We examine to what extent the characteristic slow dynamics of glass-forming liquids can be reproduced by a single-particle model without randomness. Our results show that even a single-particle Lorentz gas without explicit randomness reproduces the behavior of several key observables such as mean-square displacement, non-Gaussian parameter, and dynamical susceptibility in close agreement with those of glass-forming liquids. Notably, $\alpha$ relaxation, characterized by a stretched exponential decay in the self-intermediate scattering function, emerges in the 3D Lorentz gas with a face-centered-cubic (fcc) lattice. The Vogel-Fulcher law is also observed in the single-particle Lorentz gas; however, the full range of the Vogel-Fulcher law is reproduced only when the dimensionality of the model is increased, indicating that the Vogel-Fulcher law originates from features intrinsic to higher-dimensional systems. Finally, we discuss the implications of intermediate timescales and finite-lifetime structures in light of recent advances in dynamical systems theory.

In this work, we investigate the forces acting on a flexible fiber dragged through a granular bed. Using discrete element simulations, we observe that, after a sufficiently large displacement, the system reaches a steady state in which both the fiber's shape and the forces acting on it become, on average, constant. Under these conditions, we identify two characteristic lengths that describe the fiber's shape and propose unique scaling laws for the drag and lift forces, valid across a wide range of fiber flexibilities, from highly deformable to nearly rigid, based on these lengths. We highlight that the fiber–grains interaction is governed by a single dimensionless elastogranular parameter, defined as the ratio of the fiber's elastic properties to the granular pressure. Finally, we demonstrate that both the forces and the characteristic lengths can be expressed solely as functions of this dimensionless parameter. Our findings offer a fundamental insight into the behavior of a flexible fiber interacting with a granular medium.

For Markov jump processes on irreducible networks with a finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a given time window of observation (i.e., an ‘integrated current’ as dynamical output). Such an expression, which in itself is particularly useful for numerical calculations, is then elaborated to obtain the interrelation with the precision on the intrinsic timing of the recurrences of the forward and backward transitions. In biochemical ambits, such as enzyme catalysis and molecular motors, the precision on the timing is quantified by the so-called randomness parameter, and the above connection is established in the long time limit of monitoring and for an irreversible site-site transition; the present extension to finite time and reversibility adds a new dimension. Some kinetic and thermodynamic inequalities are also derived.

Hyperuniform systems are distinguished by an unusually strong suppression of large-scale density fluctuations and, consequently, display a high degree of uniformity at the largest length scales. In some cases, however, enhanced uniformity is expected to be present even at intermediate and, possibly, down to small length scales. There exist three different classes of hyperuniform systems, where class I and class III are the strongest and weakest forms of hyperuniformity, respectively. We utilize the local number variance ${\sigma }_N^2\left(R\right)$ associated with a window of radius $R$ as a diagnostic to quantify the approach to the asymptotic large-$R$ hyperuniform scaling of a variety of class I, II, and III hyperuniform systems across the first three Euclidean space dimensions. We find, for all the class I systems we analyzed, which include crystals, quasicrystals, disordered stealthy hyperuniform systems, and the one-component plasma, a faster approach to the asymptotic scaling of ${\sigma }_N^2\left(R\right)$, governed by corrections with integer powers of $1/R$. Thus, we conclude that this represents the highest degree of effective uniformity from small to large length scales among hyperuniform systems. Class II hyperuniform systems, such as Fermi-sphere point processes, are characterized by logarithmic $1/ln\left(R\right)$ corrections to the asymptotic scaling and, consequently, a lower degree of local uniformity compared to class I. Class III hyperuniform systems, such as perturbed lattice patterns, present an asymptotic scaling of $1/R^{\alpha }$, $0<\alpha <1$, implying, curiously, an intermediate degree of local uniformity compared to classes I and II. In addition, our study provides insight into when experimental and numerical finite systems are representative of large-scale behavior. Our findings may thereby facilitate the design of hyperuniform systems with enhanced physical properties, such as transport and mechanical properties, arising from local uniformity.

The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy.

In this work, we investigate a generalization of the separatrix map to higher dimensions, in particular, a three-dimensional (3D) symplectic map derived from the Arnold Hamiltonian, which involves a pendulum and a free rotator coupled through a time-dependent periodic perturbation. This map was originally introduced by Chirikov to study not only the chaotic layer around the separatrix of the main resonance of the system but also the diffusion along this layer, i.e., Arnold diffusion. In two limiting cases in frequency space, it was assumed that this map reduces to the 2D separatrix map, and thus all its known results are applicable, such as the layer half-width and the maximum Lyapunov exponent. Here, we focus on the dynamics of this 3D map, particularly in the frequency domain dominated by low-order resonances between the pendulum frequency near the separatrix and that of the free rotator. By means of numerical and analytical estimates, we show that in this region of the frequency space, the results differ from the expected ones. The maximum Lyapunov exponent and the metric entropy are computed and compared with analytical estimates as well as with results for the standard separatrix map.

