In this work, we investigate the possibility of suppressing injection-driven, viscous fingering instabilities in a radial Hele-Shaw cell, via the action of centrifugal forces. We consider the situation in which an inviscid fluid of negligible density is injected into a viscous and denser one, while the entire cell is rotated with constant angular velocity. Linear stability theory indicates that injection is destabilizing, while rotation tends to stabilize the expanding interface. Two linear stability criteria are proposed to determine a critical angular velocity required to stabilize the interface. The first criterion is based on a standard wavelength selection procedure, and maximizes the linear growth. A second criterion relies on the maximum of the interfacial perturbation amplitudes. Our linear stability findings indicate that the perturbation amplitude-based criterion provides a more robust condition for thorough interface stabilization. To explore the complete nonlinear dynamics of the system, and to verify the efficacy of our angular velocity-based controlling criteria, we perform fully numerical simulations, based on the level set method. Our numerical simulations show that the conventional growth-rate-based criterion is unsuccessful to predict the critical stabilizing angular velocity. On the other hand, our numerical findings validate the maximum-amplitude criterion as a proper and accurate controlling mechanism for suppressing viscous fingering. In this way, our fully nonlinear numerical results do substantiate our analytical linear stability predictions.

The interaction between flexible bodies and fluids is very complex, however, studying this mechanism helps us understand how natural plants deform in response to fluid flow to prevent structural damage. Due to the complexity of fluid-structure interaction, there is a lack of methods for quickly and quantitatively calculating the deformation and drag of flexible body systems. In this paper, the principles of variational methods are used to solve for the deformation shape and drag of a flexible fiber in a flowing fluid. The deformation shape of the fiber is treated as the primary unknown, leading to the derivation of an approximate variational equation. The results are in good agreement with those obtained from CFD methods, while requiring fewer computational resources. In terms of specific methods, the differential equation corresponding to the steady-state solution of this problem is transformed into an approximate variational equation, and parameters are adjusted by comparing it with the results of numerical simulation. Some quantitative theoretical solutions are provided, and the relevant laws are summarized. The law of drag variation is described through dimensionless velocity and drag. It is found that the nonconstant-cross-section stiffness fiber with thick fixed ends and slender free ends is more effective in preventing structural damage when facing incoming flow compared with the constant-cross-section stiffness fiber. This is manifested by the reduction of maximum stress and the movement of the position of maximum stress with the flow velocity.

The ion flux direction in a rapidly diverging magnetic field and the role of Earth's magnetic field in plasma dynamics are investigated experimentally using a low power electron cyclotron resonance thruster. The comparison between ion trajectories measured with a directional Faraday cup and the magnetic field geometry allows us to assess some of the ion flow properties. The results show that the ion trajectories follow the magnetic field lines in the center part of the plasma plume but not on its edges, defining the detachment location. Once detached, ions follow straight line trajectories, and their detachment has a divergent nature. The effect of the thruster operating condition on these properties is explored. Plasma potential measurements carried out with an emissive probe reveal the presence of a large radial electric field, pointing outward at the detachment point, that explains the divergent nature of the ion detachment. The amplitude of the induced $\mathbf{E}\times \mathbf{B}$ drift rotation of the electrons in the nozzle damps the disymmetrizing influence of Earth's magnetic field on the electron dynamics and leads to an axisymmetric plasma plume. This mechanism is demonstrated using single particle simulations.

We present experimental results of dust mobilization on a solid surface under an electron beam with grazing incidence. When the electron beam energy has a secondary electron yield greater than 1, dust particles move in the opposite direction of the electron beam. This is caused by asymmetric charging between the beam-facing and beam-shadowed sides of the particles. On the beam-facing side, the microcavity between a dust particle and the substrate surface collects beam electrons and emits beam-induced secondary electrons. In contrast, on the beam-shadowed side, the microcavity mainly collects secondary electrons. It is shown that the charge magnitude on the beam-shadowed side is larger than that on the beam-facing side, resulting in a net repulsive force pointing in the opposite direction of the beam to move the particle. When the beam energy has a secondary electron yield smaller than 1, the beam-facing side charged by primary beam electrons and the beam-shadowed side charged by backscattered beam electrons reach a similar potential close to the beam energy, resulting in the dust particles moving in random directions. These experimental results show agreement with particle-in-cell simulations.

