We investigate the competition between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices and their impact on transport and localization. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and temporal inhomogeneities are implemented via random variations of the quantum gate operations. By analyzing the return probability and the participation function, we identify that distinct quantum walking regimes such as the nonlinear parameter $\chi$ and the quantum gate parameter ${\theta }_0$ are varied. Spatial inhomogeneities weaken nonlinear self-trapping and constrict the region of robust localization. In this process, partially localized regimes emerge, characterized by the coexistence of a confined core and dispersive wave-packet components. In contrast, temporal inhomogeneities act as time-dependent perturbations that disrupt phase coherence and suppress nonlinear self-trapping, promoting dispersive spreading and delocalization. By using $\chi$ versus ${\theta }_0$ diagrams, we display a comprehensive characterization of how inhomogeneities modify the stability and extent of the prevailing dynamical regimes, elucidating the competition between nonlinearity and inhomogeneities in discrete-time quantum walks.

Classical models of collective behavior often assume that emergent dynamics result from external and observable interactions among individuals. However, how collective dynamics in human populations depend on the internal psychological processes of individuals remains underexplored. Here, we develop a mathematical model to investigate the effects of internal psychology on dynamics of collective action. Our model is grounded in the theory of planned behavior—a well-established conceptual framework in social psychology that links intrinsic beliefs to behavior. By incorporating temporal biases in social perception and individual differences in decision-making processes, we find that the interplay between internal and external drivers of behavior can produce diverse outcomes, ranging from partial participation in action-taking to rapid or delayed behavioral cascades. Predicting these outcomes is, in general, challenging because distinct outcomes can be preceded by transient dynamics that are qualitatively similar to one another. Nevertheless, in the case of two individuals, we derive a complete, analytical classification of long-term outcomes into three mutually exclusive categories. Our model provides a useful test bed for methods that aim to predict the emergence of collective action, and it lays the groundwork for studying the nuanced dynamics of collective human behavior arising from the interaction between psychological processes and observable actions.

Long QT syndrome is a potential fatal cardiac disease, whereas the mechanisms of arrhythmogenesis remain incompletely understood. In this study we use a modified FitzHugh-Nagumo model in inhomogeneous two-dimensional tissue to investigate spontaneous initiation of reentry to reveal their underlying dynamical mechanisms. We show multiple ways of spiral wave formation, depending on the bifurcation types and recovery kinetics. Through the study of pattern dynamics of inhomogeneous excitable medium, we elucidate the dynamics of spontaneous spiral wave initiation, providing mechanistic insights into arrhythmogenesis in long QT syndrome.

Active fluids, which consist of self-propelling constituent units, often exhibit viscoelastic behavior. Building upon the mean-field kinetic theory, we incorporate the Oldroyd-B constitutive equation to investigate the collective motion of active particles in a viscoelastic fluid inside a circular chamber. Specifically, by introducing both a viscoelastic stress term and an active stress term into the Navier-Stokes equations, we study spontaneous flow states and their transitions. Our results show that the addition of elasticity destabilizes the active suspension and thus promotes phase transitions. The influence of viscoelasticity is most pronounced in regimes that are critical for transitions in the Newtonian case. We further analyze the accumulation of particles near the wall and find that the viscoelastic environment enhances both the wall-directed swimming speed and the steady-state wall accumulation, which increases monotonically with the Deborah number. Extending the computational framework of Theillard et al. [Soft Matter 13, 363 (2017)], this study elucidates how viscoelastic stresses modulate collective motion under confinement and offers new insights into the behavior of active collective systems.

A common explanation for selecting the shape and size of coherent patterns based on the filtering nature of the linearized Navier-Stokes equations is investigated. The filtering properties are examined by generalized optimal perturbations. Computing generalized optimal perturbations with different structure norms in a homogeneous shear flow demonstrates that different generalized optimal perturbations take different structural forms, implying the existence of multiple filtering properties of the linearized Navier-Stokes operators dependent on the filter output. Subsequently, linear simulations with random initial conditions are conducted to further clarify the capability of generalized optimal perturbations in representing the multiple filtering properties. With nonlinearity not taken into consideration, generalized optimal perturbations well predict the temporal evolutions of structural characteristics of multiple flow patterns governed by the linearized Navier-Stokes operators, thereby offering a more refined description of the multiple filtering properties than the optimal perturbation framework. The capability of generalized optimal perturbations in describing the filtering nature of the linearized Navier-Stokes operators is further examined in real turbulence with nonlinearity taken into account. In addition to the spanwise streak spacing, comparing with the direct numerical simulation results reveals that the spanwise length scale of spanwise velocity patterns can also be well-captured by the corresponding generalized optimal perturbations. This supports the effectiveness and intuitiveness of generalized optimal perturbations in representing the selectivity of the linearized Navier-Stokes operators, which is essential in dictating some specific flow patterns in fully developed turbulence.

