The microscopic structure within a two-dimensional shock was studied using data from a dusty plasma experiment. A single layer of charged microparticles, levitated in a glow-discharge plasma, was perturbed by an electrically floating wire that was moved at a steady supersonic speed to excite a compressional shock. A rearrangement of particles was observed, from a hexagonal lattice in the preshock into a quadrilateral microstructure on the front side of the shock. This quadrilateral structure would not be stable in a monolayer of identical repulsive particles, under equilibrium conditions. Glaser-Clark polygon analysis of the microstructure helped in identifying quadrilaterals. Voronoi analysis was used to characterize the defect fraction behind the shock, as an indication of shock-induced melting.

We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schrödinger perturbation theory, we demonstrate that the principal components are related to the reciprocal lattice vectors of the hypercubic lattice, and the corresponding eigenvalues are connected to the discrete Fourier transform of the sampled configurations. From a different perspective, we show that the PCA in question can be viewed as a numerical method for computing the ensemble average of the squared moduli of the Fourier transform of physical quantities. Our results also provide a way to determine approximately the principal components of a classical system with translational invariance without the need for matrix diagonalization.

An open fully connected system of qubits at nonzero temperature is driven within a finite time interval along various paths in the space of its control parameters. The driving leads across finite-size precursors of first- and second-order quantum phase transition from factorized to entangled ground-state phases, aiming at the preparation of the complex ground state of the system at the final parameter point with maximal fidelity. During the drive, the system is coupled to a heat bath at a constant temperature, the dynamics being determined in a nonperturbative way by the method of hierarchical equations of motion. It is shown that the presence of the heat bath in combination with specific patterns of avoided crossings affecting the ground and excited states in the parameter region around the quantum phase transition may considerably improve the fidelity of preparation of the target ground state.

In the study of disordered systems, one often chooses a matrix of independent identically distributed interaction coefficients to represent the quenched random couplings between components, perhaps with some symmetry constraint or correlations between diagonally opposite pairs of elements. However, a more general set of couplings, which still preserves the statistical interchangeability of the components, could involve correlations between interaction coefficients sharing only a single row or column index. These correlations have been shown to arise naturally in systems such as the generalized Lotka-Volterra equations (gLVEs). In this work, we perform a dynamic mean-field analysis to understand how single-index correlations affect the dynamics and stability of disordered systems, taking the gLVEs as our example. We show that in-row correlations raise the level of noise in the mean-field process, even when the overall variance of the interaction coefficients is held constant. We also see that correlations between transpose pairs of rows and columns can either enhance or suppress feedback effects, depending on the sign of the correlation coefficient. In the context of the gLVEs, in-row and transpose row/column correlations thus affect both the species survival rate and the stability of ecological equilibria.

We explore the connection between migration patterns and emergent behaviors of evolving populations in spatially heterogeneous environments. Despite extensive studies in systems of ecological and medical importance, a unifying framework that clarifies this connection and makes concrete predictions remains much needed. Using a simple evolutionary model on a network of interconnected habitats with distinct fitness landscapes, we demonstrate a fundamental connection between migration feedback, emergent ecotypes, and a form of discontinuous critical transition. We show how migration feedback—via circulating migration patterns—generates spatially nonlocal niches in which emergent ecotypes specialize. Rugged fitness landscapes lead to a complex, yet understandable, phase diagram in which different sets of ecotypes coexist under different migration patterns. Under certain ecological interactions, a discontinuous transition splits into two continuous transitions—this effect suggests a sensitive experimental probe for the nature and magnitude of the underlying interactions.

In this work, we revisited the Ziff-Gullari-Barshad (ZGB) model in order to investigate its critical behavior when carbon monoxide (CO) molecules are allowed to desorb from the catalytic surface. As shown by several authors, when this kind of desorption takes place, the first-order phase transition of the standard model disappears, and an Ising-like critical point is found for a very small value of the desorption rate. However, our time-dependent Monte Carlo simulations reveal that, instead of a single critical point, there exists a critical line that appears to encompass multiple universality classes, passing through the Ising and three-state Potts points, as well as providing reasonable evidence for the four-state Potts point, resulting in an unprecedented critical line exhibiting weak universality.

In the previous paper we have shown analytically that the drift function of the $d$-dimensional Langevin equation is the Langevin function with a properly chosen scale factor when the evolution of the drift function is a martingale associated with the histories generated by the very Langevin equation. Moreover, we numerically demonstrated that those generated histories from common initial data, which become asymptotically ballistic, show their orientations to obey the classical canonical spin statistics under the external field corresponding to the initial data. In the present paper we show that the canonical density of a $d$-dimensional spin evolves as a martingale associated with the process generated by the above mentioned Langevin equation. Finally, as a by-product, we give an analytical explanation of the above numerical findings. These results elucidate a physical link between the martingale and canonical spin statistics.

