Liquid crystals (LCs) are unique heat transfer media that exhibit large anisotropy in thermal properties depending on the direction of the director ($n$) of the LC state. This phenomenon is the basis of thermal conduction in ordered soft materials, and has been extensively studied to understand thermal conduction in soft materials. In this study, we used inelastic x-ray scattering (IXS) to investigate the anisotropic thermal diffusivity and collective dynamics in the terahertz region of a pyrimidine-type LC (PYP8O8). The dispersion relations at several frequencies corresponding to the LC state were analyzed in the directions parallel and perpendicular to $n$. The results showed that there was a significant difference between the anisotropy of the sound velocity and that of the attenuation coefficient ($\mathrm{\Gamma }$) estimated from the shape parameter of the IXS spectrum. The results for the linewidth of inelastic excitation show $Q^2$ dependence that is far beyond the viscoelastic relaxation of the system, and the anisotropy in the collective dynamics predicted by Forster et al. [Phys. Rev. Lett. 26, 1016 (1971)] in the hydrodynamic region can be extensively applied to the more localized collective motion of LC systems.

The mechanical response of amorphous solids to external strains is riddled with plastic events that create topological charges in the resulting displacement field. It was recently shown that the latter lead to screening phenomena that are accompanied by the breaking of both translational and Chiral symmetries. The screening effects are quantified by two screening parameters ${\kappa }_e$ and ${\kappa }_o$, which are inverse characteristic lengths that do not exist in classical elasticity. The screening parameters (and the associated lengths) are emergent, and it is important to understand how they are selected. This Letter explores the mechanism of selection of these characteristic lengths in two examples of strain protocols that allow analytic scrutiny.

It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-$1/2$ chain models that the average eigenstate entanglement indeed approaches the random matrix result. However, the distribution of the eigenstate entanglement differs significantly. While for autonomous systems such deviations are expected, they are surprising for the more scrambling kicked systems. Similar deviations occur in a tensor-product random matrix model with all-to-all interactions. Therefore, we attribute the origin of the deviations for the kicked spin-$1/2$ chain models to the tensor-product structure of the Hilbert spaces. As a consequence, this would mean that such many body systems cannot be described by the standard random matrix ensembles.

In this work, we study alternating mixed-spin $(s,S)$ Heisenberg ladders in the magnetic field $h$ density matrix renormalization group and linear spin-wave calculations. The $h$ versus interchain coupling $J_{\perp }$ phase diagram for the $(1/2,1)$ case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of $J_{\perp }$ and of $h$ along the chain, $J_{\perp }$ and $h$ scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for $J_{\perp }>0$ and in a limited range for $J_{\perp }<0$. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.

Path optimization is a fundamental concern across various real-world scenarios, ranging from traffic congestion issues to efficient data routing over the Internet. The traffic assignment problem (TAP) is a classic continuous optimization problem in this field. This study considers the integer traffic assignment problem (ITAP), a discrete variant of TAP. ITAP involves determining optimal routes for commuters in a city represented by a graph, aiming to minimize congestion while adhering to integer flow constraints on paths. This restriction makes ITAP an NP-hard problem. While conventional TAP prioritizes repulsive interactions to minimize congestion, this work also explores the case of attractive interactions, related to minimizing the number of occupied edges. We present and evaluate multiple algorithms to address ITAP, including a message passing algorithm, a greedy approach, simulated annealing, and relaxation of ITAP to TAP, including the message passing algorithm in Yeung, Saad, and Wong [Proc. Natl. Acad. Sci. USA 110, 13717 (2013)], a greedy approach, simulated annealing, and relaxation of ITAP to TAP. Inspired by studies of random ensembles in the large-size limit in statistical physics, comparisons between these algorithms are conducted on large sparse random regular graphs with a random set of origin-destination pairs. Our results indicate that while the simplest greedy algorithm performs competitively in the repulsive scenario, in the attractive case the message-passing-based algorithm and simulated annealing demonstrate superiority. We then investigate the relationship between TAP and ITAP in the repulsive case. We find that, as the number of paths increases, the solution of TAP converges toward that of ITAP, and we investigate the speed of this convergence. Depending on the number of paths, our analysis leads us to identify two scaling regimes: In one the average flow per edge is of order one, and in another, the number of paths scales quadratically with the size of the graph, in which case the continuous relaxation solves the integer problem closely.

