Daily Papers

Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explosions, in which small perturbations at a density interface grow into chaotic, multiscale mixing as a lighter fluid accelerates into a heavier one. Standard ML models struggle with RTI, and despite over a century of theoretical, numerical, and experimental work, it carries an unresolved discrepancy between simulation and experiment: the late-time mixing growth rate, α, measured in most laboratory experiments (sim 0.06-0.07), is roughly three times the value from idealized direct numerical simulations (DNS, sim 0.02). The gap's origin remains debated. These properties make RTI a stringent test for a question that matters well beyond RTI: can foundation models trained only on simulations generalise to sparse, messy, and noisy laboratory settings? We finetune Walrus, a foundation model for continuum dynamics, on three or fewer DNS realizations and recover key RTI physics over long rollouts. Applied zero-shot to sliding-barrier laboratory data, the finetuned model leaves the DNS-like regime and enters the observed growth band, having never seen a single experimental sample. These results provide independent, data-driven evidence that initial conditions play a crucial role in the longstanding sim-experiment gap in α. The model also generalises zero-shot to stable stratification, a buoyancy regime absent from training, correctly slowing mixing-layer growth. Together, our results show that foundation models can generalise well beyond their training data, predicting laboratory behavior and unseen physical regimes, opening new ways to probe longstanding simulation-experiment gaps.

In this paper we consider a particular class of solutions of the Rayleigh-Boltzmann equation, known in the nonlinear setting as homoenergetic solutions, which have the form gleft( x,v,t right) =fleft( v-Lleft( tright)x,tright) where the matrix L(t) describes a shear flow deformation. We began this analysis in [22] where we rigorously proved the existence of a stationary non-equilibrium solution and established the different behaviour of the solutions for small and large values of the shear parameter, for cut-off collision kernels with homogeneity parameter 0leq gamma <1, including Maxwell molecules and hard potentials. In this paper, we concentrate in the case where the deformation term dominates the collision term for large times (hyperbolic-dominated regime). This occurs for collision kernels with gamma < 0 and in particular we focus on gamma in (-1,0). In such a hyperbolic-dominated regime, it appears challenging to provide a clear description of the long-term asymptotics of the solutions. Here we present a formal analysis of the long-time asymptotics for the distribution of velocities and provide the explicit form for the asymptotic profile. Additionally, we discuss the different asymptotic behaviour expected in the case of homogeneity gamma < -1. Furthermore, we provide a probabilistic interpretation describing a stochastic process consisting in a combination of collisions and shear flows. The tagged particle velocity {v(t)}_{tgeq 0} is a Markov process that arises from the combination of free flights in a shear flow along with random jumps caused by collisions.

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications.

We investigate the coupling effects of the two-phase interface, viscosity ratio, and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor-Couette turbulence at a system Reynolds number of 6000 and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets, and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, while light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. Additionally, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the turbulence modulation in two-phase flow.

Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature often decreases with height, condensation releases latent heat preferentially in regions of upflow. Due to this inhomogeneous heat source, moist convection may be more sensitive to changes in flow morphology, such as those induced by rotation, than dry Rayleigh-B\'enard convection. In order to study the effects of rotation on flows driven by latent heat release, we present a suite of numerical simulations that solve the Rainy-B\'enard equations (Vallis et al. 2019). We identify three morphological regimes: a cellular regime and a plume regime broadly analogous to those found in rotating Rayleigh B\'enard convection, and a novel funnel regime that lacks a clear analog within the regimes exhibited by dry convection. We measure energy fluxes through the system and report rotational scalings of the Reynolds and moist Nusselt numbers. We find that moist static energy transport, as measured by a moist Nusselt number, is significantly enhanced in the funnel regime without a corresponding enhancement in Reynolds number, indicating that this funnel regime produces structures with more favorable correlations between the temperature and vertical velocity.

Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics and `decide' what to do, we propose a minimal axisymmetric model of a spherical active drop, and show that simple and linear interface properties can lead to both steady self-propulsion of the droplet as well as chaotic behavior. The model includes two different mobility mechanisms, namely, diffusiophoresis and the Marangoni effect, that convert self-generated gradients of surfactant concentration into the flow at the droplet surface. In turn, surface-driven flow initiates surfactant advection that is the only nonlinear mechanism and, thus, the only source of dynamical complexity in our model. Numerical investigation of the fully-coupled hydrodynamic and advection diffusion problems reveals that strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. Our results indicate that the thresholds of these instabilities depend heavily on the balance between diffusiophoresis and the Marangoni effect. Using linear stability analysis, we demonstrate that diffusiophoresis promotes the onset of high-order modes of monotonic instability of the motionless drop. We argue that diffusiophoresis has a similar effect on the instabilities of a moving drop.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

In this paper, we consider the stability of the Lamb dipole solution of the two-dimensional Euler equations in R^{2} and question under which initial disturbance the Lamb dipole is stable, motivated by experimental work on the formation of a large vortex dipole in two-dimensional turbulence. We assume (O) odd symmetry for the x_2-variable and (N) non-negativity in the upper half plane for the initial disturbance of vorticity, and establish the stability theorem of the Lamb dipole without assuming (F) finite mass condition. The proof is based on a new variational characterization of the Lamb dipole using an improved energy inequality.

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability (MRI) as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi&Pharr, ApJ 2022), confined either between two Alfv\'enic resonances or an Alfv\'enic resonance and a boundary.

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

In this work, we consider the generalized Benjamin-Bona-Mahony equation $partial_t u+partial_x u+partial_x( |u|^pu)-partial_t partial_x^{2}u=0, quad(t,x) in R times R, with p>4. This equation has the traveling wave solutions \phi_{c}(x-ct), for any frequency c>1. It has been proved by Souganidis and Strauss Strauss-1990 that, there exists a number c_{0}(p)>1, such that solitary waves \phi_{c}(x-ct) with 1<c<c_{0}(p) is orbitally unstable, while for c>c_{0}(p), \phi_{c}(x-ct) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein Pego-1991-eigenvalue. In this paper, we prove the orbital instability in the critical case c=c_{0}(p)$.

How momentum, energy, and magnetic fields are transported in the presence of macroscopic gradients is a fundamental question in plasma physics. Answering this question is especially challenging for weakly collisional, magnetized plasmas, where macroscopic gradients influence the plasma's microphysical structure. In this paper, we introduce thermodynamic forcing, a new method for systematically modeling how macroscopic gradients in magnetized or unmagnetized plasmas shape the distribution functions of constituent particles. In this method, we propose to apply an anomalous force to those particles inducing the anisotropy that would naturally emerge due to macroscopic gradients in weakly collisional plasmas. We implement thermodynamic forcing in particle-in-cell (TF-PIC) simulations using a modified Vay particle pusher and validate it against analytic solutions of the equations of motion. We then carry out a series of simulations of electron-proton plasmas with periodic boundary conditions using TF-PIC. First, we confirm that the properties of two electron-scale kinetic instabilities -- one driven by a temperature gradient and the other by pressure anisotropy -- are consistent with previous results. Then, we demonstrate that in the presence of multiple macroscopic gradients, the saturated state can differ significantly from current expectations. This work enables, for the first time, systematic and self-consistent transport modeling in weakly collisional plasmas, with broad applications in astrophysics, laser-plasma physics, and inertial confinement fusion.

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

At high energies, the dynamics of a plasma with charged fermions can be described in terms of chiral magnetohydrodynamics. Using direct numerical simulations, we demonstrate that chiral magnetic waves (CMWs) can produce a chiral asymmetry μ_5 = μ_L - μ_R from a spatially fluctuating (inhomogeneous) chemical potential μ= μ_L + μ_R, where μ_L and μ_R are the chemical potentials of left- and right-handed electrically charged fermions, respectively. If the frequency of the CMW is less than or comparable to the characteristic growth rate of the chiral dynamo instability, the magnetic field can be amplified on small spatial scales. The growth rate of this small-scale chiral dynamo instability is determined by the spatial maximum value of μ_5 fluctuations. Therefore, the magnetic field amplification occurs during periods when μ_5 reaches temporal maxima during the CMW. If the small-scale chiral dynamo instability leads to a magnetic field strength that exceeds a critical value, which depends on the resistivity and the initial value of μ, magnetically dominated turbulence is produced. Turbulence gives rise to a large-scale dynamo instability, which we find to be caused by the magnetic alpha effect. Our results have consequences for the dynamics of certain high-energy plasmas, such as the early Universe.

