A fundamental understanding of synchronized behavior in multiagent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under nonnegligible resource constraints. Here we construct a system of coupled Kuramoto oscillators that consume or produce resources as a function of their oscillation frequency. At high coupling, we observe strongly synchronized dynamics, whereas at low coupling, we observe independent oscillator dynamics as expected from standard Kuramoto models. For intermediate coupling, which typically induces a partially synchronized state, we empirically observe that (and theoretically explain why) the system can exist in either: (i) a state in which the order parameter oscillates in time, or (ii) a state in which multiple synchronization states are simultaneously stable. Whether (i) or (ii) occurs depends upon whether the oscillators consume or produce resources, respectively. Relevant for systems as varied as coupled neurons and social groups, our paper lays important groundwork for future efforts to develop quantitative predictions of synchronized dynamics for systems embedded in environments marked by sparse resources.

We study a set of interacting individuals that conserve their total mass. In order to describe its dynamics we resort to mesoscopic equations of reaction diffusion including currents driven by attractive and repulsive forces. For the mass conservation we consider a linear response parameter that maintains the mass in the vicinity of a optimal value which is determined by the set. We use the reach and intensity of repulsive forces as control parameters. When sweeping a wide range of parameter space we find a great diversity of localized structures, stationary as well as other ones with cyclical and chaotic dynamics. We compare our results with real situations.

We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., [0,1], and a uniformly randomly chosen individual updates its opinion by partially mimicking the opinion of a uniformly randomly chosen neighbor. We numerically find that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks. In contrast, unless the individuals perfectly copy the opinion of their neighbors in each opinion updating, the convergence time is approximately independent of the system size in the case of regular random graphs, uncorrelated scale-free networks, and complete graphs. We also provide a mean-field analysis of the model to understand the case of the complete graph.

Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph formalism for transitions between gene states, and we apply analytical calculations to compare it with the equilibrium model in terms of the repression strength and expression noise. In contrast to the equilibrium approach, the new model allows us to separate two basic mechanisms of short-range repression. The first mechanism is associated with the recruiting of factors that mediate chromatin condensation, and the second one concerns the blocking of factors that mediate chromatin loosening. The nonequilibrium model demonstrates better performance on previously published gene expression data obtained for transcription factors controlling Drosophila development, and furthermore it predicts that the first repression mechanism is the most favorable in this system. The presented approach can be scaled to larger gene networks and can be used to infer specific modes and parameters of transcriptional regulation from gene expression data.

The high fidelity of DNA polymerase (DNAP) is critical for the faithful replication of DNA. There are several quantitative approaches to measure DNAP fidelity. Directly counting the error frequency in the replication products gives the true fidelity but it turns out very hard to implement in practice. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using kinetic theories combined with the measured apparent kinetic rates. However, whether it is equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies using these assays to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. In this paper, we make a comprehensive examination on the theoretical foundation of the two kinetic assays, based on the theory of DNAP fidelity recently proposed by us. Our studies show that while the conventional kinetic assays are generally valid to quantify the discrimination efficiency of DNAP, they are valid to quantify the proofreading efficiency of DNAP only when the kinetic parameters satisfy some constraints which will be given explicitly in this paper. These results may inspire more carefully-designed experiments to quantify DNAP fidelity.

We derive exact results for displacement fields that develop as a response to external pinning forces in two-dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a Green's function formalism which we use to derive exact results for displacement fields produced by localized external forces. We show that in the continuum limit the displacement fields decay as $1/r$ at large distances $r$ away from a force dipole. Finally, we extend our formulation to study correlations in the displacement fields produced by the external pinning forces. We show that uncorrelated pinned forces at each vertex give rise to long-range correlations in displacements in athermal systems, with a nontrivial system size dependence. We verify our predictions with numerical simulations of athermal networks in two dimensions.

