Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics, and machine learning. In this paper, we introduce a weighted balanced truncation method that significantly reduces the number of exponential terms required for an accurate representation of the kernel. This method shows great promise in approximating long-range kernels, achieving more than four digits of accuracy improvement for the Ewald splitting and inverse power kernels compared to classical balanced truncation. Numerical results demonstrate the attractive performance of the method and promising features for practical applications.

We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance; in particular, the density exhibits a periodic modulation. Using techniques familiar from solid-state theory, we define generalized intermediate scattering functions from fluctuating densities in wave-vector space. Exact equations of motion are derived within the Mori-Zwanzig projection-operator formalism reflecting the residual lattice symmetries. Due to the lack of rotational symmetry it is necessary to split the currents into components parallel and perpendicular to the modulation. We provide a closure of the equations in terms of a mode-coupling approximation for the force kernel. The theory reflects the usual analytic properties of correlation functions and encodes all phenomena known for mode-coupling theories. We prove that the theory reduces to the conventional mode-coupling theory in the case of vanishing amplitude of the modulation.

Stealthy hyperuniform (SHU) many-particle systems in $d$-dimensional Euclidean space are distinguished by a structure factor that vanishes not only at zero wave number (as in “standard” hyperuniform systems) but also across an extended range of wave numbers near the origin. We generate disordered SHU packings of identical and “nonoverlapping” spheres in two and three dimensions using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. Compared to SHU packings without soft-core repulsions, these SHU packings are ultradense with packing fractions ranging from 0.67 to 0.86 for $d=2$ and 0.47 to 0.63 for $d=3$, spanning a broad spectrum of structures depending on the stealthiness parameter $\chi$. We consider two-phase media composed of hard particles derived from ultradense SHU packings (phase 2) embedded in a matrix phase (phase 1) with varying stealthiness parameter $\chi$ and packing fractions $\varphi$. Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to SHU media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes for a range of small wave numbers, implying perfect transparency for the corresponding wave vectors. While a larger packing fraction yields a smaller transparency interval, we show that it also displays a reduced height of the attenuation peak. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media, showing that one leads to information about the other and vice versa. Our results demonstrate that disordered two-phase media derived from ultradense SHU packings exhibit advantageous transport and optical behaviors of both theoretical and experimental significance.

The electric polarization of ferroelectric Smectic-$C^{*}$($\mathrm{Sm}{C}^{*}$) liquid crystal is always measured on static samples confined between two fixed electrodes. Here, we study the effect of shear flow on the electric polarization of a $\mathrm{Sm}{C}^{*}$ liquid crystal. We observe three distinct regimes in the shear rate-dependent polarization curve. At a low shear rate, the polarization increases rapidly. In the intermediate shear rate range, polarization tends to saturate, and at sufficiently high shear rates, the polarization decreases. The results are discussed based on smectic layer orientations under the combined effect of shear flow and probe electric fields.

Thermodynamic constraints impose a trade-off between power and efficiency in heat engines, preventing the simultaneous achievement of high power and high efficiency. For classical microscopic engines, explicit inequalities have been discovered, demonstrating the inherent inevitability of this power-efficiency trade-off. However, extensions of these results to quantum engines have so far been limited to cases of slow operation. In this study, we derive a power-efficiency trade-off relation for a paradigmatic quantum engine operating within a finite time, specifically the Otto cycle of a quantum harmonic oscillator. By utilizing a phase-space approach based on quasiprobability representations, we establish a universal trade-off relation applicable to arbitrary time-dependent protocols during the adiabatic processes. Our results reveal that the power of the quantum engine vanishes as the efficiency approaches the quantum-mechanical efficiency bound, which is stricter than the Carnot bound. Furthermore, we identify the conditions under which the upper bound is attained, which indicate maximum power is achieved when the generation of quantum coherence is reduced, and the difference in time durations of the isochoric processes increases. These findings are validated through numerical calculations, which confirm their applicability across various types of protocols for heat engine cycles.

We theoretically investigate the glass-transition problem for a quasi-two-dimensional colloidal dense suspension modulated by a one-dimensional periodic external potential as imposed by interfering laser beams. Relying on a mode-coupling approach, we examine the nonequilibrium-state diagram for hard disks as a function of the density and the period of the modulation for various potential strengths. The competition between the local packing and the distortion of the cages induced by the potential leads to a striking nonmonotonic behavior of the glass-transition line, which allows melting of a glass state merely by changing the external fields. In particular, we find regions in the nonequilibrium-state diagram where a moderate periodic modulation stabilizes the liquid state.