The lattice Boltzmann method (LBM) is commonly implemented in lattice units, requiring conversion procedures to relate simulation parameters to physical quantities. In the pseudopotential multiphase model, this conversion becomes particularly restrictive when attempting to reproduce real-fluid properties. In this work, we extend the dimensional lattice Boltzmann framework to the pseudopotential formulation, enabling simulations directly in physical units. A dimensional form of the Shan-Chen interaction force is derived and its continuum limit analyzed, revealing the explicit dependence of the model on the grid parameters $\mathrm{\Delta }x$ and $\mathrm{\Delta }t$. From the recovered pressure tensor, analytical relations are obtained for the equilibrium interface profile, coexistence densities, and surface tension, establishing a direct connection between pseudopotential parameters and thermophysical properties. Numerical simulations using the Peng-Robinson equation of state for water validate the theory through planar interface test, static droplets, spurious currents, layered flow, pressure-induced bubble dynamics, and thermal droplet evaporation. The results show good agreement with analytical predictions and confirm that the dimensional formulation accurately reproduces bulk densities, surface tension, and viscosity, providing a transparent framework for simulating real multiphase flows with LBM.

Non-Hermitian band descriptions capture how loss, gain, and environmental coupling reshape quantum matter, yet most experimental probes remain wave based or dynamical. Here we develop an equilibrium charge-response route to spectral compression in Dirac materials. In the real-spectrum regime, invariance of the particle-number operator under the similarity transformation makes the quantum capacitance exactly that of the Hermitian partner, so the whole non-Hermitian content is carried by the Petermann factor. In a minimal nonreciprocal graphene model, hopping imbalance suppresses the Dirac velocity, enhancing the low-energy density of states and the capacitance as an exceptional point is approached. At charge neutrality the capacitance stays linear in temperature, with its slope enhanced relative to the Hermitian value. A perpendicular magnetic field recasts the same compression as a collapse of the Landau-level ladder, drawing more levels into the thermal window. In two dimensions, the capacitance enhancement relative to the Hermitian partner coincides exactly with the Petermann factor, even though the two have entirely different origins. This relation provides a controlled starting point for extending equilibrium thermodynamic probes to non-Hermitian electronic systems with interactions, disorder, and reservoir coupling.

The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by Lee and Yang in 1952. It provides powerful tools for understanding the very nature of phase transitions and critical phenomena in various spin and similar models. Sometimes, this theory is applied to models for which the theorem's validity has not been proved. By the main result of Lieb and Sokal [Commun. Math. Phys. 80, 153 (1981)] for a given ferromagnetic model, this validity is guaranteed by the same property of the single-spin partition function. Due to the anisotropy term ${\sum }_i\mathrm{\Delta }{S}_i^2$, the single-spin partition function of the Blume-Capel model fails to have the Lee-Yang property for $\beta \mathrm{\Delta }>ln2$. In this article, we show that the ferromagnetic interaction in such a model can induce the Lee-Yang property, even for these values of $\beta \mathrm{\Delta }$.

Within the framework of linear Maxwell generalized hydrodynamics, explicit expressions for the Green's functions of longitudinal and transverse modes are obtained. Using the fluctuation-dissipation theorem, the spectral densities of individual contributions to the total energy of the fluid are determined. Exact frequency integration by the residue method is performed for the kinetic and potential (elastic) energy. An explicit analytical expression for the total internal energy of the fluid as a function of the gap width in the wave-number spectrum of transverse modes is obtained. An expression for the excitation spectrum in the fluid is constructed. It is shown that the excitation spectrum in the Maxwell model does not generally have a Debye quadratic form. The results are placed in the context of the Maxwell-Frenkel theory of liquids, and comparison with existing numerical simulations is provided.

The ability to identify nanometer-scale nuclei of additional phases in atom probe tomography (APT) is often limited by the sensitivity of clustering algorithms to user-defined control parameters. Conventional approaches typically rely on the Euclidean distance metric and consider only solute atoms, thereby discarding the solvent atoms that contain most of the spatial information. Here, we introduce a coordination-number metric based on the composition and apply it to higher-order clustering. Using various metrics, we investigate percolation in typical APT structures. By scaling clustering properties to the corresponding percolation thresholds, we define a self-similar variable that is almost invariant with respect to metrics, clustering parameters, and structural disorder. This variable provides a relevant description of clustering and enables the formal transfer of optimal parameters between clustering methods. We also study the characteristic clustering behavior in small precipitates and quantify how the precipitate-matrix interface alters the composition spectrum and broadens the clustering curve. Finally, using simulations that incorporate limited spatial precision, detection efficiency, and other APT reconstruction artifacts, we show that the coordination-number-based approach effectively compensates for heterogeneous dilations and outperforms solute-density-based methods across all tested scenarios.

