A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the $n$-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply the formalism to hard disks and predict the density of two-dimensional random close packing (RCP), ${\varphi }_{\mathrm{rcp}}=0.85\pm 0.01$, and random loose packing (RLP), ${\varphi }_{\mathrm{rlp}}=0.67\pm 0.01$. Our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data.

To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior of a large number of individual microjunctions forming a macroscopic frictional interface. Each microjunction can switch in time between two states: a pinned state characterized by a displacement-dependent force and a slipping state characterized by a time-dependent force. Instead of tracking each microjunction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. This framework allows for a whole family of microjunction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the effects of the time scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity dependent, either monotonic (strengthening or weakening) or nonmonotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time weakening. Next, we show that the model predicts a nontrivial history dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final phases of the preceding sliding event. We suggest that this form of history dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this effect is expected to be experimentally observable.

We introduce a simple ecological model describing the spatial organization of two interacting populations whose individuals are indifferent to conspecifics and avoid the proximity to heterospecifics. At small population densities $\Phi$ a nontrivial structure is observed where clusters of individuals arrange into a rhomboidal bipartite network with an average degree of 4. For $\Phi \to 0$ the length scale, order parameter, and susceptibility of the network exhibit power-law divergences compatible with hyperscaling, suggesting the existence of a zero-density nontrivial critical point. At larger densities a critical threshold ${\Phi }_c$ is identified above which the evolution toward a partially ordered configuration is prevented and the system becomes jammed in a fully mixed state.

Physical features of induced phase transitions in a metastable free flow at an on-ramp bottleneck in three-phase and two-phase cellular automaton (CA) traffic-flow models have been revealed. It turns out that at given flow rates at the bottleneck, to induce a moving jam (F$\to$J transition) in the metastable free flow through the application of a time-limited on-ramp inflow impulse, in both two-phase and three-phase CA models the same critical amplitude of the impulse is required. If a smaller impulse than this critical one is applied, neither F$\to$J transition nor other phase transitions can occur in the two-phase CA model. We have found that in contrast with the two-phase CA model, in the three-phase CA model, if the same smaller impulse is applied, then a phase transition from free flow to synchronized flow (F$\to$S transition) can be induced at the bottleneck. This explains why rather than the F$\to$J transition, in the three-phase theory traffic breakdown at a highway bottleneck is governed by an F$\to$S transition, as observed in real measured traffic data. None of two-phase traffic-flow theories incorporates an F$\to$S transition in a metastable free flow at the bottleneck that is the main feature of the three-phase theory. On the one hand, this shows the incommensurability of three-phase and two-phase traffic-flow theories. On the other hand, this clarifies why none of the two-phase traffic-flow theories can explain the set of fundamental empirical features of traffic breakdown at highway bottlenecks.

Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼$L^{-2.5}$ and ∼$L^{-3}$, respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.

A hydrophilic floating sphere that is denser than water drifts to an amplitude maximum (antinode) of a surface standing wave. A few identical floaters therefore organize into antinode clusters. However, beyond a transitional value of the floater concentration $\varphi$, we observe that the same spheres spontaneously accumulate at the nodal lines, completely inverting the self-organized particle pattern on the wave. From a potential energy estimate we show (i) that at low $\varphi$ antinode clusters are energetically favorable over nodal ones and (ii) how this situation reverses at high $\varphi$, in agreement with the experiment.

Large-amplitude ion acoustic waves are excited and controlled by a chirped frequency driving perturbation. The process involves capturing into autoresonance (a continuous nonlinear synchronization) with the drive by passage through the linear resonance in the problem. The transition to autoresonance has a sharp threshold on the driving amplitude. The theory of this transition is developed beyond the Korteweg–de Vries limit by using the Whitham's averaged variational principle within the water bag model and compared with Vlasov-Poisson simulations.

Some 30 years have passed since we learned that any velocity perturbation develops into a propagating solitary wave in a granular chain, and over a decade has passed since we learned that these solitary waves break and reform upon collision, leaving behind small secondary solitary waves. The production of the latter eventually precipitates the quasiequilibrium state characterized by large energy fluctuations in dissipation-free granular systems. Here we present dynamical simulations on the effects of soft boundaries on solitary wave interaction in granular chains held between fixed walls. We show that at short time scales, a gradient in the distribution of kinetic energy between the boundaries is indeed sustained. At long times, however, such a gradient gets obliterated and there is no measurable difference between the average kinetic energies of the particles adjacent to walls. Our findings suggest that (i) the quasiequilibrium state can effectively erase small gradients of the average kinetic energies of the particles adjacent to walls in a system, (ii) Boltzmann distribution of grain speeds is realized in the system of interest, and (iii) time and space averages yield the same result, thus suggesting that the system is ergodic.

Over the last 15 years, x-ray microtomography has become a useful technique to obtain morphological, structural, and topological information on materials. Moreover, these three-dimensional (3D) images can be used as input data to assess certain properties (e.g., permeability) or to simulate phenomena (e.g., transfer properties). In order to capture all the features of interest, high spatial resolution is required. This involves imaging small samples, raising the question of the representativity of the data sets. In this article, we (i) present a methodology to analyze the microstructural properties of complex porous media from 3D images, (ii) assess statistical representative elementary volumes (REVs) for such materials; and (iii) establish criteria to delimit these REVs. In the context of cultural heritage conservation, a statistical study was done on 30 quarry samples for three sorts of stones. We first present the principles of x-ray microtomography experiments and emphasize the care that must be taken in the 3D image segmentation steps. Results show that statistical REVs exist for these media and are reached for the image sizes studied (1300 × 1300 × 1000 voxels) for two characteristics: porosity and chord length distributions. Furthermore, the estimators used (porosity, autocorrelation function, and chord length distributions) are sufficiently sensitive to quantitatively distinguish these three porous media from each other. Lastly, this study puts forward criteria based on the above-mentioned estimators to evaluate the REVs. These criteria avoid having to repeat the statistical study for each new material studied. This is particularly relevant to quantitatively monitor the modifications in materials (weathering, deformation …) or to determine the smallest 3D volume for simulation in order to reduce computing time.

