Alternating (temporally period-2) stripes, clusters, and labyrinths have been observed in chemical and biochemical reactions, in Min-protein dynamics in E. coli and in vitro systems, and in calcium alternans in cardiac myocytes. However, the mechanisms underlying the formation of these spatiotemporal patterns and the transitions among them remain incompletely understood. In this article, we use an amplitude-equation (AE) approach to perform theoretical analysis and numerical simulations to elucidate the mechanisms of the alternating pattern formation and selection, and we then use reaction-diffusion models to validate the predictions of the AE model. It was shown previously that in chemical reactions and cardiac myocytes, a global feedback loop plays a key role in the formation of alternating clusters. Based on previous AE models developed to describe cardiac alternans dynamics, we first develop an AE model that incorporates either a spatially uniform global feedback (UGF) loop or a spatially nonuniform global feedback (NUGF) loop. The NUGF is represented by a spatially Gaussian-weighted function. We then use the AE model to conduct nonlinear stability analysis to reveal the mechanisms underlying the emergence of alternating patterns under different feedback conditions. Under positive UGF, no patterns can form. When the UGF is negative, the stable patterns are only multiple stripes and circular clusters. For stripe patterns, they may be spatially periodic or random as long as they satisfy the requirements for pattern selection. For circular clusters, a medium can support one or multiple circular alternating clusters of the same radius depending on the size of the medium. Under NUGF, in addition to stripe and circular-cluster patterns, lateral instability arises when the width of the Gaussian function falls within an intermediate range, leading to transitions from stripes or circular clusters to labyrinths. Other initial-condition-dependent patterns are also observed under NUGF. Under UGF, the width of the stripe can be periodic or random, but under NUGF, the patterns become less random in space as the feedback strength increases. Finally, we incorporate the UGF and NUGF loops into several reaction-diffusion models, including the Belousov-Zhabotinsky reaction model, the carbon monoxide oxidation model, and the periodically paced FitzHugh-Nagumo model. These models successfully reproduce the alternating pattern dynamics predicted by the AE model, validating the theoretical predictions.

Swarmalators, a prototypical model that integrates temporal rhythms with spatial swarming, have been widely used to explore the collective dynamics observed in active-matter systems. Although numerical simulations have revealed a variety of collective states, a general theoretical framework for the stability and bifurcations of the states remains unavailable. Here, by the model of one-dimensional ring-structured swarmalators with general distributions of natural frequencies and velocities, we conduct a systematic theoretical analysis of the stability and bifurcations of four representative collective states observed in simulations: the desynchronization state, the phase-wave state, the synchronization state, and the mixed state. We show that the macroscopic dynamics are governed by a low-dimensional invariant manifold, namely the generalized Ott-Antonsen manifold, and further establish that the same manifold underlies the collective dynamics of high-dimensional agent models, thereby unifying these seemingly different descriptions within a common reduction framework. Building on this connection, we derive stability conditions and bifurcation boundaries for the collective states and construct a bifurcation diagram in the two-parameter coupling plane, with theoretical predictions validated by large-scale numerical simulations. Our results clarify the dynamical origins of state selection in swarmalator systems and provide a theoretical foundation for analyzing nonequilibrium phase transitions in active-matter systems with coupled internal rhythms and spatial motions.

Extracellular vesicles (EVs) hold great promise in drug delivery, disease diagnosis, and treatment; however, the inability to control EVs biogenesis critically limits their therapeutic and diagnostic potential. Although regulatory mechanisms for biochemical cues have been extensively studied, the principles governing how diverse mechanical cues from the extracellular microenvironment orchestrate EV secretion are poorly understood, hindering the development of scalable production strategies. Here, we resolve this by introducing a theoretical model that identifies membrane reservoir depletion as a universal biophysical switch for EV release. We discover that EV secretion is directly activated by the depletion of the membrane reservoir and the consequent rise in membrane tension. This tension-mediated mechanism provides a unifying framework that reconciles disparate experimental observations under various biophysical perturbations, including cell spreading, osmotic shock, contractile perturbation, and substrate stiffening. Furthermore, we identify the membrane reservoir size as a key intrinsic parameter setting the threshold for mechanical activation of EV secretion, offering a rationale for engineering high-yield producer cell lines. Our work thus establishes a unifying mechanochemical framework for EV secretion, explaining disparate experimental observations and providing a quantitative design principle for optimizing EV production.

