Using a linear hydrodynamic theory, we demonstrate that Faraday waves occur in liquid crystalline fluids. The use of already experimentally known material parameters of a $N$-(4-methoxybenzylidene)-4-butylaniline liquid crystal allows us to confirm and realize the predictions of this theory. It provides the critical wave number and necessary driving acceleration at instability wave onset. Additionally, these observables experience an abrupt change originated by Marangoni convection due to the temperature gradient at the isotropic-nematic phase transition temperature. Correspondingly, the Marangoni number versus temperature also shows a sharp change in the transition temperature.

We report the study of a self-excited converging shock structure observed in a complex plasma medium. A high-density dust cloud of melamine formaldehyde particles is created and horizontally confined by a circular ring in a dc glow discharge plasma at a particular discharge voltage and pressure. Later, as the discharge voltage is increased, a circular density crest is spontaneously generated around the outer boundary of the dust cloud. This nonlinear density structure is seen to propagate inward towards the center of the dust cloud. The properties of the excited structure are analyzed and found to follow the characteristics of a converging shock structure. A three-dimensional molecular dynamics simulation has also been performed in which a stable dust cloud is formed and levitated by the balance of forces due to gravity and an external electric field mimicking the cathode sheath electric field in the experiment. Particles are also horizontally confined by an external electric field, representing the sheath electric field of the circular ring present in the experiment. A circular shock structure has been excited by applying an external perturbation in the horizontal electric field around the outer boundary of the dust cloud. The characteristic properties of the shock are analyzed in the simulation and qualitatively compared with the experimental findings. This paper is not only of fundamental interest but has many implications concerning the study of converging shock waves excited in other media for various potential applications.

Flat band systems can yield interesting phenomena, such as dispersion suppression of waves with frequency at the band. While linear transport vanishes, the corresponding nonlinear case is still an open question. Here, we study power transmission along nonlinear sawtooth lattices due to waves with the flat band frequency injected at one end. While there is no power transfer for small intensity, there is a threshold amplitude above which a surge of power transmission occurs, i.e., supratransmission, for defocusing nonlinearity. This is due to a nonlinear evanescent wave with the flat band frequency that becomes unstable. We show that dispersion suppression and supratransmission also exist even when the band is nearly flat.

The instanton approximation is a widely used approach to construct the semiclassical theory of tunneling. The instanton path bridges the regions that are not connected by classical dynamics, but the connection can be achieved only if the two regions have the same energy. This is a major obstacle when applying the instanton method to nonintegrable systems. Here we show that the ergodicity of complex orbits in the Julia set ensures the connection between arbitrary regions and thus provides an alternative to the instanton path in the nonintegrable system. This fact is verified using the ultra-near integrable system in which none of the visible structures inherent in nonintegrability exist in the classical phase space, yet nonmonotonic tunneling tails emerge in the corresponding wave functions. The simplicity of the complex phase space allows us to explore the origin of the nontrivial tunneling tails in terms of semiclassical analysis in the time domain. In particular, it is shown that not only the imaginary part but also the real part of the classical action plays a role in creating the characteristic step structure of the tunneling tail that appears as a result of the quantum resonance.

Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model where nodes randomly distributed on a hyperbolic disk are connected to a fixed number $m$ of their nearest spatial neighbors. We introduce also a canonical version of this network (which we call “network with varied connection radius”), where maximal length of outgoing bond is space dependent and is determined by fixing the average out-degree to $m$. We study local bond length, in-degree, and reciprocity in these networks as a function of spacial coordinates of the nodes and show that the network has a distinct core-periphery structure. We show that for small densities of nodes the overall in-degree has a truncated power-law distribution. We demonstrate that reciprocity of the network can be regulated by adjusting an additional temperature-like parameter without changing other global properties of the network.

