We present an analysis of the stability, energy, and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of equilibrium solutions for the same boundary conditions, one solution is found to be stable and the other unstable to linear perturbations. Following the linearly unstable solutions into the nonlinear regime, we find they relax to the stable equilibrium. A description of this process in terms of kinetic, potential and boundary-flux energies is given, and the relation to a Hamiltonian formulation is commented on. A nonlocal torque integral theorem relating the prescribed boundary data to the average current in the domain is also provided. The results will be useful for numerical verification purposes, and understanding Bursian diodes in general.

We describe a high-speed physical random number generator based on a hybrid Boolean network with autonomous and clocked logic gates, realized on a reconfigurable chip. The autonomous logic gates are arranged in a bidirectional ring topology and generate broadband chaos. The clocked logic gates receive input from the autonomous logic gates so that random numbers are generated physically that pass standard randomness tests without further postprocessing. The large number of logic gates on reconfigurable chips allows for parallel generation of random numbers, as demonstrated by our implementation of 128 physical random number generators that achieve a real-time bit rate of $12.8\mathrm{Gbits}/\mathrm{s}$.

We consider a spin chain given by the $XXZ$ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a system has an ideal metallic behavior (infinite conductivity), by rigorously establishing strict lower bounds on the zero-temperature Drude weight, which are strictly positive. The proof is based on exact renormalization group methods allowing us to prove the convergence of the expansions and to fully take into account the irrelevant terms, which play an essential role in ensuring the correct lattice symmetries. We also prove that the Drude weight verifies the same parameter-free relations as in the absence of the integrability-breaking perturbation.

We present a simulation study of density, structural, and diffusion anomalies in a core-softened system, a remarkable model liquid that exhibits anomalous properties seen in tetrahedral liquids such as silica and water. It is widely believed that core-softened potentials demonstrate waterlike sequence of anomalies. Here, we show that the order of the region of anomalous diffusion and the regions of density and structural anomalies are inverted with increasing depth of the attractive part of the potential and have silicalike sequence. We also show that the Widom line slope is negative as in water.

Motivated by the recent interest in thermodynamics of micro- and mesoscopic quantum systems we study the maximal amount of work that can be reversibly extracted from a quantum system used to temporarily store energy. Guided by the notion of passivity of a quantum state we show that entangling unitary controls extract in general more work than independent ones. In the limit of a large number of copies one can reach the thermodynamical bound given by the variational principle for the free energy.

The motion of self-propelled particles can be rectified by asymmetric or ratchetlike periodic patterns in space. Here we show that a nonzero average drift can already be induced in a periodic potential with symmetric barriers when the self-propulsion velocity is also symmetric and periodically modulated but phase-shifted against the potential. In the adiabatic limit of slow rotational diffusion we determine the mean drift analytically and discuss the influence of temperature. In the presence of asymmetric barriers, modulating the self-propulsion can largely enhance the mean drift or even reverse it.

Attachment of lytic peptides to the lipid membrane of virions or bacteria is often accompanied by their aggregation and pore formation, resulting eventually in membrane rupture and pathogen neutralization. The membrane rupture may occur gradually via formation of many pores or abruptly after the formation of the first pore. In academic studies, this process is observed during interaction of peptides with lipid vesicles. We present an analytical model and the corresponding Monte Carlo simulations focused on the pore formation in such situations. Specifically, we calculate the time of the first nucleation-limited pore-formation event and show the distribution of this time in the regime when the fluctuations of the number of peptides attached to a vesicle are appreciable. The results obtained are used to clarify the mechanism of the pore formation and membrane destabilization observed recently during interaction of highly active $\alpha$-helical peptide with sub-100-nm lipid vesicles that mimic enveloped viruses with nanoscale membrane curvature. The model proposed and the analysis presented are generic and may be applicable to other meso- and nanosystems.

