The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, we extend this fundamental scientific question to the plastic regime by exploring the adaptations of crystalline sheets to the large uniaxial mechanical stretching. We reveal the intermittent plastic shear deformations leading to the complete fracture of the sheets wrapping the cylinder. Specifically, systematic investigations of crystalline sheets of varying geometry show that the fracture processes can be classified into defect-free and defective categories depending on the emergence of topological defects. We highlight the characteristic mechanical and geometric patterns in response to the large stretching deformation, including the shear-driven intermittent lattice tilting, the vortex structure in the displacement field, and the emergence of mobile and anchored dislocations as plastic excitations. The effects of noise and initial lattice orientation on the plastic deformation of the stretched crystalline sheet are also discussed. These results advance our understanding of the atomic level on the irreversible plastic instabilities of two-dimensional crystals under large uniaxial stretching and may have potential practical implications in the precise engineering of structural instabilities in packings of covalently bonded particulate systems.

The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often required, and the framework of the nonperturbative, or functional, renormalization group is no exception. The derivative expansion is one of the most popular approximation schemes within this framework, due to its great performance on multiple systems, as evidenced in the past few decades. Nevertheless, it has the downside of breaking conformal symmetry at a finite order. This breaking is not observed at the leading order of the expansion, denoted the local potential approximation, and it only appears once one considers, at least, the next-to-leading order of the derivative expansion [$O\left({\partial }^2\right)$] when including composite operators. In this work, we study the constraints arising from conformal symmetry for the $O\left(N\right)$ models using the derivative expansion at order $O\left({\partial }^2\right)$. We explore various values of $N$ and minimize the breaking of conformal symmetry to fix the nonphysical parameters of the approximation procedure. We compare our prediction for the critical exponents with those coming from a more usual procedure, known as the principle of minimal sensitivity.

In this paper, we consider a random search process with stochastic resetting and a partially accessible target $\mathcal{U}$. In contrast to standard search processes, we assume that when the searcher first finds the target by contacting the surface $\partial \mathcal{U}$, it does not have immediate access to the resources within the target interior. Instead, it spends a random waiting time attached to the surface, after which it either gains access to the resources or detaches and continues its search process. We also assume that the searcher requires an alternating sequence of periods of bulk diffusion interspersed with local surface interactions before being able to attach to the surface. The attachment, detachment, and target entry events are the analogs of adsorption, desorption, and absorption of a particle by a partially reactive surface in physical chemistry. Using renewal theory, we analytically derive the nonequilibrium stationary state and mean first passage time statistics for several configurations, including both the half-line and higher-dimensional geometries, and models incorporating non-Markovian absorption.

Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the $q$-state Potts model (for $q\ge 3$), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of $q$. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for $q=6$ and 8, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach.

Reconstructing the state space is a generic and basic step for studying nonlinear dynamics with partial observables. Recently, time series forecasting through an encoder-decoder artificial neural network is expected to implicitly realize this procedure. However, existing explanatory and comparative studies are insufficient to strongly support such an argument. This paper analyzes the feasibility of such a reconstruction from the predictive perspective. To produce the topologically equivalent attractor via the encoder, we generalize the conditions about the predictive range, measurement noise and model suitability. Based on these analyses, we explore an adapted reconstruction methodology from time series prediction. Moreover, we found that the inverted transformer network is more appealing for multivariate observations and the penalty function of noise amplification compensates for the deficiency of standard prediction error. We conduct an experimental comparison between the prediction-based reconstruction and typical delay coordinate reconstruction in multiple situations. The comparative outcomes demonstrate that sensible predictive designs can steadily reconstruct the attractor at the best level. Additionally, we recover the underlying dynamics from real meteorological data associated with El Niño–Southern Oscillation.

We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. The introduction of inelastic collisions between the particle and the boundary limit the unbounded energy increase after the crossover iteration observed for the conservative dynamics. The central phenomenology uses a probability distribution that satisfies the system's boundary conditions to solve the diffusion equation. From this, we express the observables and, using a set of scaling hypotheses and a generalized homogeneous function, obtain a relation between the critical exponents, leading to a scaling law validated through numerical simulations and analytical methods. This transition displays properties similar to continuous phase transitions in statistical mechanics, including scale invariance, interrelated critical exponents governed by scaling laws, and an order parameter (susceptibility) approaching zero (infinity) at the transition. Furthermore, the system exhibits a variation in velocity between collisions mediated by control parameters, known as elementary excitations, which facilitate particle diffusion. The system also does not present topological defects that could alter the probability distribution function.