In statistical physics, phase transitions are arguably among the most extensively studied phenomena. In the computational approach to this field, the development of algorithms capable of estimating entropy across the entire energy spectrum in a single execution has highlighted the efficacy of microcanonical inflection point analysis, while Fisher's zeros technique has re-emerged as a powerful methodology for investigating these phenomena. This paper presents an alternative protocol for analyzing phase transitions using a parametrization of the entropy function in the microcanonical ensemble. We also provide a clear demonstration of the relation of the linear pattern of the Fisher's zeros on the complex inverse temperature map (a circle in the complex $x=e^{-\beta \varepsilon }$ map) with the order of the transition, showing that the latent heat is inversely related to the distance between the zeros. We study various model systems, including the Lennard-Jones cluster, the Ising, the XY, and the Zeeman models. By examining the behavior of thermodynamic quantities such as entropy and its derivatives in the microcanonical ensemble, we identify key features—such as loops and discontinuities in parametric curves—which signal phase transitions' presence and nature. This approach can facilitate the classification of phase transitions across various physical systems.

In practical applications, complex networks often model scenarios involving higher-order relationships, for which hypergraphs offer a suitable representation. This paper introduces synchronizability metrics to study the synchronization of a temporal two-layer multiplex hypergraph, where temporal characteristics are captured by time-evolving incidence matrix. By transforming hyperedges into maximal cliques, we construct a temporally evolving weighted network that reproduces the dynamics on the hypergraph under simple structure and symmetric coupling. The analysis focuses on intralayer synchronizability across different spatio-temporal scales. In the short term, we observe that the synchronizability of the hypergraph is positively correlated with network stochasticity. For the long term, we derive time-averaged approximation equations for fast-switching hypergraph and conduct both linear and global stability analyses to determine the necessary conditions for intralayer synchronization. Experimental results demonstrate that fast-switching hypergraph achieve superior long-term synchronizability compared to their short-term evolving counterparts under identical conditions.

This study aims to conceptualize natural drainage networks as genuine complex networks. To overcome the limitation imposed by the regular connectivity structure of the traditional planted binary tree model—commonly employed to represent the planar configuration of fluvial systems—we introduce a line graph transformation. This mapping converts a planted binary tree into a plane tree, which can be regarded as a special class of loopless, directed graph characterized by inhomogeneous topology. From a geomorphological standpoint, our transformation naturally induces a hierarchical basin ordering that reflects the pioneering Gravelius stream order, offering insights into this scheme by projecting the hierarchy of tributary rivers onto a purely topological space. The application of complex network theory provides an explanatory perspective on river networks, yielding experimental findings that complement and extend established results in the geomorphological literature. In particular, our analysis of six catchments in southern Italy reveals previously unrecognized regularities, including a family of exact scaling laws and a surprisingly smooth width-type function that closely fits a Gamma distribution. These scaling laws emerge as power-law probability distributions for both the in-degree of nodes and the size of their in-components, which capture the scale invariance of tributary river lengths and drainage areas in tributary basins, respectively, thereby expanding the pantheon of known fluvial laws. Notably, these distributions represent sample distributions drawn from the complete populations of upstream lengths and drainage areas, with the sampling induced by our mapping through the selection of fluvial quantities corresponding to topologically well-defined elements of the plane tree. On the theoretical front, our approach is grounded in a model of directed, uncorrelated random graphs with arbitrary degree distributions. Among other things, by applying the generating function formalism to uncorrelated plane trees we derive an analytical expression for the distribution of drainage areas in tributary basins as a function of the distribution of tributary river lengths. By relying on average cluster properties, we predict the scaling exponent of the former distribution to be exactly 2 in the limit of large system sizes—a result that aligns well with both our empirical observations and previous findings in the complex network literature. Beyond the first-order approximation inherent in the model, our mapping also offers a coherent framework for interpreting the correlation structure consistently observed across all examined drainage networks.

Modeling human behavior is essential to accurately predict epidemic spread, with behaviors like vaccine hesitancy complicating control efforts. While epidemic spread is often treated as a simple contagion, vaccine uptake may follow complex contagion dynamics, where individuals' decisions depend on multiple social contacts. Recently, the concept of complex contagion has received strong theoretical underpinnings thanks to the generalization of spreading phenomena from pairwise to higher-order interactions. Although several potential applications have been suggested, examples of complex contagions motivated by real data remain scarce. Surveys on COVID-19 vaccine hesitancy in the United States suggest that vaccination attitudes may indeed depend on the vaccination status of social peers, aligning with complex contagion principles. In this work, we examine the interactions between epidemic spread, vaccination, and vaccine uptake attitudes under complex contagion. Using the susceptible-infected-removed (SIR) model with a dynamic, threshold-based vaccination campaign, we simulate scenarios on an age-structured multilayer network informed by U.S. contact data. Our results offer insights into the role of social dynamics in shaping vaccination behavior and epidemic outcomes.

