The short-wavelength paraxial asymptotic technique, known as Gaussian beam tracing, is extended to the case of two linearly coupled modes in plasmas with resonant dissipation. The system of amplitude evolution equations is obtained. Apart from purely academic interest, this is exactly what happens near the second-harmonic electron-cyclotron resonance if the microwave beam propagates almost perpendicularly to the magnetic field. Because of non-Hermitian mode coupling, the strongly absorbed extraordinary mode may partly transform into the weakly absorbed ordinary mode near the resonant absorption layer. If this effect is significant, it could impair the well-localized power deposition profile. The analysis of parameter dependencies gives insight into what physical factors affect the power exchange between the coupled modes. The calculations show a rather small impact of non-Hermitian mode coupling on the overall heating quality in toroidal magnetic confinement devices at electron temperatures above 200 eV.

Many weakly compressible models with intrinsic mechanisms for stabilizing computation have been proposed to simulate incompressible flows. The present paper analyzes several weakly compressible models to establish general mechanisms that incorporate them into a unified and simple framework. It is found that all these models contain some identical numerical dissipation terms, mass diffusion terms in the continuity equation, and bulk viscosity terms in the momentum equation. They are proven to provide general mechanisms for stabilizing computation. Referring to the general mechanisms and the computational procedures of the lattice Boltzmann flux solver, two general weakly compressible solvers for isothermal flows and thermal flows are proposed. They can be directly derived from standard governing equations and implicitly introduce those numerical dissipation terms. Detailed numerical investigations demonstrate that the two general weakly compressible solvers have good numerical stability and accuracy for both isothermal and thermal flows, which validates the general mechanisms further and the general approach of constructing general weakly compressible solvers.

The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this Research Letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide insights into the generation of hidden attractors in nonlinear dynamical systems.

The representation of complex lattice models in the form of a tensor network is a promising approach to the analysis of the thermodynamics of such systems. Once the tensor network is built, various methods can be used to calculate the partition function of the corresponding model. However, it is possible to build the initial tensor network in different ways for the same model. In this work, we have proposed two ways of constructing tensor networks and demonstrated that the construction process affects the accuracy of calculations. For demonstration purposes, we have done a brief study of the 4 nearest-neighbor (NN) and 5NN models, where adsorbed particles exclude all sites up to the fourth and fifth nearest neighbors from being occupied by another particle. In addition, we have studied a 4NN model with finite repulsions with a fifth neighbor. In a sense, this model is intermediate between 4NN and 5NN models, so algorithms designed for systems with hard-core interactions may experience difficulties. We have obtained adsorption isotherms, as well as graphs of entropy and heat capacity for all models. The critical values of the chemical potential were determined from the position of the heat capacity peaks. As a result, we were able to improve our previous estimate of the position of the phase transition points for the 4NN and 5NN models. And in the model with finite interactions, we found the presence of two first-order phase transitions and made an estimate of the critical values of the chemical potential for them.

Swimming microorganisms such as flagellated bacteria and sperm cells have fascinating locomotion capabilities. Inspired by their natural motion, there is an ongoing effort to develop artificial robotic nanoswimmers for potential in-body biomedical applications. A leading method for actuation of nanoswimmers is by applying a time-varying external magnetic field. Such systems have rich and nonlinear dynamics that call for simple fundamental models. A previous work studied forward motion of a simple two-link model with a passive elastic joint, assuming small-amplitude planar oscillations of the magnetic field about a constant direction. In this work, we found that there exists a faster, backward motion of the swimmer with very rich dynamics. By relaxing the small-amplitude assumption, we analyze the multiplicity of periodic solutions, as well as their bifurcations, symmetry breaking, and stability transitions. We have also found that the net displacement and/or mean swimming speed are maximized for optimal choices of various parameters. Asymptotic calculations are performed for the bifurcation condition and the swimmer's mean speed. The results may enable significantly improving the design aspects of magnetically actuated robotic microswimmers.

In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete equations for the longitudinal displacements and rotations of the rigid mass units. In the long wavelength regime, and applying the multiple-scales method we derive an effective nonlinear Schrödinger equation for slowly varying envelope rotational waves. We are then able to establish a map of the occurrence of MI to the parameters of the metamaterials and the wave numbers. We also highlight the key role of the rotation-displacement coupling between the two degrees of freedom in the manifestation of MI. All analytical findings are confirmed by numerical simulations of the full discrete and nonlinear lump problem. These results provide interesting design guidelines for nonlinear metamaterials offering either stability to high amplitude waves, or conversely being good candidates to observe instabilities.

