We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wave packets in both isotropic and anisotropic formulations. The resulting distribution functions show good agreement with molecular dynamics data under warm dense matter conditions, providing practical guidance for constraining the confining potential, an empirical parameter in the model. We also discuss how these distributions influence the resulting effective Coulomb interactions.

This work investigates how locally persistent crystal-like ordering in liquids influences the Debye-Waller factor. We have developed a theoretical framework based on liquid-phonon theory which introduces a phonon relaxation time, expressed as the ratio of shear viscosity to infinite-frequency shear modulus. These values are obtained using the Yukawa one-component plasma model. Within this framework, we establish expressions for the heat capacity at constant pressure and the Debye-Waller factor for the liquid state. These expressions explicitly introduce additional temperature dependence arising from the finite phonon lifetime. Anharmonicity is accounted for within the quasiparticle approximation. We compare our heat capacity results with values measured by Gathers for aluminum and copper, finding good agreement when assuming partial local crystal-type order. Comparisons with experimental heat capacities serve to validate the approach prior to its application to the study of electrical resistivity, the principal objective of this work. Using liquid-phonon Debye-Waller factors in the methodology developed earlier [Phys. Rev. E 102, 053209 (2020)] for electrical resistivity in dense matter, and comparing with experimental resistivities from Gathers, we elucidate the character of the locally persisting crystal order in liquid aluminum and liquid copper. These results indicate that the electrical resistivity measurements can serve as a valuable probe for determining both the extent and the nature of crystalline order in the liquid state.

We investigate the role of stall forces and entropic barriers in geometry-dependent polymer translocation through narrow pores. We consider two distinct geometrical constraints: forced translocation through a small pore in a flat membrane separating two semi-infinite three-dimensional spaces, and translocation from a confined region into an unconfined space, where the confinement is provided by a square-pyramidal geometry in three dimensions. The translocation dynamics is described within a lattice-based framework by mapping the process onto the diffusion of an effective virtual particle governed by a Fokker-Planck equation, with the underlying free-energy landscape obtained from exact enumeration of polymer configurations. This approach enables us to study the effects of external driving forces from entropic resistance arising due to geometry. Under their respective stall forces, translocation is markedly faster through a square pyramidal pore than through a flat membrane, demonstrating that confinement-induced changes in the entropic free-energy barrier can enhance driven polymer transport. Our results reveal the importance of a stall force in controlling polymer translocation, suggesting potential applications in nanopore-based manipulation, filtration, and sequencing technologies.

This paper presents an investigation of amplitude death and phase-locked oscillations in delay-coupled Stuart-Landau oscillators with frequency mismatch. These oscillators exhibit nonisochronism, in which the rotation velocities depend on amplitudes. We provide a simple procedure to numerically obtain the phase-locked periodic orbits and their stability for such oscillators. This procedure allows us to construct bifurcation diagrams for amplitudes and phase differences of the orbits, which include information on their stability. The bifurcation diagrams disclose the effects of frequency mismatch and nonisochronism on the global nonlinear dynamics of delay-coupled oscillators. We find that frequency mismatch can induce a stability region for amplitude death where the phase-flip phenomenon does not occur, and we reveal its mechanism. Furthermore, we show that explosive amplitude death can arise even in the presence of frequency mismatch.

Emergent geometric order characterizes social insect nests, exemplified by paper wasps, which collectively build arrays of hexagonal cells to optimize space and mechanical stability. These arrays contain topological defects in the form of nonhexagonal cells, which disrupt the order of the nest. A disclination like a single pentagon or heptagon modifies angular geometry and introduces curvature, whereas adjacent pentagon-heptagon pairs form dislocations that retain planarity by offsetting angular mismatch at the cost of translational order. Unlike the malleable wax of honeybee combs, the rigid materials like plant fibers used by wasps limit structural remodeling, making such defect management more challenging. Here, we show the migration of dislocations through a sequence of discrete steps involving splitting into different types of disclinations. Defects propagate via local rearrangements of walls and vertices, analogous to star-triangle transformations and node release events that conserve topological charge, as confirmed by Burgers circuits. The shift was likely intended to promote hexagonal cell formation, with a secondary aim of driving the defect to the boundary. This was not achieved because subsequent nest growth displaced the boundary farther away from the defect region. Our results suggest that wasps achieve global architectural coherence through local geometric transformations that preserve topology, enabling decentralized construction under material constraints.

