We present a spectral convolutional autoencoder framework to infer an integer, observation-conditioned estimate for the inertial-manifold dimension in the Kuramoto-Sivashinsky equation. Training on trajectory segments of temporal horizon $\tau$, we analyze reconstruction-error scaling with latent dimension $d$ through a local log-slope diagnostic $\gamma (d,\tau )$ and identify a robust horizon-induced change-point: once $\tau$ exceeds a mixing scale, the scaling gain localizes at a unique integer $d^{*}\left(L\right)$ and remains stable for larger horizons. Across $L=\{22,44,58,66,88,96\}$, the extracted $d^{*}$ is extensive and is well described by a linear law, $d^{*}\approx 0.366L$. Moreover, $d^{*}$ is largely insensitive to temporal-frequency truncation provided the energy-dominant low-frequency band is retained, indicating bandwidth sufficiency for stable dimension identification under the present observation scheme.

Laser-driven ion acceleration offers a promising route toward compact high-energy particle sources, yet achieving control of beam collimation, spectral width, and laser-to-ion energy conversion remains a central challenge for most applications. Using two- and three-dimensional particle-in-cell simulations, we investigate proton acceleration from a solid target consisting of a thin foil followed by a converging hollow plasma cone and irradiated by a relativistic laser pulse. The cone length critically controls the proton beam collimation and spectral width by regulating the lifetime and spatial structure of electron-driven sheath fields sustained along the cone walls. Specifically, the cone walls collapse throughout the irradiation process, and these sheath fields—enhanced by strong azimuthal magnetic fields that improve electron trapping—provide a tunable tradeoff. Matching the proton transit time to the cone collapse time reduces beam divergence, while an earlier cone collapse reduces the spectral width. Using a linearly polarized pulse in the radiation pressure acceleration plus target normal sheath acceleration regime exploits target heating to create these sheath field and magnetic field structures. These results identify cone-length-controlled sheath-field dynamics as a robust mechanism for proton beam control. Relative to the planar foil case, optimized cone lengths reduce the relative proton energy spread by approximately 63% in two-dimensional simulations and reduce the 25%-energy containment radius by approximately 46% in three-dimensional simulations after 200 µm of ballistic propagation.

Landauer's principle bounds the heat generated by logical operations, but in practice the thermodynamic cost of computation is dominated by the control systems that implement logic. Complementary metal oxide semiconductor (CMOS) gates dissipate energy far above the Landauer bound, while laboratory demonstrations of near-Landauer erasure rely on external measurement or feedback systems whose energy costs exceed that of the logic operation by many orders of magnitude. Here we use simulations to show that a genetic algorithm can program a thermodynamic computer to implement logic operations in which the total heat emitted by the control system is of a similar order of magnitude to that of the information-bearing degrees of freedom. Moreover, the computer can be programed so that heat is drawn away from the information-bearing degrees of freedom and dissipated within the control unit, suggesting the possibility of computing architectures in which heat management is an integral part of the program design.

Surface growth driven by nonmonomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P\left(s\right)\sim s^{-\tau }$. We find that the critical exponents vary continuously with $\tau$, recovering Kardar-Parisi-Zhang behavior only for $\tau \ge 3$. For $\tau <3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $\zeta$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $\xi$. The coexistence of these two relevant scales signals the breakdown of the usual Family-Vicsek scaling. These results point to an interesting phenomenology of surface growth beyond the standard scale-invariant paradigm.

The nature of spin-glass states in a magnetic field remains a major open problem in statistical physics. The existence of the de Almeida–Thouless (dAT) transition for three-dimensional (3D) spin glasses in a field is still debated. We introduce a computational method to define the spin-glass susceptibility, which is robust against the broad tail in the overlap distribution that undermines conventional analyses. Applying this approach to the Edwards-Anderson spin-glass model in 2D and 3D, and contrasting with the 3D Ising (without disorder) and mean-field spin-glass models, we find a stark difference: the locus of susceptibility maxima bends to the right in the field-temperature plane for the Ising and 2D spin-glass cases, indicating a supercritical crossover line, but bends to the left for the mean field and 3D spin glasses—a signature of the dAT line. Finite-size scaling further suggests that the peak susceptibility diverges with system size in 3D spin glasses under a field, while saturating in 2D. These results provide direct numerical evidence for the dAT transition in 3D, supporting the replica symmetry breaking scenario.

