Physical Review E最新文献

Understanding computational capabilities of simple biological circuits, such as the regulatory circuits of single-cell organisms, remains an active area of research. Recent theoretical work has shown that a simple cross-talk architecture based on end-product inhibition can exhibit predictive behavior by learning fluctuation statistics of one or two environmental parameters. Here we extend this analysis to higher dimensions, i.e., a large number of fluctuating inputs. We show that a generalized version of the cross-talk architecture can learn not only the dominant direction of fluctuations, as shown previously, but also the subdominant modes, orienting its responsiveness spectrum to the fluctuation eigenmodes. We comment on the relevance of our results to living systems at other scales of organization, such as ecosystems of species competing for fluctuating resources.

Eukaryotic cells perform chemotaxis by determining the direction of chemical gradients based on stochastic sensing of concentrations at the cell surface. To examine the efficiency of this process, previous studies have investigated the limit of estimation accuracy for gradients. However, most studies have treated a circular cell shape, and the few considering elongated shapes assume the elongated direction as fixed. This leaves the question of how adaptive regulation of cell shape affects the estimation limit. Dynamics of cell shape during gradient sensing is biologically ubiquitous and can influence the estimation by altering the way the concentration is measured, and cells may strategically regulate their shape to improve estimation accuracy. To address this gap, we investigate the estimation limits in dynamic situations where elongated cells change their orientation adaptively depending on the sensed signal. We approach this problem by analyzing the stationary solution of the Bayesian nonlinear filtering equation. By applying diffusion approximation to the ligand-receptor binding process and the Laplace method for the posterior expectation under a high signal-to-noise ratio regime, we obtain an analytical expression for the estimation limit. This expression indicates that estimation accuracy can be improved by aligning the elongated direction perpendicular to the estimated direction, which is also confirmed by numerical simulations. Our analysis provides a basis for clarifying the interplay between estimation and control in gradient sensing and sheds light on how cells optimize their shape to enhance chemotactic efficiency.

Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities χ[over ̃]_{_{V}}(k) tend to zero as the wavenumber k≡|k| tends to zero and are often described by the power-law χ[over ̃]_{_{V}}(k)∼k^{α} as k→0 where α is the so-called hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with a size ratio β=D_{L}/D_{S}, where D_{L} and D_{S} are the large and small disk diameters, respectively, and the molar ratio of the two disk sizes is 1:1. In particular, by characterizing the rattler fraction ϕ_{R}, the fraction of configurations in an ensemble with fixed β that are isostatic, and the n-fold orientational order metrics ψ_{n} of ensembles of packings with a wide range of size ratios β, we show that size ratios 1.2≲β≲2.0 produce maximally random jammed (MRJ)-like states, which we show are the most disordered strictly jammed packings according to several criteria. Using the large-R scaling of the volume fraction variance σ_{_{V}}^{2}(R) associated with a spherical sampling window of radius R, we extract the hyperuniformity scaling exponent α from these packings, and find the function α(β) is maximized at β=1.4 (with α=0.450±0.002) within the range 1.2≤β≤2.0. Just outside of this range of β values, α(β) begins to decrease more quickly, and far outside of this range the packings are nonhyperuniform, i.e., α=0. Moreover, we compute the spectral density χ[over ̃]_{_{V}}(k) and use it to characterize the structure of the binary circular-disk packings across length scales and then use it to determine the time-dependent diffusion spreadability of these MRJ-like packings. The results from this work can be used to inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder.

We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme-value statistics of unconfined stochastic processes. This mapping holds regardless of the statistics of the noise driving the dynamics. We first apply this result within Brownian motion theory, deriving the noncrossing probability of a Brownian path with a specific family of curves, from which several well-known results in the field can be recovered in a unified way. We then extend the analysis to non-Markovian processes, using the mapping to a steady-state to compute the long-time noncrossing probability of a pair of run-and-tumble and Brownian particles.

