Segmental dynamics of polymer chains in a model nanocomposite of poly(ethylene oxide) and silica nanoparticles (NPs) was investigated using quasielastic neutron scattering. The dynamics can be accurately described with the Rouse model. The bulklike polymer far from the NP surface behaves as the neat polymer. However, the slower polymer in the interface close to the NP surface is described either with a second Rouse population with different relaxation time or using the suppressed Rouse model. These simple two-population models accurately reproduce the experimental data, with the suppressed Rouse model describing topological constraints, on average, every 12 beads with an interfacial thickness up to 13.5 beads, and the effect of the interface extending to a layer of thickness comparable to the end-to-end distance of the polymer. This modeling provides an explanation for the observed reinforcement in PNC even at low loadings, consistent with current understanding of the relevance of the interphase.

Optical manipulation of metallic Janus particles via self-thermophoresis results in complex trajectories due to competing effect of space-dependent speed and optical torque with the optical trapping presumed to have less or no effect. Here we report that when the beam size is comparable to the size of the particle and the laser power is small, optical trapping becomes relevant leading to the trajectory having a trochoidal-like behavior and off-center trapping. Brownian dynamics simulation incorporating space-dependent speed proportional to the local laser intensity, the induced optical torque, and optical trapping effect captures well the experimental data.

A vibrational paradigm of atomic dynamic in dense fluids is known to provide useful insight on the transport and thermodynamic properties of fluids in three dimensions. In this paper, a vibrational model is generalized to describe the excess entropy of two-dimensional (2D) fluids. A simple practical implementation of this model is demonstrated to deliver accurate results for various systems, such as one-component plasmas with Coulomb and logarithmic interactions, a 2D fluid of dipole particles, and a 2D Yukawa fluid. The applicability limits, relevance to three-dimensional fluids, relations to other 2D phenomena, and potential practical applications are briefly discussed.

We investigate pattern formation in a driven mixture of two mutually repulsive particle species via a field-based lattice model (FLM), a hybrid model that combines aspects of the driven Widom-Rowlison lattice gas (DWRLG) and its statistical field theory [Dickman and Zia Phys. Rev. E 97, 062126 (2018); Lavrentovich, Dickman, and Zia, Phys. Rev. E 104, 064135 (2021)]. We find that the FLM effectively captures the bulk behavior of the DWRLG in both low- and high-density phases, suggesting that phase transitions in these models may share a common universality class. Under the effect of a drive, the FLM additionally reveals an intermediate regime, not reported in previous DWRLG studies, characterized by irregular stripes with widely fluctuating widths, contrasting with the regular, well-ordered stripes found at higher densities. In this intermediate phase, the system exhibits long-range order predominantly perpendicular to the drive direction. To construct a continuum description, we derive two coupled partial differential equations for the particle densities via a gradient expansion of the FLM mean mass-transfer equations, supplemented with additive noise. Designing a numerical solver using the pseudospectral method with dealiasing and stochastic time differencing, we reproduce the low-density microemulsion phase (characterized by a nonzero characteristic wavenumber $q^{*}$) and stripes perpendicular to the drive at high density. We identify the nonzero difference in the characteristic velocities of the sum and difference of the particle densities as a necessary condition for perpendicular stripe formation in the high-density phase. The continuum model exhibits novel behaviors not observed in the FLM, such as stripes aligned parallel to the drive, and chaotic patterns. This work highlights how the interplay of external drive, particle interactions, and noise can lead to a rich phenomenology in strongly driven binary mixtures.