Koopman analysis can be used to understand the dynamics of a nonlinear dynamical system in terms of a linear, but generally infinite-dimensional operator. The isostable coordinate system focuses on the slowest decaying principal Koopman eigenmodes. This work leverages the isostable coordinate framework in the identification of slow manifolds for dynamical systems with fixed point attractors, defined as surfaces for which the fastest decaying isostable coordinates are zero. Numerical challenges associated with separation between fast and slow timescales necessitate the development of new computational approaches to identify these slow manifolds. Two such strategies are developed which approximate backward-time solutions on the slow manifold starting near the fixed point and extending far beyond the linear regime. Application to a variety of examples illustrates the utility of these methods and their potential use for model order reduction purposes.

Sensory information propagates through successive processing stages in the brain, where synaptic weight patterns between stations determine how downstream neurons decode information from upstream populations. Although optimized synaptic connectivity can enhance information transmission, it requires precise weight tuning. Recent evidence depicting substantial synaptic volatility raises two fundamental questions: How does coarse-tuning of synaptic connectivity affect information transmission? What strategies could the nervous system employ to maintain reliable communication despite synaptic fluctuations? We addressed these questions by analyzing the signal-to-noise ratio ($\mathrm{SNR}$) for binary stimulus discrimination under two decoding schemes: a naive population average and an optimized linear decoder. For the naive decoder, we found that $\mathrm{SNR}$ remains largely insensitive to synaptic imprecision, since performance is already limited by correlated noise in neuronal responses. For the optimal decoder, we identified three distinct regimes, that is, weak, moderate, and strong coarse-tuning. Under weak coarse-tuning, $\mathrm{SNR}$ squared scales linearly with population size $N$. Under moderate coarse-tuning, scaling becomes sublinear. Strikingly, under strong coarse-tuning, the regime most consistent with observed neuronal heterogeneity, $\mathrm{SNR}$ saturates and cannot be improved by recruiting larger populations. This limitation persists even when incorporating feedforward or recurrent network architectures. These findings suggest that in the biologically relevant regime of strong coarse-tuning, naive and optimal decoders can achieve qualitatively similar performance. The analysis shows that effective readout under synaptic volatility is constrained to an invariant low-dimensional manifold aligned with the naive decoder, potentially pointing to a fundamental principle for robust neural computation in the face of ongoing synaptic remodeling.

Cross-field electron transport in Hall thrusters is widely attributed to high-frequency $E\times B$ instabilities, yet its net spatial pathway remains poorly resolved. Here we perform instability-resolving three-dimensional particle-in-cell simulations of a Hall thruster using a boundary-faithful and highly integrated framework. The model incorporates a realistic magnetic-field configuration, self-consistent dielectric wall charging, secondary electron emission, Monte Carlo ionization collisions, a self-consistent continuum neutral-gas evolution model, and an open near-plume outflow treatment. From the strongly oscillatory three-dimensional fields, we extract the net instability-driven transport by time and azimuthal averaging of the correlation term $\langle n_e{E}_y\rangle$ and the corresponding effective perpendicular mobility. The simulations reveal that anomalous electron transport is not distributed uniformly across the channel cross section. Instead, it self-organizes into persistent near-wall pathways connected to the near-exit region. By comparing conducting-wall, ceramic-wall-with-secondary-emission, and open-outflow closures, we show that the near-wall transport topology is robust, while the boundary treatment mainly redistributes the detailed strength of the pathway and its coupling to the exit and near-plume region. These results demonstrate a previously unresolved spatial organization of instability-driven anomalous transport in Hall thrusters and highlight the unique role of 3D PIC simulations in revealing it.

Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a full derivation of the resulting lattice Boltzmann method. We ensure that our method correctly reproduces macroscopic behavior via Chapman-Enskog analysis for a single-relaxation time collision operator. As a result, we are able to show that a properly discretized anisotropic Maxwell-Boltzmann equilibrium does macroscopically in fact lead to an anisotropic variation of the Navier-Stokes equations. All desired properties of lattice Boltzmann methods, such as locality of the collision operator, isotropic discrete position and velocity space, or mass and momentum conservation are retained. While it is explicitly shown in the context of fluid flow, the presented scheme is straightforward to adopt to advection-diffusion problems.

Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low-dimensional descriptions from high-dimensional observations. However, existing approaches sacrifice either interpretability for reconstruction accuracy or infer symbolic dynamics without relating latent coordinates to physically meaningful observables. Here we present Edwin (maximum $e$ntropy-$d$riven compression $w\mathrm{ith}$ $i$nterpretable $n$onlinear model discovery), a unified framework that simultaneously performs dimensionality reduction using the dynamic maximum entropy (DME) principle and discovers sparse symbolic models governing latent dynamics, as well as the coupling between learned features and external metadata. We validate Edwin on diverse simulated systems, including stochastic diffusion, the Ornstein-Uhlenbeck process, self-assembling particles, and neural population firing rates, as well as on a noisy experimental time series of aggregating RNA-liposome complexes. Across all systems, Edwin recovers low-dimensional symbolic models that are physically interpretable and generalize to unseen conditions. Together, these results establish Edwin as a principled framework for inferring interpretable, low-dimensional dynamics from high-dimensional nonnegative data.

Motivated by the chiral motility of microswimmers, we investigate how geometric asymmetry in a system of two self-propelled active Brownian robots coupled by a spring gives rise to rich emergent dynamics. We demonstrate that asymmetry in the robots' propulsion directions generates net torques that induce persistent rotational motion. Depending on the choice of propulsion angles ${\alpha }_1$ and ${\alpha }_2$, the system exhibits three distinct dynamical regimes—run-and-tumble motion, circular trajectories, and spinning—with the geometric configuration primarily determining the realized regime. We further show that spring stiffness and rotational noise act as additional tuning parameters governing the stability of these regimes. These results show how the interplay of mechanical coupling and activity produces diverse self-organized dynamics in simple robotic dimers, providing a bridge between artificial active systems and biological microswimmers such as bacteria, Chlamydomonas reinhardtii, and spermatozoa.

Dense, orientationally and translationally ordered two-dimensional (2D) monolayers of colloidal ellipsoids are fabricated at air-water interfaces. Kinetic arrest and disordered structures from long-range quadrupolar capillary attraction are overcome by synthesizing polystyrene microellipsoids with surface roughness, specifically nanoscale concavities, which attenuate capillary attraction. With increasing area fraction, the particle assembly shows a disorder-order transition from isotropic to plastic crystal at low ellipsoid aspect ratio (AR) and an isotropic to nematic transition at high AR, agreeing qualitatively with simulated hard ellipse close packing in two dimensions. The ordered particle assembly is successfully transferred to solid substrates via Langmuir-Blodgett deposition, demonstrating the potential of using rough particles to create anisotropically ordered 2D patterns via interfacial templating.

In classical physics, a key consequence of the Kolmogorov-Arnold-Moser (KAM) and the Poincaré-Birkhoff theorems is that invariant tori of integrable Hamiltonians with nonresonant frequencies survive sufficiently small nonintegrable perturbations as smooth deformations, whereas resonant tori are generically destroyed by breaking into elliptic and hyperbolic periodic orbits. In this contribution, we identify a quantum analog of this distinct sensitivity for 1-degree-of-freedom spin Hamiltonians subject to periodic instantaneous kicks. After detecting quantum signatures of resonances in the participation ratio and in the quasiprobability phase-space distribution of Floquet eigenstates of the perturbed Hamiltonian, we show that eigenstates of the unperturbed Hamiltonian exhibit greater sensitivity against the perturbation when they satisfy a resonant condition. The sensitivity is quantified through the fidelity between perturbed and unperturbed eigenstates. This distinct sensitivity becomes increasingly pronounced as the system size grows. Our findings are supported by numerical results and insights from analytical calculations based on unitary perturbation theory. Since the resonance conditions are set by commensurability with the driving period, this distinct sensitivity may persist in broader classes of periodically driven systems beyond kicked models, providing a preliminary step toward identifying quantum signatures of the classical breaking of resonant tori.

