We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schrödinger equation (NLS) using analytical and numerical methods. The model conserves both energy and norm, whose densities define a microcanonical energy-norm parameter space, while the nonlinear nearest-neighbor coupling is controlled by a parameter $D$. Within this space, our analysis identifies broad parameter regimes in which the dynamics is ergodic not only within but also outside the standard Gibbs region, indicating the need for a modified statistical description. At higher energies, the system instead exhibits long-lived compacton-mediated localization and signatures of weak nonergodicity, as evidenced by finite-time variances, excursion-time statistics, and probability distributions of local amplitudes. We show that stronger coupling $D$ enhances fluctuations and accelerates the crossover of the finite-time variance of the local norm density from an initial $\sim T^{-1/2}$ decay toward the faster $\sim T^{-1}$ decay characteristic of ergodic thermalization, where $T$ denotes the averaging time. In the high-energy regime, weak coupling $D\le 1$ favors persistent single-site compacton localization, whereas stronger coupling $D>1$ yields long-lived two-site localization. Our results provide insights into the interplay between thermalization, localization, and non-Gibbs statistical behavior in genuinely nonlinear systems.

Accurate reliability assessment of interconnected and interdependent systems requires explicit representation of interaction mechanisms arising from shared components, load redistribution, feedback coupling, and correlated degradation. Classical system reliability theory is formulated using real-valued probabilities and combinatorial aggregation and therefore lacks an intrinsic mathematical structure capable of encoding interaction strength, synchronization, and pathway competition. As a result, redundancy and vulnerability in highly coupled systems are often mischaracterized. This study introduces a quantum system reliability (QSR) framework that reformulates system reliability as a complex-valued field. In the proposed representation, the magnitude of each component amplitude corresponds to postevent functionality, while the phase encodes interaction induced by connectivity, redistribution, constraint release, and dependency. Because classical reliability contains no inherent phase information, this work rigorously defines reliability phase. It develops two independent extraction strategies: (1) a spectral-domain formulation based on discrete Fourier analysis of reliability fields, and (2) a quantum-field formulation derived from divergence, curl, and geometry-induced flux operators. Component reliabilities are encoded as complex amplitudes, and system reliability emerges through interference-aware aggregation rules that generalize classical series, parallel and inclusion-exclusion principles. The formulation preserves exact classical reliability under neutral-phase conditions while enabling constructive and destructive interference in the presence of dependencies. The framework is validated using benchmark networks, including cascading IEEE-118 data and interdependent graph models, demonstrating improved alignment with functional system behavior compared to classical connectivity-based metrics.

We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths—both weak and strong, at leading order in $1/N$. The second allows us to turn the kinetic equation—an integral equation—into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak-coupling end, the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong-coupling end, they asymptote to either the widely conjectured critical balance scaling or a Kolmogorov-like scaling exponent.

A laser induced fluorescence (LIF) scheme is investigated to probe singly ionized iodine ions (${\mathrm{I}}^{+}$) in electric propulsion devices. The transition $6s{}^{5}S_2^{\mathrm{o}}\to 6p{}^{5}P_3$ at 516.261 nm is considered and the theoretical computation of the weights and positions of the hyperfine structure is carried out. First, the measurement of the fluorescence signal is performed in the ionization chamber of an rf gridded ion engine, the PEGASES thruster, demonstrating that the chosen LIF scheme is well suited for the study of electric propulsion devices operating with iodine. Second, spatial measurements of the temperature, velocity, and density are taken in this plasma source for several conditions of iodine pressure from 0.5 to 10 mTorr. First, an increase of the temperature of the ionic excited population close to the antenna is observed. Second, the analysis of the Doppler shift of the LIF profile shows the acceleration of the ions in the source. Third, the comparison of the measured LIF profiles with previous measurements shows that the density of the probed lower excited state is proportional to that of the ground state in the conditions of the experiment.

