A theoretical study of the emergence of helices in the wake of precipitation fronts is presented. The precipitation dynamics is described by the Cahn-Hilliard equation and the fronts are obtained by quenching the system into a linearly unstable state. Confining the process onto the surface of a cylinder and using the pulled-front formalism, our analytical calculations show that there are front solutions that propagate into the unstable state and leave behind a helical structure. We find that helical patterns emerge only if the radius of the cylinder $R$ is larger than a critical value $R>R_c$, in agreement with recent experiments.

A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatiotemporal fractionality, and a variational solution is obtained with the help of the Lévy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.

We report a generalization of a nonequilibrium thermodynamic theory for the mesoscopic dynamics of radially symmetric interacting particles to anisotropic pairwise interactions and attain the one- and two-particle Fokker-Planck kinetics equations at a low-density limit that provides the translational-rotational coupling of their motion due to hydrodynamic interactions, from which we derived the balance equations of linear, angular momentum, and energy dissipation due to particle interactions and energy interchange with heat bath. In this low-density approximation, an already-known virial expression for the long-time translational collective diffusion coefficient of an orientational isotropic suspension in terms of the fluid equilibrium microstructure is recovered. An external shear flow induces, in the diffusive regime, vorticity effects into the rotational diffusion property of the colloidal particles. They manifest in the appearance of the particle's rotational viscosity due to vortex flow. The Smoluchowski equation that governs the dynamical relaxation of colloid microstructure due to particle's Brownian motion under stationary flow is provided.

We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual simplifying assumptions: (1) we allow edge weights to be stochastic rather than deterministic and (2) we do not assume that global knowledge of a network is available. We develop a decentralized routing algorithm that provides en route guidance for travelers on a spatial network with stochastic edge weights without the need to rely on global knowledge about the network. To guide a traveler, our algorithm uses an estimation function that evaluates cumulative arrival probability distributions based on distances between pairs of nodes. The estimation function carries a notion of proximity between nodes and thereby enables routing without global knowledge. In testing our decentralized algorithm, we define a criterion that makes it possible to discriminate among arrival probability distributions, and we test our algorithm and this criterion using both synthetic and real networks.

The stability and collision dynamics of moving solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are investigated. Two disjoint families of solitons are found on the plane of the coefficient of quintic nonlinearity versus the normalized frequency $(\eta ,{\Omega }_{\mathrm{norm}})$. Through numerical stability analysis, we have identified stability regions on the $(\eta ,{\Omega }_{\mathrm{norm}})$ plane for various values of dispersive reflectivity parameter ($m$) and velocity ($v$). The size of stability regions is found to be dependent on $m$ and $v$. Collisions of counterpropgating Type 1 and Type 2 solitons have been systematically investigated. It is found that for low to moderate values of dispersive reflectivity, the collisions of Type 1 solitons can result in various outcomes such as separation of solitons with reduced, increased, unchanged, or asymmetric velocities and generation of a quiescent soliton by merger or formation of three solitons. For strong dispersive reflectivity (e.g., $m=0.5$), the collisions of low-velocity in-phase Type 1 solitons may lead to repulsion of solitons, asymmetric separation, merger into a single soliton, or formation of three solitons (one quiescent and two moving solitons). At higher velocities collisions predominantly lead to the formation of three solitons. For $m=0.5$, in-phase Type 2 solitons may repel or form a temporary bound state of quiescent Type 1 solitons that subsequently splits into two asymmetrically separating Type 1 solitons. $\pi$-out-of-phase Type 2 solitons may also merge to form a quiescent Type 1 soliton.

We present experimental results of chaotic mixing of Newtonian fluids and yield-stress fluids using a rod-stirring protocol with a rotating vessel. We show how the mixing of yield-stress fluids by chaotic advection is reduced compared to the mixing of Newtonian fluids and explain our results, bringing to light the relevant mechanisms: the presence of fluid that only flows intermittently, a phenomenon enhanced by the yield stress, and the importance of the peripheral region. This finding is confirmed via numerical simulations. Anomalously slow mixing is observed when the synchronization of different stirring elements leads to the repetition of slow stretching for the same fluid particles.

