Multiple experiments on active systems consider oriented active suspensions on substrates or in chambers tightly confined along one direction. The theories of polar and apolar phases in such geometries were considered in A. Maitra et al. [Phys. Rev. Lett. 124, 028002 (2020)] and A. Maitra et al. [Proc. Natl. Acad. Sci. USA 115, 6934 (2018)], respectively. However, the presence of quenched random disorder due to the substrate cannot be completely eliminated in many experimental contexts possibly masking the predictions from those theories. In this paper, I consider the effect of quenched orientational disorder on the phase behavior of both polar and apolar suspensions on substrates. I show that polar suspensions have long-range order in two dimensions with anomalous number fluctuations, while their apolar counterparts have only short-range order, albeit with a correlation length that can increase with activity, and even more violent number fluctuations than active nematics without quenched disorder. These results should be of value in interpreting experiments on active suspensions on substrates with random disorder.

Using molecular dynamical simulations, compressional shocks in two-dimensional (2D) dusty plasmas are quantitatively investigated under various conditions. A universal relationship between the thermal and the drift velocities after shocks is discovered in 2D Yukawa systems. Using the equation of state of 2D Yukawa liquids, and the obtained pressure from the Rankine-Hugoniot relation, an analytical relation between the thermal and the drift velocities is derived, which well agrees with the discovered universal relationship for various conditions.

This work addresses the construction of a reduced-order model based on a multigroup maximum entropy formulation for application to high-enthalpy nonequilibrium flows. The method seeks a piecewise quadratic representation of the internal energy-state populations by lumping internal energy levels into groups and by applying the maximum entropy principle in conjunction with the method of moments. The use of higher-order polynomials allows for an accurate representation of the logarithm of the distribution of the low-lying energy states, while preserving an accurate description of the linear portions of the logarithm of the distribution function that characterize the intermediate- and high-energy states. A comparison of the quadratic and the linear reconstructions clearly demonstrates how the higher-order reconstruction provides a more accurate representation of the internal population distribution function at a modest increase in the computational cost. Numerical simulations carried out under conditions relevant to hypersonic flight reveal that the proposed model is able to capture the dynamics of the nonequilibrium distribution function using as few as three groups, thereby reducing the computational costs for simulations of nonequilibrium flows.

Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are studied using Monte Carlo simulations and analytic approximations. The Hamiltonians appearing in the Gibbs distribution describing the equilibrium properties differ for sequential and parallel updating but in both cases feature multispin and non-nearest-neighbor couplings. For parallel updating the system is a probabilistic cellular automaton and the equilibrium distribution satisfies detailed balance with respect to the dynamics [E. N. M. Cirillo, P. Y. Louis, W. M. Ruszel and C. Spitoni, Chaos Solitons Fractals 64, 36 (2014)]. In the limit of weak self-interaction for parallel dynamics, odd and even sublattices are nearly decoupled and checkerboard patterns are present in the critical and low temperature regimes, leading to singular behavior in the shape of the critical line. For sequential updating the equilibrium Gibbs distribution satisfies global balance but not detailed balance and the Hamiltonian is obtained perturbatively in the limit of weak nearest-neighbor dynamical interactions. In the limit of strong self-interaction the equilibrium properties for both parallel and sequential updating are described by a nearest-neighbor Hamiltonian with twice the interaction strength of the dynamical model.

Films made from random nanowire arrays are an attractive choice for electronics requiring flexible transparent conductive films. However, thus far there has been no unified theory for predicting their electrical conductivity. In particular, the effects of orientation distribution on network conductivity remain poorly understood. We present a simplified analytical model for random nanowire network electrical conductivity that accurately captures the effects of arbitrary nanowire orientation distributions on conductivity. Our model is an upper bound and converges to the true conductivity as nanowire density grows. The model replaces Monte Carlo sampling with an asymptotically faster computation and in practice can be computed much more quickly than standard computational models. The success of our approximation provides theoretical insight into how nanowire orientation affects electrical conductivity.

