We consider a one-dimensional classical ferromagnetic Ising model when it is quenched from a low temperature to zero temperature in finite time using Glauber or Kawasaki dynamics. Most of the previous work on finite-time quenches assume that the system is initially in equilibrium and focuses on the excess mean defect density at the end of the quench, which decays algebraically in quench time with Kibble-Zurek exponent. Here we are interested in understanding the conditions under which the Kibble-Zurek scalings do not hold and in elucidating the full dynamics of the mean defect density. We find that depending on the initial conditions and quench time, the dynamics of the mean defect density can be characterized by coarsening and/or the standard finite-time quench dynamics involving adiabatic evolution and Kibble-Zurek dynamics; the timescales for crossover between these dynamical phases are determined by coarsening time and stationary state relaxation time. As a consequence, the mean defect density at the end of the quench either is a constant or decays following coarsening laws or Kibble-Zurek scaling. For the Glauber chain, we formulate a low-temperature scaling theory and find exact expressions for the final mean defect density for various initial conditions. For the Kawasaki chain where the dynamic exponents for coarsening and stationary state dynamics are different, we verify the above findings numerically and examine the effect of unequal dynamic exponents.

Dense bacterial suspensions exhibit turbulent behavior called bacterial turbulence. The behavior of the bulk unconstrained bacterial turbulence is described well by the Toner-Tu-Swift-Hohenberg (TTSH) equation for the velocity field. However, it remains unclear how we should treat boundary conditions on bacterial turbulence in contact with some boundaries (e.g., solid walls). To be more specific, although the importance of the edge current, the flow along the boundary, has been demonstrated in several experimental studies on confined bacterial suspensions, previous numerical studies based on the TTSH equation employ nonslip boundary conditions and do not seem to properly describe the behavior of bacteria near the boundaries. In this paper, we impose a slip boundary condition on the TTSH equation to describe the bacterial motion at boundaries. We develop a method to implement the slip boundary condition. Using this method, we have successfully produced edge current and discovered that the direction of the edge current temporally oscillates. The oscillation can be attributable to the advection term in the TTSH equation. Our paper demonstrates that boundary conditions could play an important role in the collective dynamics of active systems.

In the study we thoroughly analyze diffraction effects accompanying the laser beam transmission through inhomogeneous plasma microstructures and simulate their diffraction patterns at the object output and in the near field. For this we solve the scalar Helmholtz wave equation in the first Rytov approximation and compute the diffraction spreading of the transmitted beam in free space. Diffraction effects are found to arise within the beam passage through inhomogeneous plasma microstructures even in the simplest approximations of the laser beam interaction with plasma. These effects become strong in the near-field region and significantly distort the patterns of plasma formations, as well as facilitate the appearance of various optical artifacts in the plasma images. By performing numerical simulations, we characterize in detail the features of the visualization of plasma formations in the field of a coherent laser beam registered by a lens system. The calculations are in good agreement with the experimental data. The study can find broad applications in the processing of the laser images of plasma microstructures registered by lens systems in the presence of strong diffraction effects.

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.

We discover that quantum dynamical tunneling, occurring between phase space regions in a classically forbidden way, can break conserved quantities. We rigorously prove that a conserved quantity in a class of typical pseudointegrable systems can be broken quantum mechanically. We then numerically compute the uncertainties of this broken conserved quantity, which remain nonzero for up to ${10}^5$ eigenstates and exhibit universal distributions similar to energy level statistics. Furthermore, all the eigenstates with large uncertainties show the superpositions of regular orbits with different values of the conserved quantity, showing definitive manifestation of dynamical tunneling. A random matrix model is constructed to successfully reproduce the level statistics of pseudointegrable systems.