A set of experiments in the SQ-n campaign attempts to increase the compression in layered implosions by reducing the design adiabat from 3.0 down to $\sim 2.6$. The experiments utilize nanocrystalline high density carbon ablators driven by a ramped laser pulse drive. Contrary to expectations, the lower design adiabat layered implosion reaches the same level of compression, within the measurement uncertainty, as the previous set of SQ-n layered implosions at the higher design adiabat. We examine potential explanations for this result, including incomplete melting or refreezing of the ablator after the first shock passes into the fuel layer, reproducibility, and dopant areal density. We also discuss additional potential paths to reaching lower adiabat including increased dopant areal density, ramped dopant profiles, and increased initial capsule size which are also based on experimental campaign results from the National Ignition Facility.

Inspired by recent advances in the chromosome capture techniques, a method is proposed to study the structural organization of systems of polymer rings with topological constraints. To this purpose, the system is divided into compartments and a simple condition is provided in order to determine if two compartments are in contact or not. Next, a set of contact matrices ${\overline{M}}_{ab}$ is defined that count how many times during a simulation a compartment $a$ was found in contact with a noncontiguous compartment $b$ in conformations with a given energy or temperature. Similar strategies based on correlation maps have been applied to the study of knotted polymers in the recent past. The advantage of the present approach is that is coupled with the Wang-Landau algorithm. Once the density of states is computed, it is possible to generate the contact matrices at any temperature. These matrices provide an information on the structure of knotted and linked polymers that is averaged over more than ${10}^{11}$ conformations and visualized by means of color maps. The obtained color patterns allow us to identify the main properties of the structure of the system under investigation at any temperature. The method is applied to understand the structural rearrangements following the phase transitions of a knotted polymer ring and a circular polycatenane composed by four rings in a solution. The phase transitions are detected from the plots of the specific heat capacity with respect to the temperature. It is shown that the color maps have a finite number of patterns that can be clearly associated with the different phases of the investigated systems. The results agree with the available data coming from the plots of the observables and the close inspection of snapshots of the system taken at different steps of the simulations.

We study the microscopic origins of relaxation modes revealed by spectroscopic studies of glasses. Major features in calorimetric and structural relaxation spectra, including $\alpha$ peaks, $\beta$ peaks, and excess wings, are reproduced using a distinguishable-particle lattice model. It is based on void-induced particle hops, which model stringlike particle hopping motions. Excess wings are found to be flattened variants of $\beta$ peaks when particle hopping barriers admit a wide distribution. A $\beta$ relaxation event is attributed to the hop of a particle which neighbors a void. An $\alpha$ relaxation event involves a similar process by an arbitrary particle but also includes, as a prior step, the arrival of a diffusing void to become its neighbor.

Temperature chaos is a striking phenomenon in spin glasses, where even slight changes in temperature lead to a complete reconfiguration of the spin state. Another intriguing effect is the reentrant transition, in which lowering the temperature drives the system from a ferromagnetic phase into a less ordered spin-glass or paramagnetic phase. In the present paper, we reveal an unexpected connection between these seemingly unrelated phenomena in the finite-dimensional Edwards-Anderson model of spin glasses by introducing a generalized formulation that incorporates correlations among disorder variables. Assuming the existence of a spin-glass phase at finite temperature, we establish that temperature chaos arises as a logical consequence of reentrance in the Edwards-Anderson model. Our findings uncover a previously hidden mathematical structure relating reentrance and temperature chaos, offering a new perspective on the physics of spin glasses beyond the mean-field theory.

Using in situ measurements from the 2022 World Championships, we derive the equations of motion for a track cyclist as a coupled bicycle-rider-track system. A key observation is that instantaneous pedal power does not map directly onto bicycle speed because elastic compliance within the bicycle-rider assembly stores and releases energy over the crank cycle, introducing a phase lag between input power and translational motion. To resolve this, we develop a phase-averaging framework over the pedaling period that yields an effective, stiff dynamical system driven by cycle-averaged power. The resulting reduced model predicts the evolution of speed without requiring high-frequency pedal-level inputs. A central feature is the geometric coupling between rider dynamics and velodrome shape: the equations link wheel-frame velocity to the center-of-mass velocity through the local track curvature, accounting for banking and radius variations along the lap. Applied to competition data, the framework reproduces the measured speed evolution across straights and turns. Beyond track cycling, the phase-average method provides a general route to modeling propulsion in compliant, cyclic systems where input power is periodic but motion is governed by averaged dynamics.

