Advances in controlled polymerization have enabled the synthesis of mechanically interlocked polymers like molecular knots and linear[$n$]catenane. These aesthetic macromolecules with unique topological constraints in the form of mechanical bonds are well known for their fascinating transport and rheological properties in the development of molecular machines and in knotted protein dynamics in biological applications. The diffusion dynamics of such macromolecular structures with large internal degrees of freedom are generally studied by using an equivalent size parameter, i.e., hydrodynamic radius, defined using Zimm theory. Although diffusion rates are expected to depend strongly on the intramolecular topological constraints in macromolecules, their explicit effects on translational and reorientational dynamics are still unknown. Here, we perform an in silico study on the diffusion dynamics of seven topologically distinct polymer chains in the limit of infinite dilution using multiparticle collision dynamics. The modeled polymers are linear, ring, linear[2]catenane, trefoil knot, linear[3]catenane, cyclic[3]catenane, and Borromean ring. The molecular weights of these macromolecules are selected such that the resulting hydrodynamic radius is approximately equal to each other. We show that while the translational diffusion coefficients of these topologically distinct polymer chains are approximately equal to each other in agreement with the Zimm theory, there are significant differences among the values of the corresponding rotational diffusion coefficients. We show that the presence of mechanical bonds in the polymer chains slows down the rotational diffusion significantly, thus suggesting the role of molecular topology on reaction kinetics of macromolecules.

Free energy is a crucial physical quantity in a wide range of domains, including systems at the nanoscale. The Jarzynski equality computes the equilibrium free energy difference between two states using the measurements of nonequilibrium work needed to move the system between the states. The Jarzynski equality uses the mean of the exponentiated work and thus holds true only in the limit of infinite data size. There are only a few studies estimating errors when employing the Jarzynski equality with a finite number of measurements; further, these estimates remain limited in scope. We provide nonrestrictive and rigorous confidence bounds on the free energy difference computable from samples of measured work without the need for any prior information on the work distribution. These bounds are applicable to a large variety of experimental conditions that take a system far from the equilibrium. The analytical claims are corroborated using simulations and experiments utilizing a toolbox developed in Python.

We report numerical evidence of Fermi-Pasta-Ulam-Tsingou (FPUT)-like recurrence in weakly damped, periodically driven $\alpha$-FPUT chains. In narrow regions of driving amplitude and damping, the steady-state energy is exchanged among a few low-frequency modes in a quasiperiodic (or highly regular, near-periodic) manner over long timescales. The maximum damping allowing recurrence decreases rapidly with chain length, suggesting that in the thermodynamic limit such behavior is unlikely to persist. Unlike discrete time crystals, the recurrence period is not an integer multiple of the driving period and does not correspond to spontaneous symmetry breaking. Nevertheless, these results reveal a type of coherent nonlinear dynamics in driven, open multimode systems and provide guidance for experimentally realizing long-lived quasiperiodic states.

We investigate the formation of Bernstein-Greene-Kruskal-type $\mathit{E}\times \mathit{B}$ staircase equilibrium in the presence of energetic ions. We show that such staircase solutions, which display crucial kinetic features and which propagate like coherent electrostatic structures, represent saturated states of negative mass instability. An energy transfer from these staircase structures and zonal flows takes place, which becomes resonant in the presence of a global phase synchronization process. This zonal flow amplification occurs as a bifurcation process and leads to the formation of an internal transport barrier, which is crucial for suppressing ion-temperature-gradient turbulence. We discuss numerical experiments in support of this scenario, which have been performed with a reduced model (referred to as “particle-mode” model) based on a double gyro-average over both the fast cyclotron phase and the bounce (or transit) phases.

