Using Monte Carlo simulations, we investigate the dynamical properties of the Baxter-Wu model under slow quenches, i.e., tuning the temperature slowly. For the cooling process, the scaling behavior of the excess defect density in the critical region aligns well with the predictions of the Kibble-Zurek (KZ) mechanism. However, the scaling behavior of the excess defect density after exiting the impulse regime does not follow from a simple interplay between the KZ mechanism and the coarsening dynamics; the system undergoes a decay close to a power-law form with an exponent that is significantly different from the coarsening exponent observed in instantaneous quenching. For the heating process, we show that if the system starts from its ground state, the relevant exponents describing the KZ mechanism are identical to those in the cooling scenario. Furthermore, in the heating process, we find that the system does not directly enter the adiabatic regime after leaving the impulse regime but instead passes through a crossover regime with an exponential decay of the excess defect density. If the initial state is ordered but not the ground state of the system, the defect density exhibits a good scaling behavior, but the relevant exponents do not conform to the predictions of the KZ mechanism.

Discovering constants of motion is meaningful in helping understand the dynamical systems, but it inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant of Motion Networkk (COMET), are promising in handling this scientific problem. While the COMET method improves dynamic predictions by leveraging discovered constants of motion, there remains significant room for further refinement. In this paper, we propose a neural network architecture, built using the singular-value-decomposition technique, and a two-phase training algorithm to improve the performance of COMET. Extensive experiments show that our approach not only retains the advantages of COMET, such as applying to non-Hamiltonian systems and indicating the number of constants of motion, but also can be more lightweight and noise-robust than COMET.

This study investigates the interplay between high-frequency external forcing and the intrinsic dynamics of a quantum nonlinear parametric oscillator. To analyze this system, classical equations of motion of the averages of quantum operators are derived and solved by employing suitable truncation schemes and the Blekhman perturbation method. It is observed that quantum fluctuations and oscillation amplitudes within the parametric resonance zone can be modulated through the fast external periodic forcing. Moreover, the influence of the strength of driving on the overall system dynamics is systematically explored. Finally, the theoretical predictions are validated through numerical simulations, establishing the reliability of the developed framework.

This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach introduces several tunable parameters, offering exceptional flexibility in capturing the diverse topologies and scaling behaviors found in both natural and man-made networks. The model effectively replicates their key characteristics such as fractal dimensions, power-law degree distributions, and scale-invariant properties of hierarchically nested boxes. Unlike traditional deterministic models, it incorporates stochasticity into the network growth process, overcoming limitations like discontinuities in degree distributions and rigid size constraints. The model's applicability is demonstrated through its ability to reproduce the structural features of real-world fractal networks, including the Internet, the World Wide Web, and co-authorship networks.

In this paper, the problem of helium gas transport in graphene nanochannels is investigated by a multilevel approach coupling surrogate modeling and Monte Carlo simulations. Under the rarefaction condition, the Knudsen diffusion is the dominant gas flow regime, characterized by gas-wall collisions. Furthermore, at low temperatures, helium gas atoms can be adsorbed on the surface and move like Brownian particles. To address the problem, the collision data between gas atoms and wall surfaces in equilibrium state are first generated by molecular dynamics simulations. A general statistical surrogate model based on polynomial chaos expansion accounting for adsorption and surface diffusion is constructed. The model exploits the Langevin dynamics analogy to satisfy physical constraints on the velocity distribution, the decaying time-dependent velocity correlation, and time-dependent displacement behavior. The trained model is then used in Monte Carlo simulations to compute various transport quantities in long nanochannels. Numerical results from the Monte Carlo study show that the approach can capture the size effect on the diffusion coefficient and transmission probability. Without being limited to helium and graphene, the developed method can be applied to any gas and solid couple and the problem of construction of kinetic boundary conditions.