We examine the ability of intrinsic noise to produce complex temporal dynamics in Turing pattern formation systems, with particular emphasis on the Schnakenberg kinetics. Using power spectral methods, we characterize the behavior of the system using stochastic simulations at a wide range of points in parameter space and compare with analytical approximations. Specifically, we investigate whether polarity switching of stochastic patterns occurs at a defined frequency. We find that it can do so in individual realizations of a stochastic simulation, but that the frequency is not defined consistently across realizations in our samples of parameter space. Further, we examine the effect of noise on deterministically predicted traveling waves and find them increased in amplitude and decreased in speed.

The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk et al. [High Energy Density Phys. 8, 76 (2012)]. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered.

Current-carrying string loops are adopted in astrophysics to model the dynamics of isolated flux tubes of magnetized plasma expected to arise in the gravitational field of compact objects, such as black holes. Recent studies suggest that they could provide a framework for the acceleration and collimation of jets of plasma observed in these systems. However, the problem remains of the search of physical mechanisms which can consistently explain the occurrence of such plasma toroidal structures characterized by nonvanishing charge currents and are able to self-generate magnetic loops. In this paper, the problem is addressed in the context of Vlasov-Maxwell theory for nonrelativistic collisionless plasmas subject to both gravitational and electromagnetic fields. A kinetic treatment of quasistationary axisymmetric configurations of charged particles exhibiting epicyclic motion is obtained. Explicit solutions for the species equilibrium phase-space distribution function are provided. These are shown to have generally a non-Maxwellian character and to be characterized by nonuniform fluid fields and temperature anisotropy. Calculation of the relevant fluid fields and analysis of the Ampere equation then show the existence of nonvanishing current densities. As a consequence, the occurrence of a kinetic dynamo is proved, which can explain the self-generation of both azimuthal and poloidal magnetic fields by the plasma itself. This mechanism can operate in the absence of instabilities, turbulence, or accretion phenomena and is intrinsically kinetic in character. In particular, several kinetic effects contribute to it, identified here with finite Larmor radius, diamagnetic and energy-correction effects together with temperature anisotropy, and non-Maxwellian features of the equilibrium distribution function.

We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system.

A new particle-based bottom-up method to develop coarse-grained models of polymers is presented and applied to polystyrene. The multiscale coarse-graining (MS-CG) technique of Izvekov et al. [J. Chem. Phys. 120, 10896 (2004)] is applied to a polymer system to calculate nonbonded interactions. The inverse Boltzmann inversion method was used to parametrize the bonded and bond-angle bending interactions. Molecular dynamics simulations were performed, and the CG model exhibited a significantly lower modulus compared to the atomistic model at low temperature and high strain rate. In an attempt to improve the CG model performance, several other parametrization schemes were used to build other models from this base model. The first of these models included standard frictional forces through use of the constant-temperature dissipative particle dynamics method that improved the modulus, yet was not transferrable to higher temperatures and lower strain rates. Other models were built by increasing the attraction between CG beads through direct manipulation of the nonbonded potential, where an improvement of the stress response was found. For these models, two parametrization protocols that shifted the force to more attractive values were explored. The first protocol involved a uniform shift, while the other protocol shifted the force in a more localized region. The uniformly shifted potential greatly affected the structure of the equilibrium model as compared to the locally shifted potential, yet was more transferrable to different temperatures and strain rates. Further improvements in the coarse-graining protocol to generate models that more satisfactorily capture mechanical properties are suggested.

