We present an approach to modeling the two-dimensional Brownian dynamics of semiflexible filaments in the worm-model description as uniform, isotropic, and continuously flexible. Experimental observations increasingly show that the mechanical behavior of semiflexible filament networks departs from conventional knowledge. A force-balance-based dynamic simulation of the filament networks has multiple advantages as an approach to understanding their anomalous mechanics. However, a major disadvantage is the difficulty of capturing filament hydrodynamics and bending mechanics in a computationally efficient and physically consistent manner. To that end, we propose a strategy for modeling semiflexible filaments which involves idealizing a semiflexible filament as a contiguous string of flexible rods, and considering the Brownian forces on it as Einsteinian-like point normal and tangential forces. By idealizing the filament as a string of rods, we avoid the complex hydrodynamic treatment involved in beads-on-string idealizations, and implement large-deflection beam mechanics and filament inextensibility in a natural manner, while reducing the computational size of the problem. By considering the Brownian forces as point normal and tangential forces, we decompose the Brownian forces on straight and curved segments into a combination of classical resultant forces and couples whose distribution is shown to be governed by the rod diffusion coefficients. The decomposition allows solution of the Euler beam equations to second-order continuity between segments and fifth-order continuity within segments. We show that the approach is physically consistent by capturing multiple Brownian phenomena ranging from the rigid to the semiflexible limit: the translational and rotational diffusion of rigid rods; the thermal fluctuation of semirigid cantilever filaments; and the shape, bending, and time relaxation of freely diffusing, semiflexible actin filaments.

A Hohlraum-like configuration is proposed for realizing a simple compact source for neutrons. A laser pulse enters a tiny thin-shelled hollow-sphere target through a small opening and is self-consistently trapped in the cavity. The electrons in the inner shell-wall region are expelled by the light pressure. The resulting space-charge field compresses the local ions into a thin layer that becomes strongly heated. An inward expansion of ions into the shell cavity then occurs, resulting in the formation at the cavity center of a hot spot of ions at high density and temperature, similar to that in inertial electrostatic confinement.

An experimental study of the transition to turbulence in a confined quasi-two-dimensional magnetohydrodynamic flow is presented. A pair of counterrotating vortice is electrically driven in the center of a thin horizontal liquid metal layer, enclosed in a cylindrical container and subject to a homogeneous vertical magnetic field. When the forcing is increased, the pair is displaced away from the center. Boundary layer separations from the circular wall appear that trigger a sequence of supercritical bifurcations. These are singled out in numerical calculations based on our previously developed shallow water model as well as in the experiment, and these bifurcations are shown to resemble those observed in flows past a cylindrical obstacle. For the highest forcing, the flow then ends up in a turbulent regime where the dissipation increases drastically, which we could relate to a possible transition from a laminar to a turbulent Hartmann boundary layer. Finally we show the first experimental evidence of a transition to three-dimensionality in liquid metal magnetohydrodynamics (MHD) by comparing velocity measurements on either horizontal sides of the layer as we find that columnar vortice wobble for a high enough forcing.

$K$-shell x-ray spectroscopy is used to study the interaction of small-mass copper foil targets $(>20\times 20\times 2\mu {\mathrm{m}}^3)$ with a high-intensity $(>{10}^{19}\mathrm{W}∕{\mathrm{cm}}^2)$ laser pulse. Efficient bulk heating to greater than $200\mathrm{eV}$ is demonstrated using collisional-energy transfer from recirculating fast electrons. $K$-photon yields and bulk-electron temperatures calculated by three-dimensional numerical target-heating simulations are in good agreement with the experimental measurements.

Compared to metallic composite metamaterials of double split-ring resonators with wires, double-ring resonators without additional wires are simple to engineer. In this paper, we have numerically studied the transmittance of double split- and closed-ring resonators at normal-to-plane incidence and identified their fundamental resonance modes. It is found that the antisymmetric and symmetric resonance modes originate from the out-of-phase and in-phase oscillations of surface charges in the neighboring legs of the double-ring resonators, respectively. The coupling of the antiparallel induced currents in the neighboring legs gives rise to magnetic resonance and consequently negative permeability of the antisymmetric mode. The negative refraction transmission of the double-ring resonators at normal-to-plane incidence is verified by dispersion curve and wedge-shaped model simulations. Our study provides a route to negative refraction metamaterial design by using the antisymmetric resonance mode of the simple double-ring structure at normal-to-plane incidence which is of particular importance for the terahertz and infrared domain.

Higher-order perturbative calculations in quantum (field) theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines two new coefficients are obtained corresponding to a four- and five-loop calculation. Several analytical and numerical procedures have been implemented which were crucial for obtaining reliable results.