The excess energy, entropy, and pressure of a strongly coupled Yukawa fluid are calculated from the variational approach using the fluid of hard spheres as a reference system. As in the case of the one-component plasma, the Percus-Yevick virial entropy is appropriate for such calculations and delivers remarkable agreement with available results from molecular-dynamics simulations. The agreement with the molecular-dynamics results is particularly impressive in the strongly coupled regime, making this approach a useful predictive tool when numerical data are scarce or not yet available. As an application of the variational approach, we estimate the location of the melting curve in the regime of sufficiently strong screening.

The variational approach based on the Bogoliubov inequality using the fluid of hard spheres as a reference system is implemented to evaluate instantaneous shear, bulk, and longitudinal elastic moduli, as well as related sound velocities of Yukawa fluids. The remarkable accuracy of this method is documented. In addition, we evaluate the adiabatic sound velocity from an appropriate equation of state and discuss its relation to the longitudinal and bulk sound velocities obtained from the corresponding instantaneous elastic moduli. The transition between weakly coupled and strongly coupled regimes is analyzed in detail.

Electron holes are Debye-scale kinetic structures that mediate particle trapping, field-aligned electric fields, and energy conversion in collisionless plasmas. How such coherent structures interact with one another, however, has remained difficult to resolve in situ. Using four-spacecraft Magnetospheric Multiscale electric-field measurements, we identify two head-on encounters between positive-potential electron holes in the terrestrial magnetotail. In both events, the holes accelerate toward one another during approach, a behavior consistent with the effective negative-mass dynamics of phase-space holes rather than with the traditional repulsion expected for isolated like-signed positive-potential structures. The subsequent outcomes differ: one fast-slow pair passes through, whereas one slow-slow pair coalesces into a single evolving structure. Targeted one-dimensional Vlasov-Poisson simulations reproduce both outcomes and show that attraction alone does not determine the collision result. Instead, the outcome is controlled by a dimensionless phase-space overlap parameter that compares the trapped-electron velocity width with the relative drift speed. An energetic diagnostic based on trapped-electron kinetic and potential energies supports this boundlike versus unboundlike interpretation. These observations and simulations demonstrate that electron holes can behave as attractive kinetic quasiparticles whose pairwise interactions follow a simple phase-space merger rule.

The presence of activity-silent working memory has been increasingly supported by experimental observation, and short-term synaptic facilitation is suggested to underlie this phenomenon. Originally proposed in the early 2000s, the synaptic theory of working memory was supported by a relatively simple, yet powerful, computational model. Recent advancements in simulation technology eased the introduction of heterogeneity in spiking models, which is a crucial factor in enhancing their dynamical richness and biological plausibility. However, introducing such heterogeneity often disrupts previously observed network dynamics. This work investigates the impact of synaptic heterogeneity in a spiking model of working memory sustained by short-term synaptic facilitation, observing that the model is resilient to additional variability.

