We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

We perform coupled fluid-particle simulations to understand the granular collapse in an ambient fluid (in particular, water) with a wide range of initial aspect ratios. We observe both similar and distinct features in underwater collapses compared to their dry counterparts. As aspect ratio $a$ increases, the normalized runout distance follows a piecewise power-law growth, transitioning at $a=2.5$. We associate this transition with the different growth rates of kinetic energy (with $a$) in vertical and horizontal directions. The ability of utilizing available energy for horizontal motion becomes limited when $a>2.5$. Moreover, the front propagation during underwater collapses can be well scaled by using the initial column height as length scale and considering a reduced gravity (due to buoyancy) in timescale. Under the reduced gravity, the initial fall of tall columns is found to be ballistic, consistent with dry collapses. On the other hand, underwater collapses (especially for large $a$) exhibit unique dynamics due to the presence of water. The eddies generated in water, which may carry considerable fluid inertia, tend to erode the surface of the granular layer, thus modifying the deposit morphology. The energy conversion is also affected by the ambient fluid. While water obviously consumes energy from the granular phase through fluid-particle interactions, it actually increases the efficiency of energy conversion from vertical to horizontal directions. The latter effect compensates the difference of runout distance between underwater and dry collapses.

Cross-beam energy transfer (CBET) is a laser-plasma instability that significantly impacts laser energy deposition in laser-driven inertial confinement fusion (ICF) experiments. Radiation-hydrodynamics simulations, which are used to design and tune ICF implosions, use ray-based CBET models, but existing models require artificial multipliers to conserve energy and to obtain quantitative agreement with experiments. The discretization of the ray trajectories in traditional ray-based CBET models does not account for the rapid variation in CBET gain as rays pass through caustics. We introduce a model that allows one to treat caustics much more accurately and greatly improves energy conservation. The ray-based CBET calculations show excellent agreement with laser absorption from two-dimensional wave-based calculations (0.3% difference) and a three-dimensional 60-beam OMEGA implosion (2.4% difference) without artificial multipliers.

A mechanism to generate spatially segregated territories in two dimensions consists of individuals depositing their own marks and avoiding foreign ones. This form of environment-mediated interaction, called stigmergy, makes the emerging spatiotemporal territory dynamics quite rich. Short-lived marks produce rapidly morphing and highly mobile territories. Long-lived marks yield slow territories with a narrowly defined shape distribution. The change in territory mobility depending on the time for which individual marks remain active is accompanied by a liquid-hexatic-solid transition akin to the Kosterlitz-Thouless melting scenario.

The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though in this case standard analytical tools are inapplicable, we found that in all considered cases eigenvector distributions are very well described by the generalized hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties.

We consider a separable continuous-time random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation that relates the probability distribution function (pdf) of finding a particle at a given position and time to the single-step jump length and waiting time pdfs is provided. The equation takes the form of a generalized Fokker-Planck equation when the jump length pdf of the particle has a finite variance. This generalized equation becomes a fractional Fokker-Planck equation in the case of a heavy-tailed waiting time pdf. These equations allow us to study the relationship between expansion, diffusion, and external force. We establish the conditions under which the dominant contribution to transport stems from the diffusive transport rather than from the drift due to the medium expansion. We find that anomalous diffusion processes under a constant external force in an expanding medium described by means of our continuous-time random walk model violate the generalized Einstein relation and lead to propagators that are qualitatively different from the ones found in a static medium. Our results are supported by numerical simulations.

Cascading failures may lead to dramatic collapse in interdependent networks, where the breakdown takes place as a discontinuity of the order parameter. In the cascading failure (CF) model with healing there is a control parameter which at some value suppresses the discontinuity of the order parameter. However, up to this value of the healing parameter the breakdown is a hybrid transition, meaning that, besides this first order character, the transition shows scaling too. In this paper we investigate the question of universality related to the scaling behavior. Recently we showed that the hybrid phase transition in the original CF model has two sets of exponents describing respectively the order parameter and the cascade statistics, which are connected by a scaling law. In the CF model with healing we measure these exponents as a function of the healing parameter. We find two universality classes: in the wide range below the critical healing value the exponents agree with those of the original model, while above this value the model displays trivial scaling, meaning that fluctuations follow the central limit theorem.

Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph-theoretical methods. We show that the group structure of real weighted networks is very robust under weight thresholding, as it is maintained even when most of the edges are removed. This appears to be related to the correlation between topology and weight that characterizes real networks. On the other hand, the behavior of other properties is generally system dependent.

A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and political systems, diversity in the knowledge, experience, and background among the individuals can be expected. Games in which the players do not have an identical strategy set are hypergames. Studies of hypergame dynamics have been scarce, especially those on networks. We investigate evolutionary hypergame dynamics on regular lattices using a prototypical model of three available strategies, in which the strategy set of each player contains two of the three strategies. Our computations reveal that more complex dynamical phases emerge from the system than those from the traditional evolutionary game dynamics with full knowledge of the complete set of available strategies, which include single-strategy absorption phases, a cyclic competition (“rock-paper-scissors”) type of phase, and an uncertain phase in which the dominant strategy adopted by the population is unpredictable. Exploiting the pair interaction and mean-field approximations, we obtain a qualitative understanding of the emergence of the single strategy and uncertain phases. We find the striking phenomenon of strategy revival associated with the cyclic competition phase and provide a qualitative explanation. Our work demonstrates that the diversity in the individuals' strategy set can play an important role in the evolution of strategy distribution in the system. From the point of view of control, the emergence of the complex phases offers the possibility for harnessing evolutionary game dynamics through small changes in individuals' probability of strategy adoption.

