Quantum harmonic oscillators coupled through coordinates and momenta, represented by the Hamiltonian $\widehat{H}={\sum }_{i=1}^2(\frac{{\widehat{p}}_i^2}{2m_i}+\frac{m_i{\omega }_i^2}{2}{x}_i^2)+{\widehat{H}}_{\text{int}}$, where the interaction of two oscillators ${\widehat{H}}_{\text{int}}=i{k}_1{x}_1{\widehat{p}}_2+i{k}_2{x}_2{\widehat{p}}_1+k_3{x}_1{x}_2-k_4{\widehat{p}}_1{\widehat{p}}_2$, are found in many applications of quantum optics, nonlinear physics, molecular chemistry, and biophysics. Despite this, there is currently no general solution to the Schrödinger equation for such a system. This is especially relevant for quantum entanglement of such a system in quantum optics applications. Here this problem is solved and it is shown that quantum entanglement depends on only one coefficient, $R\in (0,1)$, which includes all the parameters of the system under consideration. It has been shown that quantum entanglement can be very large at certain values of this coefficient. The results obtained have a fairly simple analytical form, which facilitates analysis.

In this work, we demonstrate that the Hindmarsh-Rose model subjected to additive white noise exhibits birhythmicity. Specifically, the system fluctuates between two distinct bursting attractors characterized by different numbers of spikes. This behavior is observed not only within the bistable region bounded by two saddle-node bifurcations of limit cycles but also beyond these boundaries. This phenomenon is associated with the ghost effect, typically observed near deterministic saddle-node bifurcations. We map the region of stochastic birhythmicity in terms of the noise intensity and a key deterministic parameter that controls the dynamics of fast ion channels. To provide an analytical foundation, we introduce a simple stochastic model with a single saddle-node bifurcation. In this model, stochastic birhythmicity is similarly characterized as a function of noise intensity and the control parameter.

We investigate the influence of adaptation disparity and phase lag on the heterogeneous nucleation leading to multi-step and single-step phase transitions in a finite-size adaptive network due to frequency disorders. We elucidate that the adaptation disparity predominates the effect of frequency disorder in seeding the heterogeneous nucleation. Further, a large phase lag facilitates almost a continuous spectrum of partially and fully synchronized frequency clusters, and multistability among them. We also find that the underlying mechanisms of heterogeneous nucleation due to the adaptation disparity and phase lag parameters are distinctly different from that observed only in the presence of disorders. Furthermore, we also analytically deduce the macroscopic evolution equations for the cluster dynamics using the collective coordinates framework and show that resulting reduced dynamics mimic the observed heterogeneous phase transitions of the adaptive network under adaptation disparity and phase lag. Further, we deduce the upper bound for the coupling strength for the existence of two intra-clusters explicitly in terms of the adaptation disparity and phase lag parameters for the onset of the abrupt single-step transition.

We study the evolution of the fastest paths (FPs) in transportation networks under increasing congestion. Moving from the common edge-based to a path-based analysis, we examine the directed FPs connecting random origin-destination pairs as traffic grows. We describe their shape through effective length, detour (maximum distance of FP from a straight line), inness (signed area between FP and straight line), and their performance through a metric measuring how fast and how far an agent travels toward its destination. The entire network is characterized by analyzing the distribution of the performance metric (and its Gini coefficient) across uniformly sampled paths. The study focuses on the traffic-loading phenomenon that takes place during the morning peak hour for eight major cities: networks start with empty edges that are progressively populated by the FPs of single vehicles. As vehicle density grows, the interactions among selfish agents becomes stronger at edge level, and travel speed linearly decreases, thus optimal paths dynamically change with traffic. We fully characterize the transition to congestion and discuss the common aspects among the cities (and some peculiarities); in particular we were able to pinpoint a critical traffic level (or a sequence) for which path shape, rejection ratio, and inequality of the performance degradation show a concurrent qualitative change. For all cities we observe large peaks for both detour and inness (and their variance) in the proximity of the critical traffic level. Inness shows that paths are slightly attracted by city centers with light traffic, but switch to a strong repulsion immediately beyond the transition. Finally, our path performance metric highlighted a strongly asymmetric behavior when the city neighborhoods act as origins or destinations.

