We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study the transport dependence on the perturbation amplitudes, relative phase, and spatial-mode choice. Using particle transmissivity as a confinement criterion, identical-mode pairs exhibit phase-controlled behavior: antiphase waves produce destructive interference and strong confinement, while in-phase waves add constructively and drive chaotic transport. Mode-mismatched pairs produce richer phase-space structure with higher-order resonances and sticky regions; the transmissivity boundaries become geometrically complex. Box-counting dimensions quantify this: integer dimension smooth boundaries for identical modes versus noninteger fractal-like dimension for distinct modes, demonstrating that phase and spectral content of waves jointly determine whether interference suppresses or promotes transport.

We use video microscopy to investigate transition kinetics among distinct topological states in four-particle colloidal clusters with short-range interactions. While steady-state distributions are captured solely by net free energy differences, observed transition rates are not. By introducing activation barriers proportional to topological changes between states, we construct a minimal thermodynamic framework that explains both transition rates and equilibrium distributions, with predictive capabilities across a range of interaction strengths. These findings have broad implications for evolutionary dynamics, protein folding, and self-assembly.

In a recent paper [M. Gül et al., Phys. Rev. E 110, 064115 (2024)], we showed that test particle sum rules, which address the excess chemical potential and isothermal compressibility, could be used to develop accurate classical density functionals for hard-sphere (HS) fluids. Here we extend our approach to the construction of HS functionals building upon the state-of-the-art White-Bear (WB) and White-Bear mark II functionals. Employing the same test particle sum rules, we determine the two free parameters in the Lutsko [J. F. Lutsko, Phys. Rev. E 102, 062137 (2020)] formulation of fundamental measure theory by minimizing the relative errors between different routes to the two thermodynamic quantities. The resulting optimized Lutsko WB functionals, especially Lutsko WB mark II, are generally more accurate and consistent than those obtained in earlier treatments.

The reducibility of quasiperiodic (QP) linear systems via Lyapunov-Perron (LP) transformation plays a pivotal role in Hamiltonian dynamics and may become a powerful tool in QP response analysis. The reducibility has received significant research interest, among which most focused on qualitative analysis of some local properties. The quantification of reducibility has been a challenging topic for decades, especially within a relatively large parametric range. In this paper, we will propose a practical and quantitative approach to assess the reducibility of the QP Hamiltonian system, based on a semi-analytical approach recently established to determine the LP transformation. The critical value of a certain parameter, of which the system can be reduced via routine LP transformation only on one side, can be determined accurately by the proposed approach. On the other side of the critical value, more importantly, an extension is proposed for the LP transformation to reduce the system, whereas the routine transformation ceases to be valid. With the critical value, the parametric space can be divided into regions where the routine LP transformation is applicable or the extended transformation needs to be employed. The extended transformation would be applicable in QP response analysis and could potentially enrich the research on QP system reducibility within a large parametric space.

The traditional regression model for dependence detection has been generalized by including the autocorrelated noise (ACN) or lagged dependent variable (LDV) to account for autocorrelation in time series. Existing studies on specifying the models with ACN or LDV are rare. We propose a statistical analysis framework of model specification and estimation, whose effectiveness is validated by simulations. As real-life cases we study the precipitation extreme dependence on temperature and temperature dependence on ${\mathrm{CO}}_2$ and demonstrate how the traditional and misspecified models may overestimate dependence by up to three times. We provide a solid statistical basis for detecting dependence in autocorrelated series.

Energy-based generative models, such as restricted Boltzmann machines (RBMs), require unbiased Boltzmann samples for effective training. Classical Markov chain Monte Carlo methods, however, converge slowly and yield correlated samples, making large-scale training difficult. We address this bottleneck by applying the analytic relation between annealing schedules and effective inverse temperature in diabatic quantum annealing. By implementing this prescription on a quantum annealer, we obtain temperature-controlled Boltzmann samples that enable RBM training with faster convergence and lower validation error than classical sampling. We further identify a systematic temperature misalignment intrinsic to analog quantum computers and propose an analytical rescaling method that mitigates this hardware noise, thereby enhancing the practicality of quantum annealers as Boltzmann samplers. In our method, the model's connectivity is set directly by the qubit connectivity, transforming the computational complexity inherent in classical sampling into a requirement on quantum hardware. This shift allows the approach to extend naturally from RBMs to fully connected Boltzmann machines, opening opportunities inaccessible to classical training methods.