We investigate the diffusion of an intruder in a granular gas, with both components modeled as smooth hard spheres immersed in a low-viscosity carrier fluid to form a particle-laden suspension. In this system, dissipative particle collisions coexist with the action of a solvent. The latter is modeled via a viscous drag force and a stochastic Langevin-like force proportional to the background fluid temperature. Building on previous kinetic theory and random-walk results of the tracer diffusion coefficient [Phys. Rev. E 108, 024903 (2023)], where random-walk predictions were compared with Chapman-Enskog results up to the second Sonine approximation, we assess the robustness of the Enskog framework by incorporating molecular dynamics simulations, using direct simulation Monte Carlo results as an intermediate reference. In particular, we focus on the intruder velocity autocorrelation function, considering intruders' different masses (from 0.01 to 100 times the mass of the granular particles), and analyze the behavior of the intruder temperature and diffusion coefficient. Our results clarify the influence of the friction parameter and the conditions under which Enskog kinetic theory reliably describes intruder diffusion in granular suspensions.

We study the size distributions (SDs) of two- and three-dimensional nuclei $(d=2,3)$ in the Ostwald ripening (OR) stage in open systems. The size-dependent attachment rates and the time-dependent total amount of monomers are taken in the power-law forms, with indices $\alpha$ and $\beta$, respectively. The OR occurs when $\beta <{\beta }_{\text{max}}$, where ${\beta }_{\text{max}}$ depends on $\alpha$ and $d$. The case of $\beta =0$ corresponds to the Lifshitz-Slezov-Wagner (LSW) theory in closed systems. The case of $\beta =1$ corresponds to open systems under constant material influx, where the SDs often adopt the Family-Vicsek (FV) scaling form. Using a unified scaling approach, we obtain analytical solutions for the critical size, average size, and the SDs depending on the three parameters $d,$ $\alpha$, and $\beta$. We show that the LSW and FV scaling for the OR process in open systems is essentially the same thing. We analyze the SD shapes and particular solutions under different conditions and reveal the effect of SD narrowing at $\alpha <1$ as $\beta$ approaches ${\beta }_{\text{max}}$. The scaled SDs are unimodal in most cases at $\alpha <1$, and monotonically decreasing at $\alpha =1$. These results should be useful for modeling the OR process in a wide range of practical systems and interesting from a fundamental viewpoint.

A large number of complex systems can be represented as directed networks, where the connections (edge weights) between nodes (system states) are such that the flux of the quantity of interest (e.g., energy or information) from node $i$ to $j$ is not equal to that from $j$ to $i$. The network Laplacian underpins a suite of techniques for studying diffusion and random walks on networks, but many such methods have been developed for undirected graphs. In this paper, we propose a method for characterizing the relative degree of directedness of a network. Our approach is based on the pseudospectrum of the Laplacian and examines the difference in the nature of the “containing pseudospectral frontier” between the Laplacian itself and a variant formed by removing its non-normal structure. The distance between the containing and comparator frontiers then characterizes relative directedness as a function of the shape of the underlying pseudospectral surface. We demonstrate how this metric's behavior is consistent with that expected for a cyclic permutation adjacency matrix and is appropriate for a network where directedness is controlled systematically. We also extend an existing definition of network directedness and then apply our method in detail to a network capturing the Lagrangian dynamics of a turbulent flow. Two local maxima for our metric arise in distinct regions of the complex plane, but the eigenvalues driving these maxima are dominated by nodes from the network that are both very similar to each other and highly atypical in terms of the physics they embody. These nodes are also very different in nature from those highlighted by a stochastic differential equation model for these dynamics that successfully captures many key features of turbulence. This highlights the sensitivity of our approach and its potential utility in model validation, in addition to network characterization.

Scientific impact emerges from citation networks shaped by nonlinear and out-of-equilibrium dynamics. By analyzing over 30 million scientific papers and 1 billion references across disciplines, we uncover a two-phase correlation structure: a long-term assortative regime, where highly cited works reinforce each other, and a short-term antiassortative regime, where transformative papers tend to draw upon under-recognized ideas. To reconcile this paradox, we introduce a single state variable—capacity—which quantifies the residual “originality budget” of prior knowledge. We demonstrate that capacity governs a universal double-exponential relationship with long-term impact, consistent across biology, chemistry, and physics. Building on this empirical regularity, we formulate a stochastic dynamical model coupling novelty erosion with capacity-driven attachment. The model accurately reproduces the observed dual-phase correlations and predicts a critical capacity that maximizes future impact. Furthermore, we show that capacity serves as a robust early indicator of scientific breakthroughs, effectively distinguishing Nobel-Prize-winning papers from the rest. Our results provide a unified theoretical framework for correlated impact dynamics, advancing our understanding of knowledge diffusion and breakthrough emergence in complex evolving networks.