We prove stability for a class of heterogeneous catalysis models in the L_p-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.

We consider the incompressible Euler and Navier-Stokes equations on the three dimensional torus, in velocity form, perturbed by a transport or transport-stretching Stratonovich noise. Closed control of the noise contributions in energy estimates are demonstrated, for any positive integer ordered Sobolev Space and the equivalent Stokes Space; difficulty arises due to the presence of the Leray Projector disrupting cancellation of the top order derivative. This is particularly pertinent in the case of a transport noise without stretching, where the vorticity form cannot be used. As a consequence we obtain, for the first time, the existence of a local strong solution to the corresponding stochastic Euler equation. Furthermore, smooth solutions are shown to exist until blow-up in L^1left([0,T];W^{1,infty}right).

We investigate magnetic-field amplification driven by the nonresonant hybrid (NRH or Bell) instability and its impact on cosmic-ray (CR) acceleration at reverse shocks of ultrafast outflows (UFOs) from active galactic nuclei (AGN). Previous kinetic studies by particle-in-cell simulations have demonstrated that when maximum CR energy is near the injection scale, NRH instability efficiently amplifies magnetic field up to the saturation level. However, the efficiency of NRH instability goes down as maximum energy increase since CR current is carried by escaping CRs near the maximum energy. We employ a one-dimensional MHD--CR framework solving telegraph-type diffusion--convection equations to trace the coupled evolution of CRs, magnetic fields, and shock dynamics under realistic parameters. We find a distinct transition with magnetic field strength: for weak background fields (B_{0}!lesssim!10^{-4},G), NRH instability efficiently amplifies upstream turbulence, driving a self-regulated state where E_{max} becomes independent of initial strength of magnetic turbulence. In contrast, for stronger background fields (B_{0}!gtrsim!10^{-3},G), the escaping CR current is too weak to drive NRH instability, and magnetic turbulence further decays through parametric instabilities, potentially reducing the acceleration efficiency. We give the physical interpretation for the transition and discuss conditions for PeV--EeV acceleration at UFO reverse shocks.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

We construct a time-dependent, incompressible, and uniformly-in-time Lipschitz continuous velocity field on T^3 that produces exponential growth of the magnetic energy along a subsequence of times, for every positive value of the magnetic diffusivity. Because this growth is not uniform in time but occurs only along a diverging sequence of times, we refer to the resulting mechanism as a limsup fast dynamo. Our construction is based on suitably rescaled Arnold-Beltrami-Childress (ABC) flows, each supported on long time intervals. The analysis employs perturbation theory to establish continuity of the exponential growth rate with respect to both the initial data and the diffusivity parameter. This proves the weak form of the fast dynamo conjecture formulated by Childress and Gilbert on T^3, but the considerably more challenging version proposed by Arnold on T^3 remains an open problem.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from data, remains a major challenge. This paper introduces a novel continuum dynamics perspective for model learning that enables formal uncertainty propagation by constructing Taylor series approximations of probabilistic events. We establish sufficient conditions for the soundness of the approach and prove its asymptotic convergence. Empirical results demonstrate the framework's effectiveness, particularly when predicting rare events.

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of κ-entropy, we rigorously justify the convergence of weak solutions toward the generalized anelastic system in a three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we establish a similar convergence result in the whole space, relying essentially on dispersive estimates for acoustic waves. Compared with the work of Fanelli and Zatorska [Commun. Math. Phys., 400 (2023), pp. 1463-1506], our analysis is conducted for the standard isentropic pressure law, thereby eliminating the need for the cold pressure term that played a crucial role in the previous approach. To the best of our knowledge, this is the first rigorous singular limit result for the compressible Navier-Stokes equations with degenerate viscosity that requires no additional regularization of the system.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

Data-driven surrogate models improve the efficiency of simulating continuous dynamical systems, yet their autoregressive rollouts are often limited by instability and spectral blow-up. While global regularization techniques can enforce contractive dynamics, they uniformly damp high-frequency features, introducing a contraction-dissipation dilemma. Furthermore, long-horizon trajectory optimization methods that explicitly correct drift are bottlenecked by memory constraints. In this work, we propose Jacobian-Adaptive Weighting for Stability (JAWS), a probabilistic regularization strategy designed to mitigate these limitations. By framing operator learning as Maximum A Posteriori (MAP) estimation with spatially heteroscedastic uncertainty, JAWS dynamically modulates the regularization strength based on local physical complexity. This allows the model to enforce contraction in smooth regions to suppress noise, while relaxing constraints near singular features to preserve gradients, effectively realizing a behavior similar to numerical shock-capturing schemes. Experiments demonstrate that this spatially-adaptive prior serves as an effective spectral pre-conditioner, which reduces the base operator's burden of handling high-frequency instabilities. This reduction enables memory-efficient, short-horizon trajectory optimization to match or exceed the long-term accuracy of long-horizon baselines. Evaluated on the 1D viscous Burgers' equation, our hybrid approach improves long-term stability, shock fidelity, and out-of-distribution generalization while reducing training computational costs.

We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across k_perpρ_{ti}sim 1. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for k_perpρ_{ti} correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.

In this paper, we study the existence and uniqueness of solutions to the Euler equations with initial conditions that exhibit analytic regularity near the boundary and Sobolev regularity away from it. A key contribution of this work is the introduction of the diamond-analyticity framework, which captures the spatial decay of the analyticity radius in a structured manner, improving upon uniform analyticity approaches. We employ the Leray projection and a nonstandard mollification technique to demonstrate that the quotient between the imaginary and real parts of the analyticity radius remains unrestricted, thus extending the analyticity persistence results beyond traditional constraints. Our methodology combines analytic-Sobolev estimates with an iterative scheme which is nonstandard in the Cauchy-Kowalevskaya framework, ensuring rigorous control over the evolution of the solution. These results contribute to a deeper understanding of the interplay between analyticity and boundary effects in fluid equations. They might have implications for the study of the inviscid limit of the Navier-Stokes equations and the role of complex singularities in fluid dynamics.

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of the solution, \(Δu |_{\partial Ω}\) and \( \partial_{n}(Δu)|_{\partial Ω}.\) We first prove that the associated system operator generates a contraction semigroup, which ensures the well-posedness of the forward problem. A key observability inequality is then derived via multiplier techniques. Building on this foundation, explicit stability estimates for the inverse problem are obtained. These estimates demonstrate that the biharmonic structure inherently enhances the stability of parameter identification, with the stability constants exhibiting an explicit dependence on the damping coefficient via the factor \( (1 + γ)^{1/2} \). This work provides a rigorous theoretical basis for applications in non-destructive testing and dynamic inversion.

The Korteweg-de Vries (KdV) equation serves as a foundational model in nonlinear wave physics, describing the balance between dispersive spreading and nonlinear steepening that gives rise to solitons. This article introduces sangkuriang, an open-source Python library for solving this equation using Fourier pseudo-spectral spatial discretization coupled with adaptive high-order time integration. The implementation leverages just-in-time (JIT) compilation for computational efficiency while maintaining accessibility for instructional purposes. Validation encompasses progressively complex scenarios including isolated soliton propagation, symmetric two-wave configurations, overtaking collisions between waves of differing amplitudes, and three-body interactions. Conservation of the classical invariants is monitored throughout, with deviations remaining small across all test cases. Measured soliton velocities conform closely to theoretical predictions based on the amplitude-velocity relationship characteristic of integrable systems. Complementary diagnostics drawn from information theory and recurrence analysis confirm that computed solutions preserve the regular phase-space structure expected for completely integrable dynamics. The solver outputs data in standard scientific formats compatible with common analysis tools and generates visualizations of spatiotemporal wave evolution. By combining numerical accuracy with practical accessibility on modest computational resources, sangkuriang offers a platform suitable for both classroom demonstrations of nonlinear wave phenomena and exploratory research into soliton dynamics.

In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data u_0in B^{s}_{p,r} and for some T>0, the solutions of the Navier--Stokes equations converge strongly in L^infty_TB^{s}_{p,r} to the Euler equations as the viscosity parameter tends to zero. We furthermore prove the failure of the uniform (with respect to the initial data) B^{s}_{p,r} convergence in the inviscid limit of a family of solutions of the Navier-Stokes equations towards a solution of the Euler equations.