Particle filtration through a porous medium is a much-studied field because of its numerous industrial or natural applications, particularly for deep-bed and cake-type filtration regimes. The percolation regime has received relatively less attention and corresponds to the continuous motion of particles in a porous environment under the principal effect of gravity and generally without any interaction other than contact with the porous matrix. In the present case, both the moving particles and the porous medium are composed of spherical particles of diameters $d$ and $D$, respectively. Dry percolation has been analyzed under such conditions and exhibits lateral diffusion, as well as a constant mean transit velocity that scales with $\sqrt{gD}$ (with $D$ the coarse grain diameter and $g$ gravity). The behavior is significantly different in the case studied here, where the porous stack is fully saturated by a liquid at rest. A previous study experimentally investigated the transition from deep filtration to the percolation regime under laminar flow conditions by matching the refractive index of the liquid to that of the particles of the porous system [C. Ghidaglia et al., Phys. Rev. E 53, R3028 (1996)]. Here, based on the same experimental technique, we focus on the particular case where there is no fluid flow and identify a different type of particle trapping, in contrast with either the dry condition or liquid flow situation. We show that this capture, which can exhibit high metastability, stems from a combination of solid friction and viscous lubrication, which strongly reduces the velocity of the moving particles and can also suppress any rebound. The complementary roles of the packing structure and both the size and shape of the particles are also highlighted.

Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as the square root of time. These sublinear fronts preserve an invariant shape, with an effective diffusion constant that diverges at the transition to linear spreading. The model applies to dense cellular aggregates of nonmotile cells consuming a diffusible nutrient. The sublinear spread results from biomass redistribution slowing due to nutrient depletion, a phenomenon supported experimentally but often neglected. Our results provide a potential explanation for the linear rather than quadratic increase of colony area with time, which has been observed for many microbes.

We propose and analyze a process that extracts useful work from a single active particle maintained at constant temperature in a harmonic potential by measuring the relative sign of the self-propulsion and the confining force, and then adjusting the stiffness of the potential. First, we show analytically that useful work can be extracted by stepwise changes of the stiffness. Then, we use a machine learning procedure to find time-dependent stiffness change protocols. We find that these protocols involve discontinuous initial changes of the stiffness opposite to the expected direction, which resemble initial jumps analytically found by Garcia-Millan et al. [Phys. Rev. Lett. 135, 088301 (2025)] in a different information-based work extraction process. The learned protocols allow to extract significantly larger amounts of useful work. The work extracted exceeds that allowed by the conventional second law for feedback-controlled processes, which can be rationalized by the nonequilibrium character of the system considered.

Accurate hydrodynamic modeling for laser-direct-drive (LDD) inertial confinement fusion (ICF) relies on precise calculations of the electron thermal conduction in all target materials. The nonlocal stopping range of electrons in ICF plasmas directly influences thermal conduction; yet, no first-principles model exists for the electron mean free path in the conduction-zone regime. This work utilized time-dependent stochastic density functional theory (TD-sDFT) to calculate the electron stopping power in deuterium-tritium (DT) plasmas at $(\rho ,T)$ conditions relevant to the conduction zone and the compressed shell in ICF. Using a combination of our TD-sDFT data and established analytical models, we developed and trained an artificial neural network to create a global model for the nonlocal electron deposition range, ${\lambda }_E$. We compared our machine learning (ML)-based model for ${\lambda }_E$ to the currently used modified Lee-More model in LDD radiation-hydrodynamic codes, such as lilac, and saw an overall decrease in the deposition range. To understand the effects of ${\lambda }_E$ on LDD ICF implosion dynamics, we implemented the ML-based model into lilac; specifically, we looked at designs consistent with a current experiment on the OMEGA laser and for a newly designed LDD-ICF target for the future OMEGA-Next facility. In both cases, we saw an overall drop in predicted ablation pressure, peak areal density, and neutron yield due to the reduced thermal conduction (smaller ${\lambda }_E$) in DT plasmas. Comparisons with the experiment on OMEGA are also made.

The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify numerical rounding errors as the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.

