While the Ising model is most often used to understand physical phenomena, its natural connection to combinatorial reasoning also makes it one of the best models to probe complex systems in science and engineering. We bring a computational lens to the study of Ising models, where our computer-science perspective is twofold: On the one hand, we show that partition function computation (#Ising) can be reduced to weighted model counting (WMC). This enables us to take off-the-shelf model counters and apply them to #Ising. We show that one model counter (TensorOrder) outperforms state-of-the-art tools for #Ising on midsize and topologically unstructured instances, suggesting the tool would be a useful addition to a portfolio of partition function solvers. On the other hand, we consider the computational complexity of #Ising and relate it to the logic-based counting of constraint-satisfaction problems or #CSP. We show that known dichotomy results for #CSP give an easy proof of the hardness of #Ising and provide intuition on where the difficulty of #Ising comes from.

Issues concerning the kinetics of phase transitions are not well established for the cases where the order parameter remains conserved with time, particularly when the interatomic interactions are long-range in nature. Here we present results on structure, growth, and aging from Monte Carlo simulations of the two-dimensional long-range Ising model. In our computer simulations, random initial configurations, for $50:50$ compositions of up and down spins, mimicking high-temperature equilibrium states, have been quenched to temperatures inside the coexistence curve. Our analyses of the simulation data, for such a protocol, show interesting dependence of the aging exponent, $\lambda$, on $\sigma$, the parameter, within the Hamiltonian, that controls the range of interaction. These nonuniversal values of $\lambda$ are compared with a theoretical result for lower bounds. For this purpose, we extracted information on relevant aspects of structural properties during the evolution. To estimate $\lambda$, as is necessary, we also calculated the average domain size and analyzed its time dependence to obtain the growth exponent $\alpha$ which also is nonuniversal. The trends in the values of $\lambda$ and $\alpha$, as well as an anomaly in structure, suggest that a crossover from the long-range to the short-range variety occurs at $\sigma \simeq 1$. The location of this boundary and the nonuniversality provide a picture that is surprisingly different from that of the corresponding static critical phenomena. Furthermore, our results suggest an important scaling law combining $\alpha$ and $\lambda$.

We consider a nonequilibrium transition that leads to the formation of nonlinear steady-state structures due to the gas flow scattering on a partially penetrable obstacle. The resulting nonequilibrium steady state (NESS) corresponds to a two-domain gas structure attained at certain critical parameters. We use a simple mean-field model of the driven lattice gas with ring topology to demonstrate that this transition is accompanied by the emergence of local invariants related to a complex composed of the obstacle and its nearest gas surrounding, which we refer to as obstacle edges. These invariants are independent of the main system parameters and behave as local first integrals, at least qualitatively. As a result, the complex becomes insensitive to the noise of external driving field within the overcritical domain. The emerged invariants describe the conservation of the number of particles inside the obstacle and strong temporal synchronization or correlation of gas states at obstacle edges. Such synchronization guarantees the equality to zero of the total edge current at any time. The robustness against external drive fluctuations is shown to be accompanied by strong spatial localization of induced gas fluctuations near the domain wall separating the depleted and dense gas phases. Such a behavior can be associated with nonequilibrium protection effect and synchronization of edges. The transition rates between different NESSs are shown to be different. The relaxation rates from one NESS to another take complex and real values in the sub- and overcritical regimes, respectively. The mechanism of these transitions is governed by the generation of shock waves at the back side of the obstacle. In the subcritical regime, these solitary waves are generated sequentially many times, while only a single excitation is sufficient to rearrange the system state in the overcritical regime.

