The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of stochastic Fermi acceleration, which subsumes all forms of nonresonant acceleration in ideal electric fields and is applicable in generic settings. It combines an exact equation connecting the energization rate to the statistics of the velocity field with a statistical model of particle transport through the structures (i.e., the regions of strong velocity gradients). In a second part, this formalism is applied to magnetohydrodynamic turbulence to obtain a comprehensive assessment of the scale-by-scale contributions to the advection and diffusion coefficients. Acceleration peaks on scales where particles can be trapped inside structures for an eddy turnaround time, or in intense structures associated with sharp bends of the magnetic field lines in large-amplitude turbulence (as reported earlier). These spatially inhomogeneous, rapid acceleration regimes pave the way for a rich phenomenology. We discuss the scalings obtained, their interpretation, and we show that the findings compare satisfactorily with existing numerical results.

We predict a phenomenon of catastrophic material failure arising suddenly within an amorphous material, with an extremely long delay time since the material was last deformed. By simulating a mesoscopic soft glassy rheology model in one dimension (1D), a mesoscopic elastoplastic model in 1D and 2D, and a continuum fluidity model in 1D, we demonstrate the basic physics to involve a dramatic ultra-delayed shear banding instability, in which strain suddenly strongly localizes within the material and the stress drops precipitously. The delay time after the long historical shear strain was applied before failure occurs increases steeply with decreasing strain amplitude, decreasing working temperature, and increasing sample annealing prior to shear. In demonstrating the same physics—which is directly testable experimentally and in particle simulations—to obtain within three different constitutive models, we suggest it may be generic across amorphous materials. The counter-intuitive prediction of catastrophic material failure long after any deformation was last applied could have important consequences for material processing and performance.

Many of the existing approaches to assess and predict the performance of players, teams, or products in competitive contests rely on the assumption that comparisons occur between pairs of such entities. There are, however, several real contests where more than two entities are part of each comparison, e.g., sports tournaments, multiplayer board and card games, and preference surveys. The Plackett-Luce (PL) model provides a principled approach to infer the ranking of entities involved in such contests characterized by multibody comparisons. Unfortunately, traditional algorithms used to compute PL rankings suffer from slow convergence, which limits the application of the PL model to relatively small-scale systems. Here, we present an alternative implementation that allows for significant speed-ups and validate its efficiency in both synthetic and real-world sets of data. Further, we perform systematic cross-validation tests concerning the ability of the PL model to predict unobserved comparisons. We find that a PL model trained on a set composed of multibody comparisons is more predictive than a PL model trained on a set of projected pairwise comparisons derived from the very same training set, emphasizing the need of properly accounting for the true multibody nature of real-world systems whenever such information is available.

The dynamical cavity method and its backtracking version provide a powerful approach to studying the properties of dynamical processes on large random graphs. This work extends these methods to hypergraphs, enabling the analysis of interactions involving more than two variables. We apply them to analyze the $k\text{−}\mathrm{XOR}\text{−}\mathrm{sat}\text{isfiability}$ problem, an important model in theoretical computer science which is closely related to the diluted $p$-spin model from statistical physics. In particular, we examine whether the quench dynamics—a deterministic, locally greedy process—can find solutions with only a few violated constraints on $d$-regular $k$-uniform hypergraphs. Our results demonstrate that the methods accurately characterize the attractors of the dynamics. It enables us to compute the energy reached by typical trajectories of the dynamical process in different parameter regimes. We show that these predictions are accurate, including cases where a classical mean-field approach fails.

We consider fluid flows for which the linearized Navier-Stokes operator is strongly nonnormal. The responses of such flows to external perturbations are spanned by a generically very large number of nonorthogonal eigenmodes. They are therefore qualified as “nonmodal” responses, to insist on the inefficiency of the eigenbasis to describe them. In the aim of the article to reduce the system to a lower-dimensional one free of spatial degrees of freedom, (eigen)modal reduction techniques, such as the center manifold, are thus inappropriate precisely because the leading-order dynamics cannot be restricted to a low-dimensional eigensubspace. However, it is often true that only a small number (we assume only one) of singular modes is sufficient to reconstruct the nonmodal responses at the leading order. By adopting the latter paradigm, we propose a general method to analytically derive a weakly nonlinear amplitude equation for the nonmodal response of a fluid flow to a small harmonic forcing, stochastic forcing, and initial perturbation, respectively. In these last two problems, we assumed a parallel base flow with a spatially monochromatic external excitation. The present approach for deriving nonmodal amplitude equations is simpler than the one we previously proposed, for neither the operator perturbation nor the ensuing compatibility condition is formally necessary. Additionally, it provides an explicit, rigorous treatment of the suboptimal responses. When applied to the stochastic response, the present method makes it possible to derive an amplitude equation that is substantially easier to solve and interpret than the one we proposed previously. Eventually, the three derived amplitude equations are tested in three distinct, two- and three-dimensional flows. For sufficiently small excitation amplitudes, yet up to values large enough for the flow to depart from the linear regime, they can systematically predict the weakly nonlinear modification of the gains as the amplitude of the external excitation is increased. This, at an extremely low numerical cost as compared to fully nonlinear techniques. However, the proposed weakly nonlinear approach, precisely because it condemns the flow spatial structure to be mostly along the leading singular mode, is often too simplistic to predict the occurrence of subcritical transitions as the excitation amplitude is increased to too large values.