We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many timescales. We find that the FPT statistics can be described by two scaling functions: one corresponds to the solution for an infinite system, and the other describes a scaling that depends on system size. We find a universal scaling relationship for the FPT moments $\langle t^q\rangle$ with respect to the domain size and the source-target distance. This scaling exhibits a transition at $q_c=\theta$, where $\theta$ is the persistence exponent. For low-order moments with $q<q_c$, convergence occurs towards the moments of an infinite system. In contrast, the high-order moments, $q>q_c$, can be derived from an infinite density function. The presented uniform approximation, connecting the two scaling functions, provides a description of the first-passage time statistics across all timescales. We extend the results to include diffusion in a confining potential in the high-temperature limit, where the potential strength takes the place of the system's size as the relevant scale. This study has been applied to various mediums, including a particle in a box, two-dimensional wedge, fractal geometries, non-Markovian processes, and the nonequilibrium process of resetting.

We study the propagation of both low- and high-amplitude ring-shaped sound waves in a two-dimensional square lattice of acoustic waveguides with Helmholtz resonators. We show that the inclusion of the Helmholtz resonators suppresses the inherent anisotropy of the system in the low-frequency regime allowing for radially symmetric solutions. By employing the electroacoustic analogue approach and asymptotic methods we derive an effective cylindrical Korteweg–de Vries equation. Low-amplitude waveforms are self-similar structures of the Airy function profile, while high-amplitude ones are of the form of cylindrical solitons. Our analytical predictions are corroborated by results of direct numerical simulations, with a very good agreement between the two.

The symbiotic relationship between the frameworks of classical game theory and evolutionary game theory is well established. However, evolutionary game theorists have mostly tapped into the classical game of complete information where players are completely informed of all other players' payoffs. Of late, there is a surge of interest in ecoevolutionary interactions where the environment's state is changed by the players' actions which, in turn, are influenced by the changing environment. However, in real life, the information about the true environmental state must pass through some noisy channel (like the usually imperfect sensory apparatus of the players) before it is perceived by the players: The players naturally are prone to sometimes perceive the true state erroneously. Given the uncertain perceived environment, the players may adopt bet-hedging kind of strategies in which they play different actions in different perceptions. In a population of such ill-informed players, a player would be confused about the information state of her opponent, and an incomplete information situation akin to a Bayesian game surfaces. In short, we contemplate the possibility of the natural emergence of the symbiotic relationship between the frameworks of Bayesian games and ecoevolutionary games when the players are equipped with inefficient sensory apparatus. Herein, we illustrate this connection using a setup of infinitely large, well-mixed population of players equipped with two actions for exploiting a resource (the environment) at two different rates so that the resource state evolves accordingly. The state of the resource impacts every player's decision of playing particular action. We investigate the continuous state environment in the presence of a Gaussian noisy channel. Employing the formalism of deterministic replicator dynamics, we find that noisy information can be effective in preventing the resource from going extinct.

Microswimmers play an important role in shaping the world around us. The squirmer is a simple model of a microswimmer whose cilia oscillations on its spherical surface induce an effective slip velocity to propel itself. The rapid development of computational fluid dynamics methods has markedly enhanced our capacity to study the behavior of squirmers in aqueous environments. Nevertheless, a unified methodology that can fully address the complexity of fluid-solid coupling at multiple scales and interface tracking for multiphase flows remains elusive, posing an outstanding challenge to the field. To this end, we investigate the potential of the smoothed particle dynamics (SPD) method as an alternative approach to simulating squirmers. The Lagrangian nature of the method allows it to effectively address the aforementioned difficulty. By introducing a novel treatment of the boundary condition and assigning appropriate slip velocities to the boundary particles, the SPD squirmer model is able to accurately represent a range of microswimmer types, including pushers, neutral swimmers, and pullers. We systematically validate the steady-state velocity of the squirmer, the resulting flow field, its hydrodynamic interactions with the surrounding environment, and the mutual collision of two squirmers. In the presence of Brownian motion, the model is also able to correctly calculate the velocity and angular velocity autocorrelation functions at the mesoscale. Finally, we simulate a squirmer within a multiphase flow by considering a droplet that encloses a squirmer and imposing a surface tension between the two flow phases. We find that the squirmer within the droplet exhibits different motion types. Since the proposed method is applicable to a wide range of complex scenarios, it has implications for a number of areas, including the design and application of micro and/or nano artificial swimmers, flow manipulation in microfluidic chips, and drug delivery in the biomedical field.