We present an analytical organizing principle underlying the dynamics of the periodically forced Duffing oscillator. In the massless limit the system reduces to a time-dependent cubic equation whose discriminant and Jacobian classify the canonical Duffing regimes and determine the number and stability of instantaneous equilibria. For the double-well oscillator, the same construction gives an exact forcing threshold $F_{\mathrm{bif}}$ separating intrawell and interwell dynamics. We show that this algebraic quantity governs the finite-mass dynamics far beyond the singular limit from which it originates: The boundary between intrawell and interwell motion converges to $F_{\mathrm{bif}}$ as $m\to 0$, and the families of pitchfork bifurcations responsible for asymmetric interwell states accumulate at a common point. Numerical simulations further show how the discontinuous jumps of the degenerate model are regularized at finite mass into short oscillatory transients that shrink as $m\to 0$. These results reveal the massless Duffing equation as the organizing center of the full finite-mass dynamics and establish a direct link between the algebraic structure of the degenerate problem and the global bifurcation structure of the oscillator.

We study a one-dimensional diffusive particle subject to stochastic resetting to its initial position, in the presence of an imperfect, localized target that can absorb (kill) the particle, modeled by a delta-function killing rate. The central question is how stochastic resetting competes with drift-induced transience and the target's finite reactivity. Exact Laplace-space expressions are derived for the non-normalized propagator and survival probability, for arbitrary diffusion coefficient $D$, resetting rate $r$, and killing strength $k$, first in the absence of drift and then under a constant drift. The long-time behavior separates into distinct regimes. Without resetting, unbiased diffusion exhibits the recurrent algebraic survival law $S\left(t\right)\sim t^{-1/2}$, whereas any nonzero drift renders the motion transient with respect to the target and leaves a nonzero ultimate survival probability. By contrast, any $r>0$ and $k>0$ repeatedly renew encounters with the target and restore eventual absorption, yielding an exponential survival law $S\left(t\right)\sim A{e}^{-\theta t}$. The decay rate $\theta$ is given by the dominant (rightmost) pole of the Laplace transform, and the surviving density converges after normalization to an explicit quasistationary profile. The driftless and perfectly absorbing limits recover standard resetting results. These formulas provide a unified description of the crossover between recurrence-controlled, transience-controlled, and renewal-controlled survival.

Random non-Hermitian matrix ensembles with double-sided rotation invariance obey, in the limit of large matrix size, the single ring theorem, which states that the support of the mean eigenvalue distribution in the complex plane is either a disk or an annulus. In contrast, rotational-invariant random normal matrix ensembles can have mean eigenvalue densities supported over any number of concentric annuli in the complex plane. In this paper we introduce and investigate, both analytically and numerically, a non-Hermitian matrix model which flows from a generic matrix distribution obeying the single ring theorem to a distribution of normal matrices by tuning a parameter which penalizes non-normality. We observe numerically breakdown of the single ring theorem as the model flows towards normality and determine the critical value of the parameter at which the transition occurs. We also study in detail the behavior of the singular values of these matrices under the flow. These singular values form a Fermi gas confined to the positive half-line. In particular, we find that at small values of the flow parameter, the interparticle spacings in the gas exhibit Wigner-Dyson repulsion, whereas for asymptotically large values of the flow parameter, at the normal matrix end point of the flow, the spacing statistics is Poissonian. The flow interpolates continuously between these two types of statistics. However, this change in statistics is not related directly to breaking of the single ring theorem, which occurs very early-on along the flow, in the regime of Wigner-Dyson statistics. Finally, we introduce a certain ensemble of random permutations associated with the gas, and make a conjecture on how to use it in order to reconstruct approximately the average density of complex eigenvalues from that of the singular values in the large-$N$ limit.

We introduce an operator to describe a random walk process on a simplicial complex. Walkers are allowed to wander across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrarily large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher-order simplices. Optimal search strategies in the presence of stochastic teleportation are addressed, and the peculiar interplay of noise with higher-order structures is unraveled.