We present a model for chi^{(2)} waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to viable fusion power is understanding plasma turbulence, which significantly impairs plasma confinement, and is vital for next-generation reactor design. Plasma turbulence is governed by the nonlinear gyrokinetic equation, which evolves a 5D distribution function over time. Due to its high computational cost, reduced-order models are often employed in practice to approximate turbulent transport of energy. However, they omit nonlinear effects unique to the full 5D dynamics. To tackle this, we introduce GyroSwin, the first scalable 5D neural surrogate that can model 5D nonlinear gyrokinetic simulations, thereby capturing the physical phenomena neglected by reduced models, while providing accurate estimates of turbulent heat transport.GyroSwin (i) extends hierarchical Vision Transformers to 5D, (ii) introduces cross-attention and integration modules for latent 3Dleftrightarrow5D interactions between electrostatic potential fields and the distribution function, and (iii) performs channelwise mode separation inspired by nonlinear physics. We demonstrate that GyroSwin outperforms widely used reduced numerics on heat flux prediction, captures the turbulent energy cascade, and reduces the cost of fully resolved nonlinear gyrokinetics by three orders of magnitude while remaining physically verifiable. GyroSwin shows promising scaling laws, tested up to one billion parameters, paving the way for scalable neural surrogates for gyrokinetic simulations of plasma turbulence.

The objective of this study is to develop a fully compressible magnetohydrodynamic solver for fast simulations of the global dynamo of the Sun using unstructured grids and GPUs. Accurate modeling of the Sun's convective layers is vital to predicting the Sun's behavior, including the solar dynamo and sunspot cycles. Currently, there are many efficient codes capable of conducting these large simulations; however, many assume an anealastic density distribution. The anelastic assumption is capable of producing accurate results for low mach numbers; however, it fails in regions with a higher mach number and a fully compressible flow must be considered. To avoid these issues, Wang et al. [1] created a Compressible High-ORder Unstructured Spectral difference (CHORUS) code for simulating fluid dynamics inside stars and planets. CHORUS++ augmented the CHORUS code to adopt a higher degree of polynomials by using cubed-sphere meshing and transfinite mapping to perform simulations on unstructured grids [2]. Recently, CHORUS++ was further developed for parallel magnetohydrodynamic (MHD) solutions on GPUs at Clarkson University. In this study the solar benchmark problems presented by Chen et al. [2] are extended to unsteady solar dynamo problems, with two different density scale heights. The CHORUS-MHD code is further accelerated by multiple GPUs and used to successfully solve these solar dynamo benchmark problems. [1] Wang, J., Liang, C., and Miesch, M. S., "A Compressible High-Order Unstructured Spectral Difference Code for Stratified Convection in Rotating Spherical Shells," Journal of Computational Physics, Vol. 290, 2015, pp. 90-111. [2] Chen, K., Liang, C., and Wan, M., "Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids," Physics of Fluids, Vol. 35, 2023, p. 086120.

Elemental abundances in the solar corona differ from those in the photosphere, with low first ionization potential (FIP) elements being enhanced, a phenomenon known as the FIP effect. This enhancement is attributed to ponderomotive forces linked to magnetohydrodynamic (MHD) waves, particularly incompressible transverse waves. Our study investigates the relationship between coronal abundance fractionation and chromospheric transverse MHD waves by examining the spatial correlation between FIP fractionation and these waves and by analyzing their properties to test the ponderomotive force model. We used H alpha data from the Fast Imaging Solar Spectrograph at the Goode Solar Telescope to detect chromospheric transverse MHD waves and Si{X} (low FIP) and S{X} (high FIP) spectra from Hinode EUV Imaging Spectrometer to determine relative abundances in an active region. Extrapolated linear force free magnetic fields from Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetograms further linked the observed chromospheric waves with coronal composition. Approximately 400 wave packets were identified and characterized by their period, velocity amplitude, propagation speed, and direction. These incompressible or weakly compressible waves were mainly observed near loop footpoints in the sunspot penumbra and superpenumbral fibrils. Regions of high FIP fractionation coincided with closed magnetic fields where these waves were present, and low-frequency, downward-propagating waves comprised about 43/% of the total. Our results demonstrate a strong correlation between coronal abundance fractionation and chromospheric transverse MHD waves, supporting the view that the FIP effect is driven by the ponderomotive force from these waves.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propulsion is increased. However, the range of self-propulsions in which a pure liquid regime exist appears to vanish upon approaching the so-called "jamming point" at which solidity of soft-sphere packings is lost. Such an "active yielding" transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existent of different universality classes for the yielding transition under different driving conditions. In addition, we present direct measurements of length and time scales for both driving scenarios. A comparison with theoretical predictions from recent literature reveals poor agreement with our numerical results.

This study investigates the hydrodynamics of droplet formation in a T-shaped cylindrical microfluidic device using micro-PIV experiments and CFD simulations. Devices of 150 micro-m internal diameter were fabricated from PDMS via a cost-effective embedded templating method. Flow visualization was conducted using immiscible silicone oil and deionized water, forming water-in-oil droplets. A mathematical model coupling the Navier-Stokes and conservative level-set equations was solved using the finite element method. Detailed flow fields (velocity, pressure, and phase distribution) were obtained over a wide range of flow-rate ratios (0.1-10) and capillary numbers (0.001-0.1) to characterize droplet formation mechanisms. Phase evolution revealed distinct breakup stages (lag, filling, necking, and pinch-off) and multiple regimes (squeezing, dripping, sausage flow, and parallel flow with tip streaming). A regime map delineating droplet and non-droplet regions was developed. Droplet size, curvature, and internal flow profiles exhibited strong dependence on Ca and Qr. Scaling analysis showed linear dependence of droplet size on Qr in the squeezing regime, with curvature nearly independent of Qr. In contrast, both size and curvature followed power-law dependence on Ca and Qr in the dripping regime. Velocity fields inside droplets were laminar and parabolic in the core. Fully developed plug-like profiles appeared in squeezing, whereas front and rear regions remained developing in dripping. Correlations for droplet length, curvature, and film thickness, including a novel thin-film model incorporating visco-inertial and capillary effects, enable predictive design within the studied range. These findings advance fundamental understanding of confined droplet dynamics and provide quantitative guidelines for optimizing droplet-based microfluidic systems.

The Jovian atmosphere contains a wide diversity of vortices, which have a large range of sizes, colors and forms in different dynamical regimes. The formation processes for these vortices is poorly understood, and aside from a few known, long-lived ovals, such as the Great Red Spot, and Oval BA, vortex stability and their temporal evolution are currently largely unknown. In this study, we use JunoCam data and a citizen-science project on Zooniverse to derive a catalog of vortices, some with repeated observations, through May 2018 to Sep 2021, and analyze their associated properties, such as size, location and color. We find that different colored vortices (binned as white, red, brown and dark), follow vastly different distributions in terms of their sizes and where they are found on the planet. We employ a simplified stability criterion using these vortices as a proxy, to derive a minimum Rossby deformation length for the planet of sim1800 km. We find that this value of L_d is largely constant throughout the atmosphere, and does not have an appreciable meridional gradient.

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum chi_{rm eq} where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at chi_{rm eq}. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

We propose a self-consistent explanation of Rieger-type periodicities, the Schwabe cycle, and the Suess-de Vries cycle of the solar dynamo in terms of resonances of various wave phenomena with gravitational forces exerted by the orbiting planets. Starting on the high-frequency side, we show that the two-planet spring tides of Venus, Earth and Jupiter are able to excite magneto-Rossby waves which can be linked with typical Rieger-type periods. We argue then that the 11.07-year beat period of those magneto-Rossby waves synchronizes an underlying conventional alpha-Omega-dynamo, by periodically changing either the field storage capacity in the tachocline or some portion of the alpha-effect therein. We also strengthen the argument that the Suess-de Vries cycle appears as an 193-year beat period between the 22.14-year Hale cycle and a spin-orbit coupling effect related with the 19.86-year rosette-like motion of the Sun around the barycenter.

Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with O(n^2) cost. In this work, we replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at O(n) cost. We prove that the approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time relaxation to Maxwellian equilibrium where the blob method fails, and delivers 50% faster runtime with 4times lower peak memory.