We construct a continuum model of a recently discovered ferroelectric smectic-A $\left({\mathrm{SmA}}_{\mathrm{F}}\right)$ liquid crystal that has a layered structure with orientational order and polarization along the layer normal. We take into account the layer order by a complex order parameter $\psi$, and the orientational order by a director $\vec{n}$. Screened electrostatic interaction of induced charges is also introduced. We carry out numerical calculations of the dynamics of phase transition from an isotropic phase directly to ${\mathrm{SmA}}_{\mathrm{F}}$ for a simple case of small screening length. Then the electrostatic interaction is reduced to splay elastic energy and can be incorporated into the variation of the splay elastic constant $\left(K_1\right)$. We show that the enhancement of the effective $K_1$ significantly promotes the coarsening dynamics of the layered structure to a uniform one by suppressing the bending of the layers. We calculated three different characteristic lengths from the correlation of $\vec{n}$, number density of the defects of $\vec{n}$, and the structure factor of $\psi$. All the characteristic lengths for different effective $K_1$ exhibit power-law time evolution whose exponent is close to $1/4$, except for the case when the effective $K_1$ is unrealistically small compared with the bend elastic constant $K_3$. Our model can be exploited to a wide class of problems concerning the structural properties of a ferroelectric ${\mathrm{SmA}}_{\mathrm{F}}$ liquid crystal.

In this study, we explore self-organization in a two-dimensional swarm model composed of two distinct swarmalator types $(A \text{and} B)$ with opposing angular velocities, focusing on the roles of stigmergy-mediated interactions, phase-dependent motion, and physical constraints, including boundary conditions and barrier effects. Unlike traditional approaches that rely on local or direct physical interactions, the proposed swarm coordinates through internal phase-based dynamics coupled with environmental phase modifications. The intrinsic angular velocity of each swarmalator determines its phase rotation, which in turn governs its orbital motion and phase interactions with the environment. The nonequilibrium simulations reveal varying degrees of segregation across different segregation stages, observed across different time horizons, which are quantified by pairwise measures of neighborhood homogeneity specific to swarmalator type $(A \mathrm{or} B)$. Corotating pairs (AA or BB) channel trajectories via stigmergy, forming uniform clusters of the same type. In contrast, counter-rotating pairs (AB or BA) induce phase mixing, cluster decay, and fluctuations at cluster peripheries. At high stigmergy-mediated coupling, dynamic ring-shaped clusters emerge, with their macroscopic rotation direction determined by the sign of the angular velocity. Our findings underscore the importance of the interplay between indirect interactions and spatial constraints in shaping emergent self-organized patterns. This work provides a blueprint for constructing bioinspired robotic systems that adapt through environmental feedback, paving the way for advanced environments designed to actively guide swarm behaviors.

Until now, quasi-isodynamic magnetic fields have been the only known stellarator configurations that, at low collisionality, give small radial neoclassical transport and zero bootstrap current for arbitrary plasma profiles, the latter facilitating control of the magnetic configuration. The recently introduced notion of piecewise omnigenous fields has enormously broadened the space of stellarator configurations with small radial neoclassical transport. In this Letter, the existence of piecewise omnigenous fields that give zero bootstrap current is proven analytically and confirmed numerically. These results establish piecewise omnigenity as an alternative approach to stellarator reactor design.

We study a lattice model of a magnetic polymer where the XY spin variables are located on a self-avoiding walk on a regular lattice in two and three dimensions. We consider the regime where both spins and conformations are dynamic; thus, the XY model is defined on a dynamic lattice and conformations generate an annealed disorder. Using Monte Carlo simulations, we characterize the globule-coil and ferromagnetic-phase transitions, and pay special attention to the vicinity of the theta point. Our numerical results suggest that the transitions are continuous in two dimensions and first order in three dimensions, which are similar to related models with Ising spins.