In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two points and focus on the role of the geometry (size and shape) of the embedding lattice, which has received very little attention. This role becomes crucial, for example, in the strong disorder (SD) limit, where the mean length of the optimal path (${\overline{\ell }}_{\text{opt}}$) for a fixed end-to-end distance $r$ diverges as the lattice size $L$ increases. We propose a unified scaling ansatz for ${\overline{\ell }}_{\text{opt}}$ in $D$-dimensional disordered lattices. Our ansatz introduces two exponents, $\phi$ and $\chi$, which respectively characterize the scaling of ${\overline{\ell }}_{\text{opt}}$ with $r$ for fixed $L$, and the scaling of ${\overline{\ell }}_{\text{opt}}$ with $L$ for fixed $r$, both in the SD limit. The ansatz is supported by a comprehensive numerical study of the problem on $2D$ lattices, yet we also present results in $D=3$. We show that it unifies well-known results in the strong and weak disorder regimes, including the crossover behavior, but it also reveals novel scaling scenarios not yet addressed. Moreover, it provides relevant insights into the origin of the universal exponents characterizing the scaling of the optimal path in the SD limit. For example, for the fractal dimension of the optimal path in the SD limit, $d_{\text{opt}}$, we find $d_{\text{opt}}=\phi +\chi$.

Swarmalators are entities that swarm through space and sync in time and are potentially considered to replicate the complex dynamics of many real-world systems. So far, the internal dynamics of swarmalators have been taken as a phase oscillator inspired by the Kuramoto model. Here we examine the internal dynamics utilizing an amplitude oscillator capable of exhibiting periodic and chaotic behaviors. To incorporate the dual interplay between spatial and internal dynamics, we propose a general model that keeps the properties of swarmalators intact. This adaptation calls for a detailed study, which we present in this paper. We establish our study with the Rössler oscillator by taking parameters from both chaotic and periodic regions. While the periodic oscillator mimics most of the patterns in the previous phase oscillator model, the chaotic oscillator brings some fascinating states.

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order relationships, which are naturally represented by hypergraphs. Here we study random walks on hypergraphs. Due to the higher-order nature of these mathematical objects, one can define more than one type of walks. In particular, we study the unbiased and the maximal entropy random walk on hypergraphs with two types of steps, emphasizing their similarities and differences. We characterize these dynamic processes by examining their stationary distributions and associated hitting times. To illustrate our findings, we present a toy example and conduct extensive analyses of artificial and real hypergraphs, providing insights into both their structural and dynamical properties. We hope that our findings motivate further research extending the analysis to different classes of random walks as well as to practical applications.

We investigate experimentally the influence of rotation on the penetration depth of a spherical projectile impacting a granular medium. We show that a rotational motion significantly increases the penetration depth achieved. Moreover, we model our experimental results by modifying the frictional term of the equation describing the penetration dynamics of an object in a granular medium. In particular, we find that the frictional drag decreases linearly with the velocity ratio between rotational (spin motion) and translational (falling motion) velocities. The good agreement between our model and our experimental measurements offers perspectives for estimating the depth that spinning projectiles reach after impacting onto a granular ground, such as happens with seeds dropped from aircraft or with landing probes.

Many engineered photonic devices can be decomposed into parts where the material properties are independent of one or more spatial variables. Numerical mode-matching methods are widely used to simulate such photonic devices due to the efficiency gained by treating the separated variables analytically. Existing mode-matching methods based on piecewise polynomials are more accurate than those based on the global Fourier basis or low-order finite difference, finite-element schemes, but they may exhibit numerical instability when a large number of eigenmodes are used. To overcome this difficulty, we introduce the spectral Galerkin mode matching method (SGMM) based on a global piecewise-polynomial basis and a Galerkin method to solve the eigenmodes. It is shown that the numerical eigenmodes of SGMM preserve the pseudo-orthogonality of the analytical eigenmodes. This property leads to linear systems that are typically well-conditioned. Numerical examples indicate that SGMM is more stable than other mode matching methods, and gives reliable results even when a large number of eigenmodes are used.