Numerical simulations of surface acoustic wave (SAW)-induced acoustic streaming are highly sensitive to the choice of second-order boundary conditions. This study systematically compares the no-slip (NS) and Stokes slip (SD) boundary conditions through different numerical approaches. Two- and three-dimensional simulations based on the Reynolds stress method are performed for standing SAW and traveling SAW devices. Results are validated against particle image velocimetry measurements of streaming patterns and velocities. We show that the SD condition yields Lagrangian velocity fields in significantly better agreement with experiments than the NS condition, accurately capturing vortex number, rotation direction, and amplitude across varying device geometries and operating conditions. In contrast, the NS condition overpredicts velocities by 1 to 2 orders of magnitude and often fails to reproduce experimentally observed vortex structures. These findings highlight the essential role of the Stokes drift boundary condition in modeling acoustic streaming and provide clear guidance for its use in future simulations of SAW-based acoustofluidic systems.

We derive the quantum potential directly from the material derivative of the osmotic velocity and formulate a two-fluid model that reproduces the Madelung equations. Interactions between the two fluids are included but remain secondary. The framework is generalized to incorporate electromagnetic fields, yielding a self-consistent description of both the Schrödinger and Klein-Gordon equations. Extension to the relativistic Klein-Gordon case demonstrates the model's flexibility and applicability to spinless relativistic quantum systems. This approach unifies hydrodynamic, kinematic, and electromagnetic perspectives, providing a clear physical interpretation of quantum potentials and forces and offering a versatile platform for modeling complex quantum systems in both nonrelativistic and relativistic regimes.

A dual-wavelength high-sensitivity laser diagnostic based on a Nd:YAG laser (532 and 1064 nm, pulse duration of 7 ns) was applied to a laboratory high-voltage atmospheric discharge. The applied voltage was 1 MV, and the discharge current reached 10 kA. The discharge gap length was 0.55 m. The electrodes consisted of a pointed cathode inside a smooth-rim cone and a hemispherical mesh anode. The voltage pulse duration was about $1\mu \mathrm{s}$ with a rise time of 150–200 ns. The closure regions of a cathode-directed leader and an anode-directed leader were visualized. Electron density profiles were obtained in both leader channels. Distinct differences in the plasma structure of the two leaders during off-axis merging were revealed.

We investigate the roles of spin and packing fraction on the dynamics of cratering when a solid projectile impacts a granular bed at different incident angles. To do so, we carried out DEM (discrete element method) computations in which we varied the magnitude and direction of the projectile spin, the impact velocity, the bed packing fraction, and the incident angle. For a given incident velocity, we found that the projectile can rebound for small angles, or be completely or partially buried for larger angles, and that when buried, it can sometimes migrate large horizontal distances depending on the incident angle. We also found that increasing the packing fraction strengthens rebounds, and that the initial spin, depending on its direction and orientation, induces rebound, burying, or transverse deviations. The crater morphology also changes with the varying parameters, acquiring circular, elliptical, goutte-like, tadpole-like, and transitional shapes, correlating well with the projectile behavior. Finally, we propose diagrams to organize and classify the observed dynamics. Our results shed new light on the different shapes of craters found in nature and the fate of the impacting material.

We investigate a system of two coupled one-dimensional Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equations which possess a global conservation law. Such a system of equations has been recently derived for the quasiparticle densities in a two-band fermionic model with a particle-number conserving dissipative protocol. As the standard FKPP equation, the studied system has one unstable and one stable homogeneous solution, with a traveling wave switching between them. We demonstrate that the conservation law enforces the synchronization of traveling waves for both densities and determines their minimal possible velocity. Surprisingly, we find the existence of jumps in the minimal velocity as a function of control parameters. We obtain that the minimal velocity of propagating fronts in the coupled FKPP equations may significantly exceed the minimal velocity for a single FKPP equation in a wide range of control parameters.