Recent work [Phys. Rev. Lett. 134, 241901 (2025); Phys. Rev. D 112, 054506 (2025); Phys. Rev. D 112, 014514 (2025)] has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others [Eur. Phys. J. A 61, 26 (2025); Phys. Rev. D 112, 074506 (2025)]. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within Hermitian subspaces, including those arising in the decompositions of non-Hermitian operators describing noisy data. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger “Prony-Ritz equivalence class,” identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

Athermal systems such as granular materials exhibit reproducible volume fluctuations despite the absence of thermal equilibration, yet a quantitative statistical-mechanical description remains incomplete. Within the Edwards ensemble, volume replaces energy as the conserved quantity and compactivity provides Boltzmann-like weighting, but the form of the intrinsic configurational density of states and the origin of experimentally observed Gamma-like volume distributions have remained unresolved. Here, we show analytically and experimentally that the intrinsic density of states of jammed granular packings follows a Gamma distribution when expressed in terms of free volume. This shows that the widely observed Gamma form originates from the underlying structural statistics of mechanically stable configurations, rather than from the measured distribution itself. Incorporating this density of states into the Edwards ensemble yields a factorized description in which structure and thermodynamic weighting are explicitly separable. The framework provides closed-form predictions for the partition function, mean volume, fluctuations, compactivity, and entropy without fitting probability distributions. Large-scale x-ray tomography experiments confirm these predictions and demonstrate thermodynamic consistency with independent fluctuation- and histogram-based measurements. These results resolve the interpretation of Gamma volume distributions and establish a quantitative statistical-mechanical foundation for jammed granular matter.

Chiral liquid crystals and chiral magnets host a wide variety of topological solitons governed by closely related continuum theories, namely the Frank-Oseen model for liquid crystals and the Dzyaloshinskii model for chiral magnets. Here we exploit this correspondence to develop a unified theoretical description of cholesteric fingers in confined liquid crystals and their magnetic counterparts. Within a continuum framework including bulk and surface anisotropies, we analyze the topology, internal structure, interactions, and collective states of the two principal finger varieties, CF-1 and CF-2. We show that cholesteric fingers can be interpreted as composite chiral solitons built from meronic constituents. In particular, CF-2 corresponds to a bimeron with unit topological charge, whereas CF-1 represents a topologically trivial composite object formed by two merons with identical vorticities. From a homotopic viewpoint these textures correspond to skyrmions and droplets, respectively. Strong homeotropic surface anchoring induces pronounced confinement effects that reshape the meron structure and redistribute the topological charge across the film thickness. Despite their composite nature, isolated fingers embedded in the homogeneous state interact repulsively and behave as particle-like objects. Periodic finger phases emerge when the eigenenergy of an isolated finger becomes negative, giving rise to nucleation-type phase transitions with a diverging lattice period. The coexistence of several energetically degenerate finger varieties allows the formation of mixed periodic sequences whose number grows combinatorially and can be classified analogously to stacking polytypes in close-packed crystals. In contrast, when embedded in the conical background the interaction between fingers becomes attractive due to the overlap of distortion regions. Finally, we demonstrate that the film thickness strongly controls the stability and internal structure of cholesteric fingers. At small thickness the solitons collapse at a critical point where their internal topological structure disappears, whereas at large thickness isolated bimerons exhibit bistability between surface-stabilized and bulklike configurations. These results establish cholesteric fingers as experimentally accessible realizations of composite chiral solitons and highlight the deep correspondence between topological textures in chiral liquid crystals and chiral magnets.

We investigate multicomponent metallic glass systems using a hybrid molecular dynamics (MD) and variance-constrained semi-grand-canonical approach. This method enables us to generate samples with properties consistent with experimental observations, at deeply supercooled states that are typically inaccessible with conventional MD simulations. Using a realistic interatomic potential, we investigate the dynamics, kinetic stability, and rheology of a ZrCu(Al) metallic glass, together with the widely studied ZrCu system, in the low-temperature glassy regime. Our results demonstrate how the hybrid method enhances relaxation and provides a generic framework for modeling realistic complex metallic glasses.