This paper theoretically investigates surface acoustic waves (SAWs) which emerge within the continuous spectrum of bulk Bloch waves in piezoelectric one-dimensional phononic crystals. Accordingly, these SAWs may be treated as an example of the bound states in the continuum (BIC). The equations which determine the existence of such BIC-SAWs have been derived. Unlike SAWs in the frequency intervals forbidden for bulk Bloch waves, BIC-SAWs are governed not by a single purely real dispersion equation but by sets of equations, so BIC-SAWs prove to be robust only to a consistent change of a definite number of free parameters characterizing the wave propagation. The form of the derived equations allows the establishment of the conditions on the frequency and other parameters under which the BIC-SAW exists. The number of conditions depends on the number of bulk waves in the frequency interval under consideration. In the case of generic crystallographic symmetry, there are three, five, and seven conditions which have to be fulfilled for a BIC-SAWs to coexist with one pair, two pairs, and three pairs of bulk Bloch waves, respectively. It is shown that the crystallographic symmetry may reduce the number of conditions to two, three and four, respectively. Numerical computations confirm analytic results.

We report a proposal to observe the two-photon Breit-Wheeler process in plasma driven by compact lasers. A high-charge electron bunch can be generated from laser plasma wakefield acceleration when a tightly focused laser pulse propagates in a subcritical density plasma. The electron bunch scatters with the laser pulse coming from the opposite direction and resulting in the emission of high brilliance x-ray pulses. In a three-dimensional particle-in-cell simulation with a laser pulse of $\sim 10$ J, one could produce an x-ray pulse with a photon number higher than $3\times {10}^{11}$ and brilliance above $1.6\times {10}^{23}$ photons/s/${\mathrm{mm}}^2$/${\mathrm{mrad}}^2$/$0.1\%\mathrm{BW}$ at 1 MeV. The x-ray pulses collide in the plasma and create more than $1.1\times {10}^5$ electron-positron pairs per shot. It is also found that the positrons can be accelerated transversely by a transverse electric field generated in the plasma, which enables the safe detection in the direction away from the laser pulses. This proposal enables the observation of the linear Breit-Wheeler process in a compact device with a single shot.

In the multiphase flow simulations based on the lattice Boltzmann equation (LBE), the spurious velocity near the interface and the inconsistent density properties are frequently observed. In this paper, a well-balanced regularized lattice Boltzmann (WB-RLB) model with Hermite expansion up to third order is developed for two-phase flows. To this end, the equilibrium distribution function and the modified force term proposed by Guo [Phys. Fluids 33, 031709 (2021)] are directly introduced into the regularization of the transformed distribution functions when considering the LBE with trapezoidal integral. First, to give a detailed comparison of the well-balanced lattice Boltzmann equation (WB-LBE), WB-RLB, and second-order mixed difference scheme (SOMDS) proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)], the theoretical analyses on the force balance of LBE with two different gradient operators, isotropic central scheme (ICS) and SOMDS, as well as the numerical simulations of the stationary droplet are carried out. The force analysis shows that SOMDS can achieve a higher accuracy than ICS for the force balance, which has been validated in the simulations of stationary droplet cases. For the stationary droplet cases, all three models (WB-LBE, WB-RLB, and SOMDS) can capture the physical equilibrium state even at a large density ratio of 1000. Also, the numerical investigations of the WB-RLB model with third-order expansion (WB-RLB3) demonstrate that adjusting the relaxation parameters of the third-order moment can further improve the accuracy and stability of the WB-RLB model. Then, both the droplet coalescence and the phase separation cases are investigated with considering the effect of different interface thickness, which demonstrates that the performance of the WB-RLB for the two-phase dynamic problems is still quite well, and it exhibits better numerical stability when compared with the WB-LBE. In addition, the contact angle problem is investigated by the present WB-RLB model; the numerical results show that the predicted values of the contact angles agree well with the analytical solutions, but the well-balance property is not validated, especially near the three-phase junction. Overall, the present WB-RLB model exhibits excellent numerical accuracy and stability for both static and dynamic interface problems.

