We study the formation of solitons of microwave self-induced transparency (M/W-SIT) which occurs under cyclotron resonance interaction of an electromagnetic pulse with an initially rectilinear magnetized electron beam. Taking into account the relativistic dependence of the gyrofrequency on the particle energy for electromagnetic wave propagating with a phase velocity different from the speed of light (i.e., far from the autoresonance conditions), such a beam can be considered as a medium of nonisochronous unexcited oscillators. Thus, similar to passing light pulses in the two-level medium, for sufficiently large amplitude and duration the incident electromagnetic pulse decomposes into one or several solitons. We find analytically the generalized solution for the M/W-SIT soliton with amplitude and duration determined, besides the soliton velocity, by the frequency self-shift parameter. The feasibility and stability of the obtained solutions are confirmed in numerical simulations of a semibounded problem describing propagation and nonlinear interaction of an incident electromagnetic pulse.

Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly growing solutions. These divergences have been treated with a variety of techniques, including the powerful dynamical renormalization group (DRG). Most of the existing DRG approaches rely on having analytic solutions up to some order in perturbation theory. However, sometimes the equations can only be solved numerically. We reformulate the DRG in the language of differential geometry, which allows us to apply it to numerical solutions of the background and perturbation equations. This formulation also enables us to use the DRG in systems with background parameter flows and, therefore, extend our results to any order in perturbation theory. As an example, we apply this method to calculate the soliton-like solutions of the Korteweg–de Vries equation deformed by adding a small damping term. We numerically construct DRG solutions which are valid on secular timescales, long after naive perturbation theory has broken down.

Anticipation is the phenomenon in which the response of a system is predictive of the stimulation. The encoding of stochastic light intensity ($x$) into spikes is investigated in an experiment with retinas from bullfrogs to understand the mechanism of anticipation of a retina. Partial information decomposition of the mutual information between the spike rates and the joint state $\{x,\dot{x}\}$ is found to be consistent with the encoding by the linear combination of $x$ and $\dot{x}$ where $\dot{x}$ is the rate of change of $x$. This spike rate encoding form indicates that a retina is capable of anticipation based on the synergistic information generation between $x$ and $\dot{x}$. Our results suggest that illusions such as the anticipation studied here during retinal perception can originate from the recombination of information extracted in the retinal network.

Genetic diversity is at the basis of the evolution process of populations and it is responsible for the populations' degree of fitness to a particular ecosystem. In marine environments many factors play a role in determining the dynamics of a population, including the amount of nutrients, the temperature, and many other stressing factors. An important and yet rather unexplored challenge is to figure out the role of individuals' dispersion, due to flow advection, on population genetics. In this paper we focus on two populations, one of which has a slight selective advantage, advanced by an incompressible two-dimensional flow. In particular, we want to understand how this advective flow can modify the dynamics of the advantageous allele. We generalize, through a theoretical analysis, previous evidence according to which the fixation probability is independent of diffusivity, showing that this is also independent of fluid advection. These findings may have important implications in the understanding of the dynamics of a population of microorganism, such as plankton or bacteria, in marine environments under the influence of (turbulent) currents.

To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.

Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long-term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce variational integrator graph networks—a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single- and many-body problems studied in the recent literature. We empirically show that the improvements arise because high-order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the partitioned Runge-Kutta method.

We show how the dynamics of the Dicke model after a quench from the ground-state configuration of the normal phase into the superradiant phase can be described for a limited time by a simple inverted harmonic oscillator model and that this limited time approaches infinity in the thermodynamic limit. Although we specifically discuss the Dicke model, the presented mechanism can also be used to describe dynamical quantum phase transitions in other systems and presents an opportunity for simulations of physical phenomena associated with an inverted harmonic oscillator.