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a non-responsive dark matter halo to perturbations like bars, spiral arms and satellite galaxy encounters. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Omega_z), radial (Omega_r) and azimuthal (Omega_phi) frequencies, giving rise to local phase-space spirals. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes super-exponential damping of the phase-spiral amplitude. The z-v_z phase-spiral is 1-armed (2-armed) for vertically anti-symmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (tau_{P}) comparable to the vertical oscillation period (tau_z sim 1/Omega_z) trigger z-v_z phase-spirals. Each (n,l,m) mode of the response to impulsive (tau_{P}<tau=1/(nOmega_z+lOmega_r+mOmega_phi)) perturbations is power law (sim tau_{P}/tau) suppressed, but that to adiabatic (tau_{P}>tau) perturbations is exponentially weak (sim left[-left(tau_{mathrm{P}/tauright)^alpharight]}) except resonant (tauto infty) modes. Slower (tau_{P}>tau_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. If the Gaia phase-spiral was triggered by a satellite, Sagittarius is the leading contender as it dominates the Solar neighborhood response of the Milky Way disk to satellite encounters. However, survival against collisional damping necessitates that the impact occurred within sim 0.6-0.7 Gyr ago. We discuss how the detailed galactic potential dictates the phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound in the outer disk and in presence of an ambient halo.

We show that Hertzian particle contacts are the underlying cause of the as-yet-unexplained noninteger power laws in weakly nonlinear rheology. In the medium amplitude oscillatory shear (MAOS) region, the cubic scaling of the leading order nonlinear shear stress (σ_3 sim γ_0^{m_3}, m_3=3) is the standard expectation. Expanding on the work by Natalia et al. [J. Rheol. 64 625-635 (2020)], we report an extensive data set of noncubical, noninteger power law scalings m_3 for particle suspensions in two immiscible fluids with a capillary attractive interaction, known as capillary suspensions. Here, we show that distinct power law exponents are found for the storage and loss moduli and these noninteger scalings occur at every secondary fluid concentration for two different contact angles. These compelling results indicate that the noninteger scalings are related to the underlying microstructure of capillary suspensions. We show that the magnitude of the third harmonic elastic stress scaling m_3,elastic originates from Hertzian-like contacts in combination with the attractive capillary force. The related third harmonic viscous stress scaling m_3,viscous is, found to be associated with adhesive-controlled friction. These observations, conducted for a wide range of compositions, can help explain previous reports of noninteger scaling for materials involving particle contacts and offers a new opportunity using the variable power law exponent of MAOS rheology to reveal the physics of particle bonds and friction in the rheological response under low deformation instead of at very high shear rates.

A large-scale database of two-dimensional UEDGE simulations has been developed to study detachment physics in KSTAR and to support surrogate models for control applications. Nearly 70,000 steady-state solutions were generated, systematically scanning upstream density, input power, plasma current, impurity fraction, and anomalous transport coefficients, with magnetic and electric drifts across the magnetic field included. The database identifies robust detachment indicators, with strike-point electron temperature at detachment onset consistently Te around 3-4 eV, largely insensitive to upstream conditions. Scaling relations reveal weaker impurity sensitivity than one-dimensional models and show that heat flux widths follow Eich's scaling only for uniform, low D and Chi. Distinctive in-out divertor asymmetries are observed in KSTAR, differing qualitatively from DIII-D. Complementary time-dependent simulations quantify plasma response to gas puffing, with delays of 5-15 ms at the outer strike point and approximately 40 ms for the low-magnetic-field-side (LFS) radiation front. These dynamics are well captured by first-order-plus-dead-time (FOPDT) models and are consistent with experimentally observed detachment-control behavior in KSTAR [Gupta et al., submitted to Plasma Phys. Control. Fusion (2025)]

We apply a Gaussian process method to the extreme gamma-ray flares of 3C 454.3 and 3C 279 to discover the variable patterns and then to investigate the physical origins of the giant flares. The kernels of stochastically driven damped simple harmonic oscillator (SHO), the damped random-walk (DRW), and Matrm ern-3/2 are respectively used to describe the adaptive-binning gamma-ray light curves of the two flares. Our findings show that both the extreme gamma-ray flares of 3C 454.3 and 3C 279 clearly prefer the SHO kernel in the over-damped mode and the Matrm ern-3/2 kernel over the DRW kernel. The resulted SHO and Matrm ern-3/2 power spectral densities (PSDs) are the same for each object, with the index changing from -4 at high frequencies to 0 at low frequencies. The patterns of the two flares are both approaching the critical damping mode with the quality factor Q approx 0.4 (i.e., the damping ratio eta approx 1.25), but with slightly different damping timescales. The characteristic timescale (corresponding to the broken frequency in the PSD) for 3C 454.3 is 2-3 days and 3-5 days for 3C 279. The variable patterns found here suggest that once the system responds to the energy injection disturbance, the release of the energy in the system is finished abruptly. The obtained timescale provides a constraint on the size of energy dissipation region for each source.

Air lubrication regimes were studied using simultaneous drag force measurements and multi-plane imaging to characterize the regimes and identify the governing mechanisms of drag reduction. A bubbly, transitional, and air layer regime are identified over a large range of freestream velocities (U_{infty}), air flow rates (Q_{air}), and Froude-depth numbers (Fr_d). For the lowest U_{infty}, drag reduction lags significantly behind the non-wetted area coverage at all cases and no simple correlation exists. Within the bubbly regime, a drag increase is found for low U_{infty} with large, slow-moving bubbles forming a single layer over the plate height. For higher velocities, bubbles become smaller and disperse vertically, while the drag starts decreasing. For higher Q_{air}, irrespective of U_{infty}, air patches start to form (transitional regime) and drag monotonically decreases, with the onset of the air layer regime at 60\% drag reduction. A new scaling of the associated critical Q_{air} is proposed, combining the air exit velocity, the liquid velocity close to the air layer and Fr_d. For a further increase of Q_{air} and low U_{infty}, a thicker and smoother air layer is formed with even lower drag; for higher U_{infty}, marginal differences are observed. The air layer morphology is significantly altered however, depending on Fr_d: for Fr_d>0.7, it is unbounded, extending beyond the current test section length, and for subcritical conditions (deep water regime, Fr_d<0.61) a closure is formed and the air layer transitions to a cavity of a specific length.

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k leq 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly inference. Consequently, quality-preserving fast sampling methods that require fewer NFEs have been an active area of research. However, prior training-free sampling methods fail to simultaneously address two key challenges: the stiffness of the ODE (i.e., the non-straightness of the velocity field) and dependence on the semi-linear structure of the DM ODE (which limits their direct applicability to flow-matching models). In this work, we introduce the Stabilized Taylor Orthogonal Runge--Kutta (STORK) method, addressing both design concerns. We demonstrate that STORK consistently improves the quality of diffusion and flow-matching sampling for image and video generation. Code is available at https://github.com/ZT220501/STORK.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

Surface bubbles are an abundant source of aerosols, with important implications for climate processes. In this context, we investigate the stability and thinning dynamics of soap films under effective gravity fields. Experiments are performed using a centrifugal thin-film balance capable of generating accelerations from 0.2 up to 100 times standard gravity, combined with thin-film interferometry to obtain time-resolved thickness maps. Across all experimental conditions, the drainage dynamics are shown to be governed by capillary suction and marginal regeneration-a mechanism in which thick regions of the film are continuously replaced by thin film elements (TFEs) formed at the meniscus. We consistently recover a thickness ratio of 0.8 - 0.9 between the TFEs and the adjacent film, in agreement with previous observations under standard gravity. The measured thinning rates also follow the predicted scaling laws. We identified that gravity has three distinct effects: (i) it induces a strong stretching of the initial film, extending well beyond the linear-elastic regime; (ii) it controls the meniscus size, and thereby the amplitude of the capillary suction and the drainage rate; and (iii) it reveals an inertia-to-viscous transition in the motion of TFEs within the film. These results are supported by theoretical modeling and highlight the robustness of marginal regeneration and capillary-driven drainage under extreme gravity conditions.

