$\mathrm{O}\left(N\right)$ vector models in three dimensions, when defined in a geometry with a compact direction and tuned to criticality, exhibit long-range fluctuations which induce a Casimir effect. The strength of the resulting interaction is encoded in the excess free-energy density, which depends on a universal coefficient: the Casimir amplitude. We present a high-precision numerical calculation of the latter by means of a nonequilibrium Monte Carlo algorithm and compare our findings with results obtained from large-$N$ expansions and from the conformal bootstrap.

We report a paradoxical phenomenon where stochasticity reverses deterministic collapse in threshold-activated systems. By using a hybrid logistic-sigmoidal map, we show that weak noise alters phase-space topology, enabling probabilistic recovery from extinction. Lyapunov and quasipotential analyses reveal noise-induced metastability and stochastic robustness absent in deterministic frameworks. These results suggest that environmental variability can stabilize nonlinear systems, offering a counternarrative to classical extinction theory.

We investigate the collective dynamics of multiplex networks of adaptively coupled Kuramoto oscillators, where distinct adaptation rules regulate the structural evolution of each layer. We uncover a wide variety of collective states, including incoherent states, antipodal-incoherent states, antipodal cluster states, antipodal-partially coherent states, mixed states, and antipodal states. These collective states are characterized using a set of intralayer and interlayer macroscopic order parameters. The former characterizes the self-organization within each layer, while the latter quantifies the dynamical correlation between the layers. Our results highlight the interplay of different adaptation mechanisms mediated via multiplexing that leads to rich collective states, which are not otherwise observed in a single-layer counterpart. Further, we provide an analytical estimate of the critical interlayer coupling strength for interlayer frequency synchronization using the collective coordinate approach, which agrees well with the simulation results.

We present a demonstration of finite-time gradient blow-ups in Israel-Stewart (IS) theories with $1+1\mathrm{D}$ plane symmetry, mathematically showing the existence of smooth initial data that can evolve into shocks across three regimes: pure bulk viscosity, shear viscosity, and diffusion. Through numerical simulations of bulk-viscous fluids, we verify that these shocks satisfy Rankine-Hugoniot conditions, exhibit characteristic velocity crossing (the Mach number obeys ${\mathcal{M}}_u>1>{\mathcal{M}}_d$), and maintain thermodynamic consistency, required for physical shocks. Our results reveal a crucial early-time dynamical phase where nonlinear effects dominate viscous damping, resolving the apparent impossibility of IS-type theories predicting shock formation. While restricted to simplified $1+1\mathrm{D}$ systems with separate viscous effects, this work establishes foundational insights for shock formation in relativistic viscous hydrodynamics, highlighting critical challenges for extending to $3+1\mathrm{D}$ systems or to a full IS theory where multiple nonlinear modes interact. The findings emphasize that both initial data structure and numerical methodology require careful consideration when studying shocks in relativistic viscous fluids.

Pickering emulsions are attracting growing attention as carriers of active ingredients or micronutrients in pharmaceutical and food applications, due to their high stability and low toxicity. The adsorption process of Pickering particles significantly affects emulsion properties and can be described using the random sequential adsorption (RSA) approach. While most studies focus on small, amorphous, spherical particles, the common use of elongated, crystalline, micron-sized particles in Pickering emulsions makes it necessary to consider the curvature and finite size of emulsion droplet surfaces to correctly understand and predict the interfacial adsorption behavior. The present study employs a Monte Carlo (MC) method to simulate the RSA process of both spherical and elongated micron-sized particles. Key factors such as particle polydispersity, emulsion droplet–particle size ratio, contact angle, and particle number are investigated. From the MC simulations, a new expression for the available surface function, $\text{ASF}\left(\varphi \right)$, with coverage-dependent exponent is proposed. Based on this, generalized coverage evolution models are established using response surface methodology to relate RSA conditions to $\text{ASF}\left(\varphi \right)$ parameters. For spherical particles, jamming coverage and desorption energy under various conditions are reported. For capsule-shaped particles, an aspect ratio of $\epsilon =2$ is found to yield higher coverage and faster adsorption. The proposed $\text{ASF}\left(\varphi \right)$ expression outperforms existing fixed-exponent expressions. The generalized coverage evolution models show good agreement with MC testing simulations. The mean absolute percentage errors are less than 2.63% for spherical particles and 6.58% for elongated ones in the validation cases.

