Physical review. E最新文献

Modeling how information or disease spreads on a network is a major problem in network science. The problem of determining seed nodes that maximize influence is called the influence maximization problem and has been well studied for various models of influence dissemination. The influence computation problem has an even more ambitious goal as it seeks to determine the exact probability of particular nodes getting influenced. H. Z. Brooks et al. [arXiv:2403.01066] introduced a model for the spreading of content on networks inspired by bounded confidence models. We show that this content-spreading model generalizes the independent cascade model and propose various influence computation and influence maximization problems. We discuss centrality measures for identifying influential nodes in the case of trees, which is analytically and computationally tractable. Finally, we train graph neural networks to predict the influence probabilities and propose this as a benchmark task to evaluate the oversquashing problem in graph neural networks.

In contrast to the central pattern generator hypothesis, which posits that neural networks generate rhythmic motor patterns without sensory feedback, recent robotics studies have demonstrated that independent oscillating agents with load-dependent feedback can organize coordinated gaits in quadrupedal robots. In this study, we develop minimal mathematical models to describe how such coordination emerges from physical interactions through the trunk and environment. By employing active rotators as limb controllers, we demonstrate their capacity to generate distinct gait patterns, including the trot, pace, and bound. We can also predict gait transitions with walking speed. These models provide insight into why different animals with specific physiques have limited gait patterns and offer suggestions for designing quadrupedal robots.

Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or filaments. Yet most existing models for spatial network formation focus on node-based growth, leaving a significant gap in our understanding of systems built from spatially extended components. Here we introduce a minimal model for spatial networks, rooted in the iterative growth and intersection of lines, a mechanism inspired by diverse systems including transportation networks, fungal hyphae, and vascular structures. Unlike classical approaches, our model constructs networks by sequentially adding lines across a domain populated with randomly distributed points. Each line grows greedily to maximize local coverage, while subject to angular continuity and the requirement to intersect existing structures. This emphasis on extended, interacting elements governed by local optimization and geometric constraints leads to the spontaneous emergence of a core-and-branches architecture. The resulting networks display a range of nontrivial scaling behaviors: the number of intersections grows subquadratically; Flory exponents and fractal dimensions emerge consistent with empirical observations; and spatial scaling exponents depend on the heterogeneity of the underlying point distribution, aligning with measurements from subway systems. Our model thus captures the key organizational features observed across diverse real-world networks, establishing a universal paradigm that goes beyond node-based approaches and demonstrates how the growth of spatially extended elements can shape the large-scale architecture of complex systems.

Coherently coupled nonlinear Schrödinger equations arise for wave interactions in media where the relative phase of the components is critical. An example is the propagation of electric fields in an optical waveguide in the weak birefringence limit. The competing factors are second-order dispersion and four-wave mixing. Doubly periodic structures of the nonlinear Schrödinger equation returning to their initial states after complex evolution have been previously studied. Recurrence for a coherently coupled system is studied here via approaches of spectral and linear instabilities. A doubly periodic solution for coherently coupled systems is established in terms of Jacobi elliptic functions, and its robustness is investigated. For spectral instability, the eigenvalues of the associated matrix are computed. For linear instability, direct numerical simulations are performed for slightly perturbed doubly periodic patterns. These patterns generally display various degrees of instability. Special disturbances favorable for recurrence phenomena arising from a continuous wave background and singly periodic solutions are identified. The agreement between spectral and linear instabilities on the trends of growth of disturbances is excellent. Knowledge gained here will be useful for studying wave evolution and instabilities in fluids and optics.

In recent years, unconventional computing architectures that transcend traditional semiconductor-based systems have witnessed far-ranging research interest. Here we propose an approach to the construction of logic gates, using active particles, specifically 1-pentanol-infused disks, exploiting the principle of the Marangoni effect. In our experimental setup, we design a channel with arms designated for inputs and an arm to observe the output. The inputs are provided by disks, where active disks infused with pentanol are considered to have a truth value of 1, while passive disks are considered to have a truth value of 0. The movement of a controller disk placed in a decision-making region determines the output. We demonstrate that the complex interplay of surface tension, drag, and repulsive and attractive forces yields the fundamental AND and OR logic responses. Interestingly, the logic function can be switched by solely changing the activity of the controller by decreasing the pentanol concentration, thus giving the same channels the capacity to morph the logic functionality. Additionally, the complementary NAND and NOR logic can be obtained with a simple change in the output encoding. Such active-matter-based logic gates have the potential to perform in fluid conditions, making them ideal for biomedical applications, bio sensing, molecular computing, and targeted drug delivery by responding to biological signals without external power sources.