The development of a hybrid fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulation method that combines the molecular dynamics of moving particles with the fluctuating hydrodynamics of solvent fields on Eulerian grid cells is presented. This method allows resolution of solute-solvent interfaces and realization of excluded volumes of particles in the presence of hydrodynamic coupling. With these capabilities, we show that the ubiquitous forces mediated by the solvent, hydrophobicity and hydrodynamics, can be linked in a mesoscopic simulation. The strategies we devise to overcome the numerical issues of mixing variables in the Eulerian and Lagrangian coordinate systems, i.e., using a pair of auxiliary fluids to realize the excluded volumes of particles and assigning collocating gridding systems on solutes to interface with solvent fields, are also presented. Simulation results show that the hybrid FHD and MD method can reproduce the solvation free energies and scaling laws of particles dynamics for hydrophobes of different sizes. The collapse of two hydrophobic particles was also simulated to illustrate that the hybrid FHD and MD method has the potential to be generally applied to study nanoscale self-assembly and dynamics-structure-function relationships of biomolecules.

Phase-field crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials processing phenomena involve a vapor phase as well. In this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena near the triple point temperature. For example, the PFC model exhibits density oscillations at liquid-vapor interfaces that compare favorably to data available for interfaces in metallic systems from both experiment and molecular-dynamics simulations. We also quantify the anisotropic solid-vapor surface energy for a two-dimensional PFC hexagonal crystal and find well-defined step energies from measurements on the faceted interfaces. Additionally, the strain field beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum models, simulations, and experimental data. Finally, we examine the dynamic case of step-flow growth of a crystal into a supersaturated vapor phase. The ability to model such a wide range of surface and bulk defects makes this PFC model a useful tool to study processing techniques such as chemical vapor deposition or vapor-liquid-solid growth of nanowires.

Many different kinds of noise are experimentally observed in the brain. Among them, we study a model of noisy chemical synapse and obtain critical avalanches for the spatiotemporal activity of the neural network. Neurons and synapses are modeled by dynamical maps. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of functionally excitable neurons with fast synapses present power-law avalanches, due to rebound spiking dynamics. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for self-organized criticality in neural networks.

We report computer simulations of oscillatory athermal quasistatic shear deformation of dense amorphous samples of a three-dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: For large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g., metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension $d_s=2ln\left(3\right)/ln(9/5)\simeq 3.74$.

We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between $R$ and $R+dR$ is proportional to $R^{-(a+1)}$, where $a>2$. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range interaction, we argue that in our problem, the critical exponents take their short-range values for $a>3-{\eta }_{sr}$ whereas they depend on $a$ for $a<3-{\eta }_{sr}$ where ${\eta }_{sr}$ is the anomalous dimension for the usual percolation problem. The mean-field regime obtained in the fluid problem corresponds to the fully covered regime, $a\le 2$, in the percolation problem. We propose an approximate renormalization scheme to determine the correlation length exponent $\nu$ and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent $\nu$ as a function of $a$. The determined values of $\nu$ show that it is independent of the parameter $a$ for $a>3-{\eta }_{sr}$ and is equal to that for the lattice percolation problem, whereas $\nu$ varies with $a$ for $2<a<3-{\eta }_{sr}$. We also determine the percolation threshold of the system as a function of the parameter $a$.

Low-velocity impact cratering experiments were conducted in a wet sand target. With the addition of interstitial water, the sand stiffens and the yield stress ${\sigma }_{\mathrm{y}}$ increases by a factor of 10 and we observe a significant change in the resulting crater shape. A small water saturation ($S\sim 0.02$) is sufficient to inhibit the crater wall collapse, which causes the crater diameter $d$ to decrease and the crater depth to increase, and results in the steepening of the crater wall. With a further addition of water ($S\sim 0.04$), the collapse is completely inhibited such that cylindrical craters form and the impactor penetration depth $\delta$ and ejecta dispersal are suppressed. However, for $S>0.7$, the wet sand becomes fluidized such that both $d$ and $\delta$ increase thereafter. Comparing the relevant stresses, we find that cylindrical craters form when the yield stress is more than about three times larger than the gravitational stress such that it can withstand collapse. Experiments with different impactor sizes $D$ and velocities indicate that for $S\le 0.02$, gravity-regime scaling applies for $d$. However, the scaling gradually fails as $S$ increases. In contrast, we find that $\delta /D$ can be scaled by the inertial stress normalized by the yield stress, for a wide range of $S$. This difference in the scaling is interpreted as arising from $d$ being affected by whether or not the crater wall collapses, whereas $\delta$ is determined by the penetration process that occurs prior to collapse. The experimental parameter space in terms of dimensionless numbers indicates that our experiments may correspond to impact cratering in small asteroids.