We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of $N$ lines with initial loads $L_1,...,L_N$ and free spaces (i.e., redundant space) $S_1,...,S_N$ that are independent and identically distributed with joint distribution $P_{LS}(x,y)=\mathbb{P}\left[L\le x,S\le y\right]$. The capacity $C_i$ is the maximum load allowed on line $i$ and is given by $C_i=L_i+S_i$. When a line fails due to overloading, it is removed from the system and $(1-\varepsilon )$ fraction of the load it was carrying is redistributed equally among all remaining lines in the system. The rest (i.e., $\varepsilon$ fraction) of the load is assumed to be lost or absorbed, e.g., due to advanced circuitry disconnecting overloaded power lines or an interconnected network or material absorbing a fraction of the flow from overloaded lines. We analyze the robustness of this flow network against random attacks that remove a $p$ fraction of the lines. Our contributions include (i) deriving the final fraction of alive lines $n_{\infty }(p,\varepsilon )$ for all $p,\varepsilon \in (0,1)$ and confirming the results via extensive simulations; (ii) showing that partial redistribution might lead to (depending on the parameter $0<\varepsilon \le 1$) the order of transition at the critical attack size $p^{★}$ changing from first to second-order; and (iii) proving analytically that flow networks achieve maximum robustness [quantified by the area ${\int }_0^1{n}_{\infty }(p,\varepsilon )dp]$ when all lines have the same free space regardless of their initial load. The optimality of equal free-space allocation is also confirmed on real-world data from the UK National Power Grid.

Collective behavior is observed in many physical and biological systems and has been studied through agent-based models, including the Vicsek model, which enforces aligned motion among agents. The behaviors produced by these models are highly dependent on the type of sensing individuals use. In nature, bats successfully use a complex form of sensing, namely, active echolocation in a relatively narrow beam and passive eavesdropping on their conspecifics' sound over a wider volume. Inspired by this system, we investigate whether augmenting an active sensing mechanism with passive sensing can improve the collective behavior of the group. A three-dimensional Vicsek-type model is presented to study the effects of combining active and passive sensing on collective behavior of a group of particles in the presence of noise. Phase transition is observed in both the presence and absence of passive sensing, yet the range of parameters for which ordered and disordered group states exist dramatically changes when passive sensing is implemented. Notably, we find numerous cases of the model for which the implementation of passive sensing increases the robustness of the collective behavior to noise.

Sunset Yellow (SSY) is an aromatic heterocycle nano-sheet functionalized by hydrophilic sulphanate groups. SSY forms chromonic stacks and liquid crystal (LC) phases in aqueous solution. The DNA oligomer 5′-GCGCTTAAGCGC-3′ is a self-complementary strand which forms duplexed B-form helices in aqueous solution, which, similarly, aggregate into chromonic stacks and form LC phases. Binary aqueous solutions of these two molecules were investigated using polarized optical microscopy, x-ray diffraction, and spectroscopy. At lower solute concentrations and/or higher temperatures these solutions form uniformly mixed single phases, including isotropic, chiral nematic, and hexagonal columnar LCs. At higher solute concentrations and/or lower temperatures, the uniform columnar solution separates into two columnar phases, one containing SSY with trace DNA and the other containing both SSY and DNA aggregates. The study of these solutions indicates that the mixed and unmixed phases are composed of single component SSY or DNA chromonic stacks, with the DNA stacks containing a small fraction of intercalated SSY, evidenced by structurally induced circular dichroism in the SSY absorption band. In the columnar monophase, the hexagonal lattice sites are occupied randomly by either DNA or SSY columns, with the column spacing varying continuously with the SSY-DNA mass ratio. The results demonstrate significant selectivity in the chromonic stacking of both molecules. The binding mode of these chromonic LCs may have applications to adaptive optics and nucleic acid chemistry.

Experimental results have shown that resistivity index can deviate from Archie's law at low conductive phase saturation. Previous works have claimed that wettability and flow history are the two main factors causing this phenomenon. Herein, we investigate how the underlying fluid morphology influences electrical resistivity. We start from digital synchrotron x-ray microcomputed tomography images at different conductive phase saturations. We then simulate two-phase flow at different Capillary numbers and wettabilities to investigate deviations in resistivity index. We discover that other than water saturation the connectivity of water quantified by Euler characteristic is an important parameter in determining electrical resistivity for intermediate to purely oil-wet conditions. Deviations in electrical resistivity are found to start at low Capillary number ($\mathrm{Ca}\sim {10}^{-5}$) for intermediate and oil-wet conditions for the full range of water saturations. We study correlations between resistivity index, saturation, and Euler characteristic by using the Pearson product-moment correlation and a linear regression model. We find a strong correlation between water saturation and resistivity index for the water-wet case while for the intermediate and oil-wet cases a strong correlation between Euler characteristic and resistivity index was observed. The results are explained in terms of percolation theory and a general relationship for resistivity index is proposed for intermediate-wet to oil-wet systems whereby the percolation parameter is normalized Euler characteristic. The findings explain previously observed deviations in resistivity index measurements and allow for a means to predict Euler characteristic from laboratory core-scale experiments using the proposed percolation model.