The brain's synaptic network, characterized by parallel connections and feedback loops, drives interaction pathways between neurons through a large system with infinitely many degrees of freedom. This system is best modeled by the graph C*-algebra of the underlying directed graph, the Toeplitz-Cuntz-Krieger (TCK) algebra, which captures the diversity of path-structured flow connectivity. Equipped with the gauge action, the TCK algebra defines an algebraic quantum system, and here we demonstrate that its thermodynamic properties provide a natural framework for describing the dynamic mappings of potential flow pathways within the network. Specifically, the KMS states of this system represent the stationary distributions of a non-Markovian stochastic process with memory decay, capturing how influence propagates along exponentially weighted paths, and yield global statistical measures of neuronal interactions. Applied to the C. elegans synaptic network, our framework reveals that neurolocomotor neurons emerge as the primary hubs of incoming path-structured flow at inverse temperatures where the entropy of KMS states peaks. This finding aligns with experimental evidence of the foundational role of locomotion in C. elegans behavior, suggesting that functional centrality may arise from the topological embedding of neurons rather than solely from local physiological properties. Our results highlight the potential of algebraic quantum methods and graph algebras to uncover patterns of functional organization in complex systems and neuroscience.

We discuss synchrotron absorption of a short electromagnetic pulse that propagates in a cold magnetized pair plasma. We show that the pulse can be absorbed when ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$, where $a_0>1$ is the strength parameter of the pulse, and $\omega$ and ${\omega }_{\mathrm{B}}$, respectively, are the frequency of the wave and the cyclotron frequency in the background magnetic field (all quantities are defined in the reference frame where the particles are at rest before being illuminated by the pulse). The condition ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$ is essentially a generalization of the cyclotron resonance to strong electromagnetic pulses with $a_0>1$. When ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$, the propagation of electromagnetic waves in a plasma can be very different with respect to the propagation in vacuum because the wave equation is strongly nonlinear. Then, it is unclear whether the particles are heated stochastically due to synchrotron absorption, as found by studying the motion of a test particle in the field of a vacuum electromagnetic wave. We discuss the implications of our results for constraining emission models of fast radio bursts.

This work investigates the influence of convective transport within a sedimenting drop on the exit time of a colloidal particle. Using Brownian dynamics simulations, we compute exit times for particles originating from various locations inside the drop over a range of Péclet numbers ($\text{Pe}$). The Péclet number quantifies the balance between the convective transport, caused by the Hadamard-Rybczynski flow field within a sedimenting drop, and the thermal fluctuations in the system. Additionally, we model the exit time as a first-passage process governed by the backward Kolmogorov equation, solving it asymptotically for $\text{Pe}\ll 1$ and $\text{Pe}\gg 1$, as well as numerically, to determine the mean exit time as a function of $\text{Pe}$.

The reflection and transmission coefficients of an electromagnetic wave interacting with an inhomogeneous plasma layer produced by multiphoton ionization of an inert gas in a magnetic field are determined. The possibility of terahertz radiation amplification is revealed. If the frequency of the probe radiation matches the electron cyclotron frequency, the field strength of the transmitted and reflected radiation can be amplified by more than two orders of magnitude. The amplification arises due to the Ramsauer-Townsend effect and the non-equilibrium energy distribution of the photoelectrons. Blurring the plasma boundary by an amount equal to a few percent of the uniform layer width results in a small decrease in radiation amplification. The energy spread of photoelectrons reduces the amplification by several times.

This study analyzes pass networks in football (soccer) using a stochastic model known as the Pólya urn. By focusing on preferential selection, it theoretically demonstrates that the time evolution of networks can be characterized by a single parameter. Building on this result, a data analysis method is proposed and applied to a large-scale public dataset of professional football matches. The statistical properties of the preferential-selection parameter are examined, demonstrating its correlation with pass accuracy and with mean pass difficulty. This method is applicable to various evolving networks.

Constraint satisfaction problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value ${\alpha }_{\text{crit}}$. Above this critical value, it is exponentially unlikely that all constraints can be mutually satisfied. We calculate the probability that constraints can all be satisfied, $P\left(\text{SAT}\right)$, for the spherical perceptron. Traditional replica methods, such as the Parisi ansatz, fall short. We find a new ansatz, the jammed Parisi ansatz, that correctly describes the behavior of the system in this regime. With the jammed Parisi ansatz, we calculate $P\left(\text{SAT}\right)$ for the first time and match previous computations of thresholds. We anticipate that the techniques developed here will be applicable to general constraint satisfaction problems and the identification of hidden structures in datasets.