A universal and rigorous ensemble framework for nonequilibrium systems remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using a matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems.

We investigate the long-term relaxation of a distribution of N point vortices in two-dimensional hydrodynamics. To focus on the regime of weak collective amplification, we embed these point vortices within a static background potential and soften their pairwise interaction on small scales. Placing ourselves within the limit of an average axisymmetric distribution, we stress the connections with generic long-range interacting systems, whose relaxation is described within angle-action coordinates. In particular, we emphasize the existence of two regimes of relaxation, depending on whether the system's profile of mean angular velocity (frequency) is a nonmonotonic (respectively, monotonic) function of radius, which we refer to as profile (1) [respectively, profile (2)]. For profile (1), relaxation occurs through two-body nonlocal resonant couplings, i.e., 1/N effects, as described by the inhomogeneous Landau equation. For profile (2), the impossibility of such two-body resonances submits the system to a "kinetic blocking." Relaxation is then driven by three-body couplings, i.e., 1/N^{2} effects, whose associated kinetic equation has only recently been derived. For both regimes, we compare extensively the kinetic predictions with large ensemble of direct N-body simulations. In particular, for profile (1), we explore numerically an effect akin to "resonance broadening" close to the extremum of the angular velocity profile. Quantitative description of such subtle nonlinear effects will be the topic of future investigations.

1-alkanols are well known to have anesthetic and penetration properties, though the mode of operation remains enigmatic. We perform extensive atomistic molecular dynamics simulation to study the penetration of 1-alkanols of different chain lengths in the dioleoyl-phosphatidylcholine (DOPC) bilayer model membrane. Our simulations show that the depth of penetration of 1-alkanol increases with chain length, n, and the deuterium order of the DOPC tail decreases with the chain length of the acyl-chain of the 1-alkanol. We find a cutoff value for the length of the acyl-chain of 1-alkanol, n=12, where 1-alkanol with a chain length greater than the cutoff value takes longer to penetrate the membrane. Our simulation study also demonstrates that the membrane exhibits clusters of 1-alkanols with acyl chains longer than the cutoff value, whereas 1-alkanols with acyl-chain shorter than the cutoff value are distributed homogeneously in the membrane and penetrate the membrane in a shorter time than longer-acyl-chain 1-alkanols. These findings add to our understanding of the anomalies in anesthetic molecule partitioning in the cell membrane and may have implications for general anesthesia.

Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustration drives structured arrays of topological defects. In the dilute limit, these systems have been shown to form a novel state of self-limiting assembly, in which the equilibrium size of multiparticle domains are finite and well defined. In this article we employ Monte Carlo simulations of a recently developed 2D lattice model of geometrically frustrated assembly [Hackney et al., Phys. Rev. X 13, 041010 (2023)10.1103/PhysRevX.13.041010] to study the phase transitions between the self-limiting and defect bulk phase driven by two distinct mechanisms: (1) increasing concentration and (2) decreasing temperature or frustration. The first transition is mediated by a concentration-driven percolation transition of self-limiting, wormlike domains into an intermediate heterogeneous network mesophase, which gradually fills in at high concentration to form a quasiuniform defect bulk state. We find that the percolation threshold is weakly dependent on frustration and shifts to higher concentration as frustration is increased, but depends strongly on the ratio of cohesion to elastic stiffness in the model. The second transition takes place between self-limiting assembly at high-temperature or frustration and phase separation into a condensed bulk state at low temperature or frustration. We consider the competing influences that translational and conformational entropy have on the critical temperature or frustration and show that the self-limiting phase is stabilized at higher frustrations and temperatures than previously expected. Taken together, this understanding of the transition pathways from self-limiting to bulk defect phases of frustrated assembly allows us to map the phase behavior of this 2D minimal model over the full range of concentration.

We analytically investigate a one-dimensional random sequential adsorption (RSA) model in which deposition probabilities are nonuniform and depend on the polarization state of the available intervals. Adsorbed segments behave as dipoles with two possible orientations, leading to orientation-dependent placement rules that combine stochastic selection with deterministic relaxation to energetically favorable positions. By generalizing the standard RSA integral equation to include polarization-dependent boundary conditions, we derive and solve uncoupled functional recurrences for the mean coverage, obtaining exact results for both deterministic and stochastic regimes. Furthermore, we compute the variance using the law of total variance, identifying distinct intracase and intercase contributions to the fluctuations. The model exhibits a continuous transition between steplike coverage profiles as the orientation probability varies, providing a tractable framework for studying interaction-driven nonuniform adsorption processes.