This study presents an algorithm to generate a saturated random packing built of identical, unoriented rectangles. The algorithm is based on tracing regions that are unavailable for placing subsequent shapes. If these regions cover the whole packing the algorithm stops because no more objects can be added to the packing; thus it is saturated. The algorithm is used to study packings built of rectangles of side-to-side length ratio $\epsilon \in [1.0,2.5]$. The densest packings are obtained for $\epsilon =1.49\pm 0.02$, and the packing fraction, in this case, reached $0.549641\pm 0.000017$. The microstructural properties of the obtained packings are studied in terms of density autocorrelation function and propagation of orientational ordering.

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the walls, respectively. The ability of our models to simulate rarefied flows are validated through comparison against previously reported results obtained using the linearized Boltzmann–Bhatnagar-Gross-Krook equation for values of the Knudsen number (Kn) up to 100. We find that recovering the nonlinear part of the velocity profile (i.e., its deviation from a linear function) at $\mathrm{Kn}\gtrsim 1$ requires high quadrature orders. We then employ the Shakhov model for the collision term to obtain macroscopic profiles for Maxwell molecules using the standard $\mu \sim T^{\omega }$ law, as well as for monatomic helium and argon gases, modeled through ab initio potentials, where the viscosity is recovered using the Sutherland model. We validate our implementation by comparison with DSMC results and find an excellent match for all macroscopic quantities for $\mathrm{Kn}\lesssim 0.1$. At $\mathrm{Kn}\gtrsim 0.1$, small deviations can be seen in the profiles of the diagonal components of the pressure tensor, the heat flux parallel to the plates, and the velocity profile, as well as in the values of the velocity gradient at the channel center. We attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.

We derive the distribution of particle currents for a system of interacting active Brownian particles in the long-time limit using large deviation theory and a weighted many-body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particles orientations and surrounding density, aligning particles and reducing their effective drag. From the distribution of currents, we compute the diffusion coefficient, which is in excellent agreement with molecular dynamics simulations over a range of self-propulsion velocities and densities. We show that mass transport is Fickian in that the diffusion constant determines the response of a small density gradient, and that nonlinear responses are similarly computable from the density dependence of the current distribution.

We study a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate in the presence of random quenched rotators. These rotators act like obstacles which rotate the orientation of the SPPs by an angle determined by their intrinsic orientations. In the zero self-propulsion limit, our model reduces to the equilibrium $XY$ model with quenched disorder, while for the clean system, it is similar to the Vicsek model for polar flock. We note that a small amount of the quenched rotators destroys the long-range order usually noted in the clean SPPs. The system shows a quasi-long range order state upto some moderate density of the rotators. On further increment in the density of rotators, the system shows a continuous transition from the quasi-long-range order to disorder state at some critical density of rotators. Our linearized hydrodynamic calculation predicts anisotropic higher order fluctuation in two-point structure factors for density and velocity fields of the SPPs. We argue that nonlinear terms probably suppress this fluctuation such that no long-range order but only a quasi-long-range order prevails in the system.

We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic timescale $D_R^{-1}$ set by the rotational diffusion constant $D_R$. We show that, at short times $t\ll D_R^{-1}$, the presence of “activeness” results in a strongly anisotropic and nondiffusive dynamics in the $\left(xy\right)$ plane. We compute exactly the marginal distributions of the $x$ and $y$ position coordinates along with the radial distribution, which are all shown to be non-Brownian. In addition, we show that, at early times, the ABP has anomalous first-passage properties, characterized by non-Brownian exponents.

In physics, biology, and engineering, network systems abound. How does the connectivity of a network system combine with the behavior of its individual components to determine its collective function? We approach this question for networks with linear time-invariant dynamics by relating internal network feedbacks to the statistical prevalence of connectivity motifs, a set of surprisingly simple and local statistics of connectivity. This results in a reduced order model of the network input-output dynamics in terms of motif structures. As an example, the formulation dramatically simplifies the classic Erdős-Rényi graph, reducing the overall network behavior to one proportional feedback wrapped around the dynamics of a single node. For general networks, higher-order motifs systematically provide further layers and types of feedback to regulate the network response. Thus, the local connectivity shapes temporal and spectral processing by the network as a whole, and we show how this enables robust, yet tunable, functionality such as extending the time constant with which networks remember past signals. The theory also extends to networks composed from heterogeneous nodes with distinct dynamics and connectivity, and patterned input to (and readout from) subsets of nodes. These statistical descriptions provide a powerful theoretical framework to understand the functionality of real-world network systems, as we illustrate with examples including the mouse brain connectome.

Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important. Here, we construct a mean-field framework to understand how compact representations are developed across layers, not only in deterministic deep networks with random weights but also in generative deep networks where an unsupervised learning is carried out. Our theory shows that the deep computation implements a dimensionality reduction while maintaining a finite level of weak correlations between neurons for possible feature extraction. Mechanisms of dimensionality reduction and decorrelation are unified in the same framework. This work may pave the way for understanding how a sensory hierarchy works.

We have performed large-scale molecular dynamics simulations on hammerhead RNA in water and observed disparity in the dynamical properties between water and RNA. The simulations are carried out above the dynamical transition temperature of RNA and is varied from below freezing to ambient temperature. Using this model, we observed different types of relaxation dynamics for water and RNA. While RNA shows a single stretched exponential decay, the water molecules show a double-exponential decay. Both water and RNA dynamics show temperature and spatial dependence on relaxation times. The RNA relaxations are many orders of magnitude slower compared to water for all temperature and spatial length scales. RNA relaxations show predominantly heterogeneous dynamics. Water dynamics in the hydration shell show a combination of interfacial water and bulk-like water properties and the water dynamics are decoupled from the RNA dynamics. These results explain the dynamics of water in the hydration shell and that of RNA.

Cyclic loading on granular packings and amorphous media leads to a transition from reversible elastic behavior to an irreversible plasticity. In the present study, we investigate the effect of oscillatory shear on polycrystalline and amorphous colloidal solids by performing molecular dynamics simulations. Our results show that close to the transition, both systems exhibit enhanced particle mobility, hysteresis, and rheological loss of rigidity. However, the rheological response shows a sharper transition in the case of the polycrystalline sample as compared to the amorphous solid. In the polycrystalline system, we see the disappearance of disclinations, which leads to the formation of a monocrystalline system, whereas the amorphous system hardly shows any ordering. After the threshold strain amplitude, as we increase the strain amplitude both systems get fluid. In addition to that, particle displacements are more homogeneous in the case of polycrystalline systems as compared to the amorphous solid, mainly when the strain amplitude is larger than the threshold value. We do not see any effect of oscillation frequency on the reversible-irreversible transition.

Evaporation of sessile droplets is a way to organize suspended particles and create surface coating. Many studies have demonstrated that suspensions with various compositions can give rise to qualitatively different dried patterns, often by focusing on the radial density profile of deposited particles. We demonstrate that a single suspension of superparamagnetic colloids can give rise to several dried patterns thanks to an external magnetic field applied during the evaporation process. We show the various patterns obtained with zero, constant, rotating, and oscillating magnetic fields, and evidence the continuous control given by the intensity of a constant magnetic field. We also show that this magnetic control has a substantial effect on the morphological details of the deposits.

Evaporation of sessile droplets is a method to organize suspended particles on solid substrates. Many studies have demonstrated that Marangoni flows caused by surface-adsorbed molecules or temperature gradients can strongly affect the dried deposit. In the present paper, we show how transitional Marangoni instabilitiy can be triggered by bulk-diluted tensioactive ions. Thanks to particle image velocimetry analysis, we identify four different flow stages. The transition between them can be understood by considering the competition between the Marangoni flow and the mass conservation flow, usually responsible for the coffee-ring pattern. We also demonstrate that the initial ionic concentration can select a coffee-ring pattern or a more homogeneous dried deposit.

We study electrostatic and phonon properties of Yukawa crystals. It is shown that in the harmonic approximation these systems which are used in the theory of dusty plasma can be described analytically by the model from the theory of neutron stars and white dwarfs. Using this approximation, we consider properties of body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and ${\mathrm{MgB}}_2$ lattices. Studies of ${\mathrm{MgB}}_2$ and hcp lattices in the context of Yukawa systems are lacking. It is shown that they never possess the smallest potential energy and the phase diagram of stable Yukawa crystals contains bcc and fcc lattices only. However, corrections to the charge density proportional to ${\left(\kappa a\right)}^4$ can noticeably change the structural diagram of Yukawa systems. The analytical model developed also allows us to describe low-temperature effects where numerical simulations are difficult.