Autoresonant (continuously phase-locked) two-phase waves of the Korteweg–de Vries equation are excited and controlled using a two-component, small amplitude, chirped frequency driving. These solutions are analyzed in the weakly nonlinear regime. The theory is based on Whitham's averaged variational principle. The problem is reduced to a fully separated two degrees of freedom dynamical problem. This separation allows for simple derivation of the autoresonant thresholds on the driving wave amplitudes. We also excite more complex four-phase autoresonant waves. The inverse scattering analysis of this case indicates again the separation of all four degrees of freedom in the associated weakly nonlinear dynamical problem.

We set ourselves the goal of obtaining the equations which govern the evolution of the mass density profile of a dense irrotational molecular cloud. We base our study on the notion of “ensemble of molecular clouds”, introduced in our previous work. We model the studied clouds making use of the “ensemble abstract representative member”—a spherically symmetric and isotropic cloud. This cloud is isothermal and radially accreting matter from its surroundings. Starting from the equations of hydrodynamics applied to a self-gravitating isothermal spherical gas cloud, we obtain a system of two first-order nonlinear partial differential equations, which govern the evolution of two unknown fields: the exponent of density profile and the accretion velocity. Under the assumption of steady state flow, we get approximate solutions, using the method of leading order terms. Far from the cloud's center we obtain density profile $\varrho ={\ell }^{-2}$, and the accretion velocity is constant, while near to the center we have $\varrho ={\ell }^{-3/2}$ and $v_{\mathrm{a}}\propto {\ell }^{-1/2}$. Through our dynamical equations, the obtained solutions coincide completely with the solutions found by using the equation of energy conservation of a fluid element (in our previous work). Also, combining the equations of energy balance for a fluid element, we arrive at the conclusion that the cloud's layers, far from the center, are in a stable dynamical state if the accretion velocity flow is sub- or trans-sonic, otherwise they are marginally stable (moderately supersonic flow) or unstable (supersonic flow). Both solutions are consistent only if the accretion flow is subsonic, and hence the outer layers are stable. Finally, under the assumption that both the accretion velocity and density scale with $\ell$ and their power-law exponents are position-independent, we show that the density scaling exponent far away from the center is $p=2$ and this value is an attractor. Hence, this value should be observable in dense molecular clouds.

Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to density functionals in weighted density forms, as, e.g., in fundamental measure theory. We implement the model with fast convolutional layers only and apply it to a system of hard disks in fully 2D inhomogeneous situations. The model is trained on a combination of smooth and steplike external potentials in the fluid phase. Pair correlation functions from test particle geometry show very satisfactory agreement with simulations although these types of external potentials have not been included in the training. The method should be fully applicable to 3D problems.

From the onset of the subject, granular media have been defying the toolkit of statistical mechanics, thus hindering our understanding of their thermodynamic and stress-strain constitutive properties and making this state of matter one of the key remaining mysteries in science. In the present work, we offer a resolution to this problem with the help of an idealized model—a collection of two-dimensional identical balls forming a static granular pile in the gravity field—that allows us to develop appropriate thermodynamics and constitutive relations from the first principles a posteriori justified via the statistical analysis of pile realizations. Besides the uncertainty due to the rough substrate on which the pile is built, we uncover another one due to ambiguities occurring in the positions of some interior balls. Both are responsible for the thermodynamic description of the granular pile, which proves to be anything but ordinary. In particular, we show that a pile is characterized by three temperatures: one is infinite, the other is negative, and the third is of higher order. Also, analyzing the fields of ball displacements $\mathit{\xi }$ and the normal force deviations $\delta \mathit{N}$ from those for the ideal-isosceles triangular structure of a regular pile reveals the hyperbolic nature of the $\mathit{\xi }$ field and the ability of the $\delta \mathit{N}$ field to change the characteristic type from hyperbolic to elliptic. The latter property not only yields new insights into the origin of force chains and offers an adequate description of the constitutive properties of the static granular pile but also turns out to be instrumental for understanding its thermodynamics. Our model may provide a basis for further grasping of granular media properties in general.