Models based on surfactant-driven instabilities have been employed to describe pattern formation by swarming bacteria. However, by definition, such models cannot account for the effect of bacterial sensing and decision making. Here we present a more complete model for bacterial pattern formation which accounts for these effects by coupling active bacterial motility to the passive fluid dynamics. We experimentally identify behaviors which cannot be captured by previous models based on passive population dispersal and show that a more accurate description is provided by our model. It is seen that the coupling of bacterial motility to the fluid dynamics significantly alters the phase space of surfactant-driven pattern formation. We also show that our formalism is applicable across bacterial species.

An analytical theory is developed for acoustic streaming induced by an acoustic wave field inside and outside a spherical fluid particle, which can be a liquid droplet or a gas bubble. The particle is assumed to undergo the monopole (pulsation) and the dipole (translation) oscillation modes. The dispersed phase and the carrier medium are considered to be immiscible, compressible, and viscous. The developed theory allows one to calculate the acoustic streaming both outside and inside the fluid particle. In contrast to earlier works, no restrictions are imposed on the thickness of the outer and inner viscous boundary layers with respect to the particle radius. A numerical implementation of the obtained analytical results is used to evaluate the acoustic streaming for different experimentally relevant configurations, such as an air bubble in water, a water droplet in oil, and a water droplet in air, considering both traveling and standing acoustic waves. The results show the richness of streaming pattern variations that arise in bubbles and droplets.

We study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, $K$ between neighboring triangular sites, and $J$ between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer-matrix calculations and Monte Carlo simulations. Our investigation covers the whole $(K,J)$ phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case $K<0$, where the model is geometrically frustrated. In particular, we find that there are, for all finite $J$, two transitions when $K$ is varied. Their critical properties are explored. In the limits $J\to \pm \infty$ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.

The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are “lattice animals,” made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density ${\theta }_{\text{J}}$ and on the temporal evolution of the coverage fraction $\theta \left(t\right)$. We analyzed all lattice animals of size $n=1$, 2, 3, 4, and 5. A significant number of objects of size $n⩾6$ were also used to confirm our findings. Approach of the coverage $\theta \left(t\right)$ to the jamming limit ${\theta }_{\text{J}}$ is found to be exponential, ${\theta }_{\text{J}}-\theta \left(t\right)\sim exp(-t/\sigma )$, for all lattice animals. It was shown that the relaxation time $\sigma$ increases with the number of different orientations $m$ that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that $\sigma \cong m\in \{1,3,4,6,8,12,24\}$. The presented results suggest that there is no correlation between the number of possible orientations $m$ of the object and the corresponding values of the jamming density ${\theta }_{\text{J}}$. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.

The Fokker-Planck equation provides a complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle's motion. This tensor, however, cannot be interpreted as a diffusion tensor; there are antisymmetric terms which give rise to fluxes perpendicular to the density gradients. Here, we show that for an inhomogeneous magnetic field these nondiffusive fluxes have finite divergence and therefore affect the density evolution of the system. Only in the special cases of a uniform magnetic field or carefully chosen initial condition with the same full rotational symmetry as the magnetic field can these fluxes be ignored in the density evolution.

Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-energy specified in this study not only relates a direct correlation function to the Gaussian smearing of each charged sphere, but also provides the electrostatic contribution to solvation free energy that shows good agreement with simulation results. Furthermore, the Ornstein-Zernike equation leads to a set of generalized Debye-Hückel equations reflecting the Gaussian distributed charges.

The Peregrine soliton is often considered as a prototype of rogue waves. After recent advances in the semiclassical limit of the one-dimensional focusing nonlinear Schrödinger equation [M. Bertola and A. Tovbis, Commun. Pure Appl. Math. 66, 678 (2013)] this conjecture can be seen from another perspective. In the present paper, connecting deterministic and statistical approaches, we numerically demonstrate the effect of the universal local emergence of Peregrine solitons on the evolution of statistical properties of random waves. Evidence of this effect is found in recent experimental studies in the contexts of fiber optics and hydrodynamics. The present approach can serve as a powerful tool for the description of the transient dynamics of random waves and provide new insights into the problem of the rogue waves formation.