The Stokes-Einstein (SE) relation links microscopic fluctuations to macroscopic dissipation. Whether it survives in driven-dissipative, strongly coupled systems far from global equilibrium remains an open question. Using a macroscopic dust vortex in a radio-frequency complex plasma, we isolate thermal velocity fluctuations from the dominant azimuthal flow and resolve the local thermodynamic state across the full radial extent of the structure. The shear-fluidized inner vortex core sustains local thermodynamic equilibrium, evidenced by isotropic Maxwell-Boltzmann distributions ($R^2>0.95$) and near-Fickian transport ($\alpha \approx 0.9$). Toward the periphery, Coulomb cages re-form and transport becomes subdiffusive, with $\alpha$ decreasing from near-Fickian values in the core to about 0.70–0.75 in the outer resolved shells, accompanied by enhanced non-Gaussian dynamic heterogeneity. Yet both a normalized SE-like ratio and the full SE product including the independently estimated macroscopic viscosity remain approximately constant over the robust shells, yielding a characteristic SE length comparable to the Coulomb cage size. While the macroscopic transport changes character, the local thermodynamic coupling between fluctuations and dissipation does not. These results reveal that fundamental thermodynamic scaling can globally persist in a strongly coupled system, even as nonequilibrium driving produces a spatial coexistence of fluidlike and caged, glassylike transport regimes, with a characteristic transport scale set by the microscopic confinement.

During alloy solidification, equiaxed dendrites often move within the solidifying liquid. As this motion is one of the main causes of macrosegregation, a deeper understanding of the behavior of suspensions containing dendrite-like particles is particularly important. Inspired by rheological investigations with dense suspensions containing spheres, pressure-imposed rheological measurements using an annular shear cell were performed and applied to suspensions containing 3D-printed dendrite-like particles. The results indicate that the concept of the friction coefficient for spheres can be adapted by using appropriate coefficients and suitably reduced mechanical coherency limits. Consequently, the particle pressure of interacting, moving dendrite-like particles in liquids can be effectively described. However, direct measurement of the shear rate was not possible due to the shallowness of the rheological cell used. Nevertheless, the viscosity of suspension containing dendrite-like particles could be estimated indirectly by adapting the dimensionless friction number originally proposed for suspensions with spheres. An increase in viscosity at the same reduced solid fraction, due to the specific morphology of the dendrite-like particles, is predicted. While spheres predominantly interact by sliding past one another, dendrite-like particles—particularly those with long sidearms—interact mainly through rotation.

We present results of experimental measurements and discrete element method simulations for granular flow in the exit region of a quasi-two-dimensional (2D) wedge-shaped hopper with glass front and back walls. The results are important from a practical viewpoint, since the mass flow rate from hoppers, widely used in industry, is determined primarily by the flow in this region. Experiments and simulations, which closely match the experiments, show that the acceleration of particles is about 20% larger than the acceleration due to gravity $\left(g\right)$ near the exit. Simulations are carried out for a 3D hopper in which the front and back walls are replaced by a periodic boundary. In this case, the effect is larger with the maximum acceleration equal to $1.75g$. The larger than gravity acceleration is shown to be a consequence of the large normal stress gradient near the exit plane. A theoretical analysis for the flow and stress distribution in the hopper is presented, predictions of which match simulation results. The theory is used to derive an expression for the mass flow rate.

We report a dynamical phase transition in the information spreading within a classical 2D deterministic interacting many-body system. Specifically, the transition is observed in a recently introduced momentum-conserving parity check cellular automaton (MCPCA) on the square lattice [Kasim and Prosen, Phys. Rev. Res. 7, 023230 (2025)]. We characterize the transition using information-theoretic quantities such as the Hamming distance and the classical decorrelator. By introducing conserved local charges of the momentum-conserving parity-check cellular automata, we show that selecting initial ensembles with specific charge values allows the system to transition from a localized information phase to a chaotic regime with ballistic information spreading. Importantly, our findings indicate that this transition is of second order, highlighting a sharp change in information spreading behavior. Furthermore, we revisit the multifractal behavior of the dynamical structure factor and show that, although present across both phases, it originates from effective local periodicities enforced by symmetry constraints.