Visual cues play crucial roles in the collective motion of animals, birds, fish, and insects. The interaction mediated by visual information is essentially nonlocal and has many-body nature due to occlusion, which poses a challenging problem in modeling the emergent collective behavior. In this paper, we introduce a Boltzmann-equation approach incorporating nonlocal visual interaction. Occlusion is treated in a self-consistent manner via a coarse-grained density field, which renders the interaction effectively pairwise. Our model also incorporates the recent finding that each organism stochastically selects a neighbor to interact at each instant. We analytically derive the order-disorder transition point, and show that the visual screening effect raises the transition threshold, which does not vanish when the density of the agents or the range of the intrinsic interaction is taken to infinity. Our analysis suggests that the model exhibits a discontinuous transition as in the local interaction models, and but the discontinuity is weakened by the nonlocality. Our study clarifies the essential role of nonlocality in the visual interactions among moving organisms.

The scaling inertial-range behavior of the single-time two-point correlation functions of the weak magnetic field, passively advected by the turbulent velocity field driven by the stochastic Navier-Stokes equation, is investigated in the framework of the field-theoretic renormalization group approach in the second order of the corresponding perturbative expansion (in the two-loop approximation in the language of quantum field theory). The explicit two-loop expressions for the corresponding scaling exponents are found and compared to those obtained in the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the simple Gaussian statistics of the turbulent velocity field. It is shown that, in general, the presence of higher correlations of the velocity field in the turbulent kinematic magnetohydrodynamics leads to more pronounced anomalous scaling behavior of the magnetic correlations deep inside the inertial interval. Moreover, the analysis of the asymptotic behavior of dimensionless ratios of the single-time two-point correlation functions of the magnetic field shows that even the persistence of anisotropy deep inside the inertial range is more pronounced in the genuine kinematic magnetohydrodynamics with the Navier-Stokes turbulent velocity field than in the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the complete absence of higher correlations of the turbulent velocity field.

The forward Kolmogorov equation corresponding to a system under the combined excitation of Gaussian and Poisson white noises is an integrodifferential equation (IDE). In our recent study, we introduced GL-PINNs, which integrates the Gauss-Legendre (GL) quadrature with the physics-informed neural networks (PINNs) framework for solving time-dependent IDEs. However, we observed that in scenarios such as insufficient learning of initial conditions or dynamical systems with strong temporal dependencies, GL-PINNs produced inaccurate solutions despite achieving low training loss values. This issue primarily stems from the GL-PINNs framework's failure to account for temporal causality. To address this limitation, we develop a deep neural network method called ATD-GLPINNs, which integrates adaptive task decomposition and progressive learning strategy. This approach decomposes the complex task along the time axis into an initial subtask and several extra tasks, which enable progressive learning through adaptive adjustment of task parameters. As an extension of the GL-PINNs, this algorithm adheres to temporal causality by prioritizing the training of early subtasks and dynamically allocating additional computational resources to subsequent ones. Numerical experiments demonstrate that our suggested method converges with significantly fewer training epochs compared to GL-PINNs, making it not only more efficient and robust, but also capable of reducing computational costs while improving prediction accuracy.