We develop a statistical theory of temporal learnability in recurrent neural networks, quantifying the maximal temporal horizon ${\mathcal{H}}_N$ over which gradient-based learning can recover lag-dependent structure at finite sample size $N$. The theory is built on the effective learning rate envelope $f\left(\ell \right)$, a function that captures how gating mechanisms and adaptive optimizers jointly shape the coupling between state-space dynamics and parameter updates during Backpropagation Through Time. Under heavy-tailed ($\alpha$-stable) fluctuations, where empirical averages concentrate at rate $N^{-1/{\kappa }_{\alpha }}$ with ${\kappa }_{\alpha }=\alpha /(\alpha -1)$, the interplay between envelope decay and statistical concentration yields explicit scaling laws for the growth of ${\mathcal{H}}_N$: logarithmic, polynomial, and exponential temporal learning regimes emerge according to the decay law of $f\left(\ell \right)$. These results identify envelope decay as the key determinant of temporal learnability. Slower attenuation of $f\left(\ell \right)$ enlarges ${\mathcal{H}}_N$, while heavy-tailed fluctuations compress it by weakening statistical concentration. Moreover, envelope geometry outweighs dataset size: slowing the envelope's decay enlarges ${\mathcal{H}}_N$ more than adding data, so more complex architectures that realize slower-decaying envelopes can be more data-efficient than simpler ones. Experiments across multiple gated architectures and optimizers corroborate these structural predictions.

Using a minimal aggregation-based model, we address the efficient information transfer observed in natural flocks during collective turns. In our system, the turning signal emitted by a single individual propagates throughout the collective primarily at a constant speed. To characterize the source of this capability, we analyze the system in the continuum limit. Thus, we demonstrate that wave-propagating features arise solely from the nonreciprocal nature of interactions. We explore spectral anomalies that emerge due to this mechanism and provide an explanation through a perturbative analysis. Remarkably, within this scenario, the description of velocity fluctuations is found to follow a structure analogous to a Born approximation. Our model can be extended to study other physical contexts exhibiting polar order, and our arguments can be tested in natural systems.

The origin of segregated axial bands for size-bidisperse particles in long rotating tumblers is a long-standing question in granular flows and a problem of both fundamental and practical interest. Using DEM simulations, we consider the streamwise and time-dependent development of the underlying instability as well as performing a broad parametric study over a wide range of particle size ratios, tumbler lengths and diameters, species fractions, and fill levels to determine the conditions under which axially segregated bands appear. We show that initial radial segregation of the small and large particles in the surface flowing layer results in a layer of mixed particles with a higher bulk density due to more efficient packing over a layer of nearly monodisperse small particles with a lower bulk density. This leads to a granular Rayleigh-Taylor-like instability that produces recirculation cells driving axial band formation. The appearance of a layer of high-density mixed particles over a layer of lower-density monodisperse particles can be directly connected to the operating conditions, explaining why axially segregated bands appear only under certain conditions. Typically, increasing the particle size ratio improves packing and increases the density of the mixed layer, enhancing the Rayleigh-Taylor instability and accelerating axial segregation.

The agile turning maneuvers of anguilliform swimmers remain one of the least studied aspects of aquatic locomotion, despite being crucial for survival in underwater environments. To change direction, animals must find a balance between minimizing their moment of inertia and maximizing torque. Anguilliform swimmers, like snakes, are highly maneuverable and accomplish this goal without the aid of limbs or pectoral fins. In this study, we quantify the differences between turning and forward swimming kinematics and hydrodynamics. We present flow field and body deformation measurements taken simultaneously by combining a volumetric three-component defocusing digital particle-tracking velocimetry system with a camera mounted above the tank for swimming kinematics. We determine how snakes manipulate their body position to change swimming direction by analyzing the swimming kinematics of six turns by six individuals as 2D projections (five Natrix maura and one Nerodia rhombifer). Analyses of the body kinematics show that snakes curl their body inwards to shift their center of mass and reduce their moment of inertia to perform faster turns. The volumetric wake measurements allow us to quantify the timing between the turning kinematics and vortex shedding and to compare it with forward swimming measurements. Our results indicate that snakes can generate substantially stronger vortices when turning; for example, the vortex force can be as much as $2.5–8.6\times$ larger when compared to forward swimming. We also use volumetric wake measurements to show that the vortices shed during a turn have the same tubular vortex pair composition as forward swimming. These results help explain how elongated anguilliform swimmers change swimming direction. They widen our understanding of how animals use transient maneuvers to navigate aquatic environments, with implications for both natural swimmers and underwater robots.