The determination of liquid atomic structure and thermophysical properties is essential for investigating the physical characteristics and phase transitions of refractory alloys. However, due to the stringent experimental requirements and underdeveloped interatomic potentials, acquiring such information through experimentation or simulation remains challenging. Here, an active learning method incorporating a deep neural network was established to generate the interatomic potential of the ${\mathrm{Hf}}_{76}{\mathrm{W}}_{24}$ refractory alloy. Then the achieved potential was applied to investigate the liquid atomic structure and thermophysical properties of this alloy over a wide temperature range. The simulation results revealed the distinctive bonding preferences among atoms, that is, Hf atoms exhibited a strong tendency for conspecific bonding, while W atoms preferred to form an interspecific bonding. The analysis of short-range order (SRO) in the liquid alloy revealed a significant proportion of icosahedral (ICO) and distorted ICO structures, which even exceeded 30% in the undercooled state. As temperature decreased, SRO structures demonstrated an increase in larger coordination number (CN) clusters and a decrease in smaller CNs. The alterations of the atomic structure indicated that the liquid alloy becomes more ordered, densely packed, and energetically favorable with decreasing temperature, consistent with the obtained fact: Both density and surface tension increase linearly. The simulated thermophysical properties were close to experimental values with minor deviations of 2.8% for density and 3.4% for surface tension. The consistency of the thermophysical properties further attested to the accuracy and reliability of active learning simulation.

A Bernoulli trial describing the escape behavior of a lamb to a safe haven in pursuit by a lion is studied under restarts. The process ends in two ways: either the lamb makes it to the safe haven (success) or is captured by the lion (failure). We study the first passage properties of this Bernoulli trial and find that only mean first passage time exists. Considering Poisson and sharp resetting, we find that the success probability is a monotonically decreasing function of the restart rate. The mean time, however, exhibits a nonmonotonic dependence on the restart rate taking a minimal value at an optimal restart rate. Furthermore, for sharp restart, the mean time possesses a local and a global minima. As a result, the optimal restart rate exhibits a continuous transition for Poisson resetting while it exhibits a discontinuous transition for sharp resetting as a function of the relative separation of the lion and the lamb. We also find that the distribution of first passage times under sharp resetting exhibits a periodic behavior.

Across many disciplines spanning from neuroscience and genomics to machine learning, atmospheric science, and finance, the problems of denoising large data matrices to recover hidden signals obscured by noise, and of estimating the structure of these signals, is of fundamental importance. A key to solving these problems lies in understanding how the singular value structure of a signal is deformed by noise. This question has been thoroughly studied in the well-known spiked matrix model, in which data matrices originate from low-rank signal matrices perturbed by additive noise matrices, in an asymptotic limit where matrix size tends to infinity but the signal rank remains finite. We first show, strikingly, that the singular value structure of large finite matrices (of size $\sim 1000$) with even moderate-rank signals, as low as 10, is not accurately predicted by the finite-rank theory, thereby limiting the application of this theory to real data. To address these deficiencies, we analytically compute how the singular values and vectors of an arbitrary high-rank signal matrix are deformed by additive noise. We focus on an asymptotic limit corresponding to an $\mathit{extensive}$ spike model, in which both the signal rank and the size of the data matrix tend to infinity at a constant ratio. We map out the phase diagram of the singular value structure of the extensive spike model as a joint function of signal strength and rank. We further exploit these analytics to derive optimal rotationally invariant denoisers to recover the hidden $\mathit{high}$-rank signal from the data, as well as optimal invariant estimators of the signal covariance structure. Our extensive-rank results yield several conceptual differences compared to the finite-rank case: (1) as signal strength increases, the singular value spectrum does not directly transition from a unimodal bulk phase to a disconnected phase, but instead there is a bimodal connected regime separating them; (2) the signal singular vectors can be partially estimated $\mathit{even}$ in the unimodal bulk regime, and thus the transitions in the data singular value spectrum do not coincide with a detectability threshold for the signal singular vectors, unlike in the finite-rank theory; (3) signal singular values interact nontrivially to generate data singular values in the extensive-rank model, whereas they are noninteracting in the finite-rank theory; and (4) as a result, the more sophisticated data denoisers and signal covariance estimators we derive, which take into account these nontrivial extensive-rank interactions, significantly outperform their simpler, noninteracting, finite-rank counterparts, even on data matrices of only moderate rank. Overall, our results provide fundamental theory governing how high-dimensional signals are deformed by additive noise, together with practical formulas for optimal denoising and covariance estimation.

