We investigate the influence of varying confinement on the dynamics of polymer translocation through a cone-shaped channel. For this, a linear polymer chain is modeled using self-avoiding walks on a square lattice. The cis side of a cone-shaped channel has a finite volume, while the trans side has a semi-infinite space. The confining environment is varied either by changing the position of the back wall while keeping the apex angle fixed or altering the apex angle while keeping the position of the back wall fixed. In both cases, the effective space $\varphi$, which represents the number of monomers in a chain relative to the total number of accessible sites within the cone, is reduced due to the imposed confinement. Consequently, the translocation dynamics are affected. We analyze the entropy of the confined system as a function of $\varphi$, which exhibits nonmonotonic behavior. We also calculate the free energy associated with the confinement as a function of a virtual coordinate for different positions of the back wall (base of the cone) along the conical axis for various apex angles. Employing the Fokker-Planck equation, we calculate the translocation time as a function of $\varphi$ for different solvent conditions across the channel. Our findings indicate that the translocation time decreases as $\varphi$ increases, but it eventually reaches a saturation point at a certain value of $\varphi$. Moreover, we highlight the possibility of controlling the translocation dynamics by manipulating the solvent quality across the channel. Furthermore, our investigation delves into the intricacies of polymer translocation through a cone-shaped channel, considering both repulsive and neutral interactions with the channel wall. This exploration unveils nuanced dynamics and sheds light on the factors that significantly impact translocation within confined channels.

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

We perform a numerical simulation of compression of a highly porous dust aggregate of monodisperse spheres. We find that the average interparticle normal force within the aggregate is inversely proportional to both the filling factor and the average coordination number and we also derive this relation theoretically. Our findings would be applicable for granular matter of arbitrary structures, as long as the constituent particles are monodisperse spheres.

Wave confinement, e.g., in waveguides, gives rise to a huge number of distinct phenomena. Among them, amplitude gain is a recurrent and relevant effect in undulatory processes. Using a general purpose protocol to solve wave equations, the boundary wall method, we demonstrate that for relatively simple geometries, namely, a few leaky or opaque obstacles inside a $\theta$ wedge waveguide (described by the Helmholtz equation), one can obtain a considerable wave amplification in certain spatially localized regions of the system. The approach relies on an expression for the wedge waveguide exact Green's function in the case of $\theta =\pi /M$ ($M=1,2,...)$, derived through the method of images allied to group theory concepts. The formula is particularly amenable to numerical calculations, greatly facilitating simulations. As an interesting by-product of the present framework, we are able to obtain the eigenstates of certain closed shapes (billiards) placed within the waveguide, as demonstrated for triangular structures. Finally, we briefly discuss possible concrete realizations for our setups in the context of matter and electromagnetic (for some particular modes and conditions) waves.

Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose the sparse invariant detector (SID), an algorithm that autodiscovers conservation laws from differential equations. Its algorithmic simplicity allows robustness and interpretability of the discovered conserved quantities. We show that SID is able to rediscover known and even discover new conservation laws in a variety of systems. For two examples in fluid mechanics and atmospheric chemistry, SID discovers 14 and 3 conserved quantities, respectively, where only 12 and 2 were previously known to domain experts.

In this article, we find that impurity in a one-dimensional harmonic chain leads to spikes in the phonon transmission. Using the Langevin equations and Green's function method (LEGF), we find the underlying mechanism of spikes, which comes from the fact that the wave energy can be transferred through uniform subchains laid between impurities without loss. Both the position and magnitude of spikes can be analytically obtained. By employing these results, we provide an analytical approach to transmission in the thermodynamic limit, thereby compensating for the limitation of LEGF that are practically confined to finite system size. Finally, we determine an expression for the localization length based on LEGF, demonstrating the equivalence between mass disorder and spatial disorder in low impurity concentration.