The induced magnetic field in an applied field magnetoplasmadynamic discharge device is a key physical quantity for plasma transport and electromagnetic feedback in the plasma discharge process. To clarify its spatial evolution and the associated driving mechanisms under steady operating conditions, a two-dimensional axisymmetric multifluid numerical model is developed and applied to an applied field magnetoplasmadynamic  (AF-MPD) discharge device designed by Joint Laboratory of Plasma and Propulsion. The results show that the flow-electromagnetic coupling in the discharge region exhibits pronounced spatial partitioning: magnetic diffusion prevails in the upstream near-axis region adjacent to the cathode; the Hall effect prevails in the midstream near-axis region; in the downstream near-axis jet region, magnetic convection has the advantage, whereas in the anode and peripheral plume region, the Hall effect becomes the dominant mode governing the azimuthal induced magnetic field. Operating conditions modify the prevailing plasma transport modes: increasing the applied magnetic field strength suppresses cross-field transport and shifts the downstream near-axis region from convection-prevailed mode toward a Hall-prevailed mode; conversely, increasing the discharge current enhances local ionization and collisional processes, reducing the relative importance of the Hall effect and gradually promoting convection-prevailed mode in the midstream and downstream near-axis regions. The axial and radial induced magnetic fields are primarily generated by the electron azimuthal current, producing paramagnetic behavior inside the cathode cavity and diamagnetic behavior outside the cathode exit. The formation of this spatial topology results from the competition between the driven terms by the electric field and the electron pressure gradient, the latter being jointly modulated by the gradients of electron temperature and number density. These results provide new insight into plasma transport and electromagnetic coupling in the AF-MPD discharge device.

Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear. We analyze hidden-state dynamics in trained long short-term memory (LSTM) networks and show that small networks near their optimal training epochs (steps) exhibit scale-free avalanche statistics and branching parameters close to unity, indicative of near-critical dynamics, while larger models remain subcritical. To explain the coexistence of subcritical branching with robust $1/f^{\beta }$ noise, we introduce a mixture branching process framework that links heterogeneous branching dynamics to long-range temporal correlations. These results identify critical-like behavior in LSTM networks as an emergent, capacity-dependent dynamical regime.

Hydrogel diffusiophoresis is the deformation of a hydrogel due to a solute gradient that leads to a gradient of pairwise interactions between the solute particles and the hydrogel polymers to trigger osmotic flux. Unlike typical osmosis, it occurs without any interface selectivity of the gel to the solute and can overcome the diffusive swelling without any structural modifications to the gel. We have recently shown this effect for linear deformations of a chemically responsive polyacrylic acid (PAA) hydrogel that releases ions upon arrival of a stimulus (acid), thus internally generating the solute gradient required for diffusiophoresis [Phys. Rev. Lett. 132, 208201 (2024)]. Here, we develop a nonlinear poroelastic theory for large diffusiophoretic gel strains in two models: Model I considers deformations of a generic gel when an external solute gradient is imposed and indicates that deformations can be stored while the stimulus gradient persists. Model II is concerned with the internal generation of the solute gradient within the gel, motivated by the coupled PAA gel, solute (copper), and stimulus (acid) system. In Model II, we investigate the nonlinear deformations for high stimulus concentrations or by changing the solute particle size to boost steric polymer-solute interactions as well as under a stimulus flow through the gel. Compared with the experimental strain rates found by Katke et al. [Phys. Rev. Lett. 132, 208201 (2024)], Model II demonstrates that varying the stimulus concentration can increase the strain rate up to four times, changing the solute particle size up to $\sim 25$ times and imposed flow up to $\sim 40$ times. Our theory couples nonlinear poroelasticity, polymer-solute interactions, and reaction-transport dynamics to predict large and fast diffusiophoretic gel deformations, which may find applications in hydrogel-based soft robotics and drug delivery.

Monomer effective charge and cationic specificity play a critical role in determining the polyelectrolyte (PE) brush responsiveness. Herein, we report a systematic simulation study to investigate how trivalent salt cation size and monomer effective charge cooperatively regulate surface morphology, chain dynamics, and internal ionic states of a planar PE brush system. Our simulations reveal a rich phase behavior governed by the competition between electrostatic bridging and excluded volume interactions. At fixed monomer charge, increasing cation size drives a nonmonotonic evolution in brush height and lateral structure, transitioning from a homogeneous collapsed state to heterogeneous pinned micelles and, ultimately, to a loosely reswollen layer. Specifically, the monomer effective charge is shown to modulate ionic correlations, reducing the critical cation size required for microphase separation and inducing the transition between intrachain and interchain bridging. Additionally, monomer lateral mobility exhibits a nonmonotonic dependence on cation size at high monomer charge, reflecting the dynamical consequences of this structural evolution. These findings provide a theoretical framework for understanding multifactor coupling in PE brush systems and offer parametric guidance for designing smart interfaces with ion-responsive properties.