A three-state Ising model properly describing crystal, liquid, and gas phases of a simple substance like argon [Phys. Rev. E 109, 014123 (2024)] is analyzed at a mean-field level in connection with metastable states and spinodal limits. This mainly comprises the stretched liquid and crystal at negative pressure, the superheated liquid and crystal, the supercooled liquid, and the metastable continuations of binodal curves. The model is consistent with available information from experiment and simulation, except for a supercooled liquid spinodal that it predicts. This defect is repaired by devising an enhanced four-state model, with the consequence that spinodal suppression is relevant to the topic of one-component liquid–liquid criticality. The present work on a simple substance thus paves the way to addressing the interplay between the crystal and supercooled liquid phases of water theoretically.

In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model exhibits noise-induced transitions. The bifurcation diagram has two distinct regions of unimodality and bimodality in which the steady-state probability distribution has one and two peaks, respectively. Apart from first-order transitions between the two regimes, a critical-point transition occurs at a cusp point with the transition belonging to the mean-field Ising universality class. The epidemic model shares these features with the well-known Horsthemke-Lefever model of population genetics. The effect of vaccination on the spread/containment of the epidemic in a stochastic setting is also studied. We further propose a general vaccine-hesitancy model, along the lines of Kirman's ant model, with the steady-state distribution of the fraction of the vaccine-willing population given by the Beta distribution. The distribution is shown to give a good fit to the COVID-19 data on vaccine hesitancy and vaccination. We derive the steady-state probability distribution of the basic reproduction number, a key parameter in epidemiology, based on a beta-distributed fraction of the vaccinated population. Our study highlights the universal features that epidemic and vaccine models share with other dynamical models.

Models of opinion dynamics describe how opinions are shaped in various environments. While these models are able to replicate general opinion distributions observed in real-world scenarios, their capacity to align with data at the user level remains mostly untested. We evaluate the capacity of the multistate voter model with zealots to capture individual opinions in a fine-grained Twitter dataset collected during the 2017 French presidential elections. Our findings reveal a strong correspondence between individual opinion distributions in the equilibrium state of the model and ground-truth political leanings of the users. Additionally, we demonstrate that discord probabilities accurately identify pairs of like-minded users. These results emphasize the validity of the voter model in complex settings and advocate for further empirical evaluations of opinion dynamics models at the user level.

The El Niño-Southern Oscillation (ENSO) significantly impacts global weather, with strong El Niño events often linked to prolonged dry conditions in Southeast Asia. While several high-impact El Niño events have coincided with prolonged dry conditions, leading to droughts, the underlying causal mechanisms remain complex and incompletely understood. In this study, we develop a minimal, data-driven model to quantify the conditions under which ENSO events amplify prolonged dry conditions risk in Southeast Asia. Unlike correlation-based approaches, our model identifies thresholds in sea surface temperatures and atmospheric water vapour content that increase the probability of prolonged dry conditions. Our results show that when ENSO-induced anomalies exceed specific temperature and atmospheric thresholds, prolonged dry conditions probability rises significantly, aligning with observed historical droughts. Additionally, the model reveals periods where this link weakens due to competing regional climate factors, suggesting that certain conditions mitigate the typical ENSO-prolonged dry conditions connection. These findings provide a more nuanced understanding of ENSO-driven prolonged dry conditions variability, offering a probabilistic predictive framework with potential applications in climate adaptation, agricultural planning, and regional resource management.

We present a minimal model to analyze the capacitive response of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the underlying electrolyte transport equations, we show that the leading-order relaxation of the transmembrane potential is governed by a capacitive timescale, ${\tau }_{\mathrm{C}}=\frac{{\lambda }_{\mathrm{D}}L}{D}\left(\frac{2+\mathrm{\Gamma }{\delta }^{\mathrm{M}}/L}{4+\mathrm{\Gamma }{\delta }^{\mathrm{M}}/{\lambda }_{\mathrm{D}}}\right)$, where ${\lambda }_{\mathrm{D}}$ is the Debye screening length, $L$ is the electrolyte width, $\mathrm{\Gamma }$ is the ratio of the permittivity of the electrolyte to the membrane, ${\delta }^{\mathrm{M}}$ is the membrane thickness, and $D$ is the ionic diffusivity. This timescale is considerably shorter than the traditional RC timescale ${\lambda }_{\mathrm{D}}L/D$ for a bare electrolyte due to the membrane's low permittivity and finite thickness. Beyond the linear regime, however, salt diffusion in the bulk electrolyte drives a secondary, nonlinear relaxation process of the transmembrane potential over a longer timescale ${\tau }_{\mathrm{L}}=L^2/4{\pi }^{2}D$. A simple equivalent-circuit model accurately captures the linear behavior, and the perturbation expansion remains applicable across the entire range of observed physiological transmembrane potentials. Together, these findings underscore the importance of the faster capacitive timescale and nonlinear effects on the bulk diffusion timescale in determining transmembrane potential dynamics for a range of biological systems.