Transverse interactions between particles can disrupt thermodynamic equilibrium, giving rise to distinctive nonequilibrium dynamics. However, the collective behavior of mixed particles with varying chiralities remains largely unexplored. In this paper, we use numerical simulations to investigate the separation and collective dynamics of binary mixtures with differing chiralities. Our results show that, even without attractive forces, chirality-induced nonhomogeneous bubble phases drive the clustering of similar particles, facilitating phase separation. Binary mixtures with opposing chirality spontaneously separate under specific conditions. We identify optimal parameters—such as the chirality, reduced inertial time, and packing fraction—that maximize the degree of separation. The chirality ratio emerges as a critical factor influencing both phase separation and collective dynamics. Furthermore, we observe that mixtures of particles sharing the same chirality direction but differing in magnitude can still achieve significant separation. In contrast, systems with completely opposite chirality do not form fully enclosed bubbles. Instead, when one particle type dominates, full bubbles emerge, with their number increasing as both the chirality and chirality ratio rise.

We consider three global chracteristic times for a one-dimensional Brownian motion $x\left(\tau \right)$ in the interval $\tau \in [0,t]$: the occupation time $t_{\mathrm{o}}$ denoting the cumulative time where $x\left(\tau \right)>0$, the time $t_{\mathrm{m}}$ at which the process achieves its global maximum in $[0,t]$, and the last-passage time $t_l$ through the origin before $t$. All three random variables have the same marginal distribution given by Lévy's arcsine law. We compute exactly the pairwise joint distributions of these three times and show that they are quite different from each other. The joint distributions display rather rich and nontrivial correlations between these times. Our analytical results are verified by numerical simulations.

In this work, we study the motion of protons under the influence of the Earth's magnetic field. We investigate the dynamics and topology of invariant spatial regions in two magnetic field models, namely, the dipolar and Luhmann tail configurations. In both cases, we analyze the motion of the protons in the relativistic regime, with kinetic energy intervals in the range $10<E<100\text{MeV}$. Specifically, we examine situations in which the protons undergo chaotic scattering due to their interaction with the Earth's magnetic field. Additionally, we consider scenarios where the protons, during their interaction, fall onto the Earth's surface. We compare the dipole and Luhmann tail cases by computing the distributions of escape and residence times, the exit basins, and the fractal dimensions of their boundaries. We present a robust symplectic numerical scheme which is suitable for analyzing the impact of the nonlinear effects and the presence of strong sensitivity to initial conditions when the model goes beyond the pure dipolar field. Surprisingly, we uncover a scaling law between the coefficient of the decay law and the energy of the protons. Furthermore, our computation of the fractal dimension of the exit basin boundaries $D$ versus the distance between the protons and the Earth $z_0$ reveals a decrease in $D$ as $z_0$ increases. We expect this work to be useful for a better understanding of the behavior of protons under the influence of the Earth's magnetic field when they are in the chaotic scattering regime.

We derive an expression for the exact probability $Pr[i\sim j]$ of a link between a node $i$ with degree $d_i$ and a node $j$ with degree $d_j$ in a graph belonging to the class of Erdős-Rényi $G(N,L)$ random graphs with $N$ nodes and $L$ links. The probability $Pr[i\sim j]$ is commonly approximated as $\frac{d_i{d}_j}{2L}$ and appears in the formula of Newman's modularity, which plays a crucial rule in community detection in networks. We show that, when applied to graphs not belonging to the class of Erdős-Rényi random graphs, our formula for $Pr[i\sim j]$ is considerably more accurate than $\frac{d_i{d}_j}{2L}$ and leads to the detection of different clusters or partitions than the original modularity formula.

