This corrects the article DOI: 10.1103/PhysRevE.111.014422.

When considering effective interactions in a many-body or thermodynamic system, it is important to recognize that the inherent character of the effective forces between two bodies already incorporates many-body effects that appear unified in a nontrivial way. Working backward to disentangle these effects into the contributions of pairs, triplets, or larger groups is generally complicated and seldom accomplished. However, this could offer essential insights into the structural architecture and self-assembly of complex systems, such as soft materials. In this contribution, we tackle this problem by employing a simulation-based method, here termed contraction of the bare forces (CBF), which, on the one hand, permits a precise evaluation of the effective interactions between colloids [de los Santos-López et al., J. Chem. Phys. 157, 074903 (2022)0021-960610.1063/5.0099919] and, on the other hand, makes it possible to quantify the many-body contributions to these effective interactions. The CBF approach is applied to calculate the depletion forces in asymmetric binary mixtures of hard spheres; the approach is sufficiently sensitive to quantify the effects of higher-order terms on the depletion forces between large particles. To assess the accuracy of our approach, we first explore and confirm the long-established prediction founded on purely geometric considerations, which states that for the particle size ratio, q, smaller than q<q_{3}=0.1547, the depletion interaction between large colloids does not depend on the concentration of large particles, provided that the chemical potential of the smaller particles is kept constant. In contrast, for mixtures with less size asymmetry, such effects become considerably influential. Specifically, we have conducted an in-depth examination of scenarios with size asymmetries values of q=0.45 and 0.60. We directly compare our results for the depletion forces with those obtained from the integral equation framework for effective interactions. Through the use of a naive approximation formulated at the level of the bridge functions, this comparison has further enabled us to identify higher-order contributions to the depletion forces between large colloids, thereby improving and sharpening the underlying theoretical approximations. More importantly, in this work, we explicitly disentangle the many-body components of the depletion forces and assess how significantly they affect the contact attraction strength as a function of both the size ratio and the concentration of the large colloids.

This Letter uncovers five distinct charge transport modes and their transitions in dual-energy electron beam diodes. We via first-principle particle-in-cell (PIC) simulations establish that the specific mode (e.g., space-charge oscillations) and the current transmitted characteristics are essentially governed by the interplay between the electron beam energy and the injected current density. The effective space-charge-limited (SCL) current (lower than the conventional SCL threshold) is unveiled due to the coupled interactions between two electron beams. A generalized analysis is conducted for n-component electron beams, and a theoretical piecewise function for the transmitted current density is proposed, which agrees well with the PIC results under designed conditions. The discovery provides a mechanistic picture of multiple electron beam transport in diodes, paving the way for novel designs of high-performance modern vacuum electronic devices.

In complex media, transport and geometric properties deeply influence the kinetics of random encounters between reactants. Here, we consider the situation in which a random walker, moving in a regularly diffusing medium, has to reach and activate a target located inside a compartment characterized by fractal (obstructed) subdiffusion. We focus on dual-site reactions, which end when two activation events occur within a given time window. Each activation event happens with a finite probability whenever the random walker visits the target. For weakly reactive targets, we demonstrate that the reaction time can be minimized for an optimal compartment size and can even be accelerated when compared to the same system without a compartment. Our analytical predictions are validated through simulations of a random walker on a cubic lattice, where some sites inside the compartment are obstructed at the critical percolation threshold. Our theory illustrates the fact that adding a crowded compartment around a target, even if it slows down the motion in its vicinity, can accelerate the kinetics of complex reactions, especially for weakly reactive targets.

We present a series of experiments investigating the local microstructure of cylindrical piles composed of highly concave particles. By systematically varying particle geometry-from spheres to strongly nonconvex polypods-as well as frictional properties and the number of branches, we explore how these parameters, together with the preparation protocol, shape the internal structure of the system. Using x-ray tomography combined with a dedicated image-analysis pipeline, we accurately extract the position, orientation, and contacts of every particle in each pile. This allows us to quantify the evolution of key structural observables as a function of particle geometry and preparation method. In particular, we measure the distributions of local packing fraction, coordination number, number of neighbors, and contact locations, along with particle-particle positional and orientational correlations. More importantly, we construct a new stability indicator that correlates perfectly with the observed pile stabilities, enabling us to identify the fundamental mechanisms responsible for geometrically induced cohesion in granular systems composed of noninterlocking particle shapes: interdigitation, rotational constraint, friction-mediated cohesion, and the ability of a pile to restabilize.