Time irreversibility (TIR) refers to the manifestation of nonequilibrium brain activity influenced by various physiological conditions; however, the influence of sleep on electroencephalogram (EEG) TIR has not been sufficiently investigated. In this paper, a comprehensive study on permutation TIR (pTIR) of EEG data under different sleep stages is conducted. Two basic ordinal patterns (i.e., the original and amplitude permutations) are distinguished to simplify sleep EEGs, and then the influences of equal values and forbidden permutation on pTIR are elucidated. To detect pTIR of brain electric signals, five groups of EEGs in the awake, stages I, II, III, and rapid eye movement (REM) stages are collected from the public Polysomnographic Database in PhysioNet. Test results suggested that the pTIR of sleep EEGs significantly decreases as the sleep stage increases ($p<0.001$), with the awake and REM EEGs demonstrating greater differences than others. Comparative analysis and numerical simulations support the importance of equal values. Distribution of equal states, a simple quantification of amplitude fluctuations, significantly increases with the sleep stage ($p<0.001$). If these equalities are ignored, incorrect probabilistic differences may arise in the forward-backward and symmetric permutations of TIR, leading to contradictory results; moreover, the ascending and descending orders for symmetric permutations also lead different outcomes in sleep EEGs. Overall, pTIR in sleep EEGs contributes to our understanding of quantitative TIR and classification of sleep EEGs.

This study explores the influence of migration costs and rewarding schemes on cooperation through the implementation of computational behavioral models in spatial public goods games. The former involves a cost for agents to migrate to a neighboring group, while the latter rewards them for remaining in the same group for multiple rounds. By analyzing these mechanisms separately and in combination, we unveil their effects on cooperative behavior. The grid-based game dynamics begins with equal size groups, and agents can adjust their contributions each round, with the option to migrate if unsatisfied. Our findings reveal that when considered separately, the rewarding scheme is not as effective in achieving full cooperation as the migration cost scheme. Combining migration costs and rewards instead yields high cooperation levels with low public goods game enhancement factors and migration probability. Our results offer valuable insights for contexts where promoting cooperative behavior is crucial, such as community engagement development and public policies.

We analyze the dynamics of room evacuation for mixed populations that include both competitive and cooperative individuals through numerical simulations using the social force model. Cooperative agents represent well-trained individuals who know how to behave in order to reduce risks within high-density crowds. We consider that competitive agents can imitate cooperative behavior when they are in close proximity to cooperators. We study the effects of the imitation of cooperative behavior on the duration and safety of evacuations, analyzing evacuation time and other quantities of interest for varying parameters such as the proportions of mixing, the aspect ratio of the room, and the parameters characterizing individual behaviors. Our main findings reveal that the addition of a relatively small number of cooperative agents into a crowd can reduce evacuation time and the density near the exit door, making the evacuation faster and safer despite an increase in the total number of agents. In particular, for long spaces such as corridors, a small number of added cooperative agents can significantly facilitate the evacuation process. We compare our results with those of systems without imitation and also study the general role of cooperation, providing further analysis for homogeneous populations. Our main conclusions emphasize the potential relevance of training people how to behave in high-density crowds.

Agent-based models were used to describe electrical signaling in bacterial biofilms in three dimensions. Specifically, wavefronts of potassium ions in Escherichia coli biofilms subjected to stress from blue light were modeled from experimental data. Electrical signaling occurs only when the biofilms grow beyond a threshold size, which we have shown to vary with the ${\mathrm{K}}^{+}$ ion diffusivity, and the ${\mathrm{K}}^{+}$ ion threshold concentration, which triggered firing in the fire-diffuse-fire model. The transport of the propagating wavefronts shows superdiffusive scaling on time. ${\mathrm{K}}^{+}$ ion diffusivity is the main factor that affects the wavefront velocity. The ${\mathrm{K}}^{+}$ ion diffusivity and the firing threshold also affect the anomalous exponent for the propagation of the wavefront determining whether the wavefront is subdiffusive or superdiffusive. The geometry of the biofilm and its relation to the mean-square displacement (MSD) of the wavefront as a function of time was investigated for spherical, cylindrical, cubical, and mushroom-like structures. The MSD varied significantly with geometry; an additional regime to the kinetics occurred when the potassium wavefront leaves the biofilm. Adding cylindrical defects to the biofilm, which are known to occur in E. coli biofilms, also gave an extra kinetic regime to the wavefront MSD for the propagation through the defect.