A comprehensive study of the effect of gravity-induced shape change on the diffusion-limited evaporation of thin sessile and pendant droplets on a horizontal substrate is performed. Specifically, theoretical predictions for the evolution, and hence the lifetime, of sessile and pendant droplets evaporating in four modes of evaporation, namely, the constant contact radius (CR), the constant contact angle (CA), the stick-slide (SS), and the stick-jump (SJ) modes, are obtained. In particular, it is shown that gravity-induced shape change can cause quantitative differences in the evolution of sessile and pendant droplets compared to that of a droplet in the absence of (or in the neglect of) the effect of gravity (a “zero-gravity droplet”). For example, whereas sessile and pendant droplets evaporating in the CR mode evolve in qualitatively the same manner as a zero-gravity droplet, the evolution of droplets evaporating in the CA mode is more complicated. Specifically, while a zero-gravity droplet evaporating in the CA mode evolves according to the well-known $d^2$ and $2/3$ laws, an initially large sessile droplet evolves according to qualitatively different $d$ and $1/2$ laws, and an initially large pendant droplet evolves with the contact radius and the volume (but not, of course, the contact angle) behaving as if the droplet was evaporating in the CR mode. It is also found, perhaps somewhat unexpectedly, that the maximum height of a sessile droplet evaporating in the CA mode is a nonmonotonic function of time when the initial volume of the droplet is sufficiently large. Furthermore, it is found that for all four modes of evaporation a sessile droplet always evaporates faster, and hence has a shorter lifetime, than a zero-gravity droplet with the same initial volume, which in turn always evaporates faster, and hence has a shorter lifetime, than a pendant droplet with the same initial volume. It is also shown that for all four modes of evaporation the lifetime of a droplet is a monotonically increasing function of the initial volume of the droplet, that the lifetime of a droplet evaporating in the CA mode is always longer than that of the same droplet evaporating in the CR mode, and that the lifetimes of droplets evaporating in the SS and SJ modes both always lie between the lifetimes of the same droplet evaporating in the extreme modes.

Radiative shocks are shock waves where radiation plays a crucial role in shaping their dynamics and structure. This study investigates the influence of advanced radiation modeling, using the M1-multigroup moment method, on the properties of radiative shocks. We identify three key effects: the shock velocity, the hydrodynamic properties of the downstream medium, and the radiative precursor. Our simulations show that approaching the spectral effect of photons with the M1 multigroup reduces the shock velocity, resulting in a lower Mach number. Additionally, we find that precise radiation modeling enlarges the regions within the radiative precursor where gas and radiation are thermodynamically out of equilibrium. Finally, we compare the downstream quantities from our simulations with predictions from the commonly used diffusion regime approximation, identifying deviations of 1 to 8% in gas temperature and 3 to 15% in density. These findings highlight the importance of accurate modeling of the interaction between radiation and matter to advance our understanding of radiative shocks.

We have performed experiments on dusty plasmas under the weightlessness conditions of parabolic flights where the dust particles form an extended homogeneous dust cloud. The three-dimensional (3D) dynamic state of the dust cloud is characterized. Therefore, the particle trajectories have been recorded using a four-camera stereoscopic camera system. From that, the 3D particle trajectories have been determined using both a machine-learning particle reconstruction technique and the deterministic shake-the-box algorithm. From the trajectories, characteristic fluid parameters, such as flow fields and finite-time Lyapunov exponent (FTLE)-based fluid structures have been calculated and analyzed. The FTLE analysis indicates that the fluid is characterized by an incompressible flow with small-scale behavior. Furthermore, it is demonstrated that the machine-learning based approach allows to reliably characterize the dynamic states by comparison with the shake-the-box algorithm.

Effective mass transport properties of porous materials, such as permeability, are heavily influenced by their three-dimensional microstructure. There are numerous models developed for the prediction of permeability from microstructural characteristics, ranging from straightforward analytical relationships to high-performing machine learning models based on neural networks. There is an inherent tradeoff between predictive performance and interpretability; analytical models do not provide the best predictive performance but are relatively simple to understand. Neural networks, on the other hand, provide better predictive performance but are harder to interpret. In this paper, we investigate a multitude of models on the performance-versus-interpretability spectrum. Specifically, we use a dataset of $90000$ microstructures developed elsewhere and consider the prediction of permeability using the microstructural descriptors porosity, specific surface area, and geodesic tortuosity. At the respective ends of the spectrum, we study analytical, power-law-type models and fully connected neural networks. In between, we study neural networks that are either separable, monotonic, or both separable and monotonic. Establishing monotonic relationships is particularly interesting considering the potential for solving the inverse microstructure design problem using gradient-based methods. In addition, we study versions of these models that are consistent and inconsistent in terms of physical dimension.