Mathematical models have provided a general framework for understanding the dynamics and control of infectious disease. Many compartmental models are limited in that they do not account for the range of behavioral feedbacks that have been observed in the response to emerging infections. Here we expand on the SIR compartmental model framework by introducing a general class of behavioral feedbacks that encompasses both individual responses and nonpharmaceutical interventions. By linking transmission dynamics and behavior, this class of models can capture the interplay of disease incidence, behavioral response, and controls such as vaccination. We prove mathematically the existence of two endemic equilibria depending on the vaccination rate: one in the presence of low vaccination but with reduced societal activity (the “new normal”), and one with return to normal activity but with vaccination rate below that required for disease elimination. Establishing the existence and stability of these equilibria is a precursor to designing control strategies that may exploit them.

An analysis of lattice wave spectra in a three-dimensional dusty plasma structure formed in a direct current gas discharge with alternating polarity under microgravity conditions is reported. The spectra are determined using the Fourier transform of microparticle velocities, measured by tracking microparticles with subpixel resolution. Both longitudinal and transverse modes are detected and analyzed. The absence of a “$k$–gap” in the long-wavelength domain of the transverse mode strongly suggests that the microparticles form a solid structure. Therefore, the experimental spectra are compared with the spectra obtained from molecular dynamics simulations for different lattice structures and their orientation. This comparison yields important dusty plasma parameters, such as the particle charge and the plasma screening length. The measured longitudinal and transverse sound velocities allow us to estimate the elastic moduli of the particle component. These are rather small in the absolute magnitude, but when normalized by the number density and the interaction energy of the particles resemble those in conventional matter.

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems.

By introducing appropriate surfactants to nonpolar solvents, charged inverse micelles can be incorporated as charge carriers, facilitating stable particle suspensions via electrostatic interactions. The presence of these charge carriers enables electric-field-induced transport phenomena, notably electrophoresis and electro-osmosis, to occur in these systems. As a consequence, these nonpolar-solvent systems are used in a wide range of applications, such as electronic paper displays and smart windows. In previously reported experimental work, we found that, under the right circumstances, electrophoresis and electro-osmosis act synergistically to transport particles unexpectedly fast. This work aims to uncover the underlying physics of experimentally observed particle velocity fields and trajectories driven by an applied electric field in a nonpolar solvent. Our approach involves a comprehensive numerical model to analyze particle motion in nonpolar solvents. By comparing simulation results of particle velocity fields and trajectories with experimental data obtained through astigmatism microparticle tracking velocimetry, we find that both electrophoresis and electro-osmosis contribute to particle motion. By quantifying the contributions of electrophoresis and electro-osmosis based on average particle velocities, we further confirm that electro-osmosis contributes significantly to particle transport. Two modes of electro-osmosis are considered, one that is caused by the electrical double layer near the glass surfaces and the other that is caused by the induced space charge in the vicinity of the driving electrodes. Additionally, enhanced particle velocities are found mainly in the center of the cell and result from the superposition of electrophoresis and electro-osmosis. Finally, we propose a scheme that explains how particle trajectories emerge as a result of the interplay between electrophoresis and electro-osmotic flows generated near the glass surface and in the vicinity of the driving electrodes. This study contributes to the fundamental understanding of the interplay between electrophoresis and electro-osmosis in nonpolar solvents and offers insights for advancing the design of enhanced electrokinetic displays.