A method for symmetry analysis of a deterministic pulsating ratchet (the so-called phase shift indexing method) is proposed, which provides a relationship between the symmetry parameters of the potential profile of a nanoparticle and the average velocity of the corresponding ratchet. The technique and capabilities of the method are demonstrated by determining the type of symmetry of the dependence of the average ratchet velocity in a general-type additive-multiplicative potential, $U(x,t)=u\left(x\right)+w\left(x\right)\sigma \left(t\right)$ ($\sigma \left(t\right)$ is a periodic function of time), on the distance (phase shift) between the axes or centers of symmetry of its stationary, $u\left(x\right)$, and fluctuating, $w\left(x\right)$, periodic contributions. It has been established that if the spatial dependence of $u\left(x\right)$ and the time dependence of $\sigma \left(t\right)$ belong to the universal type of symmetry (i.e., have both an axis and a center of symmetry mutually shifted by a quarter-period), then the average velocity as a function of the phase shift is also universally symmetric in the overdamped inertialess motion mode [taking into account the hidden Cubero-Renzoni symmetry, Cubero et al., Phys. Rev. Lett. 116, 010602 (2016)], while being only antisymmetric with inertia included. The obtained conclusions are confirmed by the results of calculations of the average velocity of pulsating ratchets in overdamped and inertial motion modes. The effectiveness of the proposed method is also compared for a number of reported cases which address the spatiotemporal dependence of potential energy in overdamped, nondissipative, and inertial-dissipative motion modes.

The study of chaotic systems, where rare events play a pivotal role, is essential for understanding complex dynamics due to their sensitivity to initial conditions. Recently, tools from large deviation theory, typically applied in the context of stochastic processes, have been used in the study of chaotic systems. Here, we study dynamical observables, $A={\sum }_{n=1}^{N}g\left({\mathit{x}}_n\right)$, defined along a chaotic trajectory $\{{\mathit{x}}_1,{\mathit{x}}_2,...,{\mathit{x}}_N\}$. For most choices of $g\left(\mathit{x}\right)$, $A$ satisfies a central limit theorem: At large sequence size $N\gg 1$, typical fluctuations of $A$ follow a Gaussian distribution with a variance that scales linearly with $N$. Large deviations of $A$ are usually described by the large deviation principle, that is, $P\left(A\right)\sim e^{-NI(A/N)}$, where $I\left(a\right)$ is the rate function. We find that certain dynamical observables exhibit a remarkable statistical similarity: even when constructed with distinct functions $g_1\left(\mathit{x}\right)$ and $g_2\left(\mathit{x}\right)$, different observables are described by the same rate function. We provide a physical interpretation for this striking similarity by showing that $g_1\left(\mathit{x}\right)-g_2\left(\mathit{x}\right)$ belongs to a class of functions that we call “derived.” Furthermore, we show that if $g\left(\mathit{x}\right)$ itself is “derived,” then the distribution of $A$ becomes independent of $N$ in the large-$N$ limit and is generally non-Gaussian (although it is mirror-symmetric). We demonstrate that the position observable for certain open maps, used to model random walks and the finite-time Lyapunov exponent for the logistic map are of this derived form, thus providing a simple explanation for some existing results.

We numerically study disease dynamics that lead to the disease switching from one host species to another, resulting in diseases gaining the ability to infect, e.g., humans. Unlike previous studies that focused on branching processes starting with the first infected humans, we begin by considering a disease pathogen that initially cannot infect humans. We model the entire process, starting from an infection in the animal population, including mutations that eventually enable the disease to cause an epidemic outbreak in the human population. We use a susceptible-infected-recovered model on a network consisting of 132 dog and 1320 human nodes, with a single parameter representing the gene of the pathogen. We use numerical large-deviation techniques, specifically the $1/t$ Wang-Landau algorithm, to calculate the potentially very small probability of the host-switching event. With this approach we are able to resolve probabilities as small as ${10}^{-120}$. Additionally, the $1/t$ Wang-Landau algorithm allows us to obtain the complete probability density function $P\left(C\right)$ of the cumulative fraction $C$ of infected humans, which is an indicator for the severity of the disease in the human population. We also calculate correlations of $C$ with selected quantities $q$ that characterize the outbreak. Due to the application of the rare-event algorithm, this is possible for the entire range of $C$ values.

Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here, we analyze the eigenspectrum of the Jacobian matrices associated to a general class of networked dynamical systems, which contains information on how perturbations to a stationary state develop over time. We find that stability is always determined by a spectral outlier, but with pronounced differences to the corresponding eigenvector in different regimes. We show that, depending on model details, instability may originate in nodes of anomalously low or high degrees, or may occur everywhere in the network at once. Importantly, the dependence on extremal degrees results in considerable finite-size effects with different scaling depending on the ensemble degree distribution. Our results have potentially useful applications in network monitoring to predict or prevent catastrophic failures, and we validate our analytical findings through applications to epidemic dynamics and gene regulatory systems.