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of $0.66\pm 0.02$. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a “jacket” of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

Colloidal rods immersed in a thermotropic liquid-crystalline solvent are at the basis of so-called hybrid liquid crystals, which are characterized by tunable nematic fluidity with symmetries ranging from conventional uniaxial nematic or antinematic to orthorhombic [Mundoor et al., Science 360, 768 (2018)]. We provide a theoretical analysis of the elastic moduli of such systems by considering interactions between the individual rods with the embedding solvent through surface-anchoring forces, as well as steric and electrostatic interactions between the rods themselves. For uniaxial systems, the presence of colloidal rods generates a marked increase of the splay elasticity, which we found to be in quantitative agreement with experimental measurements. For orthorhombic hybrid liquid crystals, we provide estimates of all 12 elastic moduli and show that only a small subset of those elastic constants play a relevant role in describing the nematoelastic properties. The complexity and possibilities related to identifying the elastic moduli in experiments are briefly discussed.

We present the results of a direct simulation of the expansion of a two-component ultracold plasma for various numbers of particles, densities, and electron temperatures. A description of the expansion process common to all plasma parameters is given. After the escape of fast electrons from the plasma cloud, the excess positive charge is localized at the outer boundary, in a narrow layer. This layer has a characteristic front shape with a sharp drop in the charge concentration. The charged layer retains the remaining electrons during the entire expansion process. As the plasma expands, the speed of movement of the charged layer becomes constant and significantly exceeds the sonic speed of ions. In addition, the dependence of the radial velocity of ions on the radius acquires a self-similar character long before the final stage of expansion. Based on the calculation results, equations and self-similar solutions are obtained. General dependencies on plasma parameters are determined, which are compared with experimental data.

We provide third to eighth virial coefficients of oblate, hard ellipsoids of revolution and hard lenses in dependence on their aspect ratio $\nu$. Employing an algorithm optimized for hard anisotropic shapes, highly accurate data are accessible with comparatively small numerical effort. For both geometries, reduced virial coefficients ${\tilde{B}}_i\left(\nu \right)=B_i\left(\nu \right)/B_2^{i-1}\left(\nu \right)$ are in first approximation proportional to the inverse excess contribution ${\alpha }^{-1}$ of their excluded volume. The latter quantity is directly accessible from second virial coefficients and analytically known for convex bodies.

This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.

Deep reinforcement learning (RL) is a data-driven, model-free method capable of discovering complex control strategies for macroscopic objectives in high-dimensional systems, making its application toward flow control promising. Many systems of flow control interest possess symmetries that, when neglected, can significantly inhibit the learning and performance of a naive deep RL approach. Using a test-bed consisting of the Kuramoto-Sivashinsky equation (KSE), equally spaced actuators, and a goal of minimizing dissipation and power cost, we demonstrate that by moving the deep RL problem to a symmetry-reduced space, we can alleviate limitations inherent in the naive application of deep RL. We demonstrate that symmetry-reduced deep RL yields improved data efficiency as well as improved control policy efficacy compared to policies found by naive deep RL. Interestingly, the policy learned by the symmetry aware control agent drives the system toward an equilibrium state of the forced KSE that is connected by continuation to an equilibrium of the unforced KSE, despite having been given no explicit information regarding its existence. That is, to achieve its goal, the RL algorithm discovers and stabilizes an equilibrium state of the system. Finally, we demonstrate that the symmetry-reduced control policy is robust to observation and actuation signal noise, as well as to system parameters it has not observed before.

A reservoir computing based echo state network (ESN) is used here for the purpose of predicting the spread of a disease. The current infection trends of a disease in some targeted locations are efficiently captured by the ESN when it is fed with the infection data for other locations. The performance of the ESN is first tested with synthetic data generated by numerical simulations of independent uncoupled patches, each governed by the classical susceptible-infected-recovery model for a choice of distributed infection parameters. From a large pool of synthetic data, the ESN predicts the current trend of infection in $5\%$ patches by exploiting the uncorrelated infection trend of $95\%$ patches. The prediction remains consistent for most of the patches for approximately 4 to 5 weeks. The machine's performance is further tested with real data on the current COVID-19 pandemic collected for different countries. We show that our proposed scheme is able to predict the trend of the disease for up to 3 weeks for some targeted locations. An important point is that no detailed information on the epidemiological rate parameters is needed; the success of the machine rather depends on the history of the disease progress represented by the time-evolving data sets of a large number of locations. Finally, we apply a modified version of our proposed scheme for the purpose of future forecasting.