Speed-accuracy tradeoffs are a common feature in several physical and biological systems. Here, we demonstrate analogous speed-performance tradeoffs in the game of cricket, where batters score runs off the balls delivered by bowlers. Leveraging extensive data from cricket, we show that a batter's run-scoring rate and probability of dismissal are related, and this relation can be approximated by a power law. Similar relation is observed for bowlers as well that links their run-conceding rate and wicket taking abilities. The exponents in these power-law relations quantify player adaptability under varying conditions and serve as a robust performance indicator. Using a drift-diffusion-decay model for run scoring and conceding, we find that players with extreme exponent values are better suited to specific game formats and match conditions than those with moderate values. These findings provide a quantitative framework for evaluating player potential, optimizing team strategy, and extending the analysis to other systems exhibiting similar speed-accuracy or performance tradeoffs.

A growing body of theoretical and empirical evidence shows that the global steady-state distributions of many equilibrium and nonequilibrium systems approximately satisfy an analog of the Boltzmann distribution, with a local dynamical property of states playing the role of energy. The correlation between the effective potential of the steady-state distribution and the logarithm of the exit rates determines the quality of this approximation. We demonstrate and explain this phenomenon in a simple one-dimensional particle system and in random dynamics of the Sherrington–Kirkpatrick spin glass by providing the first explicit estimates of this correlation. We find that, as parameters of the dynamics vary, each system exhibits a threshold above and below which the correlation dramatically differs. We explain how these thresholds arise from underlying transitions in the relationship between the local and global “parts” of the effective potential.

Diffusion in the channels with flexible moving boundaries as well as driven by time-dependent forces can be described by the generalized Fick-Jacobs (Smoluchowski) equation in the reduced 1D picture, with the Boltzmann factor $A(x,t)$ and the effective diffusion coefficient $D(x,t)$ depending not only on the longitudinal coordinate $x$, but also on time $t$. We show here that for the driving periodic in time and space, the asymptotic solution of the rocking density and the rectified current can be found consistently as a series of corrections to the adiabatic limit given by the Stratonovich formula. The solution is tested on the simplest rocking ratchet system, driven by the homogeneous sinusoidal force $F\left(t\right)=F_{0}cos\omega t$. We arrive at analytic formulas for the leading term of the ratchet current $J_{r,2}\left(\omega \right)\sim F_0^2$ for any corrugation of the channel $h\left(x\right)$.

We study the efficacy of strategies aimed at controlling the spread of deception-based cyber-threats unfolding on online social networks. We model directed and temporal interactions between users using a family of activity-driven networks featuring tunable homophily levels among gullibility classes. We simulate the spreading of cyber-threats using classic susceptible-infected-susceptible (SIS) models. We explore and quantify the effectiveness of four control strategies. Akin to vaccination campaigns with a limited budget, each strategy selects a fraction of nodes with the aim to increase their awareness and provide protection from cyber-threats. The first strategy picks nodes randomly. The second assumes global knowledge of the system selecting nodes based on their activity. The third picks nodes via egocentric sampling. The fourth selects nodes based on the outcome of standard security awareness tests, customarily used by institutions to probe, estimate, and raise the awareness of their workforce. We quantify the impact of each strategy by deriving analytically how they affect the spreading threshold. Analytical expressions are validated via large-scale numerical simulations. Interestingly, we find that targeted strategies, focusing on key features of the population such as the activity, are extremely effective. Egocentric sampling strategies, though not as effective, emerge as a clear second best despite not assuming any knowledge about the system. In addition, we find that networks characterized by highly homophilic interactions linked to gullibility might expand the range of transmissibility parameters that allows for macroscopic outbreaks. At the same time, they reduce the reach of these spreading events. Hence, rather isolated patches of the network formed by highly gullible individuals might provide fertile grounds for the propagation and survival of cyber-threats.