We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations demonstrate that in the strongly interacting regime, the system exhibits a distinct set of universal critical exponents, markedly different from those observed in the weakly interacting limit. This dichotomy aligns with experimental findings on the metal-insulator transition in 2DEGs, where high-interaction strength (low carrier density) leads to qualitatively different behavior. The analysis includes scaling of the average electron density with temperature, the power spectral density, and the statistics of electronic avalanches, including avalanche size distributions and autocorrelation functions. In all cases the extracted exponents differ significantly between the weak and strong interaction regimes, highlighting the emergence of two universality classes governed by interaction strength. These results underscore the critical role of electron correlations in the self-organized behavior of low-dimensional electronic systems.

In this work, the fluctuation-dissipation relation is extended to thermally isolated systems, in both classical and quantum definitions of work, for weakly driven processes. In the classical case, the optimal work variance is calculated, showing that it attains its minimal possible value in a so-called quasistatic variance, related to the difference between the quasistatic work and the system's Helmholtz free-energy difference. In the quantum case, the corresponding optimality condition involves higher cumulants and is expressed as a constraint on a weighted cumulant sum. The result is illustrated by the examples of the classical driven harmonic oscillator and the transverse-field quantum Ising chain. Along the way, a stronger, physically motivated definition of the arbitrary constant in the relaxation function of thermally isolated systems is derived for both the classical and quantum cases.

It was conjectured for a long time that the tectonic plates are in a self-organized state of criticality and that the Gutenberg-Richter law is a manifestation of that. It was recently shown that for a system near criticality, the inequality of their responses due to external driving would sharply rise and show universal behavior that could indicate the proximity of the system to a critical point. As a result, measures such as the Gini and Kolkata indices that quantify inequality can also serve as indicators of imminent criticality and those of diverging (system-spanning) responses. In the context of earthquakes, such a large response would correspond to events of high magnitudes. In this work, we show with numerical simulations and seismic data analysis that large earthquake events tend to follow events that are highly unequal, similar to the case of a system near a critical point. Even though this is not a proof of tectonic plate systems being near-critical, continuous monitoring of the inequality indices of the earthquake time series could be a useful tool for hazard estimates. We have applied this framework to models of earthquakes and to the earthquake time series from various seismically active regions, such as North America, Southern Japan, parts of Southeast Asia, and Indonesia. The findings indicate that the SOC picture of tectonic plates is consistent with the increase in size inequality of earthquakes, even though this cannot be treated as a rigorous proof.

We revisit the spectral statistics of the ${\mathrm{C}}_3$-symmetric billiard introduced by F. Leyvraz et al. [J. Phys. A: Math. Gen. 29, L575 (1996)], which exhibits both Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE) statistics depending on the symmetry block. Using high-precision Beyn's contour-integral method for the nonlinear Fredholm eigenvalue problem with built-in separation of irreducible subspaces, we compute $2.8\times {10}^5$ eigenvalues in each symmetry subspace, enabling statistically meaningful comparisons with random matrix theory. The improved spectra reveal clear GOE-GUE correspondence and resolve previously observed deviations in long-range spectral correlations. Furthermore, we analyze phase-space eigenstate localization through the distribution of entropy localization measures, which, for chaotic states follow a β distribution whose standard deviation decays as a power law with energy, consistent with the onset of quantum ergodicity as described by Schnirelman's theorem.

Reaching consensus on massive discussion networks is critical for reducing noise and achieving optimal collective outcomes. However, the natural tendency of humans to preserve their initial ideas constrains the emergence of global solutions. To address this, collective intelligence (CI) platforms facilitate the discovery of globally superior solutions. We introduce a dynamical system based on the standard $O\left(N\right)$ model to drive the aggregation of semantically similar ideas. The system consists of users represented as nodes in a $d=2$ lattice with nearest-neighbor interactions, where their ideas are represented by semantic vectors computed with a pretrained embedding model. We analyze the system's equilibrium states as a function of the coupling parameter $\beta$. Our results show that $\beta >0$ drives the system toward a ferromagneticlike phase (global consensus), while $\beta <0$ induces an antiferromagneticlike state (maximum dissent), where users maximize semantic distance from their neighbors. This framework offers a controllable method for managing the tradeoff between cohesion and diversity in CI platforms.