We establish that the nonequilibrium dynamics of most pure states gives rise to the same entropy production (EP) as that of the corresponding ensemble, provided the effective dimension of the ensemble is large enough. This establishes the positivity of EP under a wide variety of nonequilibrium situations. Our results follow from dynamical typicality and suitable continuity properties alone, without relying on nonintegrability, and they complement other recent efforts to establish pure state second laws. An explicit comparison with the distinctively different two-point measurement scheme is also provided.

We investigate the effective temperature of a harmonic chain whose two ends are coupled to baths at different temperatures. We propose taking a weighted average temperature as the effective temperature of the system. The weighting factors are determined by the coupling strengths between the system and two baths, as well as the asymmetry of interactions between oscillators. We revisit the thermodynamics of nonequilibrium steady states based on the weighted average temperature and find that the fundamental thermodynamic relations in such states take on similarly concise forms as those in equilibrium thermodynamics, provided that we replace the equilibrium temperature with the weighted average temperature. Additionally, we demonstrate how to explicitly calculate effective temperatures through three illustrative examples.

In this paper, we performed the comprehensive studies of magnetic frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers-Wannier transfer matrix method. The assigned challenge consisted in finding rigorous formulas for residual entropies of all possible cases of degeneration of the system without exception and also elucidating the influence of frustrations on the behavior of the thermodynamic functions of the system under discussion. The accomplished results turned out to be very rich and intricate, especially in comparison with the original undecorated square lattice, in which frustration properties are completely absent. Such an abundance of properties is due to the multiparametric problem of decorated lattice with four exchange interactions $J_x, J_y, J_{dx}$, and $J_{dy}$ taking on arbitrary continuous values and different signs: positive (ferromagnetic) and negative (antiferromagnetic), as well as with two discrete variables $d_x$ and $d_y$ (multiplicities of decorating spins in both lattice directions), corresponding to infinite natural series of numbers.

Many biological and social systems are naturally represented as edge-weighted directed or undirected hypergraphs since they exhibit group interactions involving three or more system units as opposed to pairwise interactions that can be incorporated in graph-theoretic representations. However, finding influential cores in hypergraphs is still not as extensively studied as their graph-theoretic counterparts. To this end, we develop and implement a hypergraph-curvature guided discrete time diffusion process with suitable topological surgeries and edge-weight renormalization procedures for both undirected and directed weighted hypergraphs to find influential cores. We successfully apply our framework for directed hypergraphs to seven metabolic hypergraphs and our framework for undirected hypergraphs to two social (coauthorship) hypergraphs to find influential cores, thereby demonstrating the practical feasibility of our approach. In addition, we prove a theorem showing that a certain edge weight renormalization procedure in a prior research work for Ricci flows for edge-weighted graphs has the undesirable outcome of modifying the edge weights to negative numbers, thereby rendering the procedure impossible to use. This paper formulates algorithmic approaches for finding core(s) of (weighted or unweighted) directed hypergraphs.

In this work, we investigate the swimming dynamics of a spheroidal squirmer near a flat wall for various aspect ratios using the direct-forcing fictitious domain method. Our results show that the swimming mode of a strong pusher undergoes the transition from either oscillating or escaping to crawling as the aspect ratio increases. A strong puller exhibits an opposite transition: from crawling to escaping and then to oscillating as the aspect ratio increases. The mechanism for the near-wall swimming behavior of a strong puller and pusher is explored by analyzing the hydrodynamic force and torque on a swimmer with its height and orientation fixed. The results indicate that both collision and hydrodynamic toques are important to the near-wall swimming state of the squirmer. Additionally, we found that the initial orientation angle and the release distance do not influence the swimming mode when the squirmer initially swims toward the wall at an angle smaller than $-\pi /8$.