Tensor networks are one of the best available tools to study many-body quantum systems. Tensor networks are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two aspects: the limitation in expressive power and the approximate extraction of information. Here we investigate the performance of the superposition-of-product-states (SPS) ansatz, a variational framework structurally related to canonical polyadic tensor decomposition. While the ansatz is generally not as expressive as tensor networks, it has the properties that it (i) is structurally independent of the geometry of the system, (ii) allows accurate extraction of information, (iii) is readily parallelizable, and (iv) allows analytical shortcuts. We first study the typical properties of the SPS ansatz for spin-$\frac{1}{2}$ systems, including its entanglement entropy and its trainability. We then use this ansatz for a ground-state search in tilted Ising models, including one-dimensional and three-dimensional models with short- and long-range interaction, and a random network, demonstrating that the SPS ansatz can attain high accuracy.

We study the zero-temperature quasistatically driven dynamics of the random field Blume-Emery-Griffiths model (RFBEGM) as a minimal framework to investigate the consequences of violating the no-passing property in driven disordered systems. While the random field Ising model obeys no-passing and displays Abelian relaxation dynamics, we show that this property is generically violated in the RFBEGM. By systematically exploring the full parameter space of the fully connected model, we identify the regimes in which no-passing is broken and demonstrate that, when this violation is combined with frustration induced by a repulsive biquadratic coupling, it leaves a clear dynamical signature. Specifically, the distribution of the minimal field increment required to trigger successive avalanches develops a discontinuity that is absent both in no-passing dynamics and in unfrustrated no-passing-violating regimes. We provide analytical arguments that locate the onset of this discontinuity, in excellent agreement with numerical simulations. Our results establish this discontinuity as a robust diagnostic of frustration-induced blocking in non-Abelian avalanche dynamics within a mean-field setting, without making claims about new universality classes.

Nonequilibrium dynamics play an important role in all contexts of physics, both classical and quantum as well as living and nonliving, so it is crucial to develop a foundational understanding of nonequilibrium phase transitions. In this work we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular we study how nonreciprocal coupling between two $O\left(n_i\right)$ order parameters (with $i=1,2$) affects the universality at a multicritical point, extending the analysis of J. T. Young et al. [Phys. Rev. X 10, 011039 (2020)], which considered the case $n_1=n_2=1$, i.e., a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of $n_1,n_2$ and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically relevant regimes of $n_1,n_2$, but not others, depending on whether the critical exponent $\nu$ is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Finally, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ model, which becomes nonperturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.

In this work we investigate the diffusion of a particle governed by a generalized Langevin equation subjected to active external stochastic forces. We derive the time-dependent diffusion coefficient and a generalized form of the Kubo relation that accounts for the presence of external noise, offering a broader framework for analyzing nonequilibrium stochastic systems. Based on this result, we obtain a simple and general criterion to determine whether the particle exhibits normal diffusion, subdiffusion, or superdiffusion. Our approach enables the determination of the asymptotic behavior of the diffusion coefficient based solely on the properties of the memory kernel and external noise. To illustrate the utility of this method, we apply it to three representative cases, obtaining the long-time behavior of the mean-square displacement, and from the diffusion exponent we get the diffusion regime diagram, including remarkably a region of fast superdiffusion.

The interplay between noise and higher-order interactions shapes collective dynamics in complex systems. While noise is traditionally regarded as a disordering force, this study demonstrates its dual role in the Kuramoto model with simplicial complexes. By extending the Ott-Antonsen reduction to the stochastic domain, a low-dimensional mean-field theory is developed, yielding an exact effective potential landscape. This framework reveals that common pairwise-interaction noise acts constructively, creating a concave potential correction that enhances synchronization and significantly expands the bistable region. In contrast, the impact of higher-order interaction noise is strictly gated by the pairwise coupling, creating a singularity at incoherence that either expands the bistable region or structurally protects the pure synchronized state. Furthermore, the mechanism of noise-induced explosive synchronization is quantified via mean first-passage time theory, identifying the transition as a timescale competition between barrier crossing and observation window. These findings provide a thermodynamic framework for understanding noise-controlled switching in higher-order networks, demonstrating how noise, by reshaping the effective potential, governs synchronization transitions and enables abrupt ordering under certain conditions.