We analyze a mean-field model for mixtures involving biaxial nematogens and dipolar nanoparticles, taking into account not only orientational and isotropic pair interactions between nematogens but also orientational nematogen-nanoparticle interactions. We determine bulk equilibrium phase diagrams for a wide range of interaction strengths, identifying in each case the effect of the nanoparticles on the stability of nematic phases and on the appearance of multicritical points. Special attention is given to the limit of a low concentration of nanoparticles, in which their effect on the temperatures of both the first-order uniaxial-isotropic and the continuous biaxial-uniaxial transitions is investigated in detail.

Plasma wakefield acceleration represented a breakthrough in the field of particle accelerators by pushing beams to gigaelectronvolt energies within centimeter distances. The large electric fields excited by a driver pulse in the plasma can efficiently accelerate a trailing witness bunch paving the way toward the realization of laboratory-scale applications like free-electron lasers. However, while the accelerator size is tremendously reduced, upstream and downstream of it the beams are still handled with conventional magnetic optics with sizable footprints and rather long focal lengths. Here we show the operation of a compact device that integrates two active-plasma lenses with short focal lengths to assist the plasma accelerator stage. We demonstrate the focusing and energy gain of a witness bunch whose phase space is completely characterized in terms of energy and emittance. These results represent an important step toward the accelerator miniaturization and the development of next-generation table-top machines.

We investigated self-sustained oscillation in a collapsible channel, in which a part of one rigid wall is replaced by a thin elastic wall, and synchronization phenomena in the two channels connected in parallel. We performed a two-dimensional hydrodynamic simulation in a pair of collapsible channels which merged into a single channel downstream. The stable synchronization modes depended on the distance between the deformable region and the merging point; only an in-phase mode was stable for the large distance, in-phase and antiphase modes were bistable for the middle distance, and again only an in-phase mode was stable for the small distance. An antiphase mode became stable through the subcritical pitchfork bifurcation by decreasing the distance. Further decreasing the distance, the antiphase mode became unstable through the subcritical Neimark-Sacker bifurcation. We also clarified the distance dependences of the amplitude and frequency for each stable synchronization mode.

We investigate extreme value statistics (EVS) of general discrete time and continuous space symmetric jump processes. We first show that for unbounded jump processes, the semi-infinite propagator $G_0(x,n)$, defined as the probability for a particle issued from zero to be at position $x$ after $n$ steps whilst staying positive, is the key ingredient needed to derive a variety of joint distributions of extremes and times at which they are reached. Along with exact expressions, we extract universal asymptotic behaviors of such quantities. For bounded, semi-infinite jump processes killed upon first crossing of zero, we introduce the strip probability ${\mu }_{0,\underline{x}}\left(n\right)$, defined as the probability that a particle issued from zero remains positive and reaches its maximum $x$ on its $n{\text{th}}^{}$ step exactly. We show that ${\mu }_{0,\underline{x}}\left(n\right)$ is the essential building block to address EVS of semi-infinite jump processes, and obtain exact expressions and universal asymptotic behaviors of various joint distributions.

The first-passage time for a single diffusing particle has been studied extensively, but the first-passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently. We consider two models for many-particle diffusion—one treats each particle as independent simple random walkers while the other treats them as coupled to a common space-time random forcing field that biases particles nearby in space and time in similar ways. The first-passage time of a single diffusing particle under both models shows the same statistics and scaling behavior. However, for many-particle diffusions, the first-passage time among all particles (the extreme first-passage time) is very different between the two models, effected in the latter case by the randomness of the common forcing field. We develop an asymptotic (in the number of particles and location where first passage is being probed) theoretical framework to separate the impact of the random environment with that of the sampling trajectories within it. We identify a power law describing the impact of the environment on the variance of the extreme first-passage time. Through numerical simulations, we verify that the predictions from this asymptotic theory hold even for systems with widely varying numbers of particles, all the way down to 100 particles. This shows that measurements of the extreme first-passage time for many-particle diffusions provide an indirect measurement of the underlying environment in which the diffusion is occurring.