Common moment-based radiative transfer methods, such as flux-limited diffusion (FLD) and the M1 closure, suffer from artificial interactions between crossing beams. In protoplanetary disks, this leads to an overestimation of the midplane temperature due to the merging of inward and outward vertical fluxes. Methods that avoid these artifacts typically require angular discretization, which can be computationally expensive. In the spirit of the two-stream approximation, we introduced a half-moment (HM) closure that integrates the radiative intensity over hemispheres, thereby suppressing beam interactions along a fixed spatial direction. We derived a multidimensional HM closure via entropy maximization and replaced this closure with an approximate expression that closely matches it, coinciding with it in the diffusion and free-streaming regimes while remaining expressible through simple operations. We implemented HM and M1 closures via implicit-explicit schemes, including multiple frequency groups. We tested these methods in numerical benchmarks such as computing the temperature in an irradiated disk around a T Tauri star, comparing our results with Monte Carlo (MC) radiative transfer simulations. The HM closure correctly reproduces the diffusion limit and prevents crossing flux interactions in a chosen spatial direction. In disk simulations, our multigroup HM method closely matches midplane temperature distributions obtained with classical MC methods. While the M1 closure produces midplane temperatures 44% higher than MC with one frequency group and 21% higher with 22 groups, HM reduces this discrepancy to 6% with 22 groups. Even with just three groups, HM significantly outperforms M1, with maximum departures of 8% compared to M1's 23%. Our results show that combining HM with a multigroup treatment yields more realistic disk temperatures than M1, particularly in optically thick regions.

The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the Stokes number, St_c, the amount of deposition has the unusual scaling law of exp(-1/(St-St_c)^{1/2}). The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time for the particle to reach the surface of the cylinder varying as 1/(St-St_c)^{1/2}, together with the distance away from the stagnation point (perpendicular to the flow direction) increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the amount of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead.

Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliable only inside the Taylor convergence radius of the true loss along the update direction. That radius is set not by real-line curvature alone but by the nearest complex singularity. For cross-entropy, the softmax partition function F=sum_j exp(z_j) has complex zeros -- ``ghosts of softmax'' -- that induce logarithmic singularities in the loss and cap this radius. To make this geometry usable, we derive closed-form expressions under logit linearization along the proposed update direction. In the binary case, the exact radius is ρ^*=δ^2+ π^2/Δ_a. In the multiclass case, we obtain the lower bound ρ_a=π/Δ_a, where Δ_a=max_k a_k-min_k a_k is the spread of directional logit derivatives a_k=nabla z_kcdot v. This bound costs one Jacobian-vector product and reveals what makes a step fragile: samples that are both near a decision flip and highly sensitive to the proposed direction tighten the radius. The normalized step size r=τ/ρ_a separates safe from dangerous updates. Across six tested architectures and multiple step directions, no model fails for r<1, yet collapse appears once rge 1. Temperature scaling confirms the mechanism: normalizing by ρ_a shrinks the onset-threshold spread from standard deviation 0.992 to 0.164. A controller that enforces τleρ_a survives learning-rate spikes up to 10{,} 000times in our tests, where gradient clipping still collapses. Together, these results identify a geometric constraint on cross-entropy optimization that operates through Taylor convergence rather than Hessian curvature.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

The solar wind is a medium characterized by strong turbulence and significant field fluctuations on various scales. Recent observations have revealed that magnetic turbulence exhibits a self-similar behavior. Similarly, high-resolution measurements of the proton density have shown comparable characteristics, prompting several studies into the multifractal properties of these density fluctuations. In this work, we show that low-resolution observations of the solar wind proton density over time, recorded by various spacecraft at Lagrange point L1, also exhibit non-linear and multifractal structures. The novelty of our study lies in the fact that this is the first systematic analysis of solar wind proton density using low-resolution (hourly) data collected by multiple spacecraft at the L1 Lagrange point over a span of 17 years. Furthermore, we interpret our results within the framework of non-extensive statistical mechanics, which appears to be consistent with the observed nonlinear behavior. Based on the data, we successfully validate the q-triplet predicted by non-extensive statistical theory. To the best of our knowledge, this represents the most rigorous and systematic validation to date of the q-triplet in the solar wind.

We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We apply it to the accurate numerical study of acoustic radiation in the neighborhood of a sound-hard two-dimensional staircase modeled after the El Castillo pyramid. Such staircases support trapped waves which travel along the surface and decay exponentially away from it. We use the array scanning method (Floquet--Bloch transform) to recover the scattered field as an integral over the family of quasiperiodic solutions parameterized by their on-surface wavenumber. Each such BIE solution requires the quasiperiodic Green's function, which we evaluate using an efficient integral representation of lattice sum coefficients. We avoid the singularities and branch cuts present in the array scanning integral by complex contour deformation. For each frequency, this enables a solution accurate to around 10 digits in a couple of seconds. We propose a residue method to extract the limiting powers carried by trapped modes far from the source. Finally, by computing the trapped mode dispersion relation, we use a simple ray model to explain an observed acoustic "raindrop" effect (chirp-like time-domain response).

The dynamical realisation of the equation of state p +rho =0 is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid paradigm. It is shown that an anisotropic stress must be always present. The Hamiltonian of the system in isolation resembles the one of a Pais-Uhlenbeck oscillator and linear stability requires that it cannot be positive definite. The dynamics of linear cosmological perturbations in a DCC dominated Universe is studied in detail showing that when DCC is minimally coupled to gravity no dramatic instability is present. In contrast to what happens in a cosmological constant dominated Universe, the non-relativistic matter contrast is no longer constant and exhibits an oscillator behaviour at small scales while it grows weakly at large scales. In the gravitational waves sector, at small scales, the amplitude is still suppressed as the inverse power of the scale factor while it grows logarithmically at large scales. Also the vector modes propagate, though no growing mode is found.

In this work, we prove existence and uniqueness of a bounded viscosity solution for the Cauchy problem of degenerate parabolic equations with variable exponent coefficients. We construct the solution directly using the stochastic representation, then verify it satisfies the Cauchy problem. The corresponding SDE, on the other hand, allows the drift and diffusion coefficients to respond nonlinearly to the current state through the state-dependent variable exponents, and thus, extends the expressive power of classical SDEs to better capture complex dynamics. To validate our theoretical framework, we conduct comprehensive numerical experiments comparing finite difference solutions (Crank-Nicolson on logarithmic grids) with Monte Carlo simulations of the SDE.

Stars on the AGB can exhibit acoustic pulsation modes of different radial orders, along with non-radial modes. These pulsations are essential to the mass-loss process and influence the evolutionary pathways of AGB stars. P-L relations serve as a valuable diagnostic for understanding stellar evolution along the AGB. 3D RHD simulations provide a powerful tool for investigating pulsation phenomena driven by convective processes and their non-linear coupling with stellar oscillations. We investigate multi-mode pulsations in AGB stars using advanced 3D 'star-in-a-box' simulations with the CO5BOLD code. Signatures of these multi-mode pulsations were weak in our previous 3D models. Our focus is on identifying and characterising the various pulsation modes, examining their persistence and transitions, and comparing the results with 1D model predictions and observational data where applicable. We produced a new model grid comprising AGB stars with current masses of 0.7, 0.8, and 1,M_{odot}. Fourier analysis was applied to dynamic, time-dependent quantities to extract dominant pulsation modes and their corresponding periods. Additionally, wavelet transforms were employed to identify mode-switching behaviour over time. The models successfully reproduce the P-L sequences found in AGB stars. Mode-switching phenomena are found in both the models and wavelet analyses of observational data, allowing us to infer similarities in the underlying pulsation dynamics. These 3D simulations highlight the natural emergence of multi-mode pulsations, including both radial and non-radial modes, driven by the self-consistent interplay of convection and oscillations. Our findings underscore the value of 3D RHD models in capturing the non-linear behaviour of AGB pulsations, providing insights into mode switching, envelope structures, and potential links to episodic mass-loss events.

The gamma-ray burst (GRB) GRB 211211A and GRB 060614, believed to originate from the merger of compact objects, exhibit similarities to the jetted tidal disruption event (TDE) Sw J1644+57, by showing violent variabilities in the light-curve during the decay phase. Previous studies suggest that such fluctuations in TDE may arise from the fallback of tidal disrupted debris. In this paper, we introduce the fluctuations of the mass distribution {rm d}M/{rm d}E for the debris ejected during the tidal disruption (with energy E) and study their impact on jet power. Turbulence induced by tidal force and the self-gravity of the debris may imprint variabilities in {rm d}M/{rm d}E during fallback. We model these fluctuations with a power density spectrum propto f_{rm E}^{beta}, where f_{rm E} = 1/E and beta is the power-law index. We find that the resulting light curve can preserve the fluctuation characteristics from {rm d}M/{rm d}E. In addition, the observed fluctuations in the light-curves can be reproduced for a given suitable beta. Based on the observations, we find that the value of beta should be around -1.

We present a set of numerical simulations of the dynamical evolution of compact planetary systems migrating in a protoplanetary disk whose inner edge is sculpted by the interaction with the stellar magnetic field, as described in Yu et al. (2023). We demonstrate that the resulting final distribution of neighbouring planet period ratios contains only a small surviving fraction of resonant systems, in accordance with observations. The resulting planetary architectures are largely in place by the end of the protoplanetary disk phase (within a few Myr), and do not require significant later dynamical evolution. The divergence of planetary pairs during gas disk dispersal also leads to the excitation of eccentricities when pairs cross mean motion resonances in a divergent fashion. The resulting distribution of remnant free eccentricities is consistent with the values inferred from the observation of transit durations and transit timing variations. We furthermore demonstrate that this conclusion is not significantly altered by tides, assuming standard values for tidal dissipation in Earth or Neptune-class planets. These results demonstrate that the observed spacing and residual dynamical excitation of compact planetary systems can be reproduced by migration through a protoplanetary disk, as long as the inner disk boundary is modelled as a gradual rollover, instead of a sharp transition. Such an effect can be achieved when the model accounts for the diffusion of the stellar magnetic field into the disk. The resulting divergence of planetary pairs during the magnetospheric rebound phase breaks the resonant chains, resulting in a better match to observations than disk models with more traditional inner boundaries.

We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chernov and Le (2024) as well as Harbrecht, Schmidlin, and Schwab (2024) in which the input random field is assumed to belong to a Gevrey smoothness class. This approach has the advantage of being substantially more general than models which assume a particular parametric representation of the input random field such as a Karhunen-Loeve series expansion. We consider both the Poisson equation as well as the heat equation and design randomly shifted lattice quasi-Monte Carlo (QMC) cubature rules for the computation of the expected solution under domain uncertainty. We show that these QMC rules exhibit dimension-independent, essentially linear cubature convergence rates in this framework. In addition, we complete the error analysis by taking into account the approximation errors incurred by dimension truncation of the random input field and finite element discretization. Numerical experiments are presented to confirm the theoretical rates.

Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in system identification remains limited, and existing architectures lack formal stability guarantees that globally preclude unstable modes. We address this gap by introducing an EBM framework for system identification with stable, dissipative, absorbing invariant dynamics. Unlike classical global Lyapunov stability, absorbing invariance expands the class of stability-preserving architectures, enabling more flexible and expressive EBMs. We extend EBM theory to nonsmooth activations by establishing negative energy dissipation via Clarke derivatives and deriving new conditions for radial unboundedness, exposing a stability-expressivity tradeoff in standard EBMs. To overcome this, we introduce a hybrid architecture with a dynamical visible layer and static hidden layers, prove absorbing invariance under mild assumptions, and show that these guarantees extend to port-Hamiltonian EBMs. Experiments on metric-deformed multi-well and ring systems validate the approach, showcasing how our hybrid EBM architecture combines expressivity with sound and provable safety guarantees by design.

We report observations of solar wind turbulence derived from measurements by the Parker Solar Probe. Our findings reveal the emergence of finite magnetic helicity within the transition range of the turbulence, aligning with signatures of kinetic Alfv\'en waves (KAWs). Notably, as the wave scale transitions from super-ion to sub-ion scales, the ratio of KAWs with opposing signs of magnetic helicity initially increases from approximately 1 to 6 before returning to 1. This observation provides, for the first time, compelling evidence for the transition from imbalanced kinetic Alfv\'enic turbulence to balanced kinetic Alfv\'enic turbulence.

Context. Radiation plays a significant role in solar and astrophysical environments as it may constitute a sizeable fraction of the energy density, momentum flux, and the total pressure. Modelling the dynamic interaction between radiation and magnetized plasmas in such environments is an intricate and computationally costly task. Aims. The goal of this work is to demonstrate the capabilities of the open-source parallel, block-adaptive computational framework MPI-AMRVAC, in solving equations of radiation-magnetohydrodynamics (RMHD), and to present benchmark test cases relevant for radiation-dominated magnetized plasmas. Methods. The existing magnetohydrodynamics (MHD) and flux-limited diffusion (FLD) radiative-hydrodynamics physics modules are combined to solve the equations of radiation-magnetohydrodynamics (RMHD) on block-adaptive finite volume Cartesian meshes in any dimensionality. Results. We introduce and validate several benchmark test cases such as steady radiative MHD shocks, radiation-damped linear MHD waves, radiation-modified Riemann problems and a multi-dimensional radiative magnetoconvection case. We recall the basic governing Rankine-Hugoniot relations for shocks and the dispersion relation for linear MHD waves in the presence of optically thick radiation fields where the diffusion limit is reached. The RMHD system allows for 8 linear wave types, where the classical 7-wave MHD picture (entropy and three wave pairs for slow, Alfven and fast) is augmented with a radiative diffusion mode. Conclusions. The MPI-AMRVAC code now has the capability to perform multidimensional RMHD simulations with mesh adaptation making it well-suited for larger scientific applications to study magnetized matter-radiation interactions in solar and stellar interiors and atmospheres.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

In this work we update the L-Galaxies semi-analytic model (SAM) to better follow the physical processes responsible for the growth of bulges via disc instabilities (leading to pseudo-bulges) and mergers (leading to classical bulges). We address the former by considering the contribution of both stellar and gaseous discs in the stability of the galaxy, and we update the latter by including dissipation of energy in gas-rich mergers. Furthermore, we introduce angular momentum losses during cooling and find that an accurate match to the observed correlation between stellar disc scale length and mass at z ~ 0.0 requires that the gas loses 20% of its initial specific angular momentum to the corresponding dark matter halo during the formation of the cold gas disc. We reproduce the observed trends between the stellar mass and specific angular momentum for both disc- and bulge-dominated galaxies, with the former rotating faster than the latter of the same mass. We conclude that a two-component instability recipe provides a morphologically diverse galaxy sample which matches the observed fractional breakdown of galaxies into different morphological types. This recipe also enables us to obtain an excellent fit to the morphology-mass relation and stellar mass function of different galactic types. Finally, we find that energy dissipation during mergers reduces the merger remnant sizes and allows us to match the observed mass-size relation for bulge-dominated systems.

Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. Particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to magnetic field can play an important, if not dominant role. In this study, we carry out 2D fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameter sigma_0=20, we find that the injection energy {varepsilon}_{rm inj} converges with increasing domain size to {varepsilon}_{rm inj}simeq 10m_ec^2. In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_parallel) and perpendicular (W_perp) electric fields during both the injection phase and the post-injection phase. We find that during the injection phase, the W_perp contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, both components contribute equally during the post-injection phase, insensitive to the domain size. For high energy ({varepsilon}varepsilon_{rm inj}) particles, W_perp dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

Using solar-cycle long helioseismic measurements of meridional and zonal flows in the near-surface shear layer (NSSL) of the Sun, we study their spatio-temporal variations and connections to active regions. We find that near-surface inflows towards active latitudes are part of a local circulation with an outflow away from them at depths around 0.97 R, which is also the location where the deviations in the radial gradient of rotation change sign. These results, together with opposite-signed changes over latitude and depth in the above quantities observed during the solar minimum period, point to the action of the Coriolis force on large-scale flows as the primary cause of changes in the rotation gradient within the NSSL. We also find that such Coriolis force-mediated changes in near-surface flows towards active latitudes only marginally change the amplitude of zonal flow and hence are not likely to be its driving force. Our measurements typically achieve a high signal-to-noise ratio (>5σ) for near-surface flows but can drop to 3σ near the base (0.95 R) of the NSSL. Close agreements between the depth profiles of changes in rotation gradient and in meridional flows measured from quite different global and local helioseismic techniques, respectively, show that the results are not dependent on the analysis techniques.