The aim of this paper is to construct highly accurate local absorbing boundary conditions for a linearized Korteweg–de Vries equation on unbounded domain. The local absorbing boundary conditions are derived by Padé approximation with high accuracy, and a sequence of auxiliary variables are utilized to avoid the high-order derivatives in the absorbing boundary conditions. Then the original problem on unbounded domain is replaced by an equivalent initial boundary value problem defined on a finite domain. The finite difference method is applied to solve the reduced problem on the finite computational domain. Finally, numerical results are presented to demonstrate the effectiveness and accuracy of the proposed method.

Computing two-center overlap integrals arising in Hartree-Fock-Roothaan equations is considered by using the numerical Global-adaptive method. These integrals are expressed through auxiliary functions in ellipsoidal coordinates. They involve Slater-type basis sets with noninteger principal quantum numbers. A computationally simple, efficient, and reliable program procedure is presented. Comparison is made with the results of numerical three-dimensional adaptive integration procedure presented by Ramanowski, with methods used for analytical solution via auxiliary functions and series expansions by translation to a single center. Highly accurate results can be achieved for overlap integrals by numerical approximations both for integer and noninteger principal quantum numbers also, these extended calculations are efficient with no restriction and over a wide range of orbital parameters.

Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds.

We investigated the short-wavelength longitudinal and transverse collective dynamics of the fluid and gel phases of phospholipid bilayers by means of molecular dynamics simulation. Similarly to a crystal, the spectrum of collective excitations in a bilayer consists of longitudinal and transverse acoustic modes, though modified by disorder. Beside acoustic modes, a series of broad dispersionless excitations are revealed. The dispersion curves of the observed excitations may be represented in a pseudo-Brillouin zone scheme centered around the spatial correlation peak of the acyl chains. The study provides evidence for a resonant interaction between the lowest frequency optical phonon and the longitudinal acoustic mode.

We present experiments and simulations that show a fundamental scaling for both the rheology and microstructure of flowing gels. Unique flow-SANS measurements demonstrate that the structure orients along both the neutral and compression axis. We quantify the anisotropy using a single parameter, α, that scales by a dimensionless number, $M^{\prime }$, that arises from a force balance on a particle. Simulations support the scalings and confirm the results are independent of the shape and range of the potential suggesting a universal for colloidal gels with short-ranged attractions.

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second-order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is the nonclassical value $3/2$, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.

We investigate the nonequilibrium dynamics of the two-dimensional (2D) Potts model on the square lattice after a quench below the discontinuous transition point. By means of numerical simulations of systems with $q=12$, 24, and 48, we observe the onset of a stationary regime below the temperature-driven transition, in a temperature interval decreasing with the system size and increasing with $q$. These results obtained dynamically agree with those obtained from the analytical continuation of the free energy [J. L. Meunier and A. Morel, Eur. Phys. J. B 13, 341 (2000)], from which metastability in the 2D Potts model results to be a finite-size effect.

Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. The maximum-entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. However, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuromimetic models) provide a probabilistic mapping between the stimulus, network architecture, and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuromimetic and maximum-entropy models.

Molecular motors are involved in key transport processes inside actin-based cellular protrusions. The motors carry cargo proteins to the protrusion tip which participate in regulating the actin polymerization and play a key role in facilitating the growth and formation of such protrusions. It is observed that the motors accumulate at the tips of cellular protrusions and form aggregates that are found to drift towards the protrusion base at the rate of actin treadmilling. We present a one-dimensional driven lattice model, where motors become inactive after delivering their cargo at the tip, or by loosing their cargo to a cargoless neighbor. The results suggest that the experimental observations may be explained by the formation of traffic jams that form at the tip. The model is solved using a novel application of mean-field and shock analysis. We find a new class of shocks that undergo intermittent collapses. Extensions with attachment and detachment events and relevance to experiments are briefly described.

This paper presents a modeling and experimental framework to characterize the chemotaxis of Serratia marcescens (S. marcescens) relying on two-dimensional and three-dimensional tracking of individual bacteria. Previous studies mainly characterized bacterial chemotaxis based on population density analysis. Instead, this study focuses on single-cell tracking and measuring the chemotactic drift velocity $V_C$ from the biased tumble rate of individual bacteria on exposure to a concentration gradient of l-aspartate. The chemotactic response of S. marcescens is quantified over a range of concentration gradients (${10}^{-3}$ to 5 mM/mm) and average concentrations ($0.5\times {10}^{-3}$ to 2.5 mM). Through the analysis of a large number of bacterial swimming trajectories, the tumble rate is found to have a significant bias with respect to the swimming direction. We also verify the relative gradient sensing mechanism in the chemotaxis of S. marcescens by measuring the change of $V_C$ with the average concentration and the gradient. The applied full pathway model with fitted parameters matches the experimental data. Finally, we show that our measurements based on individual bacteria lead to the determination of the motility coefficient $\mu$ ($7.25\times {10}^{-6}$ cm${}^2$/s) of a population. The experimental characterization and simulation results for the chemotaxis of this bacterial species contribute towards using S. marcescens in chemically controlled biohybrid systems.