Homophily is the principle whereby “similarity breeds connections.” We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the partition, whose entries are the number of edges of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among labeled partitions whose classes have the same cardinalities as the given one. This is the recently introduced random coloring model for network homophily. In this perspective, the value of any homophily score $\mathrm{\Theta }$, namely, a nondecreasing real-valued function in the sizes of subgraphs induced by the classes of the partition, evaluated at the observed outcome, can be thought of as the observed value of a random variable. Consequently, according to the score $\mathrm{\Theta }$, the input network is homophillic at the significance level $\alpha$ whenever the one-sided tail probability of observing a value of $\mathrm{\Theta }$ at least as extreme as the observed one is smaller than $\alpha$. Since, as we show, even approximating $\alpha$ is an NP-hard problem, we resort to classical tails inequality to bound $\alpha$ from above. These upper bounds, obtained by specializing $\mathrm{\Theta }$, yield a class of quantifiers of network homophily. Computing the upper bounds requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap. Interestingly, the matrix depends on the input partition only through the cardinalities of its classes and depends on the network only through its degrees. Furthermore all the covariances have the same sign, and this sign is a graph invariant. Plugging this structure into the bounds yields a meaningful, easy to compute class of indices for measuring network homophily. As demonstrated in real-world network applications, these indices are effective and reliable, and may lead to discoveries that cannot be captured by the current state of the art.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the $x$ direction for the first component and a 1D nonlinear optical lattice (NOL) in the $y$ direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the $y$ direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the $y$ direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.

A model of self-propelled motion in a closed compartment containing simple or complex fluids is formulated in this paper in terms of the dynamics of a point particle moving in a spherical cavity under the action of random thermal forces and exponentially correlated noise. The particle's time evolution is governed by a generalized Langevin equation (GLE) in which the memory function, connected to the thermal forces by a fluctuation-dissipation relation, is described by Jeffrey's model of viscoelasticity (which reduces to a model of ordinary viscous dynamics in a suitable limit). The GLE is transformed exactly to a Fokker-Planck equation that in spherical polar coordinates is in turn found to admit of an exact solution for the particle's probability density function under absorbing boundary conditions at the surface of the sphere. The solution is used to derive an expression (that is also exact) for the survival probability of the particle in the sphere, starting from its center, which is then used to calculate the distribution of the particle's first-passage times to the boundary. The behavior of these quantities is investigated as a function of the Péclet number and the persistence time of the athermal forces, providing insight into the effects of nonequilibrium fluctuations on confined particle motion in three dimensions.

The Sweeny algorithm for the $Q$-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As $Q$ decreases, the so-called critical speeding-up for nonlocal quantities becomes more and more pronounced. However, for some quantity of a specific local pattern, e.g., the number of half faces on the square lattice, we observe that, as $Q\to 0$, the integrated autocorrelation time $\tau$ diverges as $Q^{-\zeta }$, with $\zeta \simeq 1/2$, leading to the nonergodicity of the Sweeny method for $Q\to 0$. Such $Q$-dependent critical slowing-down, attributed to the peculiar form of the critical bond weight $v=\sqrt{Q}$, can be eliminated by a combination of the Sweeny and the Kawasaki algorithm. Moreover, by classifying the occupied bonds into bridge bonds and backbone bonds, and the empty bonds into internal-perimeter bonds and external-perimeter bonds, one can formulate an improved version of the Sweeny-Kawasaki method such that the autocorrelation time for any quantity is of order $O\left(1\right)$.

Inertial confinement fusion ignition requires high inflight shell velocity, good energy coupling between the hotspot and shell, and high areal density at peak compression. Three-dimensional asymmetries caused by imperfections in the drive symmetry or target can grow and damage the coupling and confinement. Recent high-yield experiments have shown that low-mode asymmetries are a key degradation mechanism and contribute to variability. We show the experimental signatures and impacts of asymmetry change with increasing implosion yield given the same initial cause. This letter has implications for improving robustness to a key degradation in ignition experiments.

Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge—e.g., work or heat—by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of “swap” and “reset” computations that quantitatively compares the TUT against previous generalized TURs.