A moving space-time electron grating can split a laser pulse into two parts, functioning as a pulse splitter. In this paper, the evolution of dynamic gratings generated by two counterpropagating laser pulses with different frequencies is investigated. These gratings are characterized by finite length, rapid formation, and directional movement. Specifically, the scenario in which a low-frequency $yz$-polarized pulse interacts with a high-frequency linearly $y$-polarized pulse is examined. The effects of laser parameters and plasma parameters on the reflection and transmission properties of the dynamic gratings are studied. Particle-in-cell simulations indicate that by adjusting the frequency and duration of the high-frequency pulse, the $z$ component of the low-frequency pulse can be transmitted as low-frequency pulses and reflected as high-frequency pulses while maintaining the pulse duration. Thus, the dynamic electron grating can act as a pulse splitter and frequency converter. A theory based on the four-wave mixing model involving density gratings provides predictions that support the simulation findings. This dynamic electron grating is expected to have potential value in rapid pulse splitting.

We perform discrete element method (DEM) simulations of elongated grains in a shear cell for various particle aspect ratios and contact frictions, with an additional heterogeneous force perturbation in the flow direction. For a perturbation in the form of a single Fourier mode, we show that the response of the system consists of transverse secondary flows that average onto a pattern of four vortices. We also theoretically studied this phenomenon by generalizing the granular rheology $\mu \left(I\right)$ to the case of elongated grains and computing the linear response to such a perturbation. Even if the agreement between theory and simulations remains qualitative only, we can reproduce and understand the inversion of the vortex pattern when the cell aspect ratio is increased from a vertically to a horizontally elongated cell shape, emphasizing the key role of the second normal stress difference as well as the cell geometry.

In this work, we investigate the thermophoresis of Janus nanoparticles in liquids through molecular dynamics simulations. Thermophoretic forces acting on cylindrical Janus nanoparticles are calculated through MD simulations by varying the particle size, the heterogenous surface energies, and the mean temperature of the fluid. It is found that a transition from negative thermophoresis to positive thermophoresis occurs when these parameters are varied. The surface energies and mean temperature affect both the magnitude of the thermophoretic force and the transition from negative to positive thermophoresis. However, the particle size only influences the magnitude of the thermophoretic force, not the transition from negative to positive thermophoresis. Contributions of the total energy and pressure of fluid molecules are studied by evaluating the excess enthalpy density around the particle. A general scaling relationship for the thermophoretic force is developed using dimensionless numbers. This work advances the understanding of the thermophoresis of Janus nanoparticles and offers theoretical support for manipulating Janus nanoparticles in liquids by temperature gradients.

We investigate complete wetting and drying at sinusoidally corrugated solid walls, focusing on the effects of wall geometry and interaction range. Two distinct interaction models are considered: one incorporating only short-ranged (SR) forces (applied to drying), and another including long-ranged (LR) van der Waals interactions (applied to wetting). The SR model is analyzed within the framework of nonlocal Hamiltonian theory by Parry et al., while the LR model is treated using a sharp-kink approximation. In both cases we derive scaling relations that describe the dependence of the adsorbed layer's width and morphology on the wall's geometric parameters as the system approaches two-phase coexistence. We identify distinct scaling regimes determined by the degree of wall corrugation and highlight the contrasting effects of SR and LR interactions. Theoretical predictions are corroborated by numerical results from classical density functional theory.

The persistence of populations depends on the minimum habitat area required for survival, known as the critical patch size. While most studies assume purely diffusive movement, additional movement components can significantly alter habitat requirements. Here, we investigate how critical patch sizes are affected by stochastic resetting, where each organism intermittently returns to a common fixed location, modeling behaviors such as homing, refuge-seeking, or movement toward essential resources. We analytically derive the total population growth over time and the critical patch size. Our results are validated by agent-based simulations, showing excellent agreement. Our findings demonstrate that stochastic resetting can either increase or decrease the critical patch size, depending on the reset rate, reset position, and external environmental hostility. These results highlight how intermittent relocation shapes ecological thresholds and may provide insights for ecological modeling and conservation planning, particularly in fragmented landscapes such as deforested regions.

Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.