Markov Chain Monte Carlo (MCMC) algorithms are commonly used to sample from graph ensembles. Two graphs are neighbors in the state space if one can be obtained from the other with only a few modifications, e.g., edge rewirings. For many common ensembles, e.g., those preserving the degree sequences of bipartite graphs, rewiring operations involving two edges are sufficient to create a fully connected state space, and they can be performed efficiently. We show that, for ensembles of bipartite graphs with fixed degree sequences and number of butterflies ($k_{2,2}$ bicliques), there is no universal constant $c$ such that a rewiring of at most $c$ edges at every step is sufficient for any such ensemble to be fully connected. Our proof relies on an explicit construction of a family of pairs of graphs with the same degree sequences and number of butterflies, with each pair indexed by a natural $c$, and such that any sequence of rewiring operations transforming one graph into the other must include at least one rewiring operation involving at least $c$ edges. Whether rewiring this many edges is sufficient to guarantee the full connectivity of the state space of any such ensemble remains an open question. Our result implies the impossibility of developing efficient, graph-agnostic, MCMC algorithms for these ensembles, as the necessity to rewire an impractically large number of edges may hinder taking a step on the state space.

We investigate the scaling behavior of the magnetic dynamic order parameter $Q$ in the vicinity of the dynamic phase transition (DPT) in the presence of temporal field sequences $H$($t$) that are periodic with period $P$ but lack half-wave antisymmetry. We verify by means of mean-field calculations that the scaling of $Q$ is preserved in the vicinity of the second-order phase transition if one defines a suitable generalized conjugate field $H^{*}$ that reestablishes the proper time-reversal symmetry. For the purpose of our quantitative data analysis, we employ the dynamic equivalent of the Arrott-Noakes equation of state, which allows for a simultaneous scaling analysis of the period $P$ and the conjugate-field $H^{*}$ dependence of $Q$. By doing so, we demonstrate that both the scaling behavior and universality are preserved, even if the dynamics is driven by a more general applied field sequence that lacks antisymmetry.

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.

A photonic crystal microcavity with the liquid crystal resonant layer tunable by heating has been implemented. The multiple vanishing resonant lines corresponding to optical bound states in the continuum are observed. The abrupt change in the resonant linewidth near the vanishing point can be used for temperature sensing.

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical—but not generally accepted—field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, ${\overline{S}}_e/k_B\ge 1/2\mathrm{\Delta }t$, and its inverse is the minimum time to execute the process, $\mathrm{\Delta }t\ge k_B/2{\overline{S}}_e$. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, $\overline{Q}\mathrm{\Delta }t\ge k_{B}T/2$. These bounds constrain the relationship between dissipation and time during nonstationary processes, including transient excursions from steady states.

This paper addresses the exploration-exploitation dilemma inherent in decision-making, focusing on multiarmed bandit problems. These involve an agent deciding whether to exploit current knowledge for immediate gains or explore new avenues for potential long-term rewards. We here introduce a class of algorithms, approximate information maximization (AIM), which employs a carefully chosen analytical approximation to the gradient of the entropy to choose which arm to pull at each point in time. AIM matches the performance of Thompson sampling, which is known to be asymptotically optimal, as well as that of Infomax from which it derives. AIM thus retains the advantages of Infomax while also offering enhanced computational speed, tractability, and ease of implementation. In particular, we demonstrate how to apply it to a 50-armed bandit game. Its expression is tunable, which allows for specific optimization in various settings, making it possible to surpass the performance of Thompson sampling at short and intermediary times.

We propose a dimensionless bendability parameter, ${\epsilon }^{-1}={\left[{(h/W)}^2{T}^{-1}\right]}^{-1}$, for wrinkling of thin, twisted ribbons with thickness $h$, width $W$, and tensional strain $T$. Bendability permits efficient collapse of data for wrinkle onset, wavelength, critical stress, and residual stress, demonstrating longitudinal wrinkling's primary dependence on this parameter. This parameter also allows us to distinguish the highly bendable range (${\epsilon }^{-1}>20$) from moderately bendable samples (${\epsilon }^{-1}\in (0,20]$). We identify scaling relations to describe longitudinal wrinkles that are valid across our entire set of simulated ribbons. When restricted to the highly bendable regime, simulations confirm theoretical near-threshold (NT) predictions for wrinkle onset and wavelength.

Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three-dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler–Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.