Here, we investigate the maximum power and efficiency of thermoelectric generators through devising a set of protocols for the isothermal and adiabatic processes of thermoelectricity to build a Carnot-like thermoelectric cycle, with the analysis based on fluctuation theorem. The Carnot efficiency can be readily obtained for the quasistatic thermoelectric cycle with vanishing power. The maximum power-efficiency pair of the finite-time thermoelectric cycle is derived, which is found to have the identical form to that of Brownian motors characterized by the stochastic thermodynamics. However, it is of significant discrepancy compared to the linear-irreversible and endoreversible-thermodynamics based formulations. The distinction with the linear-irreversible-thermodynamics case could result from the difference in the definitions of Peltier and Seebeck coefficients in the thermoelectric cycle. As for the endoreversible thermodynamics, we argue the applicability of endoreversibility could be questionable for analyzing the Carnot-like thermoelectric cycle, due to the incompatibility of the endoreversible hypothesis that attributes the irreversibility to finite heat transfer with thermal reservoirs, though the distinction in the mathematical expressions can vanish with the assumption that the ratio of thermoelectric power factors at the high and low temperatures $\left(\gamma \right)$ is equal to the square root of the temperature ratio, $\gamma =\sqrt{T_L/T_H}$ (this condition could significantly deviate from the practical case). Last, utilizing our models as a concise tool to evaluate the maximum power-efficiency pairs of realistic thermoelectric material, we present a case study on the $n$-type silicon.

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multiclass data set. As a by-product, a topological classifier is defined that uses an open subcovering of the data set. This subcovering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open-source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

During the intercalation of lithium in layered host materials such as graphite, lithium atoms can move within the plane between two neighboring graphene sheets, but cannot cross the sheets. Repulsive interactions between atoms in different layers lead to the existence of ordered phases called “stages,” with stage $n$ consisting of one filled layer out of $n$, the others being empty. Such systems can be conveniently described by a multilayer Cahn-Hilliard model, which can be seen as a mean-field approximation of a lattice-gas model with intra- and interlayer interactions between lithium atoms. In this paper, the dynamics of stage formation after a rapid quench to lower temperature is analyzed, both by a linear stability analysis and by numerical simulation of the full equations. In particular, the competition between stages 2 and 3 is studied in detail. The linear stability analysis predicts that stage 2 always grows the fastest, even in the composition range where stage 3 is the stable equilibrium state. This is borne out by the numerical simulations, which show that stage 3 emerges only during the nonlinear coarsening of stage 2. Some consequences of this finding for the charge-discharge dynamics of electrodes in batteries are briefly discussed.

The one-dimensional (1D) Ising model is revisited. The integral operator method is used for the model to derive the general statistical identity for multispin correlation functions. As an application of this identity to generate various correlations, recursive formulas are derived for the correlations of pairs, threes, fours, and fives of spins. Both compact clusters and disjoint sets of spins are considered. It is shown that multispin correlations for the 1D Ising model can be exactly expressed in terms of pairwise correlations using recursive procedures. For clusters with different structures, numerical calculations of multispin correlations as a function of temperature and external magnetic field are performed. The results of these calculations are presented in the figures and discussed.

We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known single site case, but exhibits a discontinuous transition as the position of one resetting site is varied while keeping the initial position of the particle fixed, or vice versa. The discontinuity vanishes at a “liquid-gas” critical point in position space. This critical point exists provided that the relative weight $m$ of the further site is comprised in the interval [2.9028...,8.5603...]. When the initial position is a random variable that follows the resetting point distribution, a discontinuous transition also exists for the optimal rate as the distance between the resetting points is varied, provided that $m$ exceeds the critical value $m_c=6.6008....$ This setup can be mapped onto an intermittent search problem with switching diffusion coefficients and represents a minimal model for the study of distributed resetting.

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: Deterministic coupling and common forcing. The inclusion of independent noise in these models typically serves to drive disorder, increasing the stability of the incoherent state. Here we show that the reverse is also possible. We propose and analyze a simple general model of purely noise coupled oscillators. In the first explicit choice of noise coupling, we find the linear response around incoherence is identical to that of the paradigmatic Kuramoto model but exhibits binary phase locking instead of full coherence. We characterize the phase diagram, stationary states, and approximate low-dimensional dynamics for the model, revealing the curious behavior of this mechanism of synchronization. In the second minimal case we connect the final synchronized state to the initial conditions of the system.

Various physical systems relax mechanical frustration through configurational rearrangements. We examine such rearrangements via Hamiltonian dynamics of simple internally stressed harmonic four-mass systems. We demonstrate theoretically and numerically how mechanical frustration controls the underlying potential energy landscape. Then, we examine the harmonic four-mass systems' Hamiltonian dynamics and relate the onset of chaotic motion to self-driven rearrangements. We show such configurational dynamics may occur without strong precursors, rendering such dynamics seemingly spontaneous.