Walkers (i.e., bouncing droplets coupled to a local Faraday wave) are sent on an orthogonal standing wave. The trajectories of successive walkers form a straight-propagating beam toward the wave that splits into three distinct paths during the interaction with the wave. At the end of the interaction, walkers' trajectories split again and are deviated into three main directions. The walkers' trajectories show sensitivity to parameters and initial conditions but remain predictable in some regions of the parameter space. The dependence of the statistical distribution of deviations on the wave amplitude markedly differs from the prediction of quantum mechanics for a particle interacting with a standing electromagnetic wave.

The fast ion (FI) on turbulent transport is one of the key topics of magnetic confinement fusion. This work focus on the impact of FI pressure gradients on turbulence in a high-β plasma scenario using gyrokinetic simulations. Linear analyses reveal that FIs strongly stabilize ion temperature gradient (ITG) modes via the thermal-ion dilution, while their influence on trapped electron modes (TEMs) is minimal. At elevated FI pressure gradients, a transition to a FI-driven BAE (FI-BAE) regime occurs, as evidenced by mode structure and frequency alignment within the Alfvénic gap. Electron β scans further demonstrate the emergence of kinetic ballooning modes at higher β, whereas an ITG-TEM hybrid turbulence dominates near experimental β values. Nonlinear simulations show that moderate FI pressure suppresses transport via zonal flow (ZF) shear, whereas strong FI drive weakens ZFs and enhances transport by destabilizing FI-BAEs. These results highlight the dual role of FIs in regulating turbulence and offer insight into multiscale transport physics relevant for high-performance plasmas.

In the present work, we review two well-established quasicontinuum models of a Fermi-Pasta-Ulam lattice with Hertzian potentials, and we utilize these two models to approximate the discrete dispersive shock waves which are numerically observed in the simulation of the lattice. To perform analysis on various characteristics of the discrete dispersive shock wave, we analytically derive the Whitham modulation equations of the two quasicontinuum models, which govern the slowly varying spatial and temporal dynamics of distinct parameters of the periodic solutions. We then perform a very useful reduction of the Whitham modulation system to gain a system of initial-value problems whose solutions can provide important insights on edge features of the dispersive shock waves such as their edge speeds. In addition, we also study the numerical rarefaction waves of the lattice based on the two quasicontinuum models. In particular, we analytically compute and compare their self-similar solutions with the numerical discrete rarefaction wave of the lattice. These comparisons made for both dispersive shock waves and rarefaction waves reveal to be reasonably good, which suggest the impressive performance of both quasicontinuum models in approximating the nonlinear dispersive wave patterns of the granular crystal lattice.

Using particle-based simulations, we study the rheology of dense, frictional, non-Brownian suspensions containing active particles. We find that the viscosity and the shear jamming point of the suspension can be tuned by varying the activity strength of the active particles. Microscopically, variations in the number of frictional contacts and the formation of a more isotropic force-chain network due to the presence of active particles underlie the viscosity changes. We introduce an effective temperature, defined through the control parameters of the active particles, that uniquely governs the viscosity of the suspensions. We also find that while activity drives the system away from jamming by hindering force-chain formation, unjamming an already jammed state by breaking existing force chains requires higher activity strength.

The Sherrington-Kirkpatrick (SK) model is a foundational model for understanding spin glass systems. It is based on the pairwise interaction between each two spins in a fully connected lattice with quenched disordered interactions. The SK model, as an infinite-range model, simplifies the study of this system by eliminating fluctuations. An advanced SK model, known as the p-spin model, introduces higher-order interactions that involve the interaction of P spins. This study focuses on the general Hamiltonian of the spin glass model with infinite-range interactions, referred to as the mixed p-spin glass model, which consists of adding all p-spin interaction terms. This study aims to derive the equations of state for this Hamiltonian, formulate the equations of state within the framework of the first replica symmetry breaking, and determine both the stability condition of the replica symmetric solution and the stability of the replicas belonging to the same group in the first step of replica symmetry breaking. Additionally, this study considers two special cases. The first case is a mixed p-spin glass model in which all interactions are normally distributed around zero. The second case focuses on the SK model compound with perturbative higher-order interactions to investigate how these interactions influence the phase transition.