In this work we study of the dynamics of large-size random neural networks. Different methods have been developed to analyze their behavior, and most of them rely on heuristic methods based on Gaussian assumptions regarding the fluctuations in the limit of infinite sizes. These approaches, however, do not justify the underlying assumptions systematically. Furthermore, they are incapable of deriving in general the stability of the derived mean-field equations, and they are not amenable to analysis of finite-size corrections. Here we present a systematic method based on path integrals which overcomes these limitations. We apply the method to a large nonlinear rate-based neural network with random asymmetric connectivity matrix. We derive the dynamic mean field (DMF) equations for the system and the Lyapunov exponent of the system. Although the main results are well known, here we present the detailed calculation of the spectrum of fluctuations around the mean-field equations from which we derive the general stability conditions for the DMF states. The methods presented here can be applied to neural networks with more complex dynamics and architectures. In addition, the theory can be used to compute systematic finite-size corrections to the mean-field equations.

We perform direct numerical simulations of a bidisperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different inertia. For a pair of particles with small difference in their inertias we compare our results with recent theoretical predictions [Meibohm et al., Phys. Rev. E 96, 061102 (2017)] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation and compare with the theoretical predictions. We observe good agreement. For a pair of particles that are very different from each other—one is heavy and the other one has negligible inertia—we give a theory to calculate their root-mean-square relative velocity. This theory also agrees well with the results of our simulations.

We study spatial clustering in a discrete-time, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $\alpha$, that plays the role of an inertia parameter. Using the fact that it suffices to consider the linearized dynamics of the model at small separations, we find that $D_q=D_2/(q-1)$ for $q=2,3,...$ . The correlation dimension $D_2$ turns out to be a nonanalytic function of the inertia parameter in this model. We calculate $D_2$ for small $\alpha$ up to the next-to-leading order in the nonanalytic term.

The random sequential adsorption (RSA) model is a classical model in statistical physics for adsorption on two-dimensional surfaces. Objects are deposited sequentially at random and adsorb irreversibly on the landing site, provided that they do not overlap any previously adsorbed object. The kinetics of adsorption ceases when no more objects can be adsorbed (jamming state). Here, we investigate the role of post-relaxation on the jamming state and percolation properties of RSA of dimers on a two-dimensional lattice. We consider that, if the deposited dimer partially overlaps with a previously adsorbed one, a sequence of dimer displacements may occur to accommodate the new dimer. The introduction of this simple relaxation dynamics leads to a more dense jamming state than the one obtained with RSA without relaxation. We also consider the anisotropic case, where one dimer orientation is favored over the other, finding a non-monotonic dependence of the jamming coverage on the strength of anisotropy. We find that the density of adsorbed dimers at which percolation occurs is reduced with relaxation, but the value depends on the strength of anisotropy.

Quantum heat engine with ideal gas has been well studied, yet the role of interaction was seldom explored. We construct a quantum Otto heat engine with $N$ repulsive bosons in a one-dimensional (1D) hard wall box. With the advantage of exact solution using the Bethe ansatz, we obtain not only the exact numerical result of efficiency in all interacting strength $c$ but also analytical results for strong interaction. We find the efficiency $\eta$ approaches to the one of noninteracting case ${\eta }_{\mathrm{non}}=1-\left(L_1/L_2\right){}^2$ for strong interaction with the asymptotic behavior $\eta \sim {\eta }_{\mathrm{non}}-4(N-1)L_1\left(L_2-L_1\right)/\left(c{L}_2^3\right)$. Here $L_1$ and $L_2$ are two trap sizes during the cycle. Such a phenomenon reflects the duality between 1D strongly repulsive bosons and free fermions. We observe and explain the appearance of a minimum efficiency at a particular interacting strength $c$ and study its dependence on the temperature.

We analyze amplitude death (AD) in large systems of globally coupled oscillators with randomly distributed time scales. We show that the distribution of characteristic eigenvalues of a large but finite system is well approximated by the continuous and discrete spectra of the system in the thermodynamic limit. The stability analysis from the continuous and discrete spectra of the infinite system provides a fairly accurate prediction for the onset of AD in the large finite system. We prove the argument by examining the stability of AD in a paradigmatic system of coupled Stuart-Landau limit cycles with mismatched time scales. The proposed technique is extended to systems of globally coupled nonlinear oscillators of a general form with time-scale diversity, which is verified in coupled chaotic Rössler oscillators. Our study provides analytical insight into the understanding of the emergence of AD in populations of globally coupled dynamical systems.