Phenomena including friction and earthquakes are complicated by the joint presence of disorder and nonlinear instabilities, such as those triggered by the presence of velocity weakening. In de Geus and Wyart [Phys. Rev. E 106, 065001 (2022)], we provided a theory for the nucleation of flow and the magnitude of hysteresis, building on recent results on disorder-free systems described by so-called rate-and-state descriptions of the frictional interface, and treating disorder perturbatively. This theory was tested for models of frictional interfaces, where long-range elastic interactions are present. Here we test it for short-range depinning, and confirm that (i) nucleation is triggered by avalanches, governed by a critical point at some threshold force $f_c$ close to the minimum of the flow curve and that (ii) due to an armoring mechanism by which the elastic manifold displays very little plasticity after a big slip event, very slowly decaying finite size effects dominate the hysteresis magnitude, with an exponent we can relate to other observables.

Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. Starting from critical configurations, such as the $\mathrm{O}\left(n\right)$ loop and fuzzy Potts models, successive coarse graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, we derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations.

We study the dynamics of a zero-temperature particle interacting linearly with a bath of hot Brownian particles. Starting with the most general model of a linearly coupled bath, we eliminate the bath degrees of freedom exactly to map the tracer dynamics onto a generalized Langevin equation, allowing for an arbitrary external potential on the tracer. We apply this result to determine the fate of a tracer connected by springs to $N$ identical bath particles or inserted within a harmonic chain of hot particles. In the former “fully connected” case, we find the tracer transitions between an effective equilibrium regime at large $N$ and a fluctuation-dissipation theorem (FDT)-violating regime at finite $N$, while in the latter “loop” model the tracer never satisfies an FDT. We then study the fully connected model perturbatively for large but finite $N$, demonstrating signatures of irreversibility such as ratchet currents, non-Boltzmann statistics, and positive entropy production. Finally, we specialize to harmonic external potentials on the tracer, allowing us to exactly solve the dynamics of both the tracer and the bath for an arbitrary linear model. We apply our findings to show that a cold tracer in a hot lattice suppresses the fluctuations of the lattice in a long-ranged manner, and we generalize this result to linear elastic field theories.

We explore the application of the nonperturbative functional renormalization group (NPFRG), within its most common approximation scheme based on truncations of the derivative expansion, to the $Z_2$-symmetric scalar ${\phi }^4$ theory as the lower critical dimension $d_{\mathrm{lc}}$ is approached. We aim to assess whether the NPFRG—a broad, nonspecialized method which is accurate in $d\ge 2$—can capture the effect of the localized (droplet) excitations that drive the disappearance of the phase transition in $d_{\mathrm{lc}}$ and control the critical behavior as $d\to d_{\mathrm{lc}}$. We extend a prior analysis to the next (second) order of the derivative expansion to check the convergence of the results and the robustness of the conclusions. The study turns out to be much more involved. Through extensive numerical and analytical work we provide evidence that the convergence to $d_{\mathrm{lc}}$ is nonuniform in the field dependence and is characterized by the emergence of a boundary layer near the minima of the fixed-point effective potential. This is the mathematical mechanism through which the NPFRG within the truncated derivative expansion reproduces nontrivial features predicted by the droplet theory of Bruce and Wallace [Phys. Rev. Lett. 47, 1743 (1981); J. Phys. A: Math. Gen. 16, 1721 (1983)], namely, the existence of two distinct small parameters as $d\to d_{\mathrm{lc}}$ that control different aspects of the critical behavior and that are nonperturbatively related. The second order of the derivative expansion fixes several issues that were encountered at the lower level and improves the compatibility with the droplet-theory predictions.

We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of synchronization. Despite its simplicity, we postulate its relevance for understanding more complex and realistic oscillator systems. In the thermodynamic limit, the model exhibits a continuous nonequilibrium phase transition between the unsynchronized and synchronized states. We show that this transition is not governed by any extremum dissipation principle—depending on system parameters, synchronization may either reduce or enhance the dissipation. Close to the phase transition, we observe a divergent behavior of fluctuations and responses with $N$ and characterize their universal scaling behavior. In particular, the covariances of the oscillator phases and the local entropy productions are shown to diverge toward $-\infty$, a phenomenon that has not been reported before. Finally, we study the behavior of information-theoretic quantities, demonstrating that mutual information and information flow between oscillators display different scaling with $N$ in synchronized and unsynchronized states, and thus can act as order parameters of synchronization.

