In this paper we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in a certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the “distance” to quantum chaos. Numerical simulations performed in the Lipkin-Meshkov-Glick model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart.

In this paper, we consider a stochastic molecular circadian oscillator described by a sequence of biological reactions and its deterministic kinetics governed by a system of ordinary differential equations in the limit of large numbers of molecules. The oscillations in the model are generated by negative feedback regulation of a gene. The focus of this paper is the entrainment of the oscillator by a periodic light signal that affects the maximal transcription rate of the gene. We introduce two scalings of the model parameters that provide independent control over the natural frequency of the oscillator and the relative noise level. We study entrainment in two ways: by visualizing the stochastic limit cycle in various projections of the discrete phase space of the system and by evaluating the maximum of the normalized cross correlation of the light signal with the number of protein molecules in the cell. The visualization method ignores the phase of the oscillator, and we find in this way that entrainment has a subtle organizing effect on the limit cycle as a whole. The cross correlation results reveal an interval of natural frequencies of the oscillator surrounding the frequency of the light signal within which maximal entrainment occurs with rather sharp drops in entrainment at the edges of this interval. The width of the interval of maximal entrainment increases with the amplitude of the light signal. These statements are applicable both to the stochastic oscillator and to its deterministic limit, but the results are most clear-cut in the deterministic case and degrade from there as the relative noise level increases.

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of $0.1–32.4\mathrm{g}{\mathrm{cm}}^{-3}$ and ${10}^4–{10}^8$ K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and $\langle Z\rangle$ to reveal the evolution of the plasma structure and ionization behavior.

Direct measurements of energy transfer across steep density and temperature gradients in a hot-dense-matter system are presented. Hot-dense-plasma conditions were generated by high-intensity laser irradiation of a thin-foil target containing a buried metal layer. Energy transfer to the layer was measured using picosecond time-resolved x-ray emission spectroscopy. The data show two x-ray flashes in time. Fully explicit, coupled particle-in-cell and collisional-radiative atomic kinetics model predictions reproduce these observations, connecting the two x-ray flashes with staged radial energy transfer within the target.

We study the accuracy of combined multiparameter measuring systems (CMPMSs) that determine several unknown quantities from measurements of a single variable at different preprogrammed conditions determined by control parameters. To reduce inaccuracies of determined quantities, we propose a mathematical method for selection of control parameters that are optimal for all possible values of determined quantities. Using the submultiplicativity of the spectral and Frobenius matrix norms, we construct the upper bound of the error function and determine the set of control parameters by minimizing this bound. To demonstrate the capability of our method for CMPMSs, we apply it to the polarized light microscopy technique called LC-PolScope, which is used for determining inhomogeneous two-dimensional fields of optical retardation and orientation of the slow optic axis in thin organic and inorganic samples. We compare the computed set of control parameters with other sets, including the one used in the PolScope, and demonstrate that our choice of control parameters works very well even though it does not take into account any specific features of the PolScope. We expect that our method will be successful in various CMPMSs, as it is applicable to any error distribution of the control parameters and measured values.

We study conserved stochastic sandpiles (CSSs), which exhibit an active-absorbing phase transition upon tuning density $\rho$. We demonstrate that a broad class of CSSs possesses a remarkable hydrodynamic structure: There is an Einstein relation ${\sigma }^2\left(\rho \right)=\chi \left(\rho \right)/D\left(\rho \right)$, which connects bulk-diffusion coefficient $D\left(\rho \right)$, conductivity $\chi \left(\rho \right)$, and mass fluctuation, or scaled variance of subsystem mass, ${\sigma }^2\left(\rho \right)$. Consequently, density large-deviations are governed by an equilibrium-like chemical potential $\mu \left(\rho \right)\sim lna\left(\rho \right)$, where $a\left(\rho \right)$ is the activity in the system. By using the above hydrodynamics, we derive two scaling relations: As $\mathrm{\Delta }=(\rho -{\rho }_c)\to 0^{+}$, ${\rho }_c$ being the critical density, (i) the mass fluctuation ${\sigma }^2\left(\rho \right)\sim {\mathrm{\Delta }}^{1-\delta }$ with $\delta =0$ and (ii) the dynamical exponent $z=2+(\beta -1)/{\nu }_{\perp }$, expressed in terms of two static exponents $\beta$ and ${\nu }_{\perp }$ for activity $a\left(\rho \right)\sim {\mathrm{\Delta }}^{\beta }$ and correlation length $\xi \sim {\mathrm{\Delta }}^{-{\nu }_{\perp }}$, respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality—not that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).