This study uses plasma-profile data from the EUROfusion pedestal database, focusing on the electron-temperature and electron-density profiles in the edge region of H-mode ELMy JET ITER-Like-Wall (ILW) pulses. We make systematic predictions of the electron-temperature pedestal, using the density profiles and engineering parameters of the pulses as inputs. We first present a machine-learning algorithm that, given more inputs than theory-based modelling and 80\% of the database as training data, can reconstruct the remaining 20\% of temperature profiles within 20\% of the experimental values, including accurate estimates of the pedestal width and location. The most important engineering parameters for these predictions are magnetic field strength, particle fuelling rate, plasma current, and strike-point configuration. This confirms the potential of accurate pedestal prediction using large databases. Next, we take a simple theoretical approach assuming a local power-law relationship between the gradients of density (R/L_{n_e}) and temperature (R/L_{T_e}): R/L_{T_e}=Aleft(R/L_{n_e}right)^α with αapprox 0.4 fits well in the steep-gradient region. When A and α are fit independently for each pedestal, a one-to-one correlation emerges, also valid for JET-C data. For α= 1, A equiv η_e, a known control parameter for turbulence in slab-ETG theory. Measured values of η_e in the steep-gradient region lie well above the slab-ETG stability threshold, suggesting a nonlinear threshold shift or a supercritical turbulent state. Finally, we test heat-flux scalings motivated by gyrokinetic simulations, and we provide best-fit parameters for reconstructing JET-ILW pedestals. These models require additional experimental inputs to reach the accuracy of the machine-learning reconstructions.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of boundary effects, both on the (small) scale of the wavelength, are observed: one at the boundaries of the slab, and one inside the domain. The former impact the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

Recent flow cessation experiments on soft materials have shown a counter-intuitive non-monotonic relaxation of the shear stress: following the switch-off of a steady imposed shear flow, the stress initially decays before later increasing again. By simulating the soft glassy rheology model in a form extended to allow steady state shear banding, we show that the presence of shear bands prior to flow cessation can give rise to this phenomenon. We give a mechanistic understanding of the basic physics involved, in terms of (i) the decay of the shear bands after flow cessation, and (ii) the evolution of frustrated local stresses, governed by different time scales for plastic relaxation in each band. In particular, an elastic recoil in the unsheared band gives rise to negative local frustrated stresses, the slow release of which can cause an increase in macroscopic stress. Given that shear banding and frustrated local stresses arise widely across disordered soft solids, we argue that non-monotonic stress relaxation after flow cessation may occur in many different materials.

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Ferrofluids show unusual hydrodynamic effects due to the magnetic nature of their constituents. For increasing magnetization a classical ferrofluid undergoes a Rosensweig instability and creates self-organized ordered surface structures or droplet crystals. A Bose-Einstein condensate with strong dipolar interactions is a quantum ferrofluid that also shows superfluidity. The field of dipolar quantum gases is motivated by the search for new phases that break continuous symmetries. The simultaneous breaking of continuous symmetries like the phase invariance for the superfluid state and the translational symmetry for a crystal provides the basis of novel states of matter. However, interaction-induced crystallization in a superfluid has not been observed. Here we use in situ imaging to directly observe the spontaneous transition from an unstructured superfluid to an ordered arrangement of droplets in an atomic dysprosium Bose-Einstein condensate. By utilizing a Feshbach resonance to control the interparticle interactions, we induce a finite-wavelength instability and observe discrete droplets in a triangular structure, growing with increasing atom number. We find that these states are surprisingly long-lived and measure a hysteretic behaviour, which is typical for a crystallization process and in close analogy to the Rosensweig instability. Our system can show both superfluidity and, as shown here, spontaneous translational symmetry breaking. The presented observations do not probe superfluidity in the structured states, but if the droplets establish a common phase via weak links, this system is a very good candidate for a supersolid ground state.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

We explore a minimal scenario where the sole Standard-Model Higgs is responsible for reheating the Universe after inflation, produces a significant background of gravitational waves and maintains the full classical stability of the electroweak vacuum. As the Higgs self-coupling runs toward negative values at high energy scales, a non-minimal interaction with curvature during a stiff background expansion era drives the Higgs fluctuations closer to the instability scale. This curvature-induced tachyonic instability leads to an intense production of Higgs particles, accompanied by a stochastic gravitational-wave background. The characteristic features of such signal can be directly correlated to the inflationary scale, the non-minimal coupling parameter and the top quark Yukawa coupling. We distinguish between three possible scenarios: absolute stability with low top quark masses, potential vacuum instability, and absolute stability with new physics above the instability scale. Our findings suggest that the detection of a peaked background of gravitational waves together with its inflationary tail has the potential to unveil the features of the Higgs effective potential at very high energy scales while providing a minimal explanation for the reheating phase and the emergence of the Standard-Model plasma in the early Universe. Unlike other studies in the literature, the generation of gravitational waves in our scenario does not depend on the quantum instability of the Standard Model vacuum.

Gravitational waves from asymmetric mass-ratio black-hole binaries carry unique information about their astrophysical environment. For instance, the Laser Interferometer Space Antenna (LISA) could potentially measure the amplitude and slope of gas torques in binaries embedded in the accretion disks of Active Galactic Nuclei, helping differentiate competing accretion disk models. However, this relies on simplified analytic models, which do not account for the stochastic variability of torques seen in hydrodynamic simulations. In this work, we use hydrodynamic simulations to create gravitational waveforms for extreme and intermediate mass-ratio inspirals in the LISA band. We then analyze these simulated waveforms using simpler templates that assume analytic torques, without stochastic time variability. By performing realistic Bayesian parameter estimation, we find no bias at 90% confidence in the binary parameters; however, estimates of accretion disk parameters, such as torque amplitude and slope, may be biased. Typically, the posterior distribution is centered around the average value of the torques, but when stochastic variability is large, the posterior can indicate no torques, even though they are present in the simulation. Our results suggest that while simplified analytic torque models work well for estimating binary parameters, caution is needed when using them to infer properties of the accretion disk. This work moves towards a more realistic assessment of one of the LISA science objectives, i.e., probing the properties of the astrophysical environments of black holes.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4+1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents a nonlinear model reduction method that employs lifting variable transformations to derive structure-preserving quadratic reduced-order models for conservative PDEs with general nonlinearities. We present an energy-quadratization strategy that defines the auxiliary variable in terms of the nonlinear term in the energy expression to derive an equivalent quadratic lifted system with quadratic system energy. The proposed strategy combined with proper orthogonal decomposition model reduction yields quadratic reduced-order models that conserve the quadratized lifted energy exactly in high dimensions. We demonstrate the proposed model reduction approach on four nonlinear conservative PDEs: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, the two-dimensional Klein-Gordon equation with parametric dependence, and the two-dimensional Klein-Gordon-Zakharov equations. The numerical results show that the proposed lifting approach is competitive with the state-of-the-art structure-preserving hyper-reduction method in terms of both accuracy and computational efficiency in the online stage while providing significant computational gains in the offline stage.

Sunspots survive on the solar surface for time-scales ranging from days to months. This requires them to be in an equilibrium involving magnetic fields and hydrodynamic forces. Unfortunately, theoretical models of sunspot equilibrium are very simplified as they assume that spots are static and possess a self-similar and axially symmetric magnetic field. These assumptions neglect the role of small scale variations of the magnetic field along the azimuthal direction produced by umbral dots, light bridges, penumbral filaments, and so forth. We aim at studying whether sunspot equilibrium is maintained once azimuthal fluctuations in the magnetic field, produced by the sunspot fine structure, are taken into account. To this end we apply the FIRTEZ Stokes inversion code to spectropolarimetric observations to infer the magnetic and thermodynamic parameters in two sunspots located at disk center and observed with two different instruments: one observed from the ground with the 1.5-meter German GREGOR Telescope and another with the Japanese spacecraft Hinode. We compare our results with three dimensional radiative magnetohydrodynamic simulations of a sunspot carried out with the MuRAM code. We infer clear variations in the gas pressure and density of the plasma directly related to fluctuations in the Lorentz force and associated with the filamentary structure in the penumbra. Similar results are obtained in the umbra despite its lack of observed filamentary structure. Results from the two observed sunspots are in excellent qualitative and quantitative agreement with the numerical simulations. Our results indicate that the magnetic topology of sunspots along the azimuthal direction is very close to magnetohydrostatic equilibrium, thereby helping to explain why sunspots are such long-lived structures capable of surviving on the solar surface for days or even full solar rotations.

We study the response of mono-energetic stellar populations with initially isotropic kinematics to impulsive and adiabatic changes to an underlying dark matter potential. Half-light radii expand and velocity dispersions decrease as enclosed dark matter is removed. The details of this expansion and cooling depend on the time scale on which the underlying potential changes. In the adiabatic regime, the product of half-light radius and average velocity dispersion is conserved. We show that the stellar populations maintain centrally isotropic kinematics throughout their adiabatic evolution, and their densities can be approximated by a family of analytical radial profiles. Metallicity gradients within the galaxy flatten as dark matter is slowly removed. In the case of strong impulsive perturbations, stellar populations develop power-law-like density tails with radially biased kinematics. We show that the distribution of stellar binding energies within the dark matter halo substantially widens after an impulsive perturbation, no matter the sign of the perturbation. This allows initially energetically separated stellar populations to mix, to the extent that previously chemo-dynamically distinct populations may masquerade as a single population with large metallicity and energy spread. Finally, we show that in response to an impulsive perturbation, stellar populations that are deeply embedded in cored dark matter halos undergo a series of damped oscillations before reaching a virialised equilibrium state, driven by inefficient phase mixing in the harmonic potentials of cored halos. This slow return to equilibrium adds substantial systematic uncertainty to dynamical masses estimated from Jeans modeling or the virial theorem.