Nonreciprocal systems can be thought of as disobeying Newton's third law—an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest toward such systems. On a fundamental level, they can be a basis of describing nonequilibrium and active states of matter, with applications ranging from physics to social sciences. However, often the first step to understanding complex nonlinear models is to linearize about the steady states. It is thus useful to develop a careful understanding of linear nonreciprocal systems, similar to our understanding of Gaussian systems in equilibrium statistical mechanics. In this work we explore simplest linear nonreciprocal models with noise and spatial extent. We describe their regions of stability and show how nonreciprocity can enhance the stability of a system. We demonstrate the appearance of exceptional and critical exceptional points with the respective enhancement of fluctuations for the latter. We show how strong nonreciprocity can lead to a finite-momentum instability. Finally, we comment how nonreciprocity can be a source of colored, 1/f type noise.

We derive the Helmholtz–Korteweg equation, which models acoustic waves in Korteweg fluids. We further derive a nematic variant of the Helmholtz–Korteweg equation, which incorporates an additional orientational term in the stress tensor. Its dispersion relation coincides with that arising in Virga's analysis of the Euler–Korteweg equations, which we extend to consider imaginary wave numbers and the effect of boundary conditions. In particular, our extensions allow us to analyze the effect of nematic orientation on the penetration depth of evanescent plane waves, and on the scattering of sound waves by obstacles. Furthermore, we make new, experimentally verifiable predictions for the effect of boundary conditions for a modification of the Mullen–Lüthi–Stephen experiment, and for the scattering of acoustic waves in nematic-Korteweg fluids by a circular obstacle.

Time-local quantum master equations that describe open quantum systems beyond the limit of ultraweak system-bath coupling are often not of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the Redfield equation approximating general open quantum systems and the Hu-Paz-Zhang equation precisely describing a damped harmonic oscillator. In this study, we demonstrate that not only the former but also the latter can be brought to pseudo-Lindblad form. This form features a dissipator resembling that of a GKSL equation, with the distinction that some of the terms have negative weights. Moreover, we systematically investigate transformations that leave the dissipator of pseudo-Lindblad equations unchanged, while changing the relative weight between its positive and negative terms. These can be used to minimize the weights of the negative terms, which is optimal both for the convergence of a recently developed quantum-trajectory unraveling of pseudo-Lindblad equations and the truncation of the negative terms to obtain a GKSL equation.

Recent experimental and theoretical results have demonstrated the possibility of accelerating electrons in the MeV range by focusing tightly a few-cycle laser beam in ambient air [S. Vallières et al., High dose-rate MeV electron beam from a tightly-focused femtosecond IR laser in ambient air, Laser Photonics Rev. 18, 2300078 (2024)]. Using Particle-In-Cell (PIC) simulations, this configuration is revisited within a more accurate modeling approach to analyze and optimize the mechanism responsible for electron acceleration. In particular, an analytical model for a linearly polarized tightly focused ultrashort laser field is derived and coupled to a PIC code, allowing us to model the interaction of laser beams reflected by high-numerical aperture mirrors with laser-induced plasmas. A set of 3D PIC simulations is performed where the laser wavelength is varied from 800 nm to $7.0\mu \mathrm{m}$ while the normalized amplitude of the electric field is varied from $a_0=3.6$ to $a_0=7.0$. The preferential forward acceleration of electrons, as well as the analysis of the laser intensity evolution in the plasma and data on electron number density, confirm that the relativistic ponderomotive force is responsible for the acceleration. We also demonstrate that the electron kinetic energy reaches a maximum of $\approx 1.6$ MeV when the central wavelength is of $2.5\mu \mathrm{m}$.

We examine a new design of reservoir computing based on an otherwise linear dynamical system subject to feedback in which a delay time linearly depends on the system's state. Despite the apparent linearity of the system under casual perusal, the system nonetheless possesses a nonlinearity that can be used for time-delay reservoir computing. We find that close multiple Hopf bifurcation points lead to a rich sawtooth-shaped transient response to input signals, which can be beneficial for computing capabilities. We benchmark the reservoir computing system's memory capacity and performance on solving delayed XOR, Iris flower classification tasks, and the Santa Fe time-series prediction task. We demonstrate how the nonlinearity and the memory capacity of the system can be tuned by changing the time-delay dependence.

We perform a thermodynamic analysis of various contributions to the size dependence of the contact-angle cosine for both axisymmetric and cylindrical sessile droplets. This shows that a commonly used method to determine the line tension from the slope of the contact-angle cosine dependence on the three-phase contact-line curvature (for axisymmetric droplets) provides a certain combination of the line tension, the adsorptions at the three interfaces, and the macroscopic contact angle. To extract the contribution related to the contact line in the leading order and determine the line tension, we propose a simple technique using droplet-size dependences of the contact angle for axisymmetric and cylindrical droplets under the same conditions.