The origin of chaos in quantum systems remains a central challenge in many-body physics. Here, we use the adiabatic gauge potential (AGP) as a tool to investigate the transition from integrability to chaos in the one-dimensional Holstein polaron model. By combining exact diagonalization with an analysis of eigenstate expectation values (EEVs) and the statistical properties of off-diagonal matrix elements, we provide a detailed characterization of thermalization indicators in this model. In the integrable regime, we observe distributions of EEVs and power-law decays of their outliers with system size, consistent with the breakdown of the eigenstate thermalization hypothesis (ETH). Notably, in the noninteracting limit, standard indicators of quantum chaos, such as the mean level spacing, fail to capture the absence of integrability breaking. As integrability is broken, the off-diagonal matrix elements exhibit Gaussian statistics with variances matching random-matrix predictions, while EEV fluctuations vanish rapidly, signaling the onset of quantum chaos. Our results establish the AGP, with matrix element statistics, as a framework to probe the crossover from integrability to chaos in electron-phonon coupled systems.

The statistical mechanics of particles that populate indistinguishable energy substates is explored. In particular, the mathematical treatment of microstates differs from conventional statistical mechanics, where, for a given degeneracy, the energy sublevels or substates are universally treated as distinguishable and differentiated by unique quantum numbers or addressed by distinct spatial locations. Results from combinatorial counting problems are adapted to derive exact distribution functions for both classical and quantum particles at a high degeneracy limit. Quantum particles obey a nonextensive entropy $\mathcal{S}\propto \sqrt{N}$ that satisfies the area law $\mathcal{S}\propto A$ in $d=2$ bulk spatial dimensions. Classical particles exhibit a definitive glass transition similar to supercooled liquids, for which the configurational entropy vanishes below a finite temperature $T_K$.

Twisted states commonly arise in nonlocally coupled ring networks. We study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics.

Synchronization in networks of coupled oscillators is a fundamental problem in the study of collective behavior. In this paper we investigate the synchronization transition in networks of coupled dynamical systems from an energetic perspective. Interactions between systems/oscillators are assumed to be governed by one of the following mechanisms: (i) the intrinsic energy $\mathbf{H}$, describing the conservative internal dynamics of isolated systems, and (ii) the dissipative energy $\dot{\mathbf{H}}$, accounting for energy losses and exchanges due to interactions and damping. An energetic threshold is introduced to modulate the network connectivity, so that the topology evolves in time according to the instantaneous energetic similarity between systems, allowing us to analyze how the balance between intrinsic and dissipative energy shapes the transition to synchronization. Using the Rössler and Lorenz systems as representative examples, while keeping the framework general and applicable to other dynamical systems, we explore three representative dynamical regimes: periodic, multiperiodic, and chaotic. This reveals that the nature of the synchronization transition strongly depends on the interplay between microscopic dynamics and the mesoscopic connectivity structure. In particular, chaotic oscillators coupled through intrinsic energy favor explosive synchronization, corresponding to a first-order transition, whereas periodic and multiperiodic dynamics lead to smooth second-order transitions. In contrast, dissipative-energy-based connectivity suppresses first-order transitions in chaotic networks but can induce second-order transition in multiperiodic systems. These findings show that explosive synchronization is not solely topology driven, as often emphasized in scale-free networks, but can also arise from an energy–dynamics–topology feedback controlled by local dynamical complexity and energy-based link activation. This work provides new insights into how internal oscillator dynamics and coupling mechanisms jointly shape collective organization and dynamical transition patterns in complex systems.