Fluids, subject to symmetry breaking by stratification, support propagation of anisotropic internal waves (IWs). In the vertical plane, rays representing energy paths obey a nonspecular reflection law, as their inclination is solely dictated by their frequency. Although satisfying the linear Poincaré equation, in basins having sloping walls, ray dynamics exhibits nonlinear effects such as convergence onto wave attractors. In contrast, in the horizontal plane of a basin with vertical walls, IWs reflect specularly and follow chaotic ray paths. Here we present an analysis of these competing effects in a 3D IW ray billiard of a stadium having sloping walls. We show and explain how varying the wall's slope shifts the ray dynamics between regimes of near ergodicity, chaotic scattering, and nonchaotic scattering with self-similar patterns, despite the basin being closed. The rich results stemming from the interplay between elliptical ergodicity and hyperbolic focusing relate to a broader context of physical phenomena.

We present the use of x-ray fluorescence spectroscopy (XFS) to a sensitive temperature diagnostic in shocked foams at temperatures of 30–75 eV. Cobalt-doped foams were shock compressed using a planar drive at the OMEGA laser facility and photo-pumped with a Zn $\mathrm{He}\alpha$ x-ray source. Analysis of the resulting cobalt $K\beta$ x-ray fluorescence spectra using collisional radiative codes allows the temperature to be determined in the shocked foams. This method provides a sensitive and robust technique to determine temperatures in high-energy-density physics experiments in the tens of electronvolts temperature range. In these experiments, we find that radiation hydrodynamic simulations predict a lower temperature in the shocked foams compared to analysis of the XFS data using collisional radiative models. Although additional experiments with an independent temperature diagnostic to absolutely calibrate XFS spectra for these conditions will be required to resolve this discrepancy, these results demonstrate the excellent temperature sensitivity of XFS spectra for high-energy-density physics experiments.

We study the phase separation kinetics of a generic amphiphilic dimer melt system using dissipative particle dynamics simulations. Each dimer consists of two incompatible amphiphilic molecule units, A- and B-type, which are connected by a photosensitive covalent bond at their terminal ends. After quenching below the critical temperature, we analyze the model system under alternate light-on and light-off cycles. The photosensitive bond cleaves into two active radicals in the light-on cycle, triggering phase separation. In the light-off state, the radicals reform the covalent bond, which returns the system to a mixed state. This competitive interplay between mixing and demixing drives the formation of a multiscale morphology. This controlled morphological variation has applications in hydrophobic agents, melanin-based material synthesis, and emulsion stabilization. We quantify key structural properties, including the correlation function, structure factor, fractal dimension, interfacial tension, and characteristic length scales. The system exhibits mass fractal characteristics during the off-cycles. The morphologies develop within the bulk, as shown by a static primary peak and an emerging secondary peak in the structure factor. The length scale follows a power-law growth that crosses over from an initial viscous hydrodynamic regime with growth exponent, $\varphi \simeq 1$, to an inertial hydrodynamic regime, $\varphi \simeq 2/3$.

Optically confined colloidal particles, when placed in close proximity, form a dissipatively coupled system through hydrodynamic interactions. The role of such interactions influencing irreversibility and energy dissipation in out-of-equilibrium systems is often not well deciphered. Here, we demonstrate—through the estimation of the entropy production rate—that the nonequilibrium features of the system with such interactions vary depending on the nature of external driving, and importantly, on the level of coarse graining. Crucially, we show that coarse graining reverses the dependence of the measured entropy production rate on the strength of the hydrodynamic interactions. Furthermore, we clarify that such interactions do not violate energy balance at the level of individual trajectories, as was believed earlier. Our results highlight a previously unnoticed effect of coarse graining in nonequilibrium systems, and have implications for the inference of entropy production in experimental contexts.

Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the particles biases their diffusion, to capture such a transition. Changes of internal states and jumps between lattice sites obey local detailed balance with respect to the same interaction energy. We unveil a crossover between two regimes: for weak interactions, the dissipation is maximal, and partial inference (namely, based on discarding the dynamics of internal states) leads to a severe underestimation; for strong interactions, the dissipation is reduced, and partial inference captures most of the dissipation. Finally, we reveal that the macroscopic dissipation, evaluated at the hydrodynamic level, coincides with the microscopic dissipation upon coarsegraining. We argue that this correspondence stems from a generic mapping of active lattice models with local detailed balance into a specific class of nonideal reaction-diffusion systems.