Using the Landau–de Gennes free-energy formalism with the fast inertial relaxation engine relaxation method, we investigate the role of geometry and anchoring conditions in nematic liquid crystal shells. Both prolate and oblate geometries are explored for four distinct anchoring configurations: degenerate planar on both surfaces, homeotropic on both surfaces, and hybrid cases with planar-homeotropic and homeotropic-planar alignments. Our simulations reveal a rich variety of topological defect arrangements, including bipolar configurations with boojums; tetrahedral patterns featuring disclination lines, boojums, and hedgehogs; Saturn-ring structures; and twisted director fields in the equatorial plane. Detailed energy analyses demonstrate that elastic distortions—splay, bend, and twist—are strongly influenced by parameters such as inner and outer radii, shell thickness, and aspect ratio, which in turn dictate the stabilization of specific defect structures. These findings provide insights into the curvature-driven mechanisms that control the formation of defects in nematic shells, with potential applications for the design of advanced photonic and sensing devices.

We study the overdamped dynamics of individual one-dimensional elastic filaments subjected to a chiral active force which propels each point of the filament at a fixed angle relative to the tangent vector of the filament at that point. Such a model is a reasonable starting point for describing the behavior of polymers such as microtubules in gliding assay experiments. We derive sixth-order nonlinear coupled partial differential equations for the intrinsic properties of the filament, namely, its curvature and metric, and show that these equations are capable of supporting multiple different stationary solutions in a comoving frame, i.e., that chiral active elastic filaments exhibit dynamic multistability in their shapes. A linear stability analysis of these solutions is carried out to determine which solutions are stable and a brief analysis of the time-dependent approach to stationary shape is considered. Finally, simulations are presented which confirm many of our predictions while also revealing additional complexity.

Motivated by intracellular phase separation, we theoretically investigate how molecular orientation and multicomponent nature affect phase behavior. We construct a minimal model for a ternary mixture composed of isotropic (I), anisotropic (A), and solvent (s) components by combining the Flory-Huggins and Maier-Saupe theories. We obtain two main results from evaluating the phase behavior and the time evolution of the density fields. First, for certain interaction parameters, two distinct binodal lines appear in the plane of the volume fractions of the I- and A-components, and merge through their respective critical points. Second, rapid droplet formation emerges due to a weakly first-order phase transition, characterized by a discontinuity of the spinodal surface. The first result indicates the possibility of continuous transformation between the two phase-separated states. The second result suggests that anisotropic molecules can regulate phase-separation kinetics. These findings might be physically general beyond biological systems.

Ion beam technology provides a powerful means for surface modification and nanostructuring of materials. In this work, slow highly charged xenon ions were used to fabricate well-defined nanopits in thin polymethyl methacrylate (PMMA) films. The pit surface density scales linearly with the applied ion fluence, demonstrating that each structure originates from a single ion impact. The formation of these nanopits is interpreted within a plasma expansion framework, in which the potential energy of an individual highly charged ion creates a transient, localized plasma within a nanometric surface region. The subsequent plasma expansion ejects material and produces a shallow surface depression. Numerical solutions of the hydrodynamic equations for the plasma components yield expansion parameters that agree with the experimentally observed pit dimensions and aspect ratios, confirming the plausibility of the proposed mechanism.

Tariffs imposed on modern global production industries, marked by deep interconnections and interdependencies, pose a critical risk of cascading economic failures. We model the impact of adding and removing tariffs on interdependent industries using a network with a hypernode framework governed by heterogeneous k-core percolation dynamics. Our analysis, using a modified generating function formalism, identifies a critical transition threshold: When tariffs remain below this value, global trade experiences only a modest reduction and fully recovers once tariffs are lifted. By contrast, tariffs that exceed the threshold trigger catastrophic collapse that spreads beyond the targeted goods into unrelated sectors. Recovery is further hindered by hysteresis, with the system in some cases failing to return to its pretariff state even after tariffs are fully removed. Moreover, multiple transition points may exist, leaving the system increasingly vulnerable to deeper failures once weakened. These findings demonstrate that the apparent reversibility of global trade under weak tariffs can foster a false sense of security, masking proximity to tipping points and the risk of irreversible collapse.