Globally coupled maps (GCMs) are prototypical examples of high-dimensional dynamical systems. Interestingly, GCMs formed by an ensemble of weakly coupled identical chaotic units generically exhibit a hyperchaotic “turbulent” state. A decade ago, Takeuchi et al. [Phys. Rev. Lett. 107, 124101 (2011)] theorized that in turbulent GCMs the largest Lyapunov exponent (LE), $\lambda \left(N\right)$, depends logarithmically on the system size $N$: ${\lambda }_{\infty }-\lambda \left(N\right)\simeq c/lnN$. We revisit the problem and analyze, by means of analytical and numerical techniques, turbulent GCMs with positive multipliers to show that there is a remarkable lack of universality, in conflict with the previous prediction. In fact, we find a power-law scaling ${\lambda }_{\infty }-\lambda \left(N\right)\simeq c/N^{\gamma }$, where $\gamma$ is a parameter-dependent exponent in the range $0<\gamma \le 1$. However, for strongly dissimilar multipliers, the LE varies with $N$ in a slower fashion, which is here numerically explored. Although our analysis is only valid for GCMs with positive multipliers, it suggests that a universal convergence law for the LE cannot be taken for granted in general GCMs.

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

Determination of the spin echo signal evolution and of transverse relaxation rates is of high importance for microstructural modeling of muscle tissue in magnetic resonance imaging. So far, numerically exact solutions for the NMR signal dynamics in muscle tissue models have been reported only for the gradient echo free induction decay, with spin echo problems usually solved by approximate methods. In this work, we modeled the spin echo signal numerically exact by discretizing the radial dimension of the Bloch-Torrey equation and expanding the angular dependency in terms of even Chebyshev polynomials. This allows us to express the time dependence of the local magnetization as a closed-form matrix expression. Using this method, we were able to accurately capture the spin echo local and total magnetization dynamics. The obtained transverse relaxation rates showed a high concordance with random walker and finite-element simulations. We could demonstrate that in cases of smaller diffusion coefficients, the commonly used strong collision approximation significantly underestimates the true value considerably. Instead, the limiting behavior in this regime is correctly described either by the full solution or by the slow diffusion approximation. Experimentally measured transverse relaxation rates of a mouse limb muscle showed an angular dependence in accordance with the theoretical prediction.

We study the relationship between topological defect formation and ground-state 2D packings in a model of repulsions in external confining potentials. Specifically we consider screened 2D Coulombic repulsions, which conveniently parameterizes the effects of interaction range, but also serves as simple physical model of confined, parallel arrays of polyelectrolyte filaments or vortices in type II superconductors. The countervailing tendencies of repulsions and confinement to, respectively, spread and concentrate particle density leads to an energetic preference for nonuniform densities in the clusters. Ground states in such systems have previously been modeled as conformal crystals, which are composed of locally equitriangular packings whose local areal densities exhibit long-range gradients. Here we assess two theoretical models that connect the preference for nonuniform density to the formation of disclination defects, one of which assumes a continuum distributions of defects, while the second considers the quantized and localized nature of disclinations in hexagonal conformal crystals. Comparing both theoretical descriptions to numerical simulations of discrete particles clusters, we study the influence of interaction range and confining potential on the topological charge, number, and distribution of defects in ground states. We show that treating disclinations as continuously distributable well captures the number of topological defects in the ground state in the regime of long-range interactions, while as interactions become shorter range, it dramatically overpredicts the growth in total defect charge. Detailed analysis of the discretized defect theory suggests that that failure of the continuous defect theory in this limit can be attributed to the asymmetry in the preferred placement of positive vs negative disclinations in the conformal crystal ground states, as well as a strongly asymmetric dependence of self-energy of disclinations on sign of topological charge.

This paper reports a mass transfer model of a reactant flowing in a large aspect ratio microfluidic chip made of a channel with electrodes on the side walls. A semianalytical solution to the two-dimensional Fickian diffusion of a reactant in a microchannel, including the electrochemical reaction at the electrode interface and the velocity profile obtained from the Navier-Stokes equations in a fully developed laminar regime, is found. The solution is written in the Laplace domain in terms of transfer functions. The proposed solution is an extension of the Lévêque approximation describing the reactant diffusion from the electrode to the middle of the microfluidic channel. The main applications of this work are the use of the obtained transfer functions for the measurement of the Faradic current density or the chemical concentration at the electrode interface. The study can also be extended to the heat transfer in microfluidic electrochemical chips (temperature or heat flux measurements at the electrode interface).

