We discuss the possibility of reaching the Carnot efficiency by heat engines (HEs) out of quasistatic conditions at nonzero power output. We focus on several models widely used to describe the performance of actual HEs. These models comprise quantum thermoelectric devices, linear irreversible HEs, minimally nonlinear irreversible HEs, HEs working in the regime of low-dissipation, overdamped stochastic HEs and an underdamped stochastic HE. Although some of these HEs can reach the Carnot efficiency at nonzero and even diverging power, the magnitude of this power is always negligible compared to the maximum power attainable in these systems. We provide conditions for attaining the Carnot efficiency in the individual models and explain practical aspects connected with reaching the Carnot efficiency at large power output. Furthermore, we show how our findings can be tested in practice using a standard Brownian HE realizable with available micromanipulation techniques.

Dynamical phase transitions are defined as nonanalytic points of the large deviation function of current fluctuations. We show that for boundary-driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase transitions in linear, rather than exponential, time.

We investigate three aspects of the importance of nodes with respect to susceptible-infectious-removed (SIR) disease dynamics: influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size), and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that (i) node separation is more important than centrality for more than one active node, (ii) vaccination and influence maximization are the most different aspects of importance, and (iii) the three aspects are more similar when the infection rate is low.

We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully thermal and nearly athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.

Time-resolved dynamics of nonspherical oscillations of micrometer-sized bubbles are captured and analyzed using high-speed imaging. The axisymmetry of the bubble shape is ensured with certainty for the first time from the recordings of two synchronous high-speed cameras located at ${90}^{\circ }$. The temporal dynamics of finite-amplitude nonspherical oscillations are then analyzed for various acoustic pressures above the instability threshold. The experimental results are compared with recent theories accounting for nonlinearities and mode coupling, highlighting particular effects inherent to these mechanisms (saturation of the instability, triggering of nonparametric shape modes). Finally, the amplitude of the nonspherical oscillations is given as function of the driving pressure both for quadrupolar and octupolar bubbles.

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

We show that the degree-degree correlations have a major impact on global synchronizability (GS) of multiplex networks, enabling the specification of synchronizability by only changing the degree-degree correlations of the mirror nodes while maintaining the connection architecture of the individual layer unaltered. If individual layers have nodes that are mildly correlated, the multiplex network is best synchronizable when the mirror degrees are strongly negatively correlated. If individual layers have nodes with strong degree-degree correlations, mild correlations among the degrees of mirror nodes are the best strategy for the optimization of GS. Global synchronization also depend on the density of connections, a phenomenon not observed in a single layer network. The results are crucial to understand, predict, and specify behavior of systems having multiple types of connections among the interacting units.

Connectivity, or the lack thereof, is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately established or removed to induce, maintain, or destroy global connectivity. Thus, there has been a great interest in understanding how to control percolation, the transition to large-scale connectivity. Previous work, however, studied control strategies assuming unlimited resources. Here, we depart from this unrealistic assumption and consider the effect of limited resources on the effectiveness of control. We show that, even for scarce resources, percolation can be controlled with an efficient intervention strategy. We derive such an efficient strategy and study its implications, revealing a discontinuous transition as an unintended side effect of optimal control.

In the present study, we have investigated the Allison mixture, a variant of the Parrondo's games where random mixing of two random sequences creates autocorrelation. We have obtained the autocorrelation function and mutual entropy of two elements. Our analysis shows that the mutual information is nonzero even if two distributions have identical average values. We have also considered the two-envelope problem and solved for its exact probability distribution.

The structure of a sentence can be represented as a network where vertices are words and edges indicate syntactic dependencies. Interestingly, crossing syntactic dependencies have been observed to be infrequent in human languages. This leads to the question of whether the scarcity of crossings in languages arises from an independent and specific constraint on crossings. We provide statistical evidence suggesting that this is not the case, as the proportion of dependency crossings of sentences from a wide range of languages can be accurately estimated by a simple predictor based on a null hypothesis on the local probability that two dependencies cross given their lengths. The relative error of this predictor never exceeds $5\%$ on average, whereas the error of a baseline predictor assuming a random ordering of the words of a sentence is at least six times greater. Our results suggest that the low frequency of crossings in natural languages is neither originated by hidden knowledge of language nor by the undesirability of crossings per se, but as a mere side effect of the principle of dependency length minimization.

We examine a rapidly solidifying binary alloy under directional solidification with nonequilibrium interfacial thermodynamics viz. the segregation coefficient and the liquidus slope are speed dependent and attachment-kinetic effects are present. Both of these effects alone give rise to (steady) cellular instabilities, mode $S$, and a pulsatile instability, mode $P$. We examine how weak imposed boundary-layer flow of magnitude $\left|\mathcal{V}\right|$ affects these instabilities. For small $\left|\mathcal{V}\right|$, mode $S$ becomes a traveling and the flow stabilizes (destabilizes) the interface for small (large) surface energies. For small $\left|\mathcal{V}\right|$, mode $P$ has a critical wave number that shifts from zero to nonzero giving spatial structure. The flow promotes this instability and the frequencies of the complex conjugate pairs each increase (decrease) with flow for large (small) wave numbers. These results are obtained by regular perturbation theory in powers of $\mathcal{V}$ far from the point where the neutral curves cross, but requires a modified expansion in powers of ${\mathcal{V}}^{1/3}$ near the crossing. A uniform composite expansion is then obtained valid for all small $\left|\mathcal{V}\right|$.