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations of a large variety of real systems whose elements interact in multiple fashions or flavors. However, multiplex networks are not always simple to observe in the real world; often, only partial information on the layer structure of the networks is available, whereas the remaining information is in the form of aggregated, single-layer networks. Recent works have proposed solutions to the problem of reconstructing the hidden multiplexity of single-layer networks using tools proper for network science. Here, we develop a machine-learning framework that takes advantage of graph embeddings, i.e., representations of networks in geometric space. We validate the framework in systematic experiments aimed at the reconstruction of synthetic and real-world multiplex networks, providing evidence that our proposed framework not only accomplishes its intended task, but often outperforms existing reconstruction techniques.

The hysteretic behavior exhibited by collagen fibrils, when subjected to cyclic loading, is known to result in both dissipation as well as accumulation of residual strain. On subsequent relaxation, partial recovery has also been reported. Cross-links have been considered to play a key role in overall mechanical properties. Here, we modify an existing coarse-grained molecular dynamics model for collagen fibril with initially cross-linked collagen molecules, which is known to reproduce the response to uniaxial strain, by incorporating reformation of cross-links to allow for possible recovery of the fibril. Using molecular dynamics simulations, we show that our model successfully replicates the key features observed in experimental data, including the movement of hysteresis loops, the time evolution of residual strains and energy dissipation, as well as the recovery observed during relaxation. We also show that the characteristic cycle number, describing the approach toward steady state, has a value similar to that in experiments. We also emphasize the vital role of the degree of cross-linking on the key features of the macroscopic response to cyclic loading.

We introduce a two dimensional system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal parameter ${\varphi }_i$. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in ${\varphi }_i$, making them similar to swarmalators used in robotic systems. In the absence of the internal parameter, the system forms a motility-induced phase separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or ant-synchronize their internal parameter values. These phases include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive antisynchronization, and a superlattice MIPS state for attractive synchronization.

We report experimental investigations of a liquid crystal comprising thiophene-based achiral bent-core banana shaped molecules. The compound exhibits the following phase sequence on cooling: Isotropic (517.4 K), $N$ (514.9 K), de Vries SmA (402 K), SmC. Practically no layer contraction was observed across the SmA to SmC transition, confirming the “de Vries” nature of the SmA phase. Interestingly, the crystallization does not occur on cooling the sample, unlike most other liquid crystals. Instead, the SmC phase undergoes a glass transition at 271 K even at a slow cooling rate. The dielectric spectroscopy studies carried out on the sample reveal the presence of a dielectric mode whose relaxation process is of the Cole-Cole type. The relaxation frequency of the mode was found to drop rapidly with decreasing temperature, confirming the glassy behavior. The variation of relaxation frequency with temperature follows the Vogel-Fulcher-Tammann equation, indicating the fragile glassy nature of the sample. This report identifies a bent-core liquid crystal exhibiting a “de Vries” SmA phase and glassy behavior at lower temperatures.

Spectral modulation of high-order harmonics generated in relativistic laser-solid interaction is investigated. Numerical simulations show that the modulation depends on surface plasma density profile, resulting in spectral envelope modulation and regular and irregular harmonic splitting. The mathematical and physical connections between the spectral modulation of high-order harmonics and the temporal modification of attosecond pulse train are explained. Based on these understandings, we propose a possible method to produce isolated attosecond pulses by tailoring surface the plasma profile.

This paper presents a numeric study of the dynamic stabilization of the ablative Rayleigh-Taylor instability (ARTI) in the presence of a temporally modulated laser pulse. The results show that the specially modulated laser produces a dynamically stabilized configuration near the ablation front. The physical features of the relevant laser-driven parameters in the unperturbed ablative flows have been analyzed to reveal the inherent stability mechanism underlying the dynamically stabilized configuration. A single-mode ARTI for the modulated laser pulse is first compared with that of the unmodulated laser pulse. The results show that the modulated laser stabilizes the surface perturbations and reduces the linear growth rate and enhancement of the cutoff wavelength. For multimode perturbations, the dynamic stabilization effect of the modulated laser pulse contributes to suppress the small-scale structure and reduce the width of the mixing layer. Moreover, the results show that the stabilization effect of the modulated laser pulse decreases as the maximum wavelength increases.

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a $d$-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in $N$-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.