Mechanochemical patterns arising in the actomyosin cortex drive many cellular processes. Here we consider a hydrodynamic model for the actomyosin cortex of cells and study the sensitivity of the emergent patterns to both physical parameters and the geometry of the confining domain. We first establish a general framework for the Galerkin analysis of such patterns far from the linear stability regime on an arbitrary two-dimensional domain. In the case of a circular disk, our analytical results predict transitions from isotropic to anisotropic patterns upon changing the strength of the active stress and the turnover rate. We confirm the existence of this secondary bifurcation of the homogeneous state by an explicit numerical analysis of our model. Extending our numerical analysis to harmonic deformations of the circular disk, we show that the emergent patterns are also sensitive to the curvature of the domain. In particular, the actomyosin patterns resulting from our study closely resemble those seen in cells confined to micropatterned substrates. Our study demonstrates the role of geometry in controlling patterns within the context of a simple model for the actomyosin cortex.

The investigation of water's glass transition and a possible liquid-liquid transition within its supercooled state is hampered by its inevitable crystallization in a temperature range, termed “no-man's land.” Here we report dielectric-spectroscopy and calorimetry measurements of pure water and various aqueous LiCl solutions, part of the latter being quenched to avoid crystallization. By investigating solutions of relatively low salt content and by covering an exceptionally broad frequency range up to THz, we find strong hints at a crossover in water from a strong to a fragile liquid, characterized by different glass-transition temperatures and different non-Arrhenius temperature dependencies of the molecular dynamics.

In this paper we examine the relative knotting probabilities in a lattice model of ring polymers confined in a cavity. The model is of a lattice knot of size $n$ in the cubic lattice, confined to a cube of side length $L$ and with volume $V={(L+1)}^3$ sites. We use Monte Carlo algorithms to estimate approximately the number of conformations of lattice knots in the confining cube. If $p_{n,L}\left(K\right)$ is the number of conformations of a lattice polygon of length $n$ and knot type $K$ in a cube of volume $L^3$, then the relative knotting probability of a lattice polygon to have knot type $K$, relative to the probability that the polygon is the unknot (the trivial knot, denoted by $0_1$), is ${\rho }_{n,L}(K/0_1)=p_{n,L}\left(K\right)/p_{n,L}\left(0_1\right)$. We determine ${\rho }_{n,L}(K/0_1)$ for various knot types $K$ up to six crossing knots. Our data show that these relative knotting probabilities are small over a wide range of the concentration $\phi =n/V$ of monomers for values of $L\le 12$ so that the model is dominated by unknotted lattice polygons. Moreover, the relative knot probability increases with $\phi$ along a curve that flattens as the Hamiltonian state is approached.

Dynamical phase transitions (DPTs) are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents (CEs) play a key role in characterizing the physics near criticality. In this paper, we aim at systematically analyzing the set of possible CEs in weak noise statistical field theories in $1+1$ dimensions, focusing on cases with a single fluctuating field. To achieve this, we develop and apply the Gaussian fluctuation method, avoiding reliance on constructing a Landau theory based on system symmetries. Our analysis reveals that the CEs can be categorized into a limited set of distinct cases, suggesting a constrained universality in weak noise-induced DPTs. We illustrate our findings in two examples: short-time large deviations of the Kardar-Parisi-Zhang equation and the weakly asymmetric exclusion process on a ring within the framework of the macroscopic fluctuation theory.

In the past 80 years, the Goldman-Hodgkin-Katz (GHK) equation has been the gold-standard framework for interpreting countless biological and physiological experiments and simulations that involve ion transport in nanopores, nanochannels, and ion-channels subjected to a combined ionic concentration and electric potential gradients. In this work, we revisit the mathematical derivation used to develop the GHK model and show that this model is internally inconsistent when the Debye length is substantially smaller than the longitudinal length of the channel. In particular, we show that its infamous assumption of a constant electric field is incorrect, which leads to substantial errors, including the inability of this model to satisfy local and global electroneutrality. Then, leveraging key insights from the field of reverse electrodialysis (RED), we derive a new internally consistent model that does not assume that the electric field is constant and satisfies electroneutrality. This new model has several advantages. First, while the mathematics are substantially more complicated, the derivation does not include ad hoc assumptions, and the model is internally consistent. Second, the new solution connects the two realms of GHK and RED, which consider the same equations but in opposing limits, negligible or substantial surface charge density effects, respectively. Third, while the expressions for the new model are complicated, the new model can be reduced to several limits, which allows for a much easier and more straightforward analysis. Finally, all of our newly derived results show remarkable correspondence to nonapproximated numerical simulations. This work provides a brand-new framework for interpreting (and reinterpreting) ion transport experiments in any charge-selective system.

Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases with increasing the length $L$ of the product chain, in a way that depends on the matrix dimension $N$ and the truncation depth $\delta N$. Here we study that dependence in the double-scaling limit $L,N\to \infty$ at the fixed ratio $\tau =L\delta N/N$. The entropy reduction crosses over from a linear to a logarithmic dependence on $\tau$ when this parameter crosses unity. The central technical result is an expression for the singular-value moments of the matrix product in terms of the Erlang function from queueing theory.

Cargo distribution in eukaryotic cells relies on active transport by molecular motors. Despite its importance, the relationship between motor transport properties and cargo binding remains inadequately understood. Moreover, improper regulation of ubiquitination, a key post-translational modification affecting protein degradation, activation, and localization, is linked to several neurodegenerative diseases. To investigate how ubiquitin-like modifications influence motor function, we use the PLM neuron of C. elegans as a model system. Through fluorescent microscopy, we examine the distribution of cargo-bound UNC-104 along the axon and probe its dynamics with FRAP experiments. We model cargo binding kinetics using a master equation and motor density dynamics via the Fokker-Planck approach. Our previous analysis showed that ubiquitin-like knockdowns enhance UNC-104's cooperative binding to cargo, but our combined experimental and theoretical analysis here demonstrates that they do not impact its transport properties, such as processivity and diffusivity. Thus, while these modifications significantly impact UNC-104's cargo binding, they do not alter its dynamics, maintaining the homeostatic distribution of motors.

The principal stress-bearing component of bacterial cell walls is the tough, covalently linked peptidoglycan network. This active material maintains the shape and integrity of bacterial cells in the presence of high turgor pressures while constantly growing. It is not well understood how its extreme material properties derive from its molecular structure. The large stress in the cell wall demands a description going beyond small-strain approximations, an approach that has not been taken in the biomaterials community. We here derive a continuum elastic model of E. coli peptidoglycan (PG) in two steps: We first reduce the complex microscopic structure of the PG layer to the spring elements of a 2D hyperelastic triangular network, and then interpret those results in the context of finite-strain continuum theory. We present a self-contained formalism to study stress-strain relationships for large deformations and arbitrary anisotropies. We obtain the minimal model compatible with the available data on E. coli morphology and mechanics. We show that the strain hardening of PG leads to a stiffness matrix that is linearly proportional to the turgor pressure of the cell.

Crystallization through vapor deposition is ubiquitous and is inevitably influenced by impurities that often impact the local structure. Interestingly, the effect of immobilizing some of the depositing particles themselves, which would preserve local structural symmetry, remains largely unexplored. Herein, we perform colloidal vapor deposition on a substrate with a few pinned adcolloids, termed “mobility impurities.” Through thermodynamic and kinematic measurements, we demonstrate that these pinned adcolloids, even though they share identical geometry and interaction with depositing particles, are disfavored as nucleation centers. Our experimental findings, supported by molecular dynamics simulations and a simple theoretical model, reveal that entropic contributions, rather than energetic ones, govern nucleation physics in the presence of mobility impurities. Moreover, tuning the mobility of colloids on the substrate adjusts the nucleation likelihood at pinned sites. In later stages of growth, pinning induces mode localization and alters the thin film's vibrational spectrum. Our work thus underscores the potential of strategically incorporating mobility impurities to engineer material properties.

Dynamics that are microscopic in space and time, where particles commit to a new position, referred to as excitations, are considered the elementary unit of relaxation in the dynamic facilitation theory of the glass transition. Meanwhile, geometric motifs known as locally favored structures are associated with vitrification in many glassformers. Recent work indicates that the probability of particles being found in both locally favored structures (LFS) and excitations decreases significantly upon supercooling, suggesting an anticorrelation between them [Ortlieb et al., Nat. Commun. 14, 2621 (2023)]. However, the spatial relationship between excitations and LFS remains unclear. By employing state-of-the-art GPU computer simulations and colloid experiments, we analyze this relationship in model glassformers. We reveal a strong anti-correlation between long-lived LFS and excitations, along with a spatial separation between the two in deeply supercooled liquids. This strong anticorrelation likely arises because well-packed LFS resist local rearrangements, and thus hindering the formation of excitations.