We present an elementary proof of the adiabatic theorem for Markov jump processes. This theorem, analogous to its quantum counterpart, states that a system starting from an instantaneous steady state remains in the instantaneous steady state if the transition rate matrix changes sufficiently slowly. Our approach adapts techniques from quantum adiabatic theorems while addressing the challenges posed by non-Hermitian dynamics. We highlight the unique properties of transition matrices that enable this proof, providing a more accessible foundation for understanding adiabatic behavior in Markov jump processes.

We analytically investigate the noise-driven response of a mechanical Duffing oscillator. Using a perturbative expansion within the Martin–Siggia–Rose–Janssen–De Dominicis path-integral formalism, we show that the fluctuation-dissipation theorem (FDT) extends to the nonlinear regime. Within renormalization theory and Feynman diagrammatic techniques, we derive the self-energy of the Duffing oscillator and the corresponding renormalized noise intensity, demonstrating the manifestation of the FDT in direct analogy with the linear oscillator. Furthermore, we illustrate how the Duffing nonlinearity enables the injection of energy by noise, allowing the excitation of higher harmonics.

Three-dimensional (3D), axisymmetric hoppers are widely used in industries for generating smooth outflow of granular materials from storage bins and it is well known that their discharge behavior is governed by the local dynamics at the orifice. Measuring the details of the outflow from a 3D hopper is challenging due to the fact that the flow is dense and the granular material is opaque. In this paper, x-ray tomography is used to image the cross section near the orifice opening. We investigate the vertical velocity, volume fraction, and particle orientations of spherical, oblate (lentil-shaped), and prolate (rice-shaped) particles for various hopper angles. We create a three-dimensional respresentation by time stacking the cross sections. We process these 3D images using standard image filtration techniques and propose simple experimental models to extract the velocity, volume fraction, and orientation angles of the particles based on their shape. We found that the hopper inclination influences both the velocity and volume fraction profiles in such a way that the magnitude of both profiles increases with increasing hopper inclination. Moreover, lentil-shaped particles achieve the highest velocity and pack more densely than the other two particles. In addition, the latter packed more orderly than the prolate (rice-shaped) particles. Finally, it is found that the independently measured experimental discharge rate has a good agreement with the discharge rate obtained from the velocity and volume fraction profiles for sphere and lentil-shaped particles.

The coercivity landscape for characterizing hysteresis in interacting systems across multiple timescales is proposed by Chen et al. in a companion paper [Phys. Rev. Lett. 136, 117102 (2026)]. For the stochastic ${\varphi }^4$ model under periodic driving of rate $v_H$, the coercivity landscape $H_c\left(v_H\right)$ exhibits plateau features at a characteristic rate $v_P$ with the corresponding coercivity $H_P$. Below this plateau ($v_H<v_P$), the $H_c\sim v_H$ scaling obtained in the near-equilibrium regime becomes inaccessible in the thermodynamic limit. Above the plateau ($v_H>v_P$), scaling in the fast-driving regime, $H_c\sim v_H^{1/2}$, is completely different from that, $H_c-H_P\sim {(v_H-v_P)}^{2/3}$, in the postplateau slow-driving regime. The emergence of the plateau with a finite-size scaling reflects the competition between the thermodynamic limit and the quasistatic limit. In this paper, we provide detailed analytical proofs and numerical evidence supporting these results. Moreover, to demonstrate the coercivity landscape in concrete physical systems, we study the magnetic hysteresis in the Curie-Weiss model and analyze its finite-size effects. We reveal that finite-time coercivity scaling shows model-specific behavior only in the fast-driving regime, while exhibiting universal characteristics elsewhere.

We explore the stationary densities and domain walls in the steady states of a pair of asymmetric exclusion processes (TASEPs) antiparallelly coupled to two particle reservoirs without any spatial extent by using the model of Haldar et al. [Phys. Rev. E 111, 014154 (2025)]. We show that the model admits a pair of delocalized domain walls, which exist for some choices of the model parameters that define the effective entry and exit rates into the TASEP lanes. Surprisingly, in the parameter space spanned by these model parameters, the region corresponding to delocalized domain walls covers an extended region, in contrast to the delocalized domain walls that appear only along a line in the relevant parameter space of the other known variants of TASEP. This implies large fluctuations in the TASEP particle numbers even in the thermodynamic limit that can be found over a range of the control parameters. The corresponding phase diagrams in the plane of the control parameters have different topology from those for an open TASEP or other models with multiple TASEPs connected to two reservoirs.