The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed “hyperuniformity”) has paved the way for the analysis of jamming as an “inverted critical point” in which the direct correlation function $c\left(\mathit{r}\right)$, rather than the total correlation function $h\left(\mathit{r}\right)$, diverges. We expand on the notion that $c\left(\mathit{r}\right)$ provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the $n\mathrm{th}$ derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of $c\left(\mathit{r}\right)$ with regards to singularities it inherits from $h\left(\mathit{r}\right)$. These relations provide a concrete means of identifying features that must be expressed in $c\left(\mathit{r}\right)$ if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c\left(\mathit{r}\right)\propto -1/r$ as $r\to 0$ that accompanies the formation of the delta function at $c\left(D\right)$ that indicates the formation of contacts in all cases, and show that this scaling behavior is, in this case, a consequence of the growing long rangedness in $c\left(\mathit{r}\right)$, e.g., $c\propto -1/r^2$ as $r\to \infty$ for disordered packings. At densities in the vicinity of the freezing density, we find striking qualitative differences in the structure factor $S\left(\mathit{k}\right)$ as well as $c\left(\mathit{r}\right)$ between TJ- and LS-generated configurations, including the early formation of a delta function at $c\left(D\right)$ in the TJ algorithm's packings, indicating the early formation of clusters of particles in near contact. Both algorithms yield structure factors that tend towards zero in the low-wave-number limit as jamming is approached. Correspondingly, we observe the expected power-law decay in $c\left(\mathit{r}\right)$ for large $r$, in agreement with previous theoretical work. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a sensitive means of monitoring for the appearance of an incipient rigid network.

The statistics and origin of the first discrete plastic event in a one-dimensional dislocation dynamics simulation are studied. This is done via a linear stability analysis of the evolving dislocation configuration up to the onset of irreversible plasticity. It is found that, via a fold catastrophe, the dislocation configuration prior to loading directly determines the stress at which the plastic event occurs and that between one and two trigger dislocations are involved. The resulting irreversible plastic strain arising from the instability is found to be highly correlated with these triggering dislocations.

Multiphase flows in porous medium systems are typically modeled at the macroscale by applying the principles of continuum mechanics to develop models that describe the behavior of averaged quantities, such as fluid pressure and saturation. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating the capillary pressure to fluid saturation and, in some cases, other topological invariants such as interfacial area and the Euler characteristic (or average Gaussian curvature). The forms that are used in traditional models, which typically consider only the relationship between capillary pressure and saturation, are hysteretic. An unresolved question is whether the inclusion of additional morphological and topological measures can lead to a nonhysteretic closure relation. Relying on the lattice Boltzmann (LB) method, we develop an approach to investigate equilibrium states for a two-fluid-phase porous medium system, which includes disconnected nonwetting phase features. A set of simulations are performed within a random close pack of 1964 spheres to produce a total of 42 908 distinct equilibrium configurations. This information is evaluated using generalized additive models to quantitatively assess the degree to which functional relationships can explain the behavior of the equilibrium data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and nonhysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. To our knowledge, this work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parametrizations investigated, and the broad set of functions examined. The conclusion of essentially nonhysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.

The confinement provided by a glass box is proving ideal for the formation of vertically aligned structures and a convenient method for controlling the number of dust particles comprising these dust structures as well as their sizes and shapes. In this paper, the electronic confinement of the glass box is mapped, and the particle interactions between the particle pairs inside the glass box are measured. The ion-wake field is shown to exist within the glass box, and its vertical and horizontal extents are measured.

Filamentation dynamics of relativistic optical vortex beams (OVBs) propagating in underdense plasma is investigated. It is shown that OVBs with finite orbital angular momentum (OAM) exhibit much more robust propagation behavior than the standard Gaussian beam. In fact, the growth rate of the azimuthal modulational instability decreases rapidly with increase of the OVB topological charge. Thus, relativistic OVBs can maintain their profiles for significantly longer distances in an underdense plasma before filamentation occurs. It is also found that an OVB would then break up into regular filament patterns due to conservation of the OAM, in contrast to a Gaussian laser beam, which in general experiences random filamentation.

We study the large deviations of the time-integrated current for a driven diffusion on the circle, often used as a model of nonequilibrium systems. We obtain the large deviation functions describing the current fluctuations using a Fourier-Bloch decomposition of the so-called tilted generator, and we also construct from this decomposition the effective (biased, auxiliary, or driven) Markov process describing the diffusion as current fluctuations are observed in time. This effective process provides a clear physical explanation of the various fluctuation regimes observed. It is used here to obtain an upper bound on the current large deviation function, which we compare to a recently derived entropic bound, and to study the low-noise limit of large deviations.

We study a one-parameter generalization of the symmetric simple exclusion process on a one-dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion constraint), annihilation and creation of pairs can occur. The system is driven out of equilibrium by two reservoirs at the boundaries. In this setting the model is still integrable: it is related to the open XXZ spin chain through a gauge transformation. This allows us to compute the full spectrum of the Markov matrix using Bethe equations. We also show that the stationary state can be expressed in a matrix product form permitting to compute the multipoints correlation functions as well as the mean value of the lattice and the creation-annihilation currents. Finally, the variance of the lattice current is computed for a finite-size system. In the thermodynamic limit, it matches the value obtained from the associated macroscopic fluctuation theory.