We carry out a detailed study of escape dynamics of a particle driven by a white noise over a metastable potential corrugated by spatial disorder in the form of zero-mean random correlated potential. The approach of double-averaging over test particles and statistic ensemble is proposed to calculate the escape rate in a finite-size random rough metastable potential, moreover, the interference mechanism of test particles multi-passing over the saddle point is considered. Through analyzing the dependence of the steady escape rate on various modelled potentials and parameters, we demonstrate that the obstruction induced by roughness leads to a decrease in the steady escape rate with the increase of rough intensity. We also add the random correlated potential into the vicinity of the saddle-point of metastable potentials of three kinds and show an enhancement phenomenon of escape rate similar to the previous study of a surmounting fluctuating sharp barrier.

Almost everything that happens in classical mechanics also shows up in quantum mechanics when we know where to look for it. A phenomenon in classical mechanics involves topological changes in action-angle loops as a result of passage around a “monodromy circuit.” This phenomenon is known by the short name “Hamiltonian monodromy” (or, more ponderously, “nontrivial monodromy of action and angle variables in integrable Hamiltonian systems”). In this paper, we show a corresponding change in quantum wave functions: These wave functions change their topological structure in the same way that the corresponding classical action-angle loops change.

Demographic and environmental heterogeneities are prevalent across many natural systems. Earlier studies on metapopulation models have mostly considered heterogeneities either in the demographic parameters or in the interaction strength and topology between the spatially separated patches. In contrast, here we study the dynamics of a metapopulation model where each of the uncoupled patches has different periods of oscillations (period mismatch). We show different synchronization dynamics governed by both period mismatch and dispersal in neighboring patches. Indeed, we find both appearance and disappearance of phase synchronization, quasiperiodic oscillations, and period doubling of limit cycle. We also quantify the effect of seasonal variation (entrainment) and dispersal on species synchrony using phase-response curve and a synchrony measure, which thereof identify the influence of stochasticity on species persistence through trade-off mechanisms. Our results show that trade-offs among period mismatch, dispersal, and external force can drive entrained oscillations as well as asynchronous population dynamics that structure ecological communities.

Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and dissolve based on multiple factors, including their lectures, interests, and friends. Such dynamic systems can be represented as multilayer networks where each layer represents a snapshot of the temporal network. In this representation, it is crucial that the links between layers accurately capture real dependencies between those layers. Often, however, these dependencies are unknown. Therefore, current methods connect layers based on simplistic assumptions that do not capture node-level layer dependencies. For example, connecting every node to itself in other layers with the same weight can wipe out dependencies between intermittent groups, making it difficult or even impossible to identify them. In this paper, we present a principled approach to estimating node-level layer dependencies based on the network structure within each layer. We implement our node-level coupling method in the community detection framework Infomap and demonstrate its performance compared to current methods on synthetic and real temporal networks. We show that our approach more effectively constrains information inside multilayer communities so that Infomap can better recover planted groups in multilayer benchmark networks that represent multiple modes with different groups and better identify intermittent communities in real temporal contact networks. These results suggest that node-level layer coupling can improve the modeling of information spreading in temporal networks and better capture intermittent community structure.

In this paper, we discuss the possible generalizations of the social influence with recurrent mobility (SIRM) model [Phys. Rev. Lett. 112, 158701 (2014)]. Although the SIRM model worked approximately satisfying when U.S. election was modeled, it has its limits: it has been developed only for two-party systems and can lead to unphysical behavior when one of the parties has extreme vote share close to 0 or 1. We propose here generalizations to the SIRM model by its extension for multiparty systems that are mathematically well-posed in case of extreme vote shares, too, by handling the noise term in a different way. In addition, we show that our method opens alternative applications for the study of elections by using an alternative calibration procedure and makes it possible to analyze the influence of the “free will” (creating a new party) and other local effects for different commuting network topologies.

We describe a mechanochemical and percolation cascade that augments myosin's regulatory network to tune cytoskeletal forces. Actomyosin forces collectively generate cytoskeletal forces during cell oscillations and ingression, which we quantify by elastic percolation of the internally driven, cross-linked actin network. Contractile units can produce relatively large, oscillatory forces that disrupt crosslinks to reduce cytoskeletal forces. A (reverse) Hopf bifurcation switches contractile units to produce smaller, steady forces that enhance crosslinking and consequently boost cytoskeletal forces to promote ingression. We describe cell-shape changes and cell ingression in terms of intercellular force imbalances along common cell junctions.

We investigated the translation of a protein through model nanopores using coarse-grained (CG) nonequilibrium molecular dynamics (NEMD) simulations and compared the mobilities with those obtained from previous coarse-grained equilibrium molecular dynamics model. We considered the effects of nanopore confinement and external force on the translation of streptavidin through nanopores of dimensions representative of experiments. As the nanopore radius approaches the protein hydrodynamic radius, $r_{\mathrm{h}}/r_{\mathrm{p}}\to 1$ (where $r_{\mathrm{h}}$ is the hydrodynamic radius of protein and $r_{\mathrm{p}}$ is the pore radius), the translation times are observed to increase by two orders of magnitude. The translation times are found to be in good agreement with the one-dimensional biased diffusion model. The results presented in this paper provide useful insights on nanopore designs intended to control the motion of biomolecules.