In this paper, two improvements to the theory of transition from brittle to ductile fracture developed by Langer [J. S. Langer, Phys. Rev. E 103, 063004 (2021)] are proposed. First, considering the drastic temperature rise near the crack tip, the temperature dependence of the shear modulus is included to better quantify the thermally sensitive dislocation entanglement. Second, the parameters of the improved theory are identified by the large-scale least-squares method. The comparison between the fracture toughness predicted by the theory and the values obtained in Gumbsch's experiments for tungsten at different temperatures [P. Gumbsch et al., Science 282, 1293 (1998)] shows good agreement.

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will detect the cue only intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work we cast this search problem in the language of a partially observable Markov decision process and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We also discuss the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits—and pitfalls—of employing a reward-shaping function.

This paper presents a numerical study of ring structural transitions in strongly coupled dusty plasma confined in a ring-shaped (quartic) potential well with a central barrier, whose axis of symmetry is parallel to the gravitational attraction. It is observed that increasing the amplitude of the potential leads to a transition from a ring monolayer structure (rings of different diameters nested within the same plane) to a cylindrical shell structure (rings of similar diameter aligned in parallel planes). In the cylindrical shell state, the ring's alignment in the vertical plane exhibits hexagonal symmetry. The ring transition is reversible, but exhibits hysteresis in the initial and final particle positions. As the critical conditions for the transitions are approached, the transitional structure states exhibit zigzag instabilities or asymmetries on the ring alignment. Furthermore, for a fixed amplitude of the quartic potential that results in a cylinder-shaped shell structure, we show that additional rings in the cylindrical shell structure can be formed by decreasing the curvature of the parabolic potential well, whose axis of symmetry is perpendicular to the gravitational force, increasing the number density, and lowering the screening parameter. Finally, we discuss the application of these findings to dusty plasma experiments with ring electrodes and weak magnetic fields.

A system can be driven out of equilibrium by both time-dependent and nonconservative forces, which gives rise to a decomposition of the dissipation into two nonnegative components, called the excess and housekeeping entropy productions. We derive thermodynamic uncertainty relations for the excess and housekeeping entropy. These can be used as tools to estimate the individual components, which are in general difficult to measure directly. We introduce a decomposition of an arbitrary current into housekeeping and excess parts, which provide lower bounds on the respective entropy production. Furthermore, we also provide a geometric interpretation of the decomposition and show that the uncertainties of the two components are not independent, but rather have to obey a joint uncertainty relation, which also yields a tighter bound on the total entropy production. We apply our results to a paradigmatic example that illustrates the physical interpretation of the components of the current and how to estimate the entropy production.

We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates. We show how to present correlation functions of interest as part of a sum-of-squares polynomial using the stationarity of the statistics. That allows us to find how the moments of the mode amplitudes depend on the degree of nonequilibrium (analog of the Reynolds number), which reveals some properties of marginal statistical distributions. By combining scaling dependence with the results of direct numerical simulations, we obtain the probability densities of both modes in a highly intermittent inverse cascade. As the Reynolds number tends to infinity, we show that the relative phase between modes tends to $\pi /2$ and $-\pi /2$ in the direct and inverse cascades, respectively, and derive bounds on the phase variance. Our approach combines computer-aided analytical proofs with a numerical algorithm applied to high-degree polynomials.

Recently, a “unified” quantum master equation was derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equation describes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equation to investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equation gives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a “V” system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equation to those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.

A phenomenological reaction-diffusion model that includes a nutrient-regulated growth rate of tumor cells is proposed to investigate the morphological instability of solid tumors during the avascular growth. We find that the surface instability could be induced more easily when tumor cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed for tumor cells in a nutrient-rich environment due to the nutrient-regulated proliferation. In addition, the surface instability is shown to be influenced by the growth moving speed of tumor rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability. A nourished length that represents the proximity is defined to illustrate its close relation to the surface instability.

In recent work, we developed a screening theory for describing the effect of plastic events in amorphous solids on its emergent mechanics. The suggested theory uncovered an anomalous mechanical response of amorphous solids where plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The theory was tested against various models of amorphous solids in two dimensions, including frictional and frictionless granular media and numerical models of amorphous glass. Here we extend our theory to screening in three-dimensional amorphous solids and predict the existence of anomalous mechanics similar to the one observed in two-dimensional systems. We conclude by interpreting the mechanical response as the formation of nontopological distributed dipoles that have no analog in the crystalline defects literature. Having in mind that the onset of dipole screening is reminiscent of Kosterlitz-Thouless and hexatic transitions, the finding of dipole screening in three dimensions is surprising.