Modeling how information or disease spreads on a network is a major problem in network science. The problem of determining seed nodes that maximize influence is called the influence maximization problem and has been well studied for various models of influence dissemination. The influence computation problem has an even more ambitious goal as it seeks to determine the exact probability of particular nodes getting influenced. H. Z. Brooks et al. [arXiv:2403.01066] introduced a model for the spreading of content on networks inspired by bounded confidence models. We show that this content-spreading model generalizes the independent cascade model and propose various influence computation and influence maximization problems. We discuss centrality measures for identifying influential nodes in the case of trees, which is analytically and computationally tractable. Finally, we train graph neural networks to predict the influence probabilities and propose this as a benchmark task to evaluate the oversquashing problem in graph neural networks.

We present the results of the molecular dynamics simulation of ultracold Xe plasma in constant homogeneous crossed electric and magnetic fields. A Simulation shows that there are two electron loss mechanisms. The first one is that the initial electron cloud splits into two lobes. The second one is that electrons leave the plasma as a beam. The beam is deformed due to the diocotron instability and drifts along the $[\mathit{E}\times \mathit{B}]$ direction with a constant velocity. A qualitative analysis of the conditions for observing the two mechanisms is provided. The result obtained may be of interest for electron microscopy.

Computed tomography (CT) is essential for studying rock microstructures and macroscopic properties, yet its imaging quality is often compromised by complex degradation factors in real-world scenarios. Superresolution (SR) reconstruction techniques for rock CT images aim to enhance image quality significantly and overcome low-resolution limitations. However, most existing SR methods rely on difficult-to-acquire paired training data or employ simulated data that inadequately reflect actual degradation processes, leading to suboptimal performance on real rock CT images. To address the challenge of high-quality three-dimensional (3D) rock CT reconstruction under real degradation conditions, this paper proposes an innovative approach that integrates a physics-driven stochastic degradation model with a lightweight network architecture. Key innovations comprise a physics-driven stochastic degradation model that dynamically utilizes randomized selection and permutation of degradation operations to emulate real-system degradation diversity—enhancing synthetic-to-real distribution alignment; synergistically integrated with a batch normalization-free lightweight 3D network where strategic elimination of batch normalization layers achieves extreme computational efficiency while preserving microstructure-critical spatial fidelity; collectively enabling a robust synthetic-to-real framework trained solely on physics-compliant synthetic data, validated through superior reconstruction quality and physical characteristic preservation. This work provides an efficient and reliable image enhancement solution for high-precision digital core analysis in petroleum exploration and related fields while offering valuable insights for geoscientific image reconstruction.

Recently, a paradoxical effect has been demonstrated in which transport of a free Brownian particle driven by active fluctuations in the form of white Poisson shot noise can be significantly enhanced when it is additionally subjected to a periodic potential. This phenomenon can emerge in an overdamped system, but it may also be inertia-induced. Here, we considerably extend previous studies and comprehensively investigate the impact of inertia on the effect of free transport enhancement observed in the overdamped system. We detect that inertia cannot only induce this phenomenon, but, depending on a parameter regime, it may also strengthen, weaken, or even destroy it. We exemplify these different scenarios and explore the parameter space to identify the corresponding regions where they emerge. The variance of the active fluctuations amplitude distribution is a key determinant of the inertia influence on the effect of free transport amplification. Our results are relevant not only for microscopic physical systems, but also for biological ones, such as living cells, where fluctuations generated by metabolic activities are active by default.

This paper studies the diffusive behaviors of the two-state model generalized Lévy walk with jumps (GLWJ) in a constant biased field. Assuming that the motion time density of the GLW process follows a power-law distribution, and the corresponding velocity is defined via a power-law coupling with its motion time, while the random jump density follows a Gaussian distribution. The diffusive behaviors are analyzed and explored through calculating the mean-squared displacement (MSD) and the probability density function (PDF). The results indicate that the MSD exhibits a crossover phenomenon driven by three distinct mechanisms and the PDF also shows a directional deviation. Notably, although the biased field endows the walker with the capability of directional transport, it does not always change the diffusion result, which contradicts our intuition. Meanwhile, since the fluctuations originate from different mechanisms, even if a diffusion term has a smaller diffusion exponent, as long as its fluctuation intensity is much stronger than the others, it can still dominate the result on a large observation timescale. This study reveals the rich diffusion phenomena of the biased GLWJ model, and can provide theoretical guidance for particle transport in the related biological and physical experimental observations.