Based on the cryptocurrency market dynamics, this study presents a general methodology for analyzing evolving correlation structures in complex systems using the $q$-dependent detrended cross-correlation coefficient $\rho (q,s)$. By extending traditional metrics, this approach captures correlations at varying fluctuation amplitudes and timescales. The method employs $q$-dependent minimum spanning trees ($q\mathrm{MSTs}$) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (January 2021–October 2024), a rolling window analysis reveals significant shifts in $q\mathrm{MSTs}$, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum and others gaining prominence. Spectral analysis confirms BTC's declining dominance and increased diversification among assets. A key finding is that medium-scale fluctuations exhibit stronger correlations than large-scale ones, with $q\mathrm{MSTs}$ based on the latter being more decentralized. Properly exploiting such facts may offer the possibility of a more flexible optimal portfolio construction. Distance metrics highlight that major disruptions amplify correlation differences, leading to fully decentralized structures during crashes. These results demonstrate $q\mathrm{MSTs}$' effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems.

Three-dimensional chromatin architecture is shaped by long-range interactions mediated by various proteins, forming a complex chromatin interaction network. However, how the topology of this network controls chromatin architecture remains unclear. Using a minimal cross-linked polymer model, we derive the spatial position distribution of chromatin fragments, the spatial distance distribution between fragments, and the joint distribution of spatial distances for two fragment pairs. Furthermore, we reveal analytical relationships linking chromatin interaction network to parameters of the derived distributions. In particular, the scale parameter of the spatial distance distribution depends solely on network topology, defined as the “effective tether length” (ETL), which can be further decomposed based on connection topology. Our results generalize the work of Gabriele et al. [Science 376, 496 (2022)] on the ETL from systems with a single long-range interaction to those with multiple interactions. On the other hand, our derived joint distribution and the corresponding correlation coefficient provide insights into the experimental observation by Fukaya et al. [Cell 166, 358 (2016)], highlighting how shared enhancer positioning regulates the coordinated dynamics of enhancer-promoter interactions. Our theoretical findings decipher the role of the topological structure of chromatin interaction networks in controlling chromatin architecture.

The study of large-scale convective flows within a spherical gap has been the focus of numerous theoretical and numerical investigations because of its relevance to geophysical applications. This is particularly true in scenarios where the inner surface is warmer than the outer surface, and the fluid is influenced by a radial force field. Various researchers have extensively analyzed the flow patterns that emerge in this simplified model, examining both nonrotating and rotating cases. In this study we present the results of numerical investigations of thermal convection within a rotating spherical gap. The inner surface maintains a higher temperature than the outer surface, $T_{\mathrm{in}}>T_{\mathrm{out}}$. The dielectrophoretic effect induces a radial force field. The convective flow can be controlled by two parameters, $\mathrm{\Delta }T$ and $V_{\mathrm{rms}}$, where $\mathrm{\Delta }T=T_{\mathrm{in}}-T_{\mathrm{out}}$, and $V_{\mathrm{rms}}$ is the mean square voltage between surfaces. In the nonrotating case, the Rayleigh number ${\mathrm{Ra}}_{\mathrm{E}}\sim V_{\mathrm{rms}}^2\mathrm{\Delta }T$, serves as the sole control parameter. The situation becomes much more complex if the system rotates. The centrifugal force can be interpreted as a buoyancy term. The key question in this work concerns whether $\mathrm{\Delta }T$ is constant and $V_{\mathrm{rms}}$ varies or vice versa. In the first case, the centrifugal force can be expressed as $f_c\sim \mathrm{Ta}$, where $\mathrm{Ta}={(2\mathrm{\Omega }{d}^2/\nu )}^2$ is the Taylor number, $d=R_{\mathrm{out}}-R_{\mathrm{in}}$ is the width of the gap, $\mathrm{\Omega }$ is the rotation rate, and $\nu$ is the kinematic viscosity. In the second case, the centrifugal force follows the relationship $f_c\sim {\mathrm{Ra}}_{\mathrm{E}}\mathrm{Ta}$. A numerical investigation is performed to analyze both cases in detail. After examining the behavior of the steady two-dimensional basic flow, a linear instability analysis is carried out to calculate the critical Rayleigh number and critical frequencies of the most dominant perturbations as functions of the Taylor number, denoted ${\mathrm{Ra}}_{\mathrm{Ec}}\left(\mathrm{Ta}\right)$ and ${\omega }_c\left(\text{Ta}\right)$, respectively. According to instability analysis, the critical Rayleigh number increases with the Taylor number. Moreover, the basic flow becomes unstable concerning nonaxisymmetric perturbations. In all the cases considered, the instability sets in as a Hopf bifurcation. Furthermore, according to the numerical analysis of the three-dimensional flow, this bifurcation is supercritical. Heat transfer is expressed in terms of the Nusselt number, which increases significantly when the Rayleigh number surpasses a critical value.