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

The average energy needed to create a magnon is high in ferromagnetic metals due to the high-strength spin stiffness, which results in strong quantization effects that could be important even at thousands of degrees. To take into account quantum statistics at such high temperatures, the associated effects of anharmonicity of the spin vibrations must be taken into account. In addition to the complex nature of such effects, anharmonicity also affects the occupation of the density of state of the vibration states in the context of quantum statistics. Thus, an unoccupied vibration state might become occupied when its spring stiffness is substantially reduced with anharmonicity. Combined effects of quantum statistics and anharmonicity are expected. In this regard, the thermodynamics of ferromagnetic metals are investigated in this paper through the example of bcc iron between 10 and 1400 K. Theoretical analysis and spin-lattice dynamic simulations are performed, through which the physics behind the complex and dramatic temperature dependence of the thermodynamic functions of bcc iron is understood.

Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers $M$. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

In a recent work [Phys. Rev. E 91, 022808 (2015)] it was reported that placing an obstacle in front of a gate has a beneficial effect in the flow of sheep through it. Here, we extend such results by implementing three different obstacle positions. We have observed that the flow is improved in two cases, while it worsens in the other one; the last instance happens when the obstacle is too close to the door. In this situation, the outcomes suggest that clogging develops between the doorjamb and the obstacle, contrary to the cases when the obstacle is farther, in which case clogging always occurs at the very door. The effectiveness of the obstacle (a strategy put forward to alleviate clogging in emergency exits) is therefore quite sensitive to its location. In addition, the study of the temporal evolution of the flow rate as the test develops makes evident a steady behavior during the entire duration of the entrance. This result is at odds with recent findings in human evacuation tests where the flow rate varies over time, therefore challenging the fairness of straightforward comparisons between pedestrian behavior and animal experimental observations.

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the $n\mathrm{th}$ cumulant of the protein number distribution depends on the $n\mathrm{th}$ moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.

In this work the coalescence of an aqueous drop with a flat aqueous-organic interface was investigated in a thin gap Hele-Shaw cell. Different concentrations of a nonionic surfactant (Span 80) dissolved in the organic phase were studied. We present experimental results on the velocity field inside a coalescing droplet in the presence of surfactants. The evolution of the neck between the drop and the interface was studied with high-speed imaging. It was found that the time evolution of the neck at the initial stages of coalescence follows a linear trend, which suggests that the local surfactant concentration at the neck region for this stage of coalescence can be considered quasiconstant in time. This neck expansion can be described by the linear law developed for pure systems when the surfactant concentration at the neck is assumed higher than in the bulk solution. In addition, velocity and vorticity fields were computed inside the coalescing droplet and the bulk homophase using a high-speed shadowgraphy technique. The significant wall effects in the Hele-Shaw cell in the transverse axis cause the two vertical velocity components towards the singularity rupture point, from the drop and from the bulk homophase, to be of the same order of magnitude. This movement together with the neck expansion creates two pairs of counteracting vortices in the drop and in the bulk phase. The neck velocity is the average of the advection velocities of the two counteracting vortex pairs on each side of the neck. The presence of the surfactant slows down the dynamics of the coalescence, affects the propagation direction of the pair of vortices in the bulk phase, and reduces their size faster compared to the system without surfactant.

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.

The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.

In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function $g_2\left(r\right)$ for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the structural characteristics analyzed in this paper.

We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws for the wave number in the bulk of the domain. Scalings are based on a description of striped patterns in semibounded domains via strain-displacement relations. We compare predictions with direct simulations in the Swift-Hohenberg, the complex Ginzburg-Landau, the Cahn-Hilliard, and reaction-diffusion equations.

Cells measure concentrations of external ligands by capturing ligand molecules with cell surface receptors. The numbers of molecules captured by different receptors co-vary because they depend on the same extrinsic ligand fluctuations. However, these numbers also counter-vary due to the intrinsic stochasticity of chemical processes because a single molecule randomly captured by a receptor cannot be captured by another. Such structure of receptor correlations is generally believed to lead to an increase in information about the external signal compared to the case of independent receptors. We analyze a solvable model of two molecular receptors and show that, contrary to this widespread expectation, the correlations have a small and negative effect on the information about the ligand concentration. Further, we show that measurements that average over multiple receptors are almost as informative as those that track the states of every individual one.

We present a detailed study of the formation of the amniotic sac in the avian embryo, and a comparison with the crocodile amniotic sac. We show that the amniotic sac forms at a circular line of stiffness contrast, separating rings of cell domains. Cells align at this boundary, and this in turn orients and concentrates the tension forces. The tissue fold which forms the amniotic sac is locked exactly along this line due to the colocalization of the stiffness contrast and of the tensile force. In addition, the tensile force plays a regenerative role when the amniotic sac is cut. The fold forming the ventral side of the embryo displays the same characteristics. This work shows that amniote embryogenesis consists of a cascade of buckling events taking place at the boundaries between regions of differing mechanical properties. Hence, amniote embryogenesis relies on a simple and robust biomechanical scheme used repeatedly, and selected ancestrally.

Employing two-dimensional molecular dynamics simulations of dense granular materials under simple shear deformations, we investigate vortex structures of particle rearrangements. Introducing vorticity fields as a measure of local spinning motions of the particles, we observe their heterogeneous distributions, where statistics of vorticity fields exhibit the highly non-Gaussian behavior and typical domain sizes of vorticity fields significantly increase if the system is yielding under quasistatic deformations. In such dense granular flows, a power-law decay of vorticity spectra can be observed at mesoscopic scale, implying anomalous local structures of kinetic energy dissipation. We explain the power-law decay, or enstrophy cascades in dense granular materials, by a dimensional analysis, where the dependence of vorticity spectra not only on the wave number, but also on the shear rate, is well explained. From our dimensional analyses, the scaling of granular temperature and rotational kinetic energy is also predicted.