We develop a dissipation-based framework for earthquake rupture on homogeneous faults that explicitly separates the onset of unstable slip from the conditions required for self-sustained rupture propagation. This distinction explains the coexistence of self-arresting earthquakes and runaway ruptures (subshear and supershear events) observed in numerical simulations and empirical studies. We identify two distinct characteristic fault sizes: a nucleation radius controlling the instability of slip, and in general a larger propagation radius controlling whether an unstable rupture can be energetically sustained. Ruptures initiated above the nucleation scale but below the propagation scale spontaneously arrest. We further derive the Gutenberg-Richter law for self-arresting earthquakes by linking rupture physics to the fractal geometry of faulting. Finally, we interpret runaway ruptures as extreme events generated by an amplifying mechanism, consistent with the dragon-king concept. These results provide a unified physical basis for earthquake initiation, arrest, and seismicity statistics.

A mechanism for the biological effects of the hypomagnetic field is proposed, based on the rotational motion of a molecule as a whole within a cavity in an enzyme. It has been shown previously that a molecular rotator about 1 nm in size can have a decoherence time of up to tens of milliseconds. On shorter timescales, the nanorotator exists in a state of quantum superposition and exhibits interference effects. The statics and dynamics of the nanorotator in a magnetic field are analyzed using the Schrödinger and Liouville–von Neumann equations, taking into account chemical kinetics and thermal relaxation. It is demonstrated that the small-scale interference of the nanorotator is highly sensitive to weak magnetic fields. The quantum nanorotator shows magnetic effects ranging from a few to several tens of percent over a wide range of realistic decoherence rates. If the nanorotator constitutes an adequate model of rotating amino acid residues in the active sites of certain enzymes involved in protein synthesis, then weak magnetic fields can exert significant biological effects, leading to the observed phenomena.

Active proteins and membrane-bound motors exert force dipole flows along fluid interfaces and lipid bilayers. We develop a Hamiltonian framework for the interactions of pusher and puller dipoles embedded in an incompressible two-dimensional membrane supported by a shallow viscous subphase. Beginning from the Brinkman-regularized Stokes equations of the membrane-subphase system, we construct the near- and far-field dipolar velocity fields and associated stream functions. For two quenched (fixed orientation) dipoles, we obtain exact analytic solutions in both the near- and far-field regimes. Although generic dipoles reorient under local membrane vorticity, we show that the far-field dipolar flow is vorticity-free; force-free motors therefore retain fixed orientations and obey a position-based Hamiltonian dynamics in which the positions of $N$ dipoles evolve via an effective Hamiltonian built from the dipolar stream function. In the near field, where the flow possesses finite vorticity, a Hamiltonian formulation is recovered in the quenched-orientation limit. For identical dipoles, the far-field Hamiltonian produces rapid clustering from random initial conditions, whereas the near-field Hamiltonian suppresses collapse leading to nonaggregating configurations. Our work thus provides a concrete realization of a position-based Hamiltonian formulation for active particles in incompressible fluid membranes and shows that hydrodynamic screening can reorganize both the dynamical phase space and the collective organization of active dipoles.

We introduce a nonequilibrium thermodynamic (NET) framework for immiscible two-phase flow in porous media, in which the total flux of both phases is driven by the gradient of an effective pressure. We show that the classical two-phase Darcy formulation emerges as a projected limit of the full linear flux-force relations under steady-state saturation constraints, with cross-coupling terms arising naturally. Large-scale lattice Boltzmann simulations reveal that the full Onsager transport matrix remains symmetric at the fundamental level, while its reduced Darcy representation can appear asymmetric because the standard force-flux pairs are not independent. Projecting onto the physically admissible subspace restores reciprocity and recovers the total phase mobility from the main- and cross-coupling coefficients. These results resolve the long-standing debate over apparent violations of Onsager symmetry and establish Darcy's law as an emergent thermodynamic limit for multiphase porous-media flow.

Collisional dissipation is expected to be the primary damping mechanism for helicon waves in low-temperature, high-density, moderate magnetic field plasmas. Combining a normal-mode analysis with high-resolution magnetic field measurements, we validate this expectation across a broad parameter space. However, we identify a distinct regime where the measured helicon damping rate is reduced by nearly a factor of 2 compared with collisional predictions. In this regime, a second harmonic at $2\omega$ is observed, contributing about 10% to the total magnetic field amplitude. A weakly nonlinear perturbative analysis shows that this component results from a resonant three-wave coupling ($\omega +\omega \to 2\omega$) that feeds back on the fundamental, accounting for the apparent underdamping and defining a predictive interaction window in helicon devices. As a controlled realization of quadratic three-wave coupling in a magnetized plasma, these results illustrate how resonant harmonic generation can redistribute wave energy and modify effective linear damping.