The intermittent stochastic motion is a dichotomous process that alternates between two distinct states. This phenomenon, observed across various physical and biological systems, is attracting increasing interest and highlighting the need for comprehensive theories to describe it. In this paper, we introduce a generalized intermittent random walk model based on a renewal process that alternates between the continuous time random walk (CTRW) state and the generalized Lévy walk (gLW) state. Notably, the nonlinear space-time coupling inherent in the gLW state allows this generalized model to encompass a variety of random walk models and makes it applicable to diverse systems. By deriving the velocity correlation function and utilizing the scaling Green-Kubo relation, the ensemble-averaged and time-averaged mean-squared displacement (MSD) is calculated, and the anomalous diffusive behavior, aging effect, and ergodic property of the model are further analyzed and discussed. The results reveal that, due to the intermittent nature, there are two diffusive terms in the expression of the MSD, and the diffusion can be intermediately characterized by the diffusive term with the largest diffusion coefficient instead of the diffusive term with the largest diffusion exponent, which is significantly different from single-state stochastic process. We demonstrate that, due to the power-law distribution of sojourn times, nonlinear space-time coupling, and intermittent characteristics, both ergodicity and nonergodicity can coexist in intermittent stochastic processes.

Isolated patterning systems have been repeatedly investigated. However, biological systems rarely work on their own. This paper presents a theoretical and quantitative analysis of a two-domain interconnected geometry, or bilayer, coupling two two-species reaction-diffusion systems mimicking interlayer communication, such as in mammary organoids. Each layer has identical kinetics and parameters, but differing diffusion coefficients. Critically, we show that despite a linear coupling between the layers, the model demonstrates nonlinear behavior; the coupling can lead to pattern suppression or pattern enhancement. Using the Routh-Hurwitz stability criterion multiple times, we investigate the pattern-forming capabilities of the uncoupled system, the weakly coupled system, and the strongly coupled system, using numerical simulations to back up the analysis. We show that although the dispersion relation of the entire system is a nontrivial octic polynomial, the patterning wave modes in the strongly coupled case can be approximated by a quartic polynomial, whose features are easier to understand.

We study the cascading failures in systems of any number of networks connected to each other via groups of supply links, which we call hyperlinks. The individual supply links of a hyperlink connect individual nodes belonging to the pair of networks connected by this hyperlink. Such a system is called a network of networks (NON). NONs based on the idea of mutual percolation have been studied for the case of dependency hyperlinks. The present model generalizes the heterogeneous $k$-core percolation for the NON, where any number of hyperlinks can be directional and any number of them can be bidirectional. We show that, by utilizing generating function formalism, the cascading process can be modeled by a set of recursive relations that are generalizations of previously studied relations in heterogeneous $k$-core percolation for single or bipartite networks. We demonstrate that the order in which failures propagate throughout the system does not matter for determining the final fraction of functional nodes, which depends only on the NON topology. We show that, in the NONs, there can be more than one transition point, defined as the discontinuous jump in the fraction of functional nodes at the end of the cascade as the strength of the initial attack on one of the networks gradually changes, and more than one critical point, defined as when the behavior changes from continuous to discontinuous. We find that the number of these points is strongly related to the number of hyperlinks in the NON. We further generalize previously studied criteria for the transition points and critical points in the bipartite network to the NONs with hyperlinks, and compare the phase diagrams of NONs with multiple critical points to the phase diagrams of protein solutions.

We show that classical DNA unzipping transition, which is equivalently described by quantum mechanical localization-delocalization transition in the ground state of non-Hermitian single impurity Hatano-Nelson Hamiltonian, is underpinned by generalized parity (P)-time reversal (T) symmetry breaking transition. We also study one-dimensional discretized version of the Hatano-Nelson model in the presence of single impurity and random disorder on a finite-size lattice. These discrete models are useful to study unzipping of a single adsorbed polymer from a surface. Our results show that the discrete models also undergo a phase transition from a PT unbroken phase to a broken phase. Interestingly, the generalized PT phase transition points coincide with the localization-delocalization transition for continuum as well as lattice models.