With exposure to air, many liquid metals spontaneously generate an oxide layer on their surface. In oscillatory rheological tests, this skin is found to introduce a yield stress that typically dominates the elastic response but can be tuned by exposing the metal to hydrochloric acid solutions of different concentration. We systematically studied the normal impact of eutectic gallium-indium (eGaIn) drops under different oxidation conditions and show how this leads to two different dynamical regimes. At low impact velocity (or low Weber number), eGaIn droplets display strong recoil and rebound from the impacted surface when the oxide layer is removed. In addition, the degree of drop deformation or spreading during impact is controlled by the oxide skin. We show that the scaling law known from ordinary liquids for the maximum spreading radius as a function of impact velocity can still be applied to the case of oxidized eGaIn if an effective Weber number We${}^{☆}$ is employed that uses an effective surface tension factoring in the yield stress. In contrast, no influence on spreading from different oxidations conditions is observed for high impact velocity. This suggests that the initial kinetic energy is mostly damped by bulk viscous dissipation. Results from both regimes can be collapsed in an impact phase diagram controlled by two variables, the maximum spreading factor $P_m=R_0/R_m$, given by the ratio of initial to maximum drop radius, and the impact number $K={\mathrm{We}}^{☆}/{\mathrm{Re}}^{4/5}$, which scales with the effective Weber number We${}^{☆}$ as well as the Reynolds number Re. The data exhibit a transition from capillary to viscous behavior at a critical impact number $K_c\approx 0.1$.

Using the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], we numerically investigate the hydrodynamics of Leidenfrost droplets under gravity in two dimensions. Some recent theoretical predictions and experimental observations are confirmed in our simulations. A Leidenfrost droplet larger than a critical size is shown to be unstable and break up into smaller droplets due to the Rayleigh-Taylor instability of the bottom surface of the droplet. Our simulations demonstrate that an evaporating Leidenfrost droplet changes continuously from a puddle to a circular droplet, with the droplet shape controlled by its size in comparison with a few characteristic length scales. The geometry of the vapor layer under the droplet is found to mainly depend on the droplet size and is nearly independent of the substrate temperature, as reported in a recent experimental study [Phys. Rev. Lett. 109, 074301 (2012)]. Finally, our simulations demonstrate that a Leidenfrost droplet smaller than a characteristic size takes off from the hot substrate because the levitating force due to evaporation can no longer be balanced by the weight of the droplet, as observed in a recent experimental study [Phys. Rev. Lett. 109, 034501 (2012)].

We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures $T_h$ and $T_c$$(<$$T_h)$, is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\eta }_C$, ${\eta }_{+}={\eta }_C^2/[{\eta }_C-(1-{\eta }_C)\ln (1-{\eta }_C)]$, with ${\eta }_C=1-T_c/T_h$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.

A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical dynamical properties of such functions. The performance of the method is assessed by presenting an application to a quartic two-dimensional oscillator whose classical dynamics are highly chaotic. We have been able to compute the eigenfunctions of the system using a small basis set. An estimate of the basis size is obtained from the mean participation ratio. A thorough analysis of the results using different indicators, such as eigenstate reconstruction in the local representation, scar intensities, participation ratios, and error bounds, is also presented.

We present direct numerical simulations of subcritical transition to turbulence in a particle-laden channel flow, with particles assumed rigid, spherical, and heavier than the fluid. The equations describing the fluid flow are solved with an Eulerian mesh, whereas those describing the particle dynamics are solved by Lagrangian tracking. Two-way coupling between fluid and particles is modeled with Stokes drag. The numerical code is first validated against previous results from linear stability: the nonmodal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for linear disturbance amplification at subcritical conditions as for the case of a single phase fluid. To analyze the full nonlinear transition, we examine two scenarios well studied in the literature: (1) transition initiated by streamwise independent counter-rotating streamwise vortices and one three-dimensional mode and (2) oblique transition, initiated by the nonlinear interaction of two symmetric oblique waves. The threshold energy for transition is computed, and it is demonstrated that for both scenarios the transition may be facilitated by the presence of particles at low number density. This is due to the fact that particles may introduce in the system detrimental disturbances of length scales not initially present. At higher concentrations, conversely, we note an increase of the disturbance energy needed for transition. The threshold energy for the oblique scenario shows a more significant increase in the presence of particles, by a factor about four. Interestingly, for the streamwise-vortex scenario the time at which transition occurs increases with the particle volume fraction when considering disturbances of equal initial energy. These results are explained by considering the reduced amplification of oblique modes in the two-phase flow. The results from these two classical scenarios indicate that, although linear stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown. These effects can be responsible of the reduced drag observed in turbulent channel flow laden with heavy particles.

We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.