Brownian particles placed sequentially in contact with distinct thermal reservoirs and subjected to external driving forces are promising candidates for the construction of reliable engine setups. In this contribution, we address the role of driving forces for enhancing the collisional machine performance. Analytical expressions for thermodynamic quantities such as power output and efficiency are obtained for general driving schemes. A proper choice of these driving schemes substantially increases both power output and efficiency and extends the working regime. Maximizations of power and efficiency, whether with respect to the strength of the force, driving scheme, or both have been considered and exemplified for two kind of drivings: generic power-law and harmonic (sinusoidal) drivings.

We study the energy transfer by exact resonances for deep-water surface gravity waves in a finite periodic spatial domain. Based on a kinematic model simulating the generation of active wave modes in a finite discrete wave number space ${\mathcal{S}}_R$, we examine the possibility of direct and inverse cascades. More specifically, we set an initially excited region which iteratively spreads energy to wave modes in ${\mathcal{S}}_R$ through exact resonances. At each iteration, we first activate new modes from scale resonances (which generate modes with new lengths), then consider two bounding situations for angle resonances (which transfer energy at the same length scale): the lower bound where no angle resonance is included and the upper bound where all modes with the same length as any active mode are excited. Such a strategy is essential to enable the computation for a large domain ${\mathcal{S}}_R$ with the maximum wave number $R\sim {10}^3$. We show that for both direct and inverse cascades, the modal propagation to the boundaries of ${\mathcal{S}}_R$ can be established when the initially excited region is sufficiently large; otherwise a frozen turbulence state occurs, with a sharp transition between the two regimes especially for the direct cascade. Through a study on the structure of resonant quartets, the mechanism associated with the sharp transition and the role of angular energy transfer in the cascades are elucidated.

We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how the sketch can be used to explicitly identify six key community events which typically occur during network evolution: growth, shrinkage, merging, splitting, birth, and death. Based on these detection techniques, we formulate a community detection algorithm which can process a network concurrently exhibiting all processes. One advantage afforded by the sketch-based algorithm is the efficient handling of large networks. Whereas detecting events in the full graph may be computationally expensive, the small size of the sketch allows changes to be quickly assessed. A second advantage occurs in networks containing clusters of disproportionate size. The sketch is constructed such that there is equal representation of each cluster, thus reducing the possibility that the small clusters are lost in the estimate. We present a new standardized benchmark based on the stochastic block model which models the addition and deletion of nodes, as well as the birth and death of communities. When coupled with existing benchmarks, this new benchmark provides a comprehensive suite of tests encompassing all six community events. We provide analysis and a set of numerical results demonstrating the advantages of our approach both in runtime and in the handling of small clusters.

We performed numerical experiments to investigate the mixing of stratified suspensions composed of different particle types by gravitational sedimentation. The mixing process is controlled by a dimensionless group ${\mathit{Y}}_{\mathrm{m}}\sim U_{\mathrm{f}}/U_{\mathrm{St}1}$, where $U_{\mathrm{f}}$ is a typical velocity of a macroscopic sedimenting finger and $U_{\mathrm{St}1}$ is the Stokes settling velocity of a single spherical particle in the upper suspension. The effects of components of ${\mathit{Y}}_{\mathrm{m}}$, in particular, terminal velocities of particles, were investigated. For ${\mathit{Y}}_{\mathrm{m}}=100$, no large difference was observed for the difference of components of ${\mathit{Y}}_{\mathrm{m}}$, and it was confirmed that the mixing rate is determined by ${\mathit{Y}}_{\mathrm{m}}$, because macroscopic (vessel-scale) mixing is dominant for large ${\mathit{Y}}_{\mathrm{m}}$. For ${\mathit{Y}}_{\mathrm{m}}=5$, macroscopic mixing and microscopic (individual particle-level) mixing due to the particle terminal velocity difference are of the same order, while completely different mixing patterns were observed for positive, zero, and negative terminal velocity differences: macroscopic mixing is promoted by the increase in apparent density due to microscopic mixing, small macroscopic mixing is suppressed by the individual particle settling, and jetting mixing occurs owing to pure liquid layer formation.

We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.