Near-term quantum algorithms are a promising route to solving partial differential equations, but gauging their true potential requires separating algorithmic performance from sampling and hardware noise. We benchmark a ground-state variational quantum eigensolver (VQE), cast as a variational quantum linear solver, against the Trotterization, variational quantum imaginary time evolution, and adaptive variational quantum dynamics simulation methods applied to the one-dimensional advection-diffusion equation in the recent quantum-dynamics study by Alipanah et al. [Phys. Rev. Res. 7, 043318 (2025)] at matched grid and problem size. On a noiseless state-vector simulator the $N=4$ VQE drives the final-time infidelity to a numerical floor ($\sim {10}^{-14}$) once the depth reaches $L\approx 5$, an algorithmic ceiling set by exact expectation values. Evaluating the same solver with a finite number $S$ of measurement shots, still without hardware noise, makes the infidelity sampling limited, following $1-f\approx c/S$ (a best-case readout-sampling estimate, with the solution's signs assumed known), providing a regime-matched comparison with the shot-based emulator of Alipanah et al. and explaining the gap to their noisy hardware runs ($>{10}^{-1}$). The benchmark thus decomposes the near-term error budget into algorithmic, sampling, and hardware contributions, with a matched-depth resource comparison. The formulation applies without modification across $N=4,5,6$ qubits and to a two-dimensional (eight-qubit, $16\times 16$) problem evolved to $t=1$, where the state-vector VQE holds a $\sim {10}^{-7}$ algorithmic-ceiling infidelity against the sampling-limited $\sim {10}^{-5}$ of the corresponding shot-based simulation, a difference of measurement regime rather than algorithmic superiority.

A new scheme with fractional particle advection is proposed for lattice Boltzmann models. This scheme recovers the same macroscopic hydrodynamics as the standard lattice Boltzmann method (LBM) under low-Mach numbers, weakly compressible and isothermal conditions. It achieves an effectively reduced Courant-Friedrichs-Lewy number so that the numerical stability is improved for simulation with a small viscosity. It overcomes the long-standing issue of increased numerical dissipation when the shear viscosity is dominant for fractional particle advection schemes and achieves accuracy of solution comparable to the standard LBM in any fractional situation. The new scheme also reveals that the origin of such increased numerical dissipation in fractional advection schemes lies in fractional advection of the nonequilibrium part of the particle distribution function. Overcoming the long-standing issue of excessive numerical dissipation when the shear viscosity is dominant due to fractional advection is a significant advancement in LBM, given the important advantages of fractional particle advection.

We investigate the dynamics of a dense raft of millimeter-sized granular particles at a vertically vibrated air-water interface, which displays a rich set of patterns and particle dynamics as we vary the vibration amplitude, frequency, and particle packing fraction. While the classical parametric instability with standing waves still occurs over a certain range of parameters, the measured wave dispersion relations indicate an increasing role of the raft's emergent elasticity at higher packing fractions, where the effective surface tension decreases and the out-of-plane bending modulus increases. At higher vibration frequencies and lower amplitudes, we identify a regime without standing waves. Instead, individual particles exhibit thermal-like motion, with transport crossing over from diffusive to subdiffusive as the packing fraction increases. The particle dynamics also display spatial and temporal heterogeneity, as in supercooled liquids. Starting from this regime, when the vibration amplitude is further increased, a large cavity eventually forms inside the raft, whose size and shape depend on the vibration frequency and the injected vibration energy. The cavitation results in the coexistence of free-surface water waves inside the cavity and thermal-like particle motion in the surrounding raft.