This study investigates the nonlinear evolution of tearing mode instabilities utilizing a quasiparticle framework integrated with spectral methods. By reformulating the resistive magnetohydrodynamic (MHD) equations via Galerkin spectral decomposition, a direct connection between MHD and quasiparticle statistics is established, where the wave-number–frequency relationship reflects the de Broglie duality ($p=\hslash k,\varepsilon =\hslash \omega$). Numerical simulations unveil three distinct stages: initial transient growth, a linear stage (${\gamma }_m\propto \left|m\right|$), and nonlinear evolution and saturation. Harmonic interactions display a growth mechanism governed by energy and momentum conservation (${\gamma }_m={\gamma }_{m^{\prime }}+{\gamma }_{m^{\prime \prime }},m=m^{\prime }+m^{\prime \prime }$). Statistical analysis indicates that the spectral energy distribution follows Maxwell-Boltzmann statistics, with the temperaturelike parameter $\beta$ evolving linearly during the linear stage. Comparisons with HL-2A experimental spectra validate the predictive capability of the model for the evolution of magnetic islands. This study bridges turbulence theory and statistical physics, offering a general mechanism for analyzing magnetic reconnection and nonlinear tearing mode instabilities in magnetized plasmas.

We investigate laser amplification in $e^{-}\text{−}{\mu }^{-}\text{−}\mathrm{ion}$ plasmas, where negative muons partially replace electrons. Theoretical results reveal a hybrid plasma wave, called $\mu$ wave, that exhibits ion-acoustic behavior in long-wavelength regime and Langmuir-like behavior in short-wavelength regime. Besides, the Landau damping of $\mu$ wave is smaller than that of Langmuir wave. Particle-in-cell (PIC) simulations confirm the theoretical results of instabilities in $e^{-}\text{−}{\mu }^{-}\text{−}\mathrm{ion}$ plasmas. The $\mu$ wave enables efficient laser amplification by suppressing pump-driven spontaneous instabilities through enhanced Landau damping of Langmuir waves. Compared to Raman amplification, $\mu$-wave amplification can maintain the Gaussian waveform of the seed laser, avoiding pulse splitting. Compared to strong-coupling Brillouin amplification, $\mu$-wave amplification exhibits weaker filamentation instability. Our theoretical model can be generalized to other plasma systems containing two species of negatively charged particles, such as two-temperature electron plasmas and negative-ion plasma. These findings establish $e^{-}\text{−}{\mu }^{-}\text{−}\mathrm{ion}$ plasma as a promising medium for advanced laser amplification schemes.

In this paper, a multiscale boundary condition for the discrete unified gas kinetic scheme (DUGKS) is developed for gas flows in all flow regimes. Based on the discrete Maxwell boundary condition (DMBC), this study addresses the limitations of the original DMBC used in DUGKS. Specifically, it is found that the DMBC produces spurious velocity slip and temperature jump, which are proportional to the mesh size and the momentum accommodation coefficient. The proposed multiscale DMBC is implemented by ensuring that the reflected original distribution function excludes collision effects. Theoretical analyses and several numerical tests show that the multiscale DMBC can achieve exactly the nonslip and nonjump conditions in the continuum limit and accurately captures nonequilibrium phenomena across a wide range of Knudsen numbers. The results demonstrate that the DUGKS with the multiscale DMBC can work properly for wall boundary conditions in all flow regimes with a fixed discretization in both space and time, without limitations on the thickness of the Knudsen layer and relaxation time.

We investigate thermal effects on density fluctuations in confined classical liquids using phonon quantization. The system is modeled via a massless scalar field between perfectly reflecting parallel planes with Dirichlet, Neumann, and mixed boundary conditions. Exact closed-form expressions are derived for the mean-square mass density, total energy density, and thermodynamic quantities including Helmholtz free energy and entropy densities. Our analysis identifies distinct regimes, namely, a low-temperature quantum regime exhibiting characteristic power-law behavior for each boundary condition, and a high-temperature classical regime where $\hslash$-independent behavior emerges as expected. A particularly interesting finding shows that while most quantities transition naturally to classical behavior, the mean-square density fluctuation requires explicit consideration of the $\hslash \to 0$ limit. The entropy density vanishes at zero temperature, in agreement with the Nernst heat theorem. Numerical analysis confirms our analytical results, particularly the asymptotic temperature behaviors and the intermediate crossover region, in which quantum and classical effects compete. This regime is governed by the energy scale $k_{B}T\sim \hslash u/a$, where $a$ is the distance between the planes and $u$ is the sound velocity.