Using a two-species quantum hydrodynamic model, we derive the quantum counterpart of magnetosonic waves, in a plasma with arbitrary degree of degeneracy and taking into account quantum diffraction effects due to the matter-wave character of the charge carriers. The weakly nonlinear aspects of the associated quantum magnetosonic wave are accessed by means of perturbation theory, with the derivation of a nonlinear evolution equation admitting solitons, namely, the Korteweg–de Vries equation. The degeneracy and quantum diffraction effects on soliton propagation are determined. A qualitative change on weakly nonlinear magnetosonic waves appears when quantum diffraction matches certain conditions, producing shock solutions instead of solitons, within the approximation level. We also include explicit numeric estimates and a discussion on the coupling (nonideality) parameter for quantum plasmas with intermediate degeneracy degree.

Reconstructing a three-dimensional (3D) structure from a single two-dimensional training image (TI) is a challenging issue. Multiple-point statistics (MPS) is an effective method to solve this problem. However, in the traditional MPS method, errors occur while statistical features of reconstruction, such as porosity, connectivity, and structural properties, deviate from those of TI. Due to the MPS reconstruction mechanism that the voxel being reconstructed is dependent on the reconstructed voxel, it may cause error accumulation during simulations, which can easily lead to a significant difference between the real 3D structure and the reconstructed result. To reduce error accumulation and improve morphological similarity, an improved MPS method based on porosity matching is proposed. In the reconstruction, we search the matching pattern in the TI directly. Meanwhile, a multigrid approach is also applied to capture the large-scale structures of the TI. To demonstrate its superiority over the traditional MPS method, our method is tested on different sandstone samples from many aspects, including accuracy, stability, generalization, and flow characteristics. Experimental results show that the reconstruction results by the improved MPS method effectively match the CT sandstone samples in correlation functions, local porosity distribution, morphological parameters, and permeability.

Complex biological and physical transport processes are often described through systems of interacting particles. The effect of excluded volume on these transport processes has been well studied; however, the interplay between volume exclusion and reactions between heterogenous particles is less well studied. In this paper we develop a framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. We consider simple reactions (unimolecular and bimolecular) that conserve the total number of particles. From an off-lattice microscopic individual-based model we use the Fokker-Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions that require particle contact the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parametrization to experimental data than existing models.

The light cone spreading of correlations following a quantum quench is obtained from first principles. Fully taking into account quantum and interaction effects, the derivation shows how light cone dynamics does not require peculiar properties of the postquench state.

The theoretical treatment of quasiperiodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a biharmonic driving and examine its asymptotic long-time limit, the limit in which features distinguishing systems with periodic and quasiperiodic driving occur. Also, in the classical case this limit is known to exhibit universal scaling, independent of the system details, with the system's reponse under quasiperiodic driving being described in terms of nearby periodically driven system results. We introduce a theoretical framework appropriate for the treatment of the quasiperiodically driven quantum system in the long-time limit and derive an expression, based on Floquet states for a periodically driven system approximating the different steps of the time evolution, for the asymptotic scaling of relevant quantities for the system at hand. These expressions are tested numerically, finding excellent agreement for the finite-time average velocity in a prototypical quantum ratchet consisting of a space-symmetric potential and a time-asymmetric oscillating force.

We propose a cascade model of wave turbulence designed to simplify the study of this phenomenon in the way that shell models simplify the study of Navier-Stokes turbulence. The model consists of resonant quartets, in which some modes are driven and damped and others are shared by pairs of quartets and transferring energy between them, mimicking the natural energy transfer mechanism in weakly turbulent waves. A set of detailed-balance conditions singles out the case of the cascade model in equilibrium, for which we can explicitly derive a Gaussian equilibrium measure and a maximum-entropy principle using a Kolmogorov forward equation. Away from equilibrium, we can approximate the second-moment dynamics of the mode amplitudes using kinetic equations. In a nonequilibrium steady state, we can also approximate the higher moments of the driven-damped mode amplitudes and characterize the distribution of the shared-mode amplitudes as Gaussian. For this latter distribution, we find an information-theoretic argument, akin to entropy maximization, which lets us conclude that arbitrary initial shared-mode amplitude distributions approach Gaussian form in forward time. The cascade model may provide insight into mechanisms governing weakly turbulent wave systems and perhaps afford computational savings as compared to direct numerical simulations of the corresponding wavelike equations.