We introduce and analyze the kinetic random-field nonreciprocal Ising model, which combines bimodal (double-delta) diffusive disorder with pairwise nonreciprocal interactions between two species. By employing mean-field and effective-field theories alongside kinetic Monte Carlo simulations (3D Glauber dynamics), we identify a nonequilibrium tricritical (Bautin) point separating continuous Hopf-type transitions from discontinuous saddle-node-of-limit-cycle (SNLC) transitions. For weak disorder below a critical value, collective oscillations (the “swap” phase) emerge via a supercritical Hopf bifurcation; above this value, the transition becomes first-order (SNLC), exhibiting hysteresis and characteristic Binder-cumulant signatures. Finite-size scaling of the susceptibility confirms the distinct critical and discontinuous behaviors in the Hopf and SNLC regimes, respectively (yielding effective exponents $\approx 1.96$ and $\approx 3.0$). In the first-order regime, the swap phase requires a threshold nonreciprocity that increases with disorder strength. The above conclusions also hold qualitatively for a random field sampled from a double-Gaussian distribution. Finally, we identify a droplet-induced swap phase at higher disorder that cycles through eight metastable states, driven by droplet nucleation in the dynamical free-energy landscape. These findings reveal how disorder and nonreciprocity generate rich nonequilibrium criticality relevant to driven and active systems.

While mutual information effectively quantifies dependence between two variables, it does not by itself reveal the complex, fine-grained interactions among variables, i.e., how multiple sources contribute redundantly, uniquely, or synergistically to a target in multivariate settings. The Partial Information Decomposition (PID) framework was introduced to address this by decomposing the mutual information between a set of source variables and a target variable into fine-grained information atoms such as redundant, unique, and synergistic components. In this work we review the axiomatic system and desired properties of the PID framework and make three main contributions. First, we resolve the two-source PID case by providing explicit closed-form formulas for all information atoms that satisfy the full set of axioms and desirable properties. Second, we prove that for three or more sources, PID suffers from fundamental inconsistencies: we review the known three-variable counterexample where the sum of atoms exceeds the total information, and extend it to a comprehensive impossibility theorem showing that no lattice-based decomposition can be consistent for all subsets when the number of sources exceeds three. Finally, we deviate from the PID lattice approach to avoid its inconsistencies, and present explicit measures of multivariate unique and synergistic information. Our proposed measures, which rely on systems of random variables that eliminate higher-order dependencies, satisfy key axioms such as additivity and continuity, provide a robust theoretical explanation of high-order relations, and show strong numerical performance in comprehensive experiments on the Ising model. Our findings highlight the need for a new framework for studying multivariate information decomposition.

Noisy pursuit in complex environments drives the emergence of collective behaviors in active matter systems. A compelling, minimal framework for studying the impact of spatially heterogeneous noise on collective motion is provided by the standard Vicsek model. In this study, we investigate the collective dynamics of Vicsek agents in a complex noise environment, comprising a central noiseless circular region surrounded by a tunable noisy outer zone with short-range mutual repulsion. By varying the outer noise intensity, we observe an emergent rotational order that peaks at higher noise levels, as revealed by phase and susceptibility plots. Global translational order follows a distinctive “U-shaped” curve: near-perfect alignment at zero outer noise, which dies down to a deep minimum around intermediate noise and reenters at high noise. The latter rise is attributed to an increase in rotational order. Strong rotational order effectively confines slower agents within the noiseless core, while faster agents escape more readily. We quantify escape dynamics through time-averaged and first-passage escape rates, demonstrating velocity-dependent retention on the probability of finding the bimotility agent flocks at a given time, resulting in segregation and trapping. Introducing a gradual noise increase from the circle's center to its outer region reduces both translational and rotational order, underscoring the impact of environmental heterogeneity and sudden annealing over gradual change. These findings offer insights into predicting and manipulating the dynamics of active agents in complex environments, with applications in both biological and synthetic swarming systems.

We investigate the formation, stability, and dynamics of three-dimensional ring-shaped and multipole vortical quantum droplets (QDs) in nonrotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDIs) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity $S$) are shaped as necklacelike modes, with the number of “beads” (multipole order) $n=2S$, up to $S=6$. The stability area of the multipoles shrinks with the increase of $S$. For higher values of $S$ the centrifugal effect associated with the phase winding destabilizes the ring-shaped QDs and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy, and peak density on the norm (number of particles) and $S$ is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the nonrotating configurations.