We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction $\mu$ is an increasing function of the inertial number $I$, and we systematically investigate the dependence of $\mu$ on the particle aspect ratio $Q$, as well as that of the normal stress differences, the volume fraction, and the coordination number. We show in particular that the quasistatic friction coefficient is nonmonotonic with $Q$: from the spherical case $Q=1$, it first sharply increases, reaches a maximum around $Q\simeq 1.05$, and then gently decreases until $Q=3$, passing its initial value at $Q\simeq 2$. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps.

In this article, we present a numerical study of the dynamics of two disks sedimenting in a narrow vertical channel filled with an Oldroyd-B fluid. Two kinds of particle dynamics are observed: (i) a periodic interaction between the two disks, and (ii) the formation of a two-disk chain. For the periodic interaction of the two disks, two different motions are observed: (a) the two disks stay far apart and interact periodically, and (b) the two disks interact closely and then far apart in a periodic way, like the drafting, kissing, and tumbling of two disks sedimenting in a Newtonian fluid, due to a weak elastic force. Concerning the formation of a two-disk chain occurring at higher values of the elasticity number, either a tilted chain or a vertical chain is observed. Our simulations show that, as expected, the values of the elasticity and Mach numbers are the determining factors concerning the particle chain formation and its orientation.

An implementation of the polynomial chaos expansion is introduced as a fast solver of the equations of beam and spin motion of charged particles in electromagnetic fields. We show that, based on the stochastic Galerkin method, our computational framework substantially reduces the required number of tracking calculations compared to the widely used Monte Carlo method.

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the $\mathrm{SU}\left(2\right)$ nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the Ablowitz-Kaup-Newell-Segur formalism; however, efficient numerical algorithms that could be employed in practical applications are still unavailable. In this paper, we present a unified framework for the forward and inverse NFT using exponential one-step methods which are amenable to FFT-based fast polynomial arithmetic. Within this discrete framework, we propose a fast Darboux transformation (FDT) algorithm having an operational complexity of $O\left(KN+N{log}^{2}N\right)$ such that the error in the computed $N$-samples of the $K$-soliton vanishes as $O\left(N^{-p}\right)$ where $p$ is the order of convergence of the underlying one-step method. For fixed $N$, this algorithm outperforms the classical DT (CDT) algorithm which has a complexity of $O\left(K^{2}N\right)$. We further present an extension of these algorithms to the general version of DT which allows one to add solitons to arbitrary profiles that are admissible as scattering potentials in the ZS problem. The general CDT and FDT algorithms have the same operational complexity as that of the $K$-soliton case and the order of convergence matches that of the underlying one-step method. A comparative study of these algorithms is presented through exhaustive numerical tests.

In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)]. First, we emphasize that the replacement of $\mathbf{\nabla }·\left(\lambda \mathbf{\nabla }T\right)/\phantom{\mathbf{\nabla }·\left(\lambda \mathbf{\nabla }T\right)\rho c_V}\rho c_V$ with $\mathbf{\nabla }·\left(\chi \mathbf{\nabla }T\right)$ is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ${\partial }_{t_0}\left(T\mathbf{v}\right)+\mathbf{\nabla }·\left(T\mathbf{vv}\right)$, which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of $\mathbf{\nabla }·\left(\lambda \mathbf{\nabla }T\right)/\phantom{\mathbf{\nabla }·\left(\lambda \mathbf{\nabla }T\right)\rho c_V}\rho c_V$ with $\mathbf{\nabla }·\left(\chi \mathbf{\nabla }T\right)$ leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by the statistics of the placement of micrometer-thin parallel permeable barriers, and the time-dependent diffusion coefficient was measured by NMR methods over three orders of magnitude in time. The relation between the structural exponent, characterizing disorder universality class, and the dynamical exponent of the diffusion coefficient is experimentally verified. The experimentally established relation between structure and transport exemplifies the hierarchical nature of structural complexity—dynamics are mainly determined by the universality class, whereas microscopic parameters affect the nonuniversal coefficients. These results open the way for noninvasive characterization of structural correlations in porous media, complex materials, and biological tissues via a bulk diffusion measurement.

The distribution of the hypervolume $V$ and surface $\partial V$ of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than $P={10}^{-1000}$ to estimate large deviation properties. For arbitrary dimensions and large walk lengths $T$, we suggest a scaling behavior of the distribution with the length of the walk $T$ similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in $d=3$ and $d=4$ dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large $T$.