Topological properties play a crucial role in the collective dynamics of coupled oscillators. In this Letter, we reveal a topology-induced phenomenon, including sparsity-induced stochastic resonance (SR) and coherence resonance (CR), in coupled noisy networks. The network sparsity alters the stochastic switching rates in coupled bistable systems and modulates the mean-field coherence in coupled excitable systems. The responses achieve maxima or minima at moderate sparsity (i.e., the optimal sparsity), implying the occurrence of sparsity-induced SR and CR. In particular, we discover the existence of invariant sparsity (domain) regarding sparsity-induced SR (CR). When the system size exceeds a threshold, the optimal sparsity (domain) is invariant with respect to system size, the five types of networks, and the frequency of the periodic force. By introducing a sparsity-dependent effective coupling, mean-field theory predicts sparsity-induced SR. These findings provide new insight into the collective dynamics of brain networks, especially explaining the pruning of neural connections by astrocytes.

Rapidly oscillating, inhomogeneous electromagnetic field from laser exert a force that repels charged particles from regions of high light intensity. We propose and analyze a flat-bottomed hollow-beam ponderomotive optical trap for an ultracold neutral plasma (UNP), driven by a high-power ${\mathrm{CO}}_2$ laser. Molecular dynamics simulations show that the plasma and Rydberg atoms are effectively trapped within a nearly uniform dark region bounded by repulsive light walls. In contrast to RF traps, flat-bottomed traps yield a small density-weighted mean ponderomotive energy per electron, while the UNP collision frequency is far below the laser frequency, thereby making collisional absorption negligible and does not limit the lifetime of the trap. This approach could enhance antimatter production and storage.

In this work, we quantify the timescales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual information across lagged embeddings of time series localized by wave number. For our chosen weakly turbulent system, the algorithm finds asymmetries in the information flow across wave numbers, reflecting what are typically described as forward and inverse cascades. However, our approach goes beyond typical heuristic arguments and provides quantitative insight into the intricate multiwave mixing dynamics necessary to maintain the steady statistical state characterizing weak turbulence. Our work then provides a detailed and fully nonlinear statistical analysis of a weakly turbulent system. The flexibility of our approach points to broader applicability in real-world data coming from chaotic or turbulent dynamical systems.

Pattern-forming instabilities are fundamental to spatiotemporal dynamics in complex biological systems, yet the role of instability modes in the manifestation of pattern formation remains poorly understood. We develop and analyze a generalized Hindmarsh-Rose network model that integrates (1) normal and abnormal diffusion via Laplacian and pseudo-inverse coupling and (2) both synaptic delay and distributed memory kernels. Linear stability analysis yields explicit criteria for Turing and delay-induced instabilities, highlighting how the network spectrum—through the eigenvalues of the coupling operator—governs stability boundaries and transversality. We show that mean delay reshapes which spectral modes set the critical synaptic delay threshold, switching control from the most negative to the most positive Laplacian eigenmodes as memory increases. Direct simulations on random networks reveal that the number of spatial instability modes scales with the number of neuronal spikes via a robust power law, providing a quantitative marker of seizure intensity. Abnormal diffusion and strong coupling promote pathological pattern selection, while increased connectivity enhances robustness and suppresses abnormal discharges. These results establish instability modes as a mechanistic bridge between network spectra, delay mechanisms, and epileptiform activity, and suggest tunable control parameters for prediction and mitigation in delayed, network-organized dynamical systems.

A network's community structure commonly impacts its functions. For instance, networks seeking synchronization will see this process follow the topology's hierarchical and community structuring. Herein, the interplay of network adjacency and Laplacian eigenspectra is shown to uncover hierarchical influence and community structure. Ring networks embedded with hubs of high connectivity are first analyzed to characterize the differing insights of the adjacency and Laplacian eigenspectra. This understanding is then transferred to the case study of satellite networks composed of intersecting rings. From these scenarios, it is found that where the adjacency reflects a network's structure, the Laplacian detects nodes' influence profiles. The adjacency identifies the number and relative sizes of salient network structures, for example hubs of high connectivity. In contrast, the Laplacian decomposes these structures in sets of nodes with equivalent influence profiles, where influence emerges due to variations in nodes' connectivity.