While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to the stability of the grid, are traditionally studied numerically with the conventional viewpoint of two regimes of extended (inter-area) or localized (intra-area) modes. In this article we introduce an analogy based on stochastic quantum models and demonstrate its applicability to power systems. We show from simple models that at low frequency the mean free path induced by disorder is inversely cubic in the frequency. This stems from the Courant-Fisher-Weyl theorem [Teschl, Mathematical methods in quantum mechanics (American Mathematical Soc., 2014), Vol. 157], a characterization of the eigenvectors of the Laplacian of the network, which provides an intuitive understanding of how eigenvectors organize themselves into nodal domains resistant to disorder at low frequency. As a consequence, a power oscillation, induced by some local disruption of the grid, can propagate in a ballistic, diffusive, or localized regime. In contrast with the conventional viewpoint, the existence of these three regimes is confirmed in a realistic model of the European power grid.

For a system of N≫1 spinless quantum particles, the projection operator is introduced, which, surprisingly, exactly transforms the inhomogeneous (with irrelevant initial correlations term) Nakajima-Zwanzig generalized master equation (GME) into completely closed (homogeneous) GME with initial correlations included into the kernel governing its evolution. The obtained equation is equivalent to the closed linear evolution equation for an S-particle (S

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they focus solely on pairwise interactions. In this study, we employ adaptive higher-order networks to describe these systems by proposing a general framework by incorporating both adaptivity and group interactions. We demonstrate that global synchronization can exist in those complex structures and we provide the necessary conditions for the emergence of a stable synchronous state. We first study the setting in which both pairwise and higher-order interactions are allowed, but only the former adapt in time. We then extend this framework by including higher-order adaptive interactions. In both analyzed settings, we show that the necessary condition is strongly related to the master stability equation, allowing to separate the dynamical and structural properties. We illustrate our theoretical findings through the relevant examples involving adaptive higher-order networks of coupled generalized Kuramoto oscillators with phase lag, coupled with an all-to-all and a nonlocal ring-like structure. We also show that the interplay of group interactions and adaptive connectivity results in the formation of stability regions that can induce transitions between synchronization and desynchronization. Our findings also reveal that the introduction of higher-order adaptation significantly alters the synchronization stability compared to the case with constant higher-order interactions.

Rogue waves, presented in numerous fields of science, are attracting significant attention. We study the excitation of electromagnetic rogue waves in magnetized plasmas caused by the thermal electron anisotropic loss cone distribution. The Krylov-Bogoliubov-Mitropolsky method is used to derive the nonlinear Schrödinger equation (NLSE) from collisionless magnetohydrodynamics equations satisfied by electrons. By solving numerically the one-dimensional NLSE, the rogue waves can be excited owing to their association with modulational instability. We can obtain the initial magnetic field conditions necessary for the excitation of electromagnetic rogue waves from the plane wave solution satisfied by the vector potential. Meanwhile, we apply a 2.5D fully kinetic particle-in-cell (PIC) method to simulate the excitation of electromagnetic rogue waves in magnetized plasmas. The PIC simulation results show that the excitation of electromagnetic rogue waves is primarily caused by the instability of the transverse perturbation components.

The fundamental theoretical problem of the existence of plasma equilibrium in a nonsymmetric magnetic field with nested magnetic surfaces is resolved. The lack of examples of smooth solutions to the equilibrium equations with no symmetry of the configuration has for many years served as the argument supporting the hypothesis by Harold Grad that nondegenerated three-dimensional plasma equilibrium does not exist. This paper first presents explicit analytical counterexamples to Grad's hypothesis. Within the standard formulation of the plasma equilibrium problem, we obtain the family of smooth solutions to the equilibrium equations. These solutions describe the set of "true" nonsymmetric magnetic surfaces compatible with continuous profiles of plasma pressure and rotational transform. The convenient system of equilibrium equations is used in the form generalizing the Grad-Shafranov approach to the case of nonaxisymmetric magnetic configurations without involving the formalism of flux coordinates. The inapplicability of simple prototype models of slab or cylindrical topologies for the predictive conclusions about the equilibrium of toroidal plasma is also revealed and clearly demonstrated. The developed formalism proves the fallacy of Grad's hypothesis and opens opportunities for adequate modeling of three-dimensional equilibrium plasma configurations.

We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We consider a scalar model of light propagation in the medium. We employ the theory of reproducing kernel Hilbert spaces, together with regularization to recover the susceptibility of two- and three-dimensional scattering media. Numerical examples illustrate the effectiveness of the proposed reconstruction method.