The target performance of laser direct-drive inertial confinement fusion (ICF) can be limited by the development of hydrodynamic instabilities resulting from the nonhomegeneous laser absorption at the target surface, i.e., the laser imprint on the ablator. To understand and describe the formation of these instabilities, the early ablator evolution during the laser irradiation should be considered. In this work, an improved modeling of the solid-to-plasma transition of a polystyrene ablator for laser direct-drive ICF is proposed. This model is devoted to be implemented in hydrocodes dedicated to ICF which generally assume an initial plasma state. The present approach consists of the two-temperature model coupled to the electron, ion and neutral dynamics including the chemical fragmentation of polystyrene. The solid-to-plasma transition is shown to significantly influence the temporal evolution of both free electron density and temperatures, which can lead to different shock formation and propagation compared with an initial plasma state. The influence of the solid-to-plasma transition on the shock dynamics is evidenced by considering the scaling law of the pressure with respect to the laser intensity. The ablator transition is shown to modify the scaling law exponent compared with an initial plasma state.

A model describing the evolution of the average plasma temperature inside a discharge capillary device including Ohmic heating, heat loss to the capillary wall, and ionization and recombination effects is developed. Key to this approach is an analytic quasistatic description of the radial temperature variation which, under local thermal equilibrium conditions, allows the radial behavior of both the plasma temperature and the electron density to be specified directly from the average temperature evolution. In this way, the standard set of coupled partial differential equations for magnetohydrodynamic (MHD) simulations is replaced by a single ordinary differential equation, with a corresponding gain in simplicity and computational efficiency. The on-axis plasma temperature and electron density calculations are benchmarked against existing one-dimensional MHD simulations for hydrogen plasmas under a range of discharge conditions and initial gas pressures, and good agreement is demonstrated. The success of this simple model indicates that it can serve as a quick and easy tool for evaluating the plasma conditions in discharge capillary devices, particularly for computationally expensive applications such as simulating long-term plasma evolution, performing detailed input parameter scans, or for optimization using machine-learning techniques.

Random walks are frequently used as a model for very diverse physical phenomena. The Monte Carlo method is a versatile tool for the study of the properties of systems modeled as random walks. Often, each walker is associated with a statistical weight, used in the estimation of observable quantities. Weights are typically assumed to be positive; nonetheless, some applications require the use of positive and negative weights or complex weights and often pose particular challenges with convergence. In this paper we examine such a case from the field of nuclear reactor physics, where the negative particle weights prevent the power iteration algorithm from converging on the sought fundamental eigenstate of the Boltzmann transport equation. We demonstrate how the use of weight cancellation allows convergence on the physical eigenstate. To this end, we develop a method to perform weight cancellation in an exact manner, in three spatial dimensions. The viability of this algorithm is then demonstrated on a reactor physics problem.

In the present study, a numerical model based on the lattice Boltzmann method (LBM) is proposed to simulate multiphase mass transfer, referred to as the CST-LB model. This model introduced continuum species transfer (CST) formulation by an additional collision term to model the mass transfer across the multiphase interface. The boundary condition treatment of this model is also discussed. In order to verify the applicability, the CST-LB model is combined with the pseudopotential multiphase model to simulate a series of benchmark cases, including concentration jump near the interface, gas dissolution in a closed system, species transport during drainage in a capillary tube, and multiphase species transport in the porous media. This CST-LB model can also be coupled with other multiphase LBMs since the model depends on the phase fraction field, which is not explicitly limited to specified multiphase models.

The noise in nonequilibrium systems commonly contains more outliers as compared to equilibrium systems and is often best described with a Lévy distribution. Many systems in which there are fluctuations around a steady-state throughput can be modeled as a Lévy-noise-subjected particle in a parabolic potential. We consider an overdamped particle in a parabolic potential that is subjected to noise. Microscopic reversibility and time-reversal symmetry apply if the particle is subject to Gaussian distributed noise, but are violated if the noise is Lévy. A parameter to detect this violation is formulated. We, furthermore, develop an understanding for how the time-reversal asymmetry depends on the time $\mathrm{\Delta }t$ between the sample points and on the stability index, $\alpha$, of the Lévy noise. With solar flare data it is shown how the time-reversal asymmetry parameter of a signal can be used to obtain the $\alpha$ of the underlying noise.