Deciphering the formation mechanism and fine structures of ion tracks in polymers is crucial for understanding ion-matter interactions and exploring new applications, particularly when they are in proximity. Here, two sequentially generated and closely spaced ion tracks in polyimide are investigated at the atomic scale. We reveal that the occurrence of the first track breaks the cylindrical symmetry of transverse atomic displacement during the second track formation, leading to non-uniformity in track size and deformed shape that significantly deviates from the well-recognized core-halo concentric structure of an isolated track. More interestingly, this anisotropic atomic displacement induces a low-density region between two tracks. This region is fundamentally different from the isolated track cores, where mass loss occurs primarily through radiolytic outgassing. Mechanistic analysis further discloses that these direction-dependent atomic displacement dynamics are driven by the distinct chemical and mechanical responses of the pre-existing track and bulk material to ion energy deposition.

Macromolecular crowding is an organizing principle in soft matter and biological systems where high concentrations of macromolecules generate depletion forces that drive collective processes such as compaction, self-assembly, and phase separation. While the classical Asakura-Oosawa (AO) theory has been widely used to describe depletion interactions, it neglects crowder-crowder interactions and is unable to account for enhanced depletion observed in systems with attractive crowders. Here, we investigate the depletion potential of colloids immersed in Lennard-Jones crowders, which at modest crowder-crowder attraction form transient, correlated clusters, enhancing and extending the depletion range beyond classical AO predictions. We develop a cluster AO theory which treats clusters as effectively larger depletants, incorporating contributions from individual crowders and interactions between clusters. The resulting theoretical predictions mimic those obtained from umbrella sampling simulations, outperforming the predictions of classical AO theory, static polydisperse models, and traditional liquid-state-like superposition approximations without requiring costly sampling of colloid-crowder systems. Our findings highlight that prior knowledge of emergent cluster statistics suffices to predict depletion interactions in systems with interacting crowders, offering a tractable route to study crowding behavior in complex fluids.

Slowly forced nonlinear systems are known to exhibit delayed transitions beyond static bifurcation thresholds, a phenomenon that can be substantially modified by additive noise. In this work, we investigate how stochastic fluctuations modulate bifurcation delay and tipping dynamics in two representative models: the FitzHugh-Nagumo (FHN) neuronal excitable system and the Stommel model of Atlantic Meridional Overturning Circulation collapse. Both systems are analyzed within a unified first-passage framework. For the FHN model, we combine deterministic delay scaling with channel-resolved first-passage statistics and eigenvector-based noise projection. Our analysis reveals that noise acting on the fast and slow variables reduces the bifurcation delay through qualitatively distinct mechanistic pathways. Fast-variable noise induces a sharp onset window for pre-Hopf activation, whereas slow-variable noise acts via projection onto the slow manifold over the relaxation timescale, producing a broader onset region in the phase map. These differences give rise to distinct rate-noise crossover regimes that reflect the underlying geometry of the attractor. For the stochastic Stommel model, the same first-passage framework identifies a sharp crossover from delayed tipping to noise-induced early collapse. Near the crossover noise amplitude, the mean delay $(-2.9 \mathrm{yr})$, median delay (3.4 yr), and interquartile range (2.05 kyr) provide markedly different characterizations of the same first-passage distribution. This striking discrepancy exposes the limitations of single-statistic summaries in saddle-node geometries and underscores the need for multistatistical descriptions of tipping times. Across both systems, we construct rate-noise phase maps and first-passage observables that establish a common basis for comparing delayed Hopf bifurcations (oscillation onset) with delayed saddle-node bifurcations (circulation collapse). The analytical framework developed here, including delay scaling laws, activation windows, and crossover estimates, is directly testable against numerical simulations and is readily extendable to other slowly forced bifurcations, including pitchfork and transcritical cases.

We study the role of heterogeneous volatility in a networked wealth dynamics model and its impact on the wealth condensation transition. Extending the Bouchaud–Mézard framework, we introduce binary volatility in networks and investigate how its configuration affects the effective power-law tail exponent of the wealth distribution. Using a stochastic block model, we control the mixing between volatility groups and show that the effective exponent is governed not only by the global parameter $\mathrm{\Lambda }=2J/{\beta }^2$ but also by the volatility configuration in the network. We find that local interactions between nodes with different volatility induce the neutralization of group-wise exponents, which lowers the aggregate tail exponent and yields a condensation transition across ${\gamma }_{\mathrm{c}}=2$. Our results identify volatility mixing as another control mechanism for wealth condensation and highlight the importance of noise heterogeneity in nonequilibrium systems on networks.