We study canonical-equilibrium properties of random field $\text{O}\left(n\right)$ models involving classical continuous vector spins of $n$ components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we employ two complementary approaches: the mean-field approximation, valid for any disorder distribution, and the replica trick, applicable when the disordered fields are sampled from a Gaussian distribution. On the basis of an exact analysis, we demonstrate that when replica symmetry holds, both the approaches yield identical expression for the free energy per spin of the system. As consequences, we study the case of $n=2$ ($XY$ spins) and that of $n=3$ (Heisenberg spins) for two representative choices of the disorder distribution, namely, a Gaussian and a symmetric bimodal distribution. For both $n=2$ and $n=3$, we demonstrate that while the magnetization exhibits a continuous phase transition as a function of temperature for the Gaussian case, the transition could be either continuous or first order with an emergent tricriticality when the disorder distribution is bimodal. We also discuss in the context of our models the issue of self-averaging of extensive variables near the critical point of a continuous phase transition.

The phenomena of senescence are widely observed during the process of cell mitosis at the cellular level. From the perspective of statistical mechanics, the senescence can be formulated by a random walk process whose dynamic and transitional properties decay as the number of transitions increases. To explore the impact of the senescence effects on anomalous diffusion, we propose a new subordinator by adding a senescence term $f\left(s\right)$ to the classical $\alpha$-stable subordinator and then establish the subordinated Langevin equation to characterize the subdiffusion with senescence effects. By taking the senescence term $f\left(s\right)$ in the specific form of power law, we evaluate the ensemble average and time average of the mean-squared displacements and derive the Fokker-Planck equations of the propagators. The quantitative analyses reveal different diffusion regimes for the scenarios of weak senescence and strong senescence. The results show that the strong senescence effect has a damping influence and slows down the subdiffusion, while the weak senescence effect has no impact on the subdiffusion at large-time limit. The proposed Langevin equation and the quantitative analyses provide a new perspective for studying the senescence effects in anomalous diffusion phenomena.

We present a method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the usual single-electron self-energy ${\mathrm{\Sigma }}_{\sigma }(\vec{k},i{\omega }_n|\mu )$ with chemical potential $\mu$, in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wave vector and spin labeled virtual energies ${\xi }_{\vec{k}\sigma }$. These, thermodynamically derived virtual energies, are solutions of the set of equations ${\xi }_{k\sigma }={\varepsilon }_{\sigma }\left(\vec{k}\right)-\frac{1}{2}U+{\mathrm{\Sigma }}_{\sigma }(\vec{k},i\frac{\pi }{\beta }|{\xi }_{k\sigma }+\frac{1}{2}U-i\frac{\pi }{\beta })=0$. Examples of the method in simplified situations are provided.

Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatiotemporal chaos and turbulence. Finding these UPOs is, however, notoriously difficult. Matrix-free loop convergence algorithms deform entire space-time fields (loops) until they satisfy the evolution equations. Initial guesses for these robust variational convergence algorithms are thus periodic space-time fields in a high-dimensional state space, rendering their generation highly challenging. Usually guesses are generated with recurrency methods, which are most suited to shorter and more stable periodic orbits. Here we propose an alternative, data-driven method for generating initial guesses, enabled by the periodic nature of the guesses for loop convergence algorithms: While the dimension of the space used to discretize fluid flows is prohibitively large to construct suitable initial guesses, the dissipative dynamics will collapse onto a chaotic attractor of far lower dimension. We use an autoencoder to obtain a low-dimensional representation of the discretized physical space for the one-dimensional Kuramoto-Sivashinksy equation in chaotic and hyperchaotic regimes. In this low-dimensional latent space, we construct loops based on the latent POD modes with random periodic coefficients, which are then decoded to physical space and used as initial guesses. These loops are found to be realistic initial guesses and, together with variational convergence algorithms, these guesses help us to quickly converge to UPOs. We further attempt to “glue” known UPOs in the latent space to create guesses for longer ones. This gluing procedure is successful and points towards a hierarchy of UPOs where longer UPOs shadow sequences of shorter ones.