Corotating Interaction Regions (CIRs) are recurring structures in the solar wind, characterized by interactions between fast and slow solar wind streams that compress and heat plasma. This study investigates the polytropic behavior of distinct regions in and around CIRs: uncompressed slow solar wind, compressed slow solar wind, compressed fast solar wind, and uncompressed fast solar wind. Using Wind spacecraft data and an established methodology for calculating the polytropic index ({\gamma}), we analyze 117 CIR events. Results indicate varying {\gamma} values across regions, with heating observed in compressed regions driven by Alfv\'en wave dissipation originating from fast streams. In the uncompressed fast solar wind, {\gamma} exceeds adiabatic values the most and correlates well with strong Alfv\'enic wave activity.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

A primary challenge in using neural networks to approximate nonlinear dynamical systems governed by partial differential equations (PDEs) is transforming these systems into a suitable format, especially when dealing with non-linearizable dynamics or the need for infinite-dimensional spaces for linearization. This paper introduces DyMixOp, a novel neural operator framework for PDEs that integrates insights from complex dynamical systems to address this challenge. Grounded in inertial manifold theory, DyMixOp transforms infinite-dimensional nonlinear PDE dynamics into a finite-dimensional latent space, establishing a structured foundation that maintains essential nonlinear interactions and enhances physical interpretability. A key innovation is the Local-Global-Mixing (LGM) transformation, inspired by convection dynamics in turbulence. This transformation effectively captures both fine-scale details and nonlinear interactions, while mitigating spectral bias commonly found in existing neural operators. The framework is further strengthened by a dynamics-informed architecture that connects multiple LGM layers to approximate linear and nonlinear dynamics, reflecting the temporal evolution of dynamical systems. Experimental results across diverse PDE benchmarks demonstrate that DyMixOp achieves state-of-the-art performance, significantly reducing prediction errors, particularly in convection-dominated scenarios reaching up to 86.7\%, while maintaining computational efficiency and scalability.

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique H^s- energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and Marchand for the dissipative SQG equation are not necessarily unique. Second, this establishes nonuniqueness below the Ladyzhenskaya-Prodi-Serrin class for the 2D Navier-Stokes equation, as well as below the Constantin-Wu and Dong-Chen-Zhao-Liu classes for the dissipative SQG equation.

We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput comparable to legacy static implementations while retaining high-level flexibility. We investigate the Laplacian growth instability across varying injection geometries and walker concentrations. Our analysis confirms the robustness of the standard fractal dimension D_f approx 1.71 for dilute regimes, consistent with the Witten-Sander universality class. However, we report a distinct crossover to Eden-like compact growth (D_f approx 1.87) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized Rényi dimensions and lacunarity metrics to quantify the monofractal character and spatial heterogeneity of the aggregates. This work establishes a reproducible, open-source testbed for exploring phase transitions in non-equilibrium statistical mechanics.

In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and 2, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler fluids.

The transfer of a star's angular momentum to its atmosphere is a topic of considerable and wide-ranging interest in astrophysics. This letter considers the effect of kinetic and magnetic turbulence on the solar wind's angular momentum. The effects are quantified in a theoretical framework that employs Reynolds-averaged mean field magnetohydrodynamics, allowing for fluctuations of arbitrary amplitude. The model is restricted to the solar equatorial (\(r-\phi\)) plane with axial symmetry, which permits the effect of turbulence to be expressed in analytical form as a modification to the classic Weber & Davis (1967) theory, dependent on the \(r,\phi\) shear component of the Reynolds stress tensor. A solar wind simulation with turbulence transport modeling and Parker Solar Probe observations at the Alfv\'en surface are employed to quantify this turbulent modification to the solar wind's angular momentum, which is found to be ~ 3% - 10% and tends to be negative. Implications for solar and stellar rotational evolution are discussed.

We consider the convected Helmholtz equation modeling linear acoustic propagation at a fixed frequency in a subsonic flow around a scattering object. The flow is supposed to be uniform in the exterior domain far from the object, and potential in the interior domain close to the object. Our key idea is the reformulation of the original problem using the Prandtl--Glauert transformation on the whole flow domain, yielding (i) the classical Helmholtz equation in the exterior domain and (ii) an anisotropic diffusive PDE with skew-symmetric first-order perturbation in the interior domain such that its transmission condition at the coupling boundary naturally fits the Neumann condition from the classical Helmholtz equation. Then, efficient off-the-shelf tools can be used to perform the BEM-FEM coupling, leading to two novel variational formulations for the convected Helmholtz equation. The first formulation involves one surface unknown and can be affected by resonant frequencies, while the second formulation avoids resonant frequencies and involves two surface unknowns. Numerical simulations are presented to compare the two formulations.

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. {For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner.} The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

A faster than real time forecast system for solar wind and interplanetary magnetic field transients that is driven by hourly updated solar magnetograms is proposed to provide a continuous nowcast of the solar corona (<0.1AU) and 24-hours forecast of the solar wind at 1 AU by solving a full 3-D MHD model. This new model has been inspired by the concept of relativity of simultaneity used in the theory of special relativity. It is based on time transformation between two coordinate systems: the solar rest frame and a boosted system in which the current observations of the solar magnetic field and tomorrow's measurement of the solar wind at 1 AU are simultaneous. In this paper we derive the modified governing equations for both hydrodynamics (HD) and magnetohydrodynamics (MHD) and present a new numerical algorithm that only modifies the conserved quantities but preserves the original HD/MHD numerical flux. The proposed method enables an efficient numerical implementation, and thus a significantly longer forecast time than the traditional method.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

We prove existence of weak and strong solutions and uniqueness for a viscous dyadic model driven by additive white noise in time using a path-wise approach. Existence of invariant measures also established and a simple balance relation among the mean rates of energy injection, dissipation and flux is derived and we investigate the asymptotic exponents zeta_{p} of the p-order structure functions.

I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for this system given bounded initial data. In particular, this shows that the model does not allow for thermal blow-up. If the initial temperature and fuel density also satisfy certain integrability conditions, the L^2-norms of these global solutions are uniformly bounded in time. Additionally, I use a bootstrap argument to show that small initial temperatures give rise to solutions that decay to zero as time goes to infinity, proving the existence of initial states that do not develop into travelling combustion waves.

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the extreme near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the near-contact limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the capsize determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

We present the first general-relativistic resistive magnetohydrodynamics simulations of self-consistent, rotating neutron stars with mixed poloidal and toroidal magnetic fields. Specifically, we investigate the role of resistivity in the dynamical evolution of neutron stars over a period of up to 100 ms and its effects on their quasi-equilibrium configurations. Our results demonstrate that resistivity can significantly influence the development of magnetohydrodynamic instabilities, resulting in markedly different magnetic field geometries. Additionally, resistivity suppresses the growth of these instabilities, leading to a reduction in the amplitude of emitted gravitational waves. Despite the variations in magnetic field geometries, the ratio of poloidal to toroidal field energies remains consistently 9:1 throughout the simulations, for the models we investigated.

Despite the increasing availability of high-performance computational resources, Reynolds-Averaged Navier-Stokes (RANS) simulations remain the workhorse for the analysis of turbulent flows in real-world applications. Linear eddy viscosity models (LEVM), the most commonly employed model type, cannot accurately predict complex states of turbulence. This work combines a deep-neural-network-based, nonlinear eddy viscosity model with turbulence realizability constraints as an inductive bias in order to yield improved predictions of the anisotropy tensor. Using visualizations based on the barycentric map, we show that the proposed machine learning method's anisotropy tensor predictions offer a significant improvement over all LEVMs in traditionally challenging cases with surface curvature and flow separation. However, this improved anisotropy tensor does not, in general, yield improved mean-velocity and pressure field predictions in comparison with the best-performing LEVM.