A two-dimensional Brownian fluid confined, in equilibrium, to a closed surface is necessarily a finite system that consequently does not fit the benchmark of an extensive thermodynamic system (ETS). Considering the particular case of a spherical surface, and in the absence of external fields, one gets a uniform arrangement which in the thermodynamic limit obeys the Euler equation that defines an ETS: the Landau (grand) potential becomes identical to the negative of the surface pressure times the area. The best-known upshot from this condition is the proportionality of the isothermal (surface) compressibility to the particle number fluctuations. The present study implements a bespoke Brownian dynamics approach, complemented with the customary methods from statistical mechanics, to show the extent to which a system with a finite radius (still defined by its lack of boundaries) departs from these ETS criteria. An experimental realization of this kind of system can be found in Pickering emulsions, which are stabilized by charged surfactant nanoparticles adsorbed to each one of the spherical oil droplets immersed in water. It is thus shown, by applying a model pair potential suitable for the interactions among these adsorbates (whose intensity can be adjusted), that the deviation from the ETS reference grows rapidly as the repulsion among the nanoparticles increases. Moreover, it is also demonstrated that this has important implications for the closure relations employed for the determination of the pair-correlation functions within typical liquid theory approaches.

We numerically study the rectification and collective dynamics of active particles driven by misaligned perception-dependent motility within an asymmetric channel. The swirling motion induced by misaligned perception can be effectively harnessed and converted into directed motion through a ratchet mechanism. Notably, the direction of motion is dictated solely by the channel's asymmetry and is independent of the misalignment angle's orientation. For identical particles, suitable parameters lead to the formation of a cluster that simultaneously rotates and exhibits directed motion as a whole within the channel. This cluster rotation, driven by misalignment, significantly enhances particle rectification. Optimal rectification occurs at specific values of key parameters, including channel width, self-propulsion speed, visual cone half-angle, and perception threshold, at which the average velocity is maximized. In binary mixtures of oppositely misaligned particles, simultaneous rectification and spontaneous separation are observed. The rectification effect is maximized when the two particle types are completely separated. These findings provide insights into controlling active matter through misaligned perception-dependent motility and asymmetric environments.

Nonlinear responses of physical systems to strong perturbations are notoriously difficult to tackle analytically. Here, we present analytic results for the nonlinear response of magnetic nanoparticles to large-amplitude oscillatory magnetic fields based on a particular model for the magnetization dynamics. A number of characteristic features of the in-phase and out-of-phase higher harmonic response are found and analyzed. In particular, we find that the magnitude of higher harmonic contributions $R_n$ depends on the field amplitude and frequency only via a single scaling variable that combines the two quantities. The decrease of $|R_n|$ with increasing order $n$ of harmonics is a key quantity monitored in biomedical applications such as magnetic particle spectroscopy and magnetic particle imaging. Except for the first few harmonics, we find that this decrease is exponential with a rate that depends on the scaling variable only. For not too high frequencies and not too large amplitudes, we find that these exact results for one particular model of magnetization dynamics hold approximately also for other, more frequently used models. Our results therefore offer not only deeper insight into strongly nonlinear responses of magnetic nanoparticles, especially for higher harmonics that are very difficult to determine numerically, but also suggest analyzing data in terms of a scaling variable.

We consider a family of totally asymmetric simple exclusion processes (TASEPs), consisting of particles on a lattice that require binding by a “token” in various physical configurations to advance over the lattice. Using a combination of theory and simulations, we address the following questions: (i) How does token binding kinetics affect the current-density relation on the lattice? (ii) How does this current-density relation depend on the scarcity of tokens? (iii) How do tokens propagate the effects of the locally imposed disorder (such as a slow site) over the entire lattice? (iv) How does a shared pool of tokens couple concurrent TASEPs running on multiple lattices? and (v) How do our results translate to TASEPs with open boundaries that exchange particles with the reservoir? Since real particle motion (including in biological systems that inspired the standard TASEP model, e.g., protein synthesis or movement of molecular motors) is often catalyzed, regulated, actuated, or otherwise mediated, the token-driven TASEP dynamics analyzed in this paper should allow for a better understanding of real systems and enable a closer match between TASEP theory and experimental observations.