We calculate the swimming speed of a Taylor sheet in a smectic-$A$ liquid crystal. Assuming that the amplitude of the wave propagating on the sheet is much smaller than the wave number, we solve the governing equations using the method of series expansion up to the second order in amplitude. We find that the sheet can swim much faster in smectic-$A$ liquid crystals than in Newtonian fluids. The elasticity associated with the layer compressibility is responsible for the enhanced speed. We also calculate the power dissipated in the fluid and the flux of the fluid. The fluid is pumped opposite to the direction of the wave propagation.

Entry of micro- or nanosized objects into cells or vesicles made of lipid membranes occurs in many processes such as entry of viruses into host cells, microplastics pollution, drug delivery, or biomedical imaging. Here we investigate the microparticle crossing of lipid membranes in giant unilamellar vesicles in the absence of strong binding interactions (e.g., streptavidin-biotin binding). In these conditions, we observe that organic and inorganic particles can always penetrate inside the vesicles provided an external piconewton force is applied and for relatively low membrane tensions. In the limit of vanishing adhesion, we identify the role of the membrane area reservoir and show that a force minimum exists when the particle size is comparable to the bendocapillary length.

Predicting future evolution based on incomplete information of the past is still a challenge even though data-driven machine learning approaches have been successfully applied to forecast complex nonlinear dynamics. The widely adopted reservoir computing (RC) can hardly deal with this since it usually requires complete observations of the past. In this paper, a scheme of RC with $(D+1)$-dimension input and output (I/O) vectors is proposed to solve this problem, i.e., the incomplete input time series or dynamical trajectories of a system, in which certain portion of states are randomly removed. In this scheme, the I/O vectors coupled to the reservoir are changed to $(D+1)$-dimension, where the first $D$ dimensions store the state vector as in the conventional RC, and the additional dimension is the corresponding time interval. We have successfully applied this approach to predict the future evolution of the logistic map and Lorenz, Rössler, and Kuramoto-Sivashinsky systems, where the inputs are the dynamical trajectories with missing data. The dropoff rate dependence of the valid prediction time (VPT) is analyzed. The results show that it can make forecasting with much longer VPT when the dropoff rate $\theta$ is lower. The reason for the failure at high $\theta$ is analyzed. The predictability of our RC is determined by the complexity of the dynamical systems involved. The more complex they are, the more difficult they are to predict. Perfect reconstructions of chaotic attractors are observed. This scheme is a pretty good generalization to RC and can treat input time series with regular and irregular time intervals. It is easy to use since it does not change the basic architecture of conventional RC. Furthermore, it can make multistep-ahead prediction just by changing the time interval in the output vector into a desired value, which is superior to conventional RC that can only do one-step-ahead forecasting based on complete regular input data.

We study the elastic enhancement factor and the two-point correlation function of the scattering matrix obtained from measurements of reflection and transmission spectra of a three-dimensional (3D) wave-chaotic microwave cavity in regions of moderate and large absorption. They are used to identify the degree of chaoticity of the system in the presence of strongly overlapping resonances, where other measures such as short- and long-range level correlations cannot be applied. The average value of the experimentally determined elastic enhancement factor for two scattering channels agrees well with random-matrix theory predictions for quantum chaotic systems, thus corroborating that the 3D microwave cavity exhibits the features of a fully chaotic system with preserved time-reversal invariance. To confirm this finding we analyzed spectral properties in the frequency range of lowest achievable absorption using missing-level statistics.

It is well known that helical magnetohydrodynamic (MHD) turbulence exhibits an inverse transfer of magnetic energy from small to large scales, which is related to the approximate conservation of magnetic helicity. Recently, several numerical investigations noticed the existence of an inverse energy transfer also in nonhelical MHD flows. We run a set of fully resolved direct numerical simulations and perform a wide parameter study of the inverse energy transfer and the decaying laws of helical and nonhelical MHD. Our numerical results show only a small inverse transfer of energy that grows as with increasing Prandtl number (Pm). This latter feature may have interesting consequences for cosmic magnetic field evolution. Additionally, we find that the decaying laws $E\sim t^{-p}$ are independent of the scale separation and depend solely on Pm and Re. In the helical case we measure a dependence of the form $p_b\approx 0.6+14/\mathrm{Re}$. We also make a comparison between our results and previous literature and discuss the possible reason for the observed disagreements.