We introduce an Ising spin-glass model with correlated disorder which continuously interpolates between the pure ferromagnetic Ising model and the Edwards-Anderson model with symmetric disorder. For this model, we prove that a Nishimori line (NL) can be defined, analogously to the Edwards-Anderson model, on which physical quantities can be expressed exactly in terms of those of the pure Ising model at a well-defined effective temperature on any lattice in any dimension. For example, the energy on the NL is equal to the energy of the pure Ising model at the effective temperature up to a constant and a trivial factor. More remarkably, the specific heat on the NL equals the energy, not the specific heat, of the pure Ising model at the effective temperature, again up to a constant and a trivial factor. Gauge-noninvariant quantities such as the magnetization and correlation functions are exactly equal to the corresponding quantities of the pure Ising model at the effective temperature. These exact relations imply that the leading critical behavior at that multicritical point for the disorder-correlated model is pure-Ising-like, in contrast to the conventional multicritical universality class of the standard Edwards-Anderson model. Our results motivate further investigations of the relatively unexplored topic of correlations in disorder in spin glasses and related problems.

E-values have recently emerged as a robust and flexible alternative to p-values for hypothesis testing, especially under optional continuation, i.e., when additional data from further experiments are collected. In this work we define optimal e-values for testing between maximum entropy models, in both the microcanonical (hard constraints) and canonical (soft constraints) settings. We show that, when testing between two hypotheses that are both microcanonical, the so-called growth-rate optimal e-variable admits an exact analytical expression, which also serves as a valid e-variable in the canonical case. For canonical tests, where exact solutions are typically unavailable, we introduce a microcanonical approximation and verify its excellent performance via both theoretical arguments and numerical simulations. We then consider constrained binary models, focusing on 2×k contingency tables-an essential framework in statistics and a natural representation for various models of complex systems. Our microcanonical optimal e-variable performs well in both settings, constituting a tool that remains effective even in the challenging case when the number k of groups grows with the sample size, as in models with growing features used for the analysis of real-world heterogeneous networks and time series.

A slightly tilted permanent magnet rotating at high speed can induce a magnetic field capable of trapping another permanent magnet in a gravity independent levitated bound state, bypassing Earnshaw's theorem. During levitation, the floater magnet is locked in a conical orbit at the same frequency as the rotor. This rotation allows the sides of the same polarity of each magnet to face each other, which is responsible for the dynamic equilibrium of the floater magnet. Here, we theoretically explain the motion of the floater in-axis and off-axis and highlight levitation stability conditions and their dependence on the size of the floater and the speed of the rotor. We also experimentally studied the levitation conditions with respect to the rotational speed of the rotor for various floater's sizes and shapes. We observed and analyzed the lower and upper limits of levitation. Finally, we explained the off-axis motion of the center of mass of the floater from its equilibrium position by an extension of the dipole moment model.

Promoter-proximal pausing is a key regulatory checkpoint in RNA polymerase II transcription, yet current models lack a unified description of how arrival-state-dependent pause heterogeneity shapes nascent transcriptional occupancy, completion flux, and steady-state mature mRNA levels. We introduce a mechanistic framework in which the promoter-proximal pause gate is a continuous-time Markov chain that modulates an M/G/∞ queue. Each initiation event samples a gate-at-initiation state that fixes the entire episode lifetime-pause waiting, early elongation, and termination-yielding exact analytical expressions for transient and steady-state nascent concurrency, and the completion flux. From this structure, we derive an explicit gate-induced pause-initiation limit: a maximal productive initiation rate determined solely by the finite capacity and residence time of the promoter-proximal window. This bound provides a mechanistic explanation for experimentally inferred ceilings on transcriptional activation and clarifies how perturbations affecting pause duration, elongation speed, or termination latency move genes along the same constraint. We further obtain interpretable formulas for the promoter-proximal pausing index and its dependence on pause-state composition. Together, our results establish a compact mathematical theory linking microscopic pausing kinetics to macroscopic transcriptional outputs, offering general principles for how promoter-proximal regulation shapes gene expression dynamics.

By extending the Sanchez-Lacombe lattice-fluid model for mixtures to the case of polymer blends containing solid fillers, we calculate the excess thermodynamic quantities arising from the presence of fillers. These results are then used to derive the spinodal stability condition of a filled polymer blend. In the low-compressibility limit, this condition reduces to a remarkably simple analytical expression that is derived self-consistently within the present framework. Comparison between the exact and approximate spinodal curves shows excellent agreement, with deviations in the spinodal temperature of less than 4K, thereby validating the proposed approximation. The obtained analytical approximation enables a straightforward evaluation of the spinodal temperature without the extensive numerical calculations required to determine the exact spinodal condition. Both the exact and approximate spinodal conditions yield good quantitative agreement with experimental data for filled and unfilled blends.