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant $\gamma$, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

Characterizing the transport properties of individual nanoparticles in pores is an important challenge for materials, environmental, and biological sciences. In this article, we analyze the diffusion of spherical particles within a long pore featuring a varying cross-section to demonstrate how geometric variations influence mass transport. We consider two distinct double-cone pore configurations. The first consists of two truncated cones joined at their wide ends, resulting in a pore that expands to its maximum width at the midpoint and then narrows. The second configuration involves two truncated cones joined at their narrow ends—apex to apex—producing a pore that narrows to its minimum width at the center and then widens again. Our findings reveal that the nature of effective diffusion depends on the initial geometry of the channel: when the pore initially widens, superdiffusive behavior is observed; conversely, when it initially narrows, subdiffusive behavior emerges. In addition to the analysis of the mean squared displacement, we examine the mean first passage time and its symmetries, showing that reversal of the channel slope does not change the exit time. We conduct some analytical analysis to evaluate the quality of the approximation provided by the Fick-Jacobs equation, revealing that this approach underestimates the mean first passage times. Furthermore, we demonstrate that the approximation worsens with the increasing number of spatial dimensions.

We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a canonical ensemble whose equilibrium distribution yields Gompertz-like and Maxwell-Boltzmann-like shapes. By reverse-engineering the associated energy landscape, we define an effective potential and derive a dynamical Lagrangian formulation. The resulting field theory captures key features of emergent behaviors in sociotechnical systems, from early suppression to peak dynamics and late decline. We interpret effective temperature, entropy, and equilibrium points and show how these systems exhibit hybrid thermodynamic-statistical signatures.

The confinement of anisotropic particles can lead to entropy-driven structural phases not observed in bulk systems. Using a density functional theory framework, we explore the rich phase diagram of hard cylindrical disks confined within a slit pore. Our investigation reveals complex structural phenomena driven by the interplay of particle geometry and density. A key finding is a concentration-driven reentrant anchoring transition for thin disks ($0.3\le \frac{L}{D}<0.5$), where the system switches from a homeotropic (face-on) to a planar (edge-on) alignment and back to a homeotropic alignment with increasing packing fraction. Furthermore, at high densities and sufficient pore widths, we identify a stable hybrid T-type structure, where layers with orthogonal particle orientations coexist. The phase diagrams are also characterized by sequences of first-order layering transitions and the formation of biaxial planar phases for thicker disks. Our results demonstrate that geometric constraints in athermal colloidal systems produce a diverse range of structural phases.

In this work, the surface tension ($\gamma$) of nanoconfined water between planar interfaces was evaluated using atomistic simulations combined with the test-area method. To elucidate the role of spatial restriction, two types of confinement were considered: solid and liquid. In the case of solid surfaces, a strong increase in surface tension was observed compared to the unconfined case—i.e., water in contact with a single interface. In contrast, no significant change in surface tension was found under hydrophobic liquid confinement, indicating that spatial restriction alone does not fully account for the increase in $\gamma$. Our results demonstrate that the enhancement of surface tension arises from a synergistic interplay between confinement and excluded volume effects, amplified by a lack of miscibility between the two phases. These findings highlight the importance of interfacial structure and phase compatibility in determining the interfacial properties of confined fluids.

We examine a nontrivial generalization of the coupled Kuramoto model with both symmetry-breaking interaction and time delay coupling. We show that this model exhibits three unique dynamical behaviors: incoherent state, stationary synchronized state, and standing wave state. In contrast to the symmetry-preserving coupling, time delay in the symmetry-breaking interaction results in three multistability regions. We elucidate that the latter two bistable regions emerge only in the presence of time delay in the symmetry-breaking coupling. The stability of the stationary synchronized state remains unaffected by the time delay interaction in the system. We deduce the low-dimensional equations for the complex order parameters using the Ott-Antonsen ansatz. We also deduce the Hopf, pitchfork, and saddle-node bifurcation curves from the evolution equations for the complex order parameters mediating the dynamical transitions. Simulation results of the original discrete set of equations for the generalized Kuramoto model agree well with the analytical bifurcation curves.