Absolute negative mobility, where particles move opposite to the direction as governed by the external load, is an anomalous transport property of a Brownian ratchet and has technological implications in mass separation and bioanalytical applications. We numerically investigated here the effect of roughness in symmetric periodic potential on the negative mobility of a driven inertial Brownian ratchet in the presence of an external load. We show that the microscopic spatial heterogeneity of the potential can generate negative mobility which would not otherwise be possible under smooth potential in the concerned parameter space. We determined the optimal condition in terms of parameter space for such anomalous behavior. Our calculations indicate that the shift of balance towards the negative velocity phase in the temporal oscillations of velocity and weakly chaotic dynamics are responsible factors for roughness-induced negative mobility. These calculations highlight a constructive role of roughness in the anomalous transport properties of Brownian ratchet.

To understand the complicated transport processes that occur in biological and physical systems, we investigate a constrained totally asymmetric simple exclusion process with a stochastic defect particle. The defect particle might randomly emerge or vanish, resulting in a dynamic defect, and slows down the flow of moving particles when attached to the lattice. Using a mean-field technique, we examine the steady-state characteristics and boundary-layer analysis is provided to comprehend the properties of finite system. In a simplification, our theoretical method unifies three different parameter used to define the defect dynamics into one parameter termed the obstruction factor. It is found that the defect kinetics lead to emergence of phases where the current is defect restricted. The system shows nine phases overall, including bulk-induced and boundary-induced shock phases, with the phase schema showing no more than eight phases depending on the dynamics. We found that variation of obstruction does not lead to qualitative transition in the system, whereas the change in constraint on total particles affect the system qualitatively. All the theoretical outcomes have been validated using extensive Monte Carlo simulations.

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatiotemporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and by exploiting symmetry properties infers entire bifurcation diagrams.

Mechanical computing has seen resurgent interest recently owing to the potential to embed sensing and computation into new classes of programmable metamaterials. To realize this, however, one must push signals from one part of a device to another and do so in a way that can be reset robustly. We investigate the propagation of signals in a bistable mechanical cascade uphill in energy. By identifying a penetration length for perturbations, we show that signals can propagate uphill for finite distances and map out parameters for this to occur. Experiments on soft elastomers corroborate our results.

The presence of higher-order interactions (simplicial complexes) on globally coupled systems yield abrupt first-order transitions to synchronization. We discover that simplicial complexes on multilayer systems can yield multiple basins of attraction, leading to multiple abrupt first-order transitions to (de)synchronization for associated coupled dynamics. Using the Ott-Antonsen approach, we develop an analytical framework for simplicial complexes on multilayer systems, reducing the high-dimensional evolution equation to a low-dimensional manifold, which thoroughly explains the origin and stability of all possible dynamical states, including multiple synchronization transitions. The study illustrating rich dynamical behaviors could be pivotal in comprehending the impacts of higher-order interactions on dynamics of complex real-world networks, such as brain, social, and technological, which have inherent multilayer architectures.

We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in which at each time step a node addition and random attachment step takes place with probability $P_{\mathrm{add}}$ and a random node deletion step takes place with probability $P_{\mathrm{del}}=1-P_{\mathrm{add}}$. The balance between the growth and contraction processes is captured by the parameter $\eta =P_{\mathrm{add}}-P_{\mathrm{del}}$. The case of pure network growth is described by $\eta =1$. In the case that $0<\eta <1$, the rate of node addition exceeds the rate of node deletion and the overall process is of network growth. In the opposite case, where $-1<\eta <0$, the overall process is of network contraction, while in the special case of $\eta =0$ the expected size of the network remains fixed, apart from fluctuations. Using the master equation and the generating function formalism, we obtain a closed-form expression for the time-dependent degree distribution $P_t\left(k\right)$. The degree distribution $P_t\left(k\right)$ includes a term that depends on the initial degree distribution $P_0\left(k\right)$, which decays as time evolves, and an asymptotic distribution $P_{\mathrm{st}}\left(k\right)$ which is independent of the initial condition. In the case of pure network growth ($\eta =1$), the asymptotic distribution $P_{\mathrm{st}}\left(k\right)$ follows an exponential distribution, while for $-1<\eta <1$ it consists of a sum of Poisson-like terms and exhibits a Poisson-like tail. In the case of overall network growth ($0<\eta <1$) the degree distribution $P_t\left(k\right)$ eventually converges to $P_{\mathrm{st}}\left(k\right)$. In the case of overall network contraction ($-1<\eta <0$) we identify two different regimes. For $-1/3<\eta <0$ the degree distribution $P_t\left(k\right)$ quickly converges towards $P_{\mathrm{st}}\left(k\right)$. In contrast, for $-1<\eta <-1/3$ the convergence of $P_t\left(k\right)$ is initially very slow and it gets closer to $P_{\mathrm{st}}\left(k\right)$ only shortly before the network vanishes. Thus, the model exhibits three phase transitions: a structural transition between two functional forms of $P_{\mathrm{st}}\left(k\right)$ at $\eta =1$, a transition between an overall growth and overall contraction at $\eta =0$, and a dynamical transition between fast and slow convergence towards $P_{\mathrm{st}}\left(k\right)$ at $\eta =-1/3$. The analytical results are found to be in very good agreement with the results obtained from computer simulations.

The stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break $\mu$ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of $\mu$; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a nonlinear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the three-body problem, the KdV equation, and nonlinear Schrödinger equation.

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equations of the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid them by using an ad hoc convolutional architecture featuring an interchannel averaging layer. The main testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the interchannel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of sidebands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this Letter, we show that phase-shift localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers, and thus by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such a focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.

Noncollisional current sheets that form during the nonlinear development of spontaneous magnetic reconnection are characterized by a small thickness, of the order of the electron skin depth. They can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. In this work, we investigate the marginal stability conditions for the development of plasmoids when the forming current sheet is purely collisionless and in the presence of a strong guide field. We analyze the geometry that characterizes the reconnecting current sheet, and what promotes its elongation. Once the reconnecting current sheet is formed, we identify the regimes for which it is plasmoid unstable. Our study shows that plasmoids can be obtained, in this context, from current sheets with an aspect ratio much smaller than in the collisional regime, and that the plasma flow channel of the marginally stable current layers maintains an inverse aspect ratio of 0.1.

The general properties of time dependent autocorrelations in many-body quantum systems are here analyzed at thermodynamic equilibrium in the Boltzmann canonical ensemble at temperature $T$, by means of the exponential expansion theory (EET). It is shown that the Kubo-Martin-Schwinger (KMS) symmetry applied to the exponential expansion of the correlation leads to the existence of two different sets of decay modes (channels) here indicated as “Matsubara modes” and “system modes,” respectively. The Matsubara modes are a series of pure decay channels with time constants representing a direct action of the thermostat upon the correlation, with a characteristic principal decay time ${\tau }_1=\hslash /\left(2\pi k_{\mathrm{B}}T\right)$, where $\hslash$ and $k_{\mathrm{B}}$ are the Planck and Boltzmann constants, and $T$ is the temperature. Moreover, the KMS condition implies that the amplitudes pertaining to the even and odd contribution of the system modes to the quantum correlation are not independent. These two properties are quantum mechanical in nature and “universal,” in the sense that they are present for any autocorrelation of a quantum system at equilibrium at a temperature $T$. The Matsubara modes' contribution to the time behavior of a quantum correlation is limited to times of the order of ${\tau }_1$, which however can be comparable with some of the characteristic decay times of the system modes. In addition, since the parameters representing the overall time behavior of the quantum correlation can be given in terms of the parameters of its Kubo transform, the EET representation turns out to be useful in calculations exploiting the outputs of some widespread quantum simulation methods. A discussion of the properties of these relations is described in detail with numerical examples. The case of the velocity autocorrelation function of para hydrogen at low temperature is also reported as a final example for a real system.

We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wave number and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the framework of random matrix theory for quantum chaotic scattering systems.

A twisted state is an important yet simple form of collective dynamics in an oscillatory medium. Here we describe a nontrivial type of twisted state in a system of nonlocally coupled Stuart-Landau oscillators. The nontrivial twisted state (NTS) is a coherent traveling wave characterized by inhomogeneous profiles of amplitudes and phase gradients, which can be assigned a winding number. To further investigate its properties, several methods are employed. We perform a linear stability analysis in the continuum limit and compare the results with Lyapunov exponents obtained in a finite-size system. The determination of covariant Lyapunov vectors allows us to identify collective modes. Furthermore, we show that the NTS is robust to small heterogeneities in the natural frequencies and present a bifurcation analysis revealing that NTSs are born or annihilated in a saddle-node bifurcation and change their stability in Hopf bifurcations. We observe stable NTSs with winding number 1 and 2. The latter can lose stability in a supercritical Hopf bifurcation, leading to a modulated 2-NTS.