Cu foils, $200\mu \mathrm{m}$ in thickness, were heated in two stages by a $\sim 100$-ns-long monoenergetic electron bunch at 19.8 MeV and a current of 1.7 kA ($8.5\times {10}^{14} e^{-}$) in a 2-mm-spot to $T_e\sim 1$ eV. After 45 ns of isochoric heating, the pressure in the foil builds up to $>20$ GPa (200 kbar), it begins to hydrodynamically disassemble, and a velocity spread is measured. Near the end of the electron pulse, the 1550 nm probe is cut off or absorbed. Photonic Doppler velocimetry measurements were made to quantify the expansion velocity, hydrodynamic disassembly time, and pressure of the foil prior to cutoff. Measurements indicate foil motion begins the instant electrons pass through the foil and continues until the particle velocity approaches the ambient sound velocity of Cu and the bulk density exceeds the critical density of the probe. Once the density of the plasma drops below the critical threshold and begins reflecting again, an expansion velocity of the classical plasma is also measured, similar to the point-source solution.

Invasion of Turing patterns into a region of bulk oscillations was investigated in the Belousov-Zhabotinsky-Aerosol OT reverse microemulsion system. Three distinct mechanisms for the formation of Turing structures at the expense of the bulk oscillation region were observed: frozen waves, which have been reported previously in this system, and reflecting waves and Turing-Hopf fronts, which have not. Turing-Hopf fronts appeared as the outer rings in this quasi-two-dimensional system with an amplitude intermediate between those of the Turing pattern and the phase waves in the bulk oscillation region. Three-dimensional (3D) Turing-Hopf shells (outer layers of 3D balls) were also observed.

This paper presents a nonequilibrium, first-principles, thermodynamic-ensemble-based model for the relaxation process of interacting nonequilibrium systems. This model is formulated using steepest-entropy-ascent quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical ensemble and is applied to a many-particle system of classical or indistinguishable particles. Two kinds of interactions are discussed, including pure heat diffusion and heat and mass diffusion together. Since no local equilibrium assumption is made, the conjugate fluxes and forces are intrinsic to the subspaces of the state space of one system and/or of the state space of two interacting systems. They are derived via the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space of a single system and/or of the state space of two interacting systems. The Onsager relations are shown to be thermodynamic kinematic features of the system and are found without knowledge of the detailed mechanics of the dynamic process. A fundamental thermodynamic explanation for the measurement of each intensive property of a system in a nonequilibrium state is given. The fundamental thermodynamic definition of reservoir is also discussed. In addition, the equation of motion for a system undergoing multiple interactions is provided, which permits the modeling of a network of local systems in nonequilibrium at any spatial and temporal scale. Finally, the physical features of a nonequilibrium measurement is illustrated via a case study, and the general validity of the equal probability condition is discussed.

The method of choice to study one-dimensional strongly interacting many-body quantum systems is based on matrix product states and operators. Such a method allows one to explore the most relevant and numerically manageable portion of an exponentially large space. It also allows one to accurately describe correlations between distant parts of a system, an important ingredient to account for the context in machine learning tasks. Here we introduce a machine learning model in which matrix product operators are trained to implement sequence-to-sequence prediction, i.e., given a sequence at a time step, it allows one to predict the next sequence. We then apply our algorithm to cellular automata (for which we show exact analytical solutions in terms of matrix product operators) and to nonlinear coupled maps. We show advantages of the proposed algorithm when compared to conditional random fields and a bidirectional, long, short-term-memory neural network. To highlight the flexibility of the algorithm, we also show that it can readily perform classification tasks.

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasiperiodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.

In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling strength is greatly above the synchronization threshold. We investigate the general class of nearly identical complex oscillators connected into network in a context of a phase reduction approach. By treating each oscillator as a black-box possessing a single-input single-output, we provide a practical and simply realizable control algorithm to attain the in-phase synchrony of the network. For a general diffusive-type coupling law and any value of a coupling strength (even greatly below the synchronization threshold) the delayed feedback control with specially adjusted time-delays can provide in-phase synchronization. Such adjustment of the delay times performed in an automatic fashion by the use of an adaptive version of the delayed feedback algorithm when time-delays become time-dependent slowly varying control parameters. Analytical results show that there are many arrangements of the time-delays for the in-phase synchronization, therefore we supplement the algorithm by an additional requirement to choose an appropriate set of the time-delays, which minimize power of a control force. Performed numerical validations of the predictions highlights the usefulness of our approach.