A model for the collisional stopping of ions on free electrons in warm dense matter is developed and explored. It is based on plasma kinetic theory, but with modifications to address the warm dense matter regime. Specifically, it uses the Boltzmann-Uehling-Uhlenbeck kinetic equation to incorporate effects of Fermi degeneracy of electrons. The cross section is computed from quantum scattering of electrons and ions occuring via the potential of mean force derived from an average atom model, which incorporates effects of strong Coulomb correlations. Predictions from this model show comparable accuracy to results from time-dependent density functional theory calculations for deuterium near solid density and a temperature of several electronvolts, at a fraction of the computational cost. Further, the model captures the transition of a plasma from the classical limit to the degenerate limit, including qualitative behaviors of solid state theory.

The phenomenological Landau–de Gennes (LdG) model is a powerful continuum theory to describe macroscopic liquid crystal (LC) phases. However, it is invariably less accurate and less physically informed than molecular-level models. We propose a neural network-based tensor (NN-tensor) model for LCs, supervised by an underlying molecular model. Our NN-tensor model not only attains energy precision comparable to the molecular model, but it also accurately captures the isotropic-nematic phase transition, which the LdG model cannot achieve. By embedding the NN-tensor model within a second neural network, we can efficiently compute stable LC configurations in a domain-free and mesh-free manner. We validate this approach with multiple examples for nematic LCs, demonstrating its ability to find physically relevant nematic configurations in diverse scenarios. We further apply the NN-tensor model to the more complex smectic LC phase. Strikingly, the NN-tensor model can quantitatively predict the smectic layer thickness and capture intricate microstructures such as Omega and T-shaped grain boundaries—features that current conventional approaches fail to resolve. These results demonstrate that the NN-tensor framework is a unified, efficient, and physically faithful route for computing rich LC configurations across multiple phases.

The process of aging following a hard quench into a glassy state is characterized universally, for a wide class of materials, by logarithmic evolution of state variables and a power-law decay of two-time correlation functions that collapse only for the ratio of those times. This stands in stark contrast with relaxation in equilibrium materials, where time-translational invariance holds. It is by now widely recognized that these aging processes, which ever so slowly relax a complex disordered material after a quench, are facilitated by activated events. Yet, theories often cited to describe such a nonequilibrium process can be shown to miss pertinent aspects that are inherent to many experiments. A case in point are recent experiments on crumpling sheets of mylar loaded by a weight whose acoustic emissions are measured while the material buckles. Using extensive simulations to generate long time-series of such buckling events, we show that crumpling is a log-Poisson process activated by increasingly rare record-sized fluctuations in a slowly stiffening material characterized by a logarithmically growing length scale. Crumpling thus adds to a range of glassy materials exhibiting the log-Poisson property, which can be used to discriminate between theories.

We study universal aspects of thermalization induced by Trotterization, a procedure routinely used in gate-based quantum computation. We use the reduced-Bardeen-Cooper-Schrieffer model—quantum integrable with a classically integrable mean-field limit—where the effects of Trotter chaos are expected to be particularly stark. The resulting Trotterized chaotic dynamics is characterized by its Lyapunov spectrum and rescaled Kolmogorov-Sinai entropy. The chaos quantifiers depend on the Trotterization time step $\tau$. We observe a Trotter transition at a finite step value ${\tau }_c\approx \sqrt{N}$. While the dynamics is weakly chaotic for time steps $\tau \ll {\tau }_c$, the regime of large Trotterization steps is characterized by short temporal correlations. We derive two different scaling laws for the two different regimes by numerically fitting the maximum Lyapunov exponent data. The scaling law of the large $\tau$ limit agrees well with the one derived from the kicked top map. Beyond its relevance to current quantum computers, our work opens other directions—such as probing observables like the Loschmidt echo, which lie beyond standard mean-field description–-across the Trotter transition we uncover.