In the context of first-passage percolation, we investigate the statistical properties of the selected link times (SLTs)—the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on weakly disordered square lattices, whose geodesics are known to fall under the Kardar-Parisi-Zhang (KPZ) universality class. Our analysis reveals universal power-law decays with the end-to-end distance for both the average and the standard deviation of the SLTs, along with an intricate pattern of long-range correlations, whose scaling exponents are directly linked to KPZ universality. Crucially, the SLT distributions for diagonal and axial paths exhibit significant differences, which we trace back to the distinct directed and undirected nature, respectively, of the underlying geodesics. Moreover, we demonstrate that the SLT distribution violates the conditions of the central limit theorem. Instead, SLT sums follow the Tracy-Widom distribution characteristic of the KPZ class, which we associate with evidence for the emergence of high-order long-range correlations in the ensemble.

The underlying processes governing dynamical systems could create very long transient dynamics. In particular, in ecological systems, it is often difficult to distinguish this transient behavior from similar persistent dynamics. Chaotic transient is a typical class of long transients. However, even in low-dimensional dynamical systems, the formation mechanism and timescale of chaotic transients have not yet been fully understood. In this study, we establish a resilience metric for bounded parametric noise perturbations. It is shown that the parametric noise below the crisis point can induce chaos-related critical transitions. Chaotic transients for parametric noise-induced critical transitions are shown to be prolonged in the sense that the transient occurs on a timescale much longer than that of the regular chaotic transient. We further reveal the formation mechanism of prolonged chaotic transients and the transition pathway of escaped trajectories. The most striking fact is that in the vicinity of the critical noise, the average lifetime of chaotic transients follows a new scaling law as $exp\left\{\alpha {[ln(\delta -{\delta }_c)]}^2\right\}$, where ${\delta }_c$ is the noise threshold leading to the critical transition, and the $\alpha$ can be estimated by the reciprocal of the critical exponent of the corresponding deterministic crisis. We demonstrate the applicability of this scaling law using several classic maps and explore its applicable boundary.

An autoresonant approach for the excitation and control of one- and two-phase waves of a weakly nonlinear Klein-Gordon equation is proposed. It employs chirped-frequency driving waves passing through linear resonances in the system. Under certain conditions, the excited wave phase-locks to the drives, and its amplitude increases to maintain resonance as the wave enters the nonlinear stage. In the single-phase autoresonance, a slow-varying, growing-amplitude traveling wave emerges. Two-wave autoresonance leads to the formation of phase-locked space-time quasicrystals. The theory is based on Whitham's averaged variational approach and is supported by fully nonlinear simulations. It describes different autoresonant scenarios depending on the parameters in the system. Furthermore, the theory establishes threshold values of the driving amplitudes required for autoresonant excitation.

We study the interaction of exploding dissipative solitons (DSs) in the framework of two coupled cubic-quintic Ginzburg-Landau equations. We find several classes of behavior as a function of the cross-coupling between counterpropagating DSs, $|c_r|$, by varying the initial conditions for fixed approach velocity. We use three quantities to characterize the resulting behavior as a function of $|c_r|$: (a) the maximum value of the effective amplitude reached during the interaction process, (b) the time interval between the end of the interaction process between exploding DSs and the start-up of new explosions, and (c) the quantity $\mathrm{\Psi }$ related to the effective time of interpenetration obtained by integrating the maximum amplitude over time during the interaction. The differences observed by varying the initial conditions can be traced back to the fact that exploding DSs are intrinsically chaotic as a function of time. Therefore, variations in the phase of the initial conditions or, equivalently, in the initial distance before the start of the collisions, can lead to qualitatively different results. Remarkably one of the possible outcomes, which is particularly sensitive to changes in the initial conditions, is partial annihilation of exploding DSs over a range of $|c_r|$. The fact that either the left or the right pulse survives the collision highlights the deterministic character of the dynamics, even though the system is inherently chaotic. However, for all three types of initial conditions studied a unique behavior emerges as the transition to compound states is approached as a function of $|c_r|$ for all three quantities used to characterize the results. For example, the quantity $\mathrm{\Psi }$ diverges as the critical value of $|c_r|$ is approached.