We present a full investigation into shock-wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range $1.0–11.0$. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focused mainly on the density profile across the shock, here we also include temperature profiles as well as non-negativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bivelocity (or volume and mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

In this paper, a multiple-relaxation-time finite-difference lattice Boltzmann method (MRT-FDLBM) is developed for the nonlinear convection-diffusion equation (NCDE). Through designing the equilibrium distribution function and the source term properly, the NCDE can be recovered exactly from MRT-FDLBM. We also conduct the von Neumann stability analysis on the present MRT-FDLBM and its special case, i.e., single-relaxation-time finite-difference lattice Boltzmann method (SRT-FDLBM). Then, a simplified version of MRT-FDLBM (SMRT-FDLBM) is also proposed, which can save about 15% computational cost. In addition, a series of real and complex-value NCDEs, including the isotropic convection-diffusion equation, Burgers-Fisher equation, sine-Gordon equation, heat-conduction equation, and Schrödinger equation, are used to test the performance of MRT-FDLBM. The results show that both MRT-FDLBM and SMRT-FDLBM have second-order convergence rates in space and time. Finally, the stability and accuracy of five different models are compared, including the MRT-FDLBM, SMRT-FDLBM, SRT-FDLBM, the previous finite-difference lattice Boltzmann method [H. Wang, B. Shi et al., Appl. Math. Comput. 309, 334 (2017)], and the lattice Boltzmann method (LBM). The stability tests show that the sequence of stability from high to low is as follows: MRT-FDLBM, SMRT-FDLBM, SRT-FDLBM, the previous finite-difference lattice Boltzmann method, and LBM. In most of the precision test results, it is found that the order from high to low of precision is MRT-FDLBM, SMRT-FDLBM, SRT-FDLBM, and the previous finite-difference lattice Boltzmann method.

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to testing vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to carefully select the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.

Finding hidden layers in complex networks is an important and a nontrivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multilayer system exist and if so then what is their extent, i.e., how many unknown layers are there. Assuming that the only information available is the time evolution of a wave propagation on a single layer of a network it is indeed possible to uncover that which is hidden by merely observing the dynamics. We present evidence on both synthetic and real-world networks that the frequency spectrum of the wave dynamics can express distinct features in the form of additional frequency peaks. These peaks exhibit dependence on the number of layers taking part in the propagation and thus allowing for the extraction of said number. We show that, in fact, with sufficient observation time, one can fully reconstruct the row-normalized adjacency matrix spectrum. We compare our propositions to a machine learning approach using a wave packet signature method modified for the purposes of multilayer systems.

Being a dual purpose enzyme, the DNA polymerase is responsible for elongation of the newly formed DNA strand as well as cleaving the erroneous growth in case of a misincorporation. The efficiency of replication depends on the coordination of the polymerization and exonuclease activity of DNA polymerase. Here, we propose and analyze a minimal kinetic model of DNA replication and determine exact expressions for the velocity of elongation and the accuracy of replication. We first analyze the case without exonuclease activity. In that case, accuracy is determined by a kinetic competition between stepping and unbinding, with discrimination between correct and incorrect nucleotides in both transitions. We then include exonuclease activity and ask how different modes of additional discrimination in the exonuclease pathway can improve the accuracy while limiting the detrimental effect of exonuclease on the speed of replication. In this way, we ask how the kinetic parameters of the model have to be set to coordinate the two activities of the enzyme for high accuracy and high speed. The analysis also shows that the design of a replication system does not universally have to follow the speed-accuracy trade-off rule, although it does in the biologically realized parameter range. The accuracy of the process is mainly controlled by the crucial role of stepping after erroneous incorporation, which has impact on both polymerase and exonuclease activities of DNA polymerase.

A long-standing puzzle in the rheology of living cells is the origin of the experimentally observed long-time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.