In every network, a distance between a pair of nodes can be defined as the length of the shortest path connecting these nodes, and therefore one may speak of a ball, its volume, and how it grows as a function of the radius. Spatial networks tend to feature peculiar volume scaling functions, as well as other topological features, including clustering, degree-degree correlation, clique complexes, and heterogeneity. Here we investigate a nongeometric random graph with a given degree distribution and an additional constraint on the volume scaling function. We show that such structures fall into the category of $m$-colored random graphs and study the percolation transition by using this theory. We prove that for a given degree distribution the percolation threshold for weakly connected components is not affected by the volume growth function. Additionally, we show that the size of the giant component and the cyclomatic number are not affected by volume scaling. These findings may explain the surprisingly good performance of network models that neglect volume scaling. Even though this paper focuses on the implications of the volume growth, the model is generic and might lead to insights in the field of random directed acyclic graphs and their applications.

We study the annealing and rejuvenation behavior of a two-dimensional amorphous solid model under oscillatory shear. We show that, depending on the cooling protocol used to create the initial configuration, the mean potential energy can either decrease or increase under subyield oscillatory shear. For post-yield oscillatory shear, the mean potential energy increases and is independent on the initial conditions. We explain this behavior by modeling the dynamics using a simple model of forced dynamics on a random energy landscape and show that the model reproduces the qualitative behavior of the mean potential energy and mean-square displacement observed in the particle based simulations. This suggests that some important aspects of the dynamics of amorphous solids can be understood by studying the properties of random energy landscapes and without explicitly taking into account the complex real-space interactions which are involved in plastic deformation.

An alternative analysis approach, namely, orthogonal detrended fluctuation analysis (ODFA), is proposed to quantify the long-range correlation exponent. This method uses an orthogonal polynomial to attenuate any trends and quantify the (auto-) correlations in the data. The method is tested using numerically simulated data with long-range correlation. A matrix formalism of this approach is also proposed. Furthermore, the extension to high-order polynomial detrending is discussed. The proposed approach quantifies the long-range exponent with an error rate of about 8% for short datasets (3000 samples) and an error rate of about 1% for long datasets (100 000 samples). ODFA can find applications that involve processing long datasets as well as in real-time processing.

We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm.

In this work, we study the performance of a quasistatic and quantum-adiabatic magnetic Otto cycles with a working substance composed of a single graphene quantum dot modeled by the continuum approach with the use of the zigzag boundary condition. Modulating an external or perpendicular magnetic field, in the quasistatic approach, we found a constant behavior in the total work extracted that is not present in the quantum-adiabatic formulation. We find that, in the quasistatic approach, the engine yielded a greater performance in terms of total work extracted and efficiency as compared with its quantum-adiabatic counterpart. In the quasistatic case, this is due to the working substance being in thermal equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic strokes.

An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Brańka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.

Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical switching with transistorlike performance, for example, realized with polaritons in a planar quantum-well semiconductor microcavity. Here we focus on a specific configuration which takes advantage of the intricate polarization dependencies in the interacting optically driven polariton system. Besides detailed numerical simulations of the coupled light-field exciton dynamics, in the present paper we focus on the derivation of a simplified population competition model giving detailed insight into the underlying mechanisms from a nonlinear dynamical systems perspective. We show that such a model takes the form of a generalized Lotka-Volterra system for two competing populations explicitly including a source term that enables external control. We present a comprehensive analysis of both the existence and stability of stationary states in the parameter space spanned by spatial anisotropy and external control strength. We also construct phase boundaries in nontrivial regions and characterize emerging bifurcations. The population competition model reproduces all key features of the switching observed in full numerical simulations of the rather complex semiconductor system and at the same time is simple enough for a fully analytical understanding.

We analyze the stationary current of bosonic carriers in the Bose-Hubbard chain of length $L$ where the first and the last sites of the chain are attached to reservoirs of Bose particles acting as a particle source and sink, respectively. The analysis is carried out by using the pseudoclassical approach which reduces the original quantum problem to the classical problem for $L$ coupled nonlinear oscillators. It is shown that an increase of oscillator nonlinearity (which is determined by the strength of interparticle interactions) results in a transition from the ballistic transport regime, where the stationary current is independent of the chain length, to the diffusive regime, where the current is inversely proportional to $L$.