In this paper, we address the problem of wave propagation within an unbounded time-modulated magnetized plasma in a Faraday configuration. We present an analysis formulated by coupling Maxwell's equations with the hydrodynamic evolution equation for the plasma current density, and casting the resulting system into a first-order state-space representation that governs the time evolution of the electromagnetic fields. This formulation shows that the temporal modulation of the magnetized plasma can lead to conversion of the polarization state. In addition, we extend our previously presented energy conservation framework to the case of time-modulated magnetized plasmas and show that energy conservation is satisfied when the collapse-source model introduced in our previous work is applied during the plasma decay phase.

We investigate radiation-induced drag, lift, and torque on circular Janus cylinders under transverse-magnetic plane-wave illumination, considering metallodielectric and purely dielectric configurations. The lattice Boltzmann method (LBM) is employed with absorption neglected, isolating scattering as the sole momentum-transfer mechanism. For metallodielectric Janus cylinders, analytical expressions for radiation force and torque are derived and used to validate the LBM, showing excellent agreement across a wide range of dielectric constants and interface orientations. For dielectric Janus cylinders, material inhomogeneity induces asymmetric scattering giving rise to nonzero lift and torque under plane-wave illumination, with nonmonotonic dependence on interface orientation and dielectric contrast. Two mechanisms govern the observed variations: resonance-driven energy amplification and scattered field redistribution. The computed force and torque maps serve as design diagrams for predicting the optomechanical response. Coupling these with viscous dynamics at low Reynolds number reveals diverse particle trajectories, including curved paths during reorientation and nearly straight motion once torque-free equilibria are reached. The system is externally actuated and results represent scattering-dominated dynamics under idealized conditions, providing physical insight into optomechanical responses of Janus particles with implications for trajectory shaping in optofluidic systems.

We describe the motions of an elastic chain submitted to an external periodic potential, without dissipation. Initially, the energy is injected in a single eigenmode of the chain. We show that this eigenmode acts as a parametric forcing of the other modes, and since there is no external energy source we speak of autoparametric forcing. If the chain is trapped in the potential well, then the motion of the center of mass is the lowest frequency mode. We show that this mode induces autoparametric resonances of the higher-frequency modes. We also exhibit specific conditions under which a mode of higher frequency induces autoparametric resonances of some other modes. Generically, a high-frequency mode in a trapped chain induces some coupling between other modes, with coupling coefficients that are periodic time functions. As a consequence, autoparametric internal resonances between one forcing mode and two forced modes take place under conditions on the relevant modes indices that we provide explicitly. When enough kinetic energy is injected into the motion of the center of mass for the chain to slide over the potential, we show that the basically translational motion of the chain may induce an autoparametric resonance of any vibrational mode of the chain. We also show that two modes can simultaneously display autoparametric resonance. Therefore, we generalize the notion of autoparametric resonance to systems of arbitrary size.

Despite extensive progress in characterizing the emergent behavior of active matter, the microscopic origins of self-diffusion in interacting active systems remain poorly understood. Here, we develop a framework that quantitatively links self-diffusion to collisional forces and their temporal correlations in active fluids. We show that transport is governed by two contributions: an equal-time suppression of motion arising from anisotropic collisional forces, and a memory correction associated with the temporal persistence of these forces. Together, these effects yield an exact expression for the self-diffusivity in terms of measurable force statistics and correlation times. We apply this framework to purely repulsive active Brownian particles and find that self-diffusion is always reduced as a function of packing fraction and activity. We identify the regimes in which equal-time force fluctuations and collisional memory dominate and how their relative contributions vary with activity and packing fraction. Our results establish a direct connection between microscopic force correlations and macroscopic transport, providing a general mechanical perspective for interpreting self-diffusion in active matter.