Metal conductors pulsed with intense electrical current are of fundamental importance to physics and engineering, yet their motion, equation-of-state (EOS), and electrical conductivity during the solid-liquid phase transition are not fully understood. Photon Doppler velocimetry (PDV) measurements of electrically thick aluminum, copper, and nickel conductors pulsed by intense current reveal that the reflective surface undergoes distinct changes in acceleration throughout the current rise. Metal surfaces were measured with sufficient resolution to capture radial magnetic compression and changes in radial acceleration that, in a model-assisted framework, diagnose the duration of the solid-liquid phase transition. Parylene-N-coated copper and nickel loads exhibited different compression dynamics. These experimental measurements serve as a benchmark, guiding the selection of EOS and conductivity tables for improved modeling and simulation accuracy.

We investigate thermal avalanche dynamics in amorphous solids using elastoplastic models with local activation rules and no external driving. Dynamical heterogeneities, quantified through persistence measurements and the associated four-point susceptibility ${\chi }_4$, reveal the emergence of correlated spatiotemporal rearrangements as temperature is varied. As temperature increases, avalanche statistics evolve from scale-free behavior with exponential cutoffs to regimes dominated by system-spanning runaway events. We identify a system-size-dependent critical temperature $T_c\left(L\right)$ that separates intermittent avalanche dynamics from thermally assisted flow, where self-sustained avalanches transiently fluidize the system. We show that $T_c\left(L\right)$ decreases algebraically with increasing system size, suggesting that in the thermodynamic limit arbitrarily small but finite temperatures may destabilize the intermittent regime. The relation between avalanche size and duration resembles that in sheared systems, whereas the statistics of minimal distances to yielding reveal a temperature-driven reorganization of marginal stability absent in strictly driven overdamped dynamics. Our results demonstrate that thermal activation alone can generate a finite-size-controlled instability scale in disordered elastic media.

In current-driven metal loads, a nonlinear magnetic-diffusion wave carries current and Joule heating inward from the electrical skin-depth layer, coupling the electromagnetic drive to material compression, melting, and expansion. Photon Doppler velocimetry of electrically thick aluminum measures premelt radial magnetic compression of $34.8\pm 2.1$ nm and an acceleration transition during surface melting. Interpreted with one-dimensional magnetohydrodynamic calculations, the measured velocity history gives a model-assisted solid-liquid transition duration of $4.5\pm 0.7\mathrm{ns}$. The result is a validation-relevant surface-motion constraint for integrated current-driven material models, complementary to direct pressure-density-temperature measurements of aluminum.

We present an exact analysis of a spin-pseudospin sawtooth chain that incorporates three distinct valence states of copper ions and serves as a minimal model for one-dimensional cuprates composed of corner-sharing copper triangles. The model includes magnetic exchange and electrostatic coupling constants both along the base sites and between base and apex sites capturing the competition between spin and charge degrees of freedom. Using the transfer-matrix method, we derive exact expressions for the free energy and obtain an analytical condition defining the pseudocritical line associated with pronounced thermodynamic anomalies. The ground-state analysis reveals, besides an antiferromagnetic phase, three frustrated phases characterized by distinct residual entropies. At finite temperatures, these zero-temperature phase boundaries evolve into narrow entropy ridges signaling pseudotransitions between the corresponding quasiphases. The specific heat and the avoided-crossing scale exhibit sharp but continuous peaks at the pseudocritical temperature, whereas the physical correlation length may be controlled by a different subleading eigenvalue. Local correlation functions uncover a cooperative rearrangement from charge-dominated to magnetically correlated regimes. Our results demonstrate that the sawtooth geometry promotes frustration and short-range coherence leading to pronounced pseudotransition behavior.