedded in a non-Markovian heat bath and under the action of crossed electric and magnetic fields is investigated. The aforementioned theorem is verified to be valid within the context of the generalized Langevin equation with an arbitrary memory kernel and arbitrary dragging in the potential minimum. The fluctuation-dissipation relation of the second kind is assumed to be valid and shows that the non-Markovian stochastic dynamics associated with the particle, in the absence of the external time-dependent electric field, reaches an equilibrium state, as is precisely demanded by such a relation. The Jarzynski equality in this problem is also analyzed.

The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is strong near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. USA 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.

We compare the photoinduced reorientation of the easy axis on rubbed polyimide surfaces for the nematic E7 doped with three isomers of methyl red; ortho, meta, and para. Using optical techniques, the angle and the pitch of the director at the polymer surface were measured before, during, and after photoexcitation of the dye. Optical absorbances were also measured before and after photoexcitation. Extrapolation lengths, hence anchoring energies, were determined with the on/off application of a magnetic field for meta- and para-methyl red-doped nematics. Because of an elastic reorientation of the easy axis in the presence of the magnetic field, we could not determine the extrapolation length of the ortho-methyl red-doped nematic. Our results confirm that photoinduced reorientation is facilitated by desorption of all dyes from the polymer surface. While there is little evidence of weak photoinduced adsorption of meta- and para-methyl red to the surface during photoexcitation, there is strong evidence of photoinduced adsorption of ortho-methyl red, which is long lasting.

Molecular simulation of adsorption of water molecules in nanoporous amorphous biopolymers, e.g., cellulose, reveals nonlinear swelling and nonlinear mechanical response with the increase in fluid content. These nonlinearities result from hydrogen bond breakage by water molecules. Classical poroelastic models, employing porosity and pore pressure as basic variables for describing the “pore fluid,” are not adequate for the description of these systems. There is neither a static geometric structure to which porosity can sensibly be assigned nor arrangements of water molecules that are adequately described by giving them a pressure. We employ molar concentration of water and chemical potential to describe the state of the “pore fluid” and stress-strain as mechanical variables. A thermodynamic description is developed using a model energy function having mechanical, fluid, and fluid-mechanical coupling contributions. The parameters in this model energy are fixed by the output of the initial simulation and validated with the results of further simulation. The poroelastic properties, e.g., swelling and mechanical response, are found to be functions both of the molar concentration of water and the stress. The basic fluid-mechanical coupling coefficient, the swelling coefficient, depends on the molar concentration of water and stress and is interpreted in terms of porosity change and solid matrix deformation. The difference between drained and undrained bulk stiffness is explained as is the dependence of these moduli on concentration and stress.

We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer-to-substrate modulus ratio is varied from above unity toward zero, we find a first transition from supercritical smooth folding followed by cusping of the valleys to direct subcritical cusped folding, then another to supercritical cusped folding. Beyond threshold, the high-amplitude fold spacing converges to about four layer thicknesses for many modulus ratios. In three dimensions, the instability gives rise to a wide variety of morphologies, including almost degenerate zigzag and triple-junction patterns that can coexist when the layer and substrate are of comparable softness. Our study unifies these results providing understanding for the complex and diverse fold morphologies found in biology, including the zigzag precursors to intestinal villi, and disordered zigzags and triple junctions in mammalian cortex.

DNA-binding protein searches for its target, a specific site on DNA, by means of diffusion. The search process consists of many recurrent steps of one-dimensional diffusion (sliding) along the DNA chain and three-dimensional diffusion (hopping) after dissociation of a protein from the DNA chain. Here we propose a computational method that allows extracting the contribution of sliding and hopping to the search process in vivo from the measurements of the kinetics of the target search by the lac repressor in Escherichia coli [P. Hammar et al., Science 336, 1595 (2012)]. The method combines lattice Monte Carlo simulations with the Brownian excursion theory and includes explicitly steric constraints for hopping due to the helical structure of DNA. The simulation results including all experimental data reveal that the in vivo target search is dominated by sliding. The short-range hopping to the same base pair interrupts one-dimensional sliding while long-range hopping does not contribute significantly to the kinetics of the search of the target in vivo.

The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle $\theta$ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection ($\theta \approx 0^{\circ }$), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for $\theta \approx 0^{\circ }$ disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration ($\theta ={90}^{\circ }$). We confirm the existence of critical angles during the transition $\theta :0^{\circ }\to {90}^{\circ }$, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-$\theta$ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

Dust acoustic waves in the bulk of a dust cloud in complex plasma of low-pressure gas discharge under microgravity conditions are considered. The complex plasma is assumed to conform to the ionization equation of state (IEOS) developed in our previous study. This equation implies the ionization similarity of plasmas. We find singular points of IEOS that determine the behavior of the sound velocity in different regions of the cloud. The fluid approach is utilized to deduce the wave equation that includes the neutral drag term. It is shown that the sound velocity is fully defined by the particle compressibility, which is calculated on the basis of the used IEOS. The sound velocities and damping rates calculated for different three-dimensional complex plasmas both in ac and dc discharges demonstrate a good correlation with experimental data that are within the limits of validity of the theory. The theory provides interpretation for the observed independence of the sound velocity on the coordinate and for a weak dependence on the particle diameter and gas pressure. Predictive estimates are made for the ongoing PK-4 experiment.