The detailed Josephson-Anderson relation, which equates instantaneously the volume-integrated vorticity flux and the work by pressure drop, has been the key to drag reduction in superconductors and superfluids. We employ a classical version of this relation to investigate the dynamics of polymer drag-reduced channel flows, particularly in the high-extent drag reduction (HDR) regime which is known to exhibit strong space-time intermittency. We show that high drag is not created instantaneously by near-wall coherent vortex structures as assumed in prior works. These predominantly spanwise near-wall vortex structures can produce a net “up-gradient” flux of vorticity toward the wall, which instead reduces instantaneous drag. Increase of wall vorticity and skin friction due to this up-gradient flux occurs after an apparent lag of several advection times, increasing with the Weissenberg number. This increasing lag appears to be due to polymer damping of up-gradient nonlinear vorticity transport that arises from large-scale eddies in the logarithmic layer. The relatively greater polymer damping of down-gradient transport due to small-scale eddies results in lower net vorticity flux and hence lower drag. The Josephson-Anderson relation thus provides an exact tool to diagnose the mechanism of polymer drag reduction in terms of vorticity dynamics and it explains also prior puzzling observations on transient drag reduction, as for centerline-release experiments in pipe flow.

We show that connectivity within the high-dimensional recurrent layer of a reservoir network is crucial for its performance. To this end, we systematically investigate the impact of network connectivity on its performance, i.e., we examine the symmetry and structure of the reservoir in relation to its computational power. Reservoirs with random and asymmetric connections are found to perform better for an exemplary Mackey-Glass time series than all structured reservoirs, including biologically inspired connectivities, such as small-world topologies. This result is quantified by the information processing capacity of the different network topologies which becomes highest for asymmetric and randomly connected networks.

Inhomogeneous flows and shear banding are of interest for a range of applications but have been eluding a comprehensive theoretical understanding, mostly due to the lack of a framework comparable to equilibrium statistical mechanics. Here we revisit models of fluids that reach a stationary state obeying mechanical equilibrium. Starting from a nonlocal constitutive relation, we apply the idea of a “mechanical phase transition” and map the constitutive relation onto a dynamical system through an integrating factor. We illustrate this framework for two applications: shear banding in strongly thinning complex fluids and the coexistence of a solid with its sheared melt. Our results contribute to the growing body of work following a mechanical route to describe inhomogeneous systems away from thermal equilibrium.

This study investigates the throw of slender elastic projectiles. By integrating experimental data, numerical simulations, and theoretical analyses, we explore the acceleration and ejection dynamics of these projectiles. We considered various conditions, including the amplitude and frequency of the thrower, as well as the geometrical and mechanical properties of the projectile and its mass distribution. Conversely to homogeneous projectiles, weighted projectiles with a mass at the leading edge exhibit strong lateral deformations that substantially influence their dynamics. This results in an increase in kinetic energy compared to rigid objects. This superpropulsion effect is maximum at a particular value of a dimensionless factor, namely, the ratio between the Euler's critical load of the beam and the acceleration force imposed by the thrower. For heavily weighted projectiles with a mass ratio of 2 between the leading and trailing edges, this maximum corresponds to a 160% increase of kinetic energy. Our results contribute to a deeper understanding of the mechanical behaviors influencing elastic energy transfer in slender structures, with potential applications in sports and robotics.

The excessive dendritic development during the electrochemical evolution of the microstructures in rechargeable batteries can ultimately cause a short circuit, thermal instability, or runaway, and loss of active material. We initially develop a computational framework to quantify the bias of the electrodeposition on the roughened interface favoring the convex zones. Subsequently, we impose a countering temperature effect to enhance the diffusion on the trailing concave zones. Consequently, we establish a stability criterion for controlling surface roughening where the visualized space of parameters establishes a relationship between the geometry of the interface, the physical properties of the electrolyte, and the charging conditions. The developed framework could be useful for controlling the propagation of the microstructures and the prevention of runaway, during prolonged cycles, particularly when the surface roughness gets pronounced in the later stage of cycle life.

The descent of dense intruder disks through granular material fluidized by vertical gas flow and vibration is investigated experimentally and computationally. Single intruders descend with a velocity which oscillates based on distance above the bottom of the system, which simulations show is due to a spatially dependent void fraction in the granular material changing the effective drag force on the intruder. Two vertically aligned intruders undergo a drafting-kissing-tumbling analog which forms because the bottom intruder decelerates due to particle compaction from the weight of the top intruder.