We study experimentally the distribution of local stresses in a granular material confined inside a vertical cylinder. We use an image correlation technique to measure the displacement field of the container induced by the forces exerted by the grains on the inner wall. We describe an optimization procedure based on the linear theory of elastic shells to deduce the distribution of these forces from the measured displacement field. They correspond to the stress field of the granular material close to the container's inner wall. We first confirm the validity of Janssen's description for various experiments, including the influence of the bead diameter and the effect of an additional mass on top of the granular column. We then apply this method to determine the stress field during the gravity-driven discharge of a silo through an aperture.

We investigate the spatiotemporal distribution of microscopic relaxation events, defined through particle hops, in a model polymer glass using molecular dynamics simulations. We introduce an efficient algorithm to directly identify hops during the simulation, which allows the creation of a map of relaxation events for the whole system. Based on this map, we present density-density correlations between hops and directly extract correlation scales. These scales define collaboratively rearranging groups of particles and their size distributions are presented as a function of temperature and age. Dynamical heterogeneity is spatially resolved as the aggregation of hops into clusters, and we analyze their volume distribution and growth during aging. A direct comparison with the four-point dynamical susceptibility ${\chi }_4$ reveals the formation of a single dominating cluster prior to the ${\chi }_4$ peak, which indicates maximally correlated dynamics. An analysis of the fractal dimension of the hop clusters finds slightly noncompact shapes in excellent agreement with independent estimates from four-point correlations.

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.

We report a study of the effects of pressure on the diffusivity of water molecules confined in single-wall carbon nanotubes (SWNT) with average mean pore diameter of $\sim 16$ Å. The measurements were carried out using high-resolution neutron scattering, over the temperature range $220\le T\le 260$ K, and at two pressure conditions: ambient and elevated pressure. The high pressure data were collected at constant volume on cooling, with $P$ varying from $\sim 1.92$ kbar at temperature $T=260$ K to $\sim 1.85$ kbar at $T=220$ K. Analysis of the observed dynamic structure factor $S(Q,E)$ reveals the presence of two relaxation processes, a faster diffusion component (FC) associated with the motion of “caged” or restricted molecules, and a slower component arising from the free water molecules diffusing within the SWNT matrix. While the temperature dependence of the slow relaxation time exhibits a Vogel-Fulcher-Tammann law and is non-Arrhenius in nature, the faster component follows an Arrhenius exponential law at both pressure conditions. The application of pressure remarkably slows down the overall molecular dynamics, in agreement with previous observations, but most notably affects the slow relaxation. The faster relaxation shows marginal or no change with pressure within the experimental conditions.

We present a unified description of interface kinetic effects in phase-field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase-field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross-coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase-field models. We derive general expressions (independent of the details of the phase-field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin-interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase-field model. We discuss in detail the possibility of a nonpositive definite matrix of kinetic coefficients, i.e., a negative effective interface dissipation, although being in the range of stability of the underlying phase-field model. Numerically we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase-field simulations with the analytical predictions of the macroscopic approach.

Using a dynamic light scattering technique, we measure the damping rate of thermal fluctuations of the nematic director for the so-called disklike nematic $N$${}_D$ phase of both the ternary lyotropic K-laurate–1-decanol–H${}_2$O system and the quaternary one of similar composition except for the addition of salt (K${}_2$SO${}_4$). By varying the scattering angle in suitable geometries and polarizations, we are able to measure the orientational diffusivities associated with the pure deformations of splay and twist. A previous study made in the $N$${}_D$ phase of the same ternary system yielded a large deviation between the splay and twist diffusivities. The effect was then interpreted in terms of the anisotropy between their associated viscosities due to induced flows, or backflow. In the present work we observe a strong increase of the backflow as an effect of the added salt. In addition, we make auxiliary measurements of shear viscosity and magnetic instabilities, which help to characterize the effect of the salt in the orientational diffusivities as they are mixed quantities involving elastic constants and viscosity coefficients.

We performed mutual tapping experiments between two humans to investigate the conditions required for synchronized motion. A transition from an alternative mode to a synchronization mode was discovered under the same conditions as when a subject changed from a reactive mode to an anticipation mode in single tapping experiments. The experimental results suggest that the cycle time for each tapping motion is tuned by a proportional control that is based on synchronization errors and cycle time errors. As the tapping frequency increases, a mathematical model based on feedback control in the sensory-motor closed loop predicts a discrete transition of the mode as the gain factors of the proportional control decrease. The conditions for synchronization are shown as a consequence of the coupled dynamics based on the next feedback loop in the sensory-motor system.