Discrete heat equations for the multilayered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in $\omega -k$ space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, and phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers. These functions demonstrate unusual behavior at high frequency compared to the continuum case. Furthermore, the maximum allowed frequency and wave number for the discrete heat equation are limited, whereas there are no such limits in a continuum. The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and timescales the discrete approach is preferable. This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing one to study ultrafast wavelike heat conduction regimes in periodic multilayered metamaterials.

Fiedler value, as the minimal real part of (or the minimal) nonzero Laplacian eigenvalue, garners significant attention as a metric for evaluating network topology and its dynamics. In this paper, we address the quantification relation between Fiedler value and each edge in a directed complex network, considering undirected networks as a special case. We propose an approach to measure the dynamical contribution value of each edge. Interestingly, these contribution values can be both positive and negative, which are determined by the left and right Fiedler vectors. Further, we show that the cumulated dynamical contribution value of all edges is exactly the Fiedler value. This provides a promising angle on the Fiedler value in terms of dynamics and network structure. Therefore, the percentage of contribution of each edge to the Fiedler value is quantified. Numerical results reveal that network dynamics is significantly influenced by a small fraction of edges, say, one single directed edge contributes to over 90% of the Fiedler value in the Cat Cerebral Cortex network.

We present a formula for determining synchronizability in large, randomized, and weighted simplicial complexes. This formula leverages eigenratios and costs to assess complete synchronizability under diverse network topologies and intensity distributions. We systematically vary coupling strengths (pairwise and three body), degree, and intensity distributions to identify the synchronizability of these simplicial complexes of the identical oscillators with natural coupling. We focus on randomized weighted connections with diffusive couplings and check synchronizability for different cases. For all these scenarios, eigenratios and costs reliably gauge synchronizability, eliminating the need for explicit connectivity matrices and eigenvalue calculations. This efficient approach offers a general formula for manipulating synchronizability in diffusively coupled identical systems with higher-order interactions simply by manipulating degrees, weights, and coupling strengths. We validate our findings with simplicial complexes of Rössler oscillators and confirm that the results are independent of the number of oscillators, connectivity components, and distributions of degrees and intensities. Finally, we validate the theory by considering a real-world connection topology using chaotic Rössler oscillators.

The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the $(2+\delta )$-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the $(2+\delta )$-dimensional theory that captures potential differences across and electric fields within lipid membranes. This model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

Can topography be used to control bacteria accumulation? We address this question in the model system of smooth-swimming and run-and-tumble Escherichia coli swimming near a sinusoidal surface, and show that the accumulation of bacteria is determined by the characteristic curvature of the surface. For low curvatures, cells swim along the surface due to steric alignment and are ejected from the surface when they reach the peak of the sinusoid. Increasing curvature enhances this effect and reduces the density of bacteria in the curved surface. However, for curvatures larger than ${\kappa }^{*}\approx 0.25\mu {\mathrm{m}}^{-1}$, bacteria become trapped in the valleys, where they can remain for long periods of time. Minimal simulations considering only steric interactions with the surface reproduce these results and give insights into the physical mechanisms defining the critical curvature, which is found to scale with the inverse of the bacterial length. We show that for curvatures larger than ${\kappa }^{*}$, the otherwise stable alignment with the wall becomes unstable while the stable orientation is now perpendicular to the wall, thus predicting accurately the onset of trapping at the valleys.

We study the condensation of fluids confined by a pair of nonparallel plates of finite height $H$. We show that such a system experiences two types of condensation, termed single and double pinning, which can be characterized by one (single-pinning) or two (double-pinning) edge contact angles describing the shape of menisci pinned at the system edges. For both types of capillary condensation, we formulate the Kelvin-like equation and determine the conditions under which the given type of condensation occurs. We construct the global phase diagram revealing a reentrant phenomenon pertinent to the change of the capillary condensation type upon varying the inclination of the walls. Asymptotic properties of the system are discussed and a link with related phase phenomena in different systems is made. Finally, we show that the change from a single- to a double-pinned state is a continuous transition, the character of which depends on the wetting properties of the walls.