We simulate a ferromagnetic Ising model with aperiodic interactions in three dimensions using the Monte Carlo method. When the strength of aperiodicity is weak, the systems exhibit behavior similar to that of a pure system. As we increase the value of $r$, we observe that the heat capacity develops a multipeak structure for all sequences. For both marginal and relevant sequences, we observe a region of divergent susceptibility, indicating the existence of a Griffiths phase. We find that the extent of this region is related to the wandering exponent and the strength of aperiodicity.

This article investigates spatiotemporally discrete or continuous stochastic descriptions, where we focus on differences in heat naturally defined between the particle level and the density field. Both descriptions are found to generally make the heat differences by the entropic term expressed just with the number density through spatial projection from the many particles' positions onto the density field. The transformation from the Langevin to Dean-Kawasaki equations is considered as the projection in the continuous descriptions, where the emergent heat differences undergo little temporal variations due to the sparse distributions of the point particles. On the other hand, the analogous formalisms constructed in the discrete models may exhibit the explicit temporal evolutions of the entropic term. Furthermore, we develop arguments about the interpretation and applicability of the heat differences as well as the perspectives to a many-polymer system.

The $q\text{−}\mathrm{state}$ clock model, sometimes called the discrete $XY$ model, is known to show a second-order (symmetry-breaking) phase transition in two dimensions for $q\le 4$ ($q=2$ corresponds to the Ising model). On the other hand, the $q\to \infty$ limit of the model corresponds to the $XY$ model, which shows the infinite order (non-symmetry-breaking) Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions. Interestingly, the two-dimensional clock model with $q\ge 5$ is predicted to show three different phases and two associated phase transitions. There are varying opinions about the actual characters of phases and the associated transitions. In this work, we develop the basic and higher-order mean-field (MF) theories to study the $q$-state clock model systematically. Our MF calculations reaffirm that, for large $q$, there are three phases: (broken) ${\mathbb{Z}}_q$ symmetric ferromagnetic phase at the low temperature, emergent $U\left(1\right)$ symmetric BKT phase at the intermediate temperature, and paramagnetic (disordered) phase at the high temperature. The phase transition at the higher temperature is found to be of the BKT type, and the other transition at the lower temperature is argued to be a large-order spontaneous symmetry-breaking type (the largeness of transition order yields the possibility of having some of the numerical characteristics of a BKT transition). The higher-order MF theory developed here better characterizes phases by estimating the spin-spin correlation between two neighbors.

A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a nondipolar BECs. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et al., Nature (London) 631, 289 (2024)], with dipolar interaction stronger by more than an order of magnitude compared with that of Dy atoms, we demonstrate that, in a very strongly dipolar NaCs BEC, it is possible to have a two- and a four-droplet metastable soliton, axially free along the polarization $z$ direction. In this study, we employ imaginary-time propagation of an improved mean-field model, including the Lee-Huang-Yang interaction. The dipolar solitons are subject to an expulsive Gaussian potential at the center and a harmonic potential, both acting in the $x\text{−}y$ plane. The phase-coherent solitons, possessing the isolated droplets, are free to move along the $z$-axis without any relative motion between the droplets. The dynamical stability and mobility of these solitons are demonstrated by real-time propagation employing the converged imaginary-time wave function as the initial state.

The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoidance of the numerical spectral unfolding. Like the use of the Rosenzweig-Porter approach to obtain the Berry-Robnik distribution of level spacings in mixed-type systems, in this paper, we extend this approach to analytically derive the distribution of spacing ratios for random matrices comprised of independent integrable blocks and chaotic blocks. We have numerically confirmed this analytical result using random matrix theory in paradigmatic models such as the quantum kicked rotor and the Hénon-Heiles system.

An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected cascade size is a time-dependent quantity and so enables the identification of nodes that are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalizes the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks.