The dynamic nature of a system gives rise to dynamical features of epidemic spreading, such as oscillation and bistability. In this paper, by studying the epidemic spreading in growing networks, in which susceptible nodes may adaptively break the connections with infected ones yet avoid being isolated, we reveal a phenomenon, epidemic reemergence, where the number of infected nodes is incubated at a low level for a long time and then erupts for a short time. The process may repeat several times before the infection finally vanishes. Simulation results show that all three factors, namely the network growth, the connection breaking, and the isolation avoidance, are necessary for epidemic reemergence to happen. We present a simple theoretical analysis to explain the process of reemergence in detail. Our study may offer some useful insights, helping explain the phenomenon of repeated epidemic explosions.

Numerical simulation of two-dimensional bulk instability of the one-dimensional conduction state in an electrolyte confined between a pair of cation-exchange membranes subjected to an external voltage is conducted under an assumption of constant current. By employing variable grids, we resolve the problem of sensitive dependence of the numerical solutions to the grid refinement in particular at a current close to the limiting value. In fact, the full range of parameters, i.e., Schmidt number, Peclet number, diffusivity ratio, and current, is considered in this study in obtaining the stability chart. It turns out that the Schmidt number exerts almost no influence on the results. From the neutral curves in the chart of the parameter space (current versus diffusivity ratio, i.e., cation diffusivity divided by anion diffusivity) we confirm that the system tends to be unstable at high Peclet numbers, high currents, and low diffusivity ratios. As the diffusivity ratio is increased the instability mode switches from the monotonic to the oscillatory type, and the critical diffusivity ratio for the switching is found to be decreased as the Peclet number decreases. At the switching, no jump in the neutral curves is found, contrary to the earlier result, because the wave number is set free to change in this study. The stability chart obtained in this study represents the true boundaries in discriminating the stable from the unstable parameter sets because the critical eigenvalues constituting the chart are sought for the entire possible range of the wave numbers and the frequencies.

Dust immersed in plasma quickly charges to a potential where the ion and electron currents to its surface balance; this is the floating potential. In order to accurately determine dust behavior, the floating potential must be known. The charging of dust grains that are small with respect to electron Debye length (${\lambda }_D$) may be adequately approximated using the orbital-motion-limited (OML) approach. A modified version of OML is presented for large dust grains in both stationary and flowing plasmas. This modified OML is compared with simulation and found to be in good agreement. The modified OML is applied to large grains charging under tokamak conditions and found to have an appreciable effect on the drag force.

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of nonideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. [J. Comput. Phys. 152, 642 (1999)]. Numerical tests show that, in the case of a one-component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two-component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, such as the susceptibilities and thermal average values. The quality of the bounds is checked against the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single-impurity Kondo model. It is shown that, when divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.

Energy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiency ${\eta }_{\mathrm{CA}}$ is commonly believed to be an absolute reference for real heat engines; however, a different but general expression for the case of stochastic heat engines, ${\eta }_{\mathrm{SS}}$, was recently found and then extended to low-dissipation engines. The discrepancy between ${\eta }_{\mathrm{CA}}$ and ${\eta }_{\mathrm{SS}}$ is here analyzed considering different irreversibility sources of heat engines, of both internal and external types. To this end, we choose a thermoelectric generator operating in the strong-coupling regime as a physical system to qualitatively and quantitatively study the impact of the nature of irreversibility on the efficiency at maximum output power. In the limit of pure external dissipation, we obtain ${\eta }_{\mathrm{CA}}$, while ${\eta }_{\mathrm{SS}}$ corresponds to the case of pure internal dissipation. A continuous transition between from one extreme to the other, which may be operated by tuning the different sources of irreversibility, also is evidenced.

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two values. In the isothermal regime, it can operate as a rechargeable battery by generating an electric current against the applied bias in response to the stochastic driving and then redelivering work in the reverse cycle. This behavior is reminiscent of the Parrondo paradox. If there is a thermal gradient the device can function as a work-generating thermal engine or as a refrigerator that extracts heat from the cold reservoir via the work input of the stochastic driving. The efficiency of the machine at maximum power output is investigated for each mode of operation, and universal features are identified.

We study two firing properties to characterize the activities of a neuron: frequency-current ($f$-$I$) curves and phase response curves (PRCs), with variation in the intrinsic temperature scaling parameter ($\mu$) controlling the opening and closing of ionic channels. We show a peak of the firing frequency for small $\mu$ in a class I neuron with the $I$ value immediately after the saddle-node bifurcation, which is entirely different from previous experimental reports as well as model studies. The PRC takes a type II form on a logarithmic $f$-$I$ curve when $\mu$ is small. Then, we analyze the synchronization phenomena in a two-neuron network using the phase-reduction method. We find common $\mu$-dependent transition and bifurcation of synchronizations, regardless of the values of $I$. Such results give us helpful insight into synchronizations tuned with a sinusoidal-wave temperature modulation on neurons.

The fluid media surrounding many microorganisms are often mixtures of multiple materials with very different physical properties. The composition and rheology of the mixture may strongly affect the related locomotive behaviors. We study the classical Taylor's swimming sheet problem within a two-fluid model, which consists of two intermixed viscous fluids with different viscosities, with both numerical experiments and analysis. Our results indicate that both the swimming speed and efficiency may be decreased substantially relative to those for a single-phase fluid.

Cylindrical implosions driven by intense heavy ion beams should be instrumental in the near future for study of high-energy-density matter. By rotating the beam by means of a high-frequency wobbler, it should be possible to deposit energy in the outer layers of a cylinder, compressing the material deposited in its core. The beam's temporal profile should, however, generate an inevitable irradiation asymmetry likely to feed the Rayleigh-Taylor instability (RTI) during the implosion phase. In this paper, we compute the Fourier components of the target irradiation in order to make the connection with previous works on the RTI performed in this setting. Implementing one- and two-dimensional beam models, we find that these components can be expressed exactly in terms of the Fourier transform of the temporal beam profile. If $T$ is the beam duration and $\Omega$ its rotation frequency, “magic products” $\Omega T$ can be identified which cancel the first harmonic of the deposited density, resulting in an improved irradiation symmetry.

We give a prescription for finding optimized correlation functions for the extraction of the gap to the first excited state within quantum Monte Carlo simulations. We demonstrate that optimized correlation functions provide a more accurate reading of the gap when compared to other “nonoptimized” correlation functions and are generally characterized by considerably larger signal-to-noise ratios. We also analyze the cost of the procedure and show that it is not computationally demanding. We illustrate the effectiveness of the proposed procedure by analyzing several exemplary many-body systems of interacting spin-$1/2$ particles.

Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an “exact” formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.

We present a complete-quantum description of a multiparticle Szilard engine that consists of a working substance and a Maxwell's demon. The demon is modeled as a multilevel quantum system with specific quantum control, and the working substance consists of identical particles obeying Bose-Einstein or Fermi-Dirac statistics. In this description, a reversible scheme to erase the demon's memory by a lower-temperature heat bath is used. We demonstrate that (1) the quantum control of the demon can be optimized for a single-particle Szilard engine so that the efficiency of the demon-assisted thermodynamic cycle could reach the Carnot cycle's efficiency and (2) the low-temperature behavior of the working substance is very sensitive to the quantum statistics of the particles and the insertion position of the partition.

We employ the techniques of microparticle image velocimetry and full-field birefringence microscopy combined with mechanical measurements of the pressure drop to perform a detailed characterization of the extensional rheology and elastic flow instabilities observed for a range of wormlike micellar solutions flowing through a microfluidic cross-slot device. As the flow rate through the device is increased, the flow first bifurcates from a steady symmetric to a steady asymmetric configuration characterized by a birefringent strand of highly aligned micellar chains oriented along the shear-free centerline of the flow field. At higher flow rates the flow becomes three dimensional and time dependent and is characterized by aperiodic spatiotemporal fluctuations of the birefringent strand. The extensional properties and critical conditions for the onset of flow instabilities in the fluids are highly dependent on the fluid formulation (surfactant concentration and ionic strength) and the resulting changes in the linear viscoelasticity and nonlinear shear rheology of the fluids. By combining the measurements of critical conditions for the flow transitions with the viscometric material properties and the degree of shear-thinning characterizing each test fluid, it is possible to construct a stability diagram for viscoelastic flow of complex fluids in the cross-slot geometry.

In this paper we use the Birkhoff–von Neumann decomposition of the diffusion kernel to compute a polytopal measure of graph complexity. We decompose the diffusion kernel into a series of weighted Birkhoff combinations and compute the entropy associated with the weighting proportions (polytopal complexity). The maximum entropy Birkhoff combination can be expressed in terms of matrix permanents. This allows us to introduce a phase-transition principle that links our definition of polytopal complexity to the heat flowing through the network at a given diffusion time. The result is an efficiently computed complexity measure, which we refer to as flow complexity. Moreover, the flow complexity measure allows us to analyze graphs and networks in terms of the thermodynamic depth. We compare our method with three alternative methods described in the literature (Estrada's heterogeneity index, the Laplacian energy, and the von Neumann entropy). Our study is based on 217 protein-protein interaction (PPI) networks including histidine kinases from several species of bacteria. We find a correlation between structural complexity and phylogeny (more evolved species have statistically more complex PPIs). Although our methods outperform the alternatives, we find similarities with Estrada's heterogeneity index in terms of network size independence and predictive power.

Traveling waves in an extended reactor, whose width cannot be neglected, represent a three-dimensional (3D) reaction-diffusion-convection system. We investigate the effects of buoyancy-driven convection in such a setting. The 3D waves traveled through horizontal layers of the iodate–arsenous acid (IAA) reaction solution containing excess of arsenous acid. The depth of the reaction solution was the examined parameter. An increase in the intensity of buoyancy-driven flow caused an increase of the traveling wave velocities. Convection distorted the front of the chemical waves. For layers deeper than $h>13$ mm, heat release became smaller than heat production causing the emergence of Rayleigh-Bénard convection cells. At the interface, a dependency of wave shape on solution depth was observed. For $h<7$ mm, the waves adopted a stable $\mathsf{V}$-like shape, while for $h>13$ mm a parabolic shape dominated. For $7<h<13$ mm, both shapes were realized with the same probability. Finally, an intermittent switch between stoichiometric regimes is observed as an unexpected effect of the buoyancy-driven convection. The switch is expressed by iodine enrichment in the product. Hence, the experiments demonstrate that the buoyancy-driven convective flow can cause long-lived, but nevertheless transient, changes in the chemical composition by inducing a local transition between different regimes of the IAA reaction.

The phase of the electronic wave function is not directly measurable but, quite remarkably, it becomes accessible in pairs of isospectral shapes, as recently proposed in the experiment by Moon et al. [Science 319, 782 (2008)]. The method is based on a special property, called transplantation, which relates the eigenfunctions of the isospectral pairs, and allows us to extract the phase distributions, if the amplitude distributions are known. We numerically simulate such a phase extraction procedure in the presence of disorder, which is introduced both as Anderson disorder and as roughness at edges. With disorder, the transplantation can no longer lead to a perfect fit of the wave functions, however we show that a phase can still be extracted—defined as the phase that minimizes the misfit. Interestingly, this extracted phase coincides with (or differs negligibly from) the phase of the disorder-free system, up to a certain disorder amplitude, and a misfit of the wave functions as high as $\sim$$5\%$, proving a robustness of the phase extraction method against disorder. However, if the disorder is increased further, the extracted phase shows a puzzle structure, no longer correlated with the phase of the disorder-free system. A discrete model is used, which is the natural approach for disorder analysis. We provide a proof that discretization preserves isospectrality and the transplantation can be adapted to the discrete systems.

In this paper, we study many geometrical properties of contour loops to characterize the morphology of synthetic multifractal rough surfaces, which are generated by multiplicative hierarchical cascading processes. To this end, two different classes of multifractal rough surfaces are numerically simulated. As the first group, singular measure multifractal rough surfaces are generated by using the $p$ model. The smoothened multifractal rough surface then is simulated by convolving the first group with a so-called Hurst exponent, $H^{*}$. The generalized multifractal dimension of isoheight lines (contours), $D\left(q\right)$, correlation exponent of contours, $x_l$, cumulative distributions of areas, $\xi$, and perimeters, $\eta$, are calculated for both synthetic multifractal rough surfaces. Our results show that for both mentioned classes, hyperscaling relations for contour loops are the same as that of monofractal systems. In contrast to singular measure multifractal rough surfaces, $H^{*}$ plays a leading role in smoothened multifractal rough surfaces. All computed geometrical exponents for the first class depend not only on its Hurst exponent but also on the set of $p$ values. But in spite of multifractal nature of smoothened surfaces (second class), the corresponding geometrical exponents are controlled by $H^{*}$, the same as what happens for monofractal rough surfaces.