We study the control of noise-induced spatiotemporal current density patterns in a semiconductor nanostructure (double-barrier resonant tunneling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of noise-induced oscillations compared to single time feedback, rendering the system more sensitive to variations in the delay time $\tau$. The coherence of noise-induced oscillations measured by the correlation time exhibits sharp resonances as a function of $\tau$, and can be strongly increased by optimal choices of $\tau$. Similarly, the peaks in the power spectral density are sharpened. We provide analytical insight into the control mechanism by relating the correlation times and mean frequencies of noise-induced breathing oscillations to the stability properties of the deterministic stationary current density filaments under the influence of the control loop. Moreover, we demonstrate that the use of multiple time delays enlarges the regime in which the deterministic dynamical properties of the system are not changed by delay-induced bifurcations.

Based on multivariate Langevin processes we present a realization of Lévy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity-dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Lévy flights. Our procedure is similar to the treatment of the Kramers-Fokker-Planck equation in the Smoluchowski limit. The proposed approach may open a way to treat Lévy flights in inhomogeneous media or systems with boundaries in the future.

We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte Carlo simulations for times up to ${10}^{10}$ and system sizes up to $8000\times 8000$ sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because, according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.

Simulation results for the asymptotic scaled capture-zone distribution (CZD) for the case of irreversible nucleation and growth of point islands are presented for substrate dimension $d=1$, 2, 3, and 4 and compared with a recent conjecture based on the Wigner distribution. Poor agreement is found between the predicted Wigner distributions and the asymptotic CZD in the limit of infinite $D∕F$ (corresponding to the ratio of monomer hopping rate $D$ to deposition rate $F$). Our results also indicate that for $d=2$ and 3 the asymptotic CZD for point islands is independent of model details and dimension. However, for $d=1$ and $d=4$ the resulting distribution is significantly more sharply peaked. We also find that in contrast to the island-size distribution, for which mean-field-like behavior is observed in $d=3$ and above, the asymptotic CZD is significantly broadened by fluctuations even in $d=4$.

The dynamic glass transition ($\alpha$ relaxation, structural relaxation) of ultrathin polysulfone films prepared between aluminum electrodes is investigated by dielectric relaxation spectroscopy. As a main result, it is found that the glass transition temperature $T_g$ does not depend on the thickness of the polymeric layer down to a thickness of $10\mathrm{nm}$. For thicknesses lower than $10\mathrm{nm}$, an increase of $T_g$ is observed. A more detailed analysis of the temperature dependence of the relaxation rates reveals that the Vogel temperature increases and the fragility decreases systematically with decreasing film thickness $d$. Further, the dielectric strength $\Delta \epsilon$ decreases with decreasing $d$. This is discussed by the formation of a surface layer of adsorbed polysulfone segments having a reduced molecular mobility with regard to the time scale characteristic of the glassy dynamics of bulk polysulfone. Plotted versus inverse film thickness $\Delta \epsilon$ decreases linearly with $1∕d$ and becomes zero for an extrapolated length scale of $10\mathrm{nm}$. From that it is concluded that the thickness of the adsorbed boundary layer is about $5\mathrm{nm}$. Contact-angle measurements were carried out to confirm the strong interaction between aluminum and polysulfone. It is also shown that preparation details like annealing conditions strongly influence the glass transition of supported ultrathin films.

In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.

Motivated by many recent experimental studies of nonclassical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii $b$ and $a$ $(b<a)$ subtending an angle $\beta$, with $0⩽\beta ⩽2\pi$. The case $\beta =2\pi$ corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges $(b=0)$ with $\beta >\pi$, we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for any nonzero value of the angular velocity. Implications of our results for experiments on “supersolid” behavior in solid ${}^4\mathrm{He}$ are discussed. A number of mathematical issues are pointed out and resolved.

In this paper we present a closed analytical description for few-cycle, focused electromagnetic pulses of arbitrary duration and carrier-envelope phase. Because of the vectorial character of light, not all thinkable one-dimensional shapes for the transverse electric field or vector potential can be realized as finite energy three-dimensional (3D) structures. We cope with this problem by using a second potential, which is defined as a primitive to the vector potential. This allows one to construct fully consistent 3D wave-packet solutions for the Maxwell equations, given a solution of the scalar wave equation. The wave equation is solved for ultrashort, Gaussian, and related pulses in paraxial approximation. The solution is given in a closed and numerically convenient form, based on the complex error function. All results undergo thorough numerical testing, validating their correctness and accuracy. A reliable and accurate representation of few-cycle pulses is, e.g., crucial for analytical and numerical theory of vacuum particle acceleration.

Axisymmetric thermal flow is of fundamental interest and practical importance. However, the work to design suitable and efficient lattice Boltzmann models on axisymmetric thermal flows is quite rare. In order to bridge the gap, a simple lattice Boltzmann model for axisymmetric thermal flow is proposed in this paper. In the present study, we show how to transform the governing equation for temperate field in the cylindrical coordinate system to the pseudo-Cartesian representation in the same way as that for the flow field. Therefore the flow field and the temperature field both are solved by the two-dimensional five-speed (D2Q5) lattice Boltzmann model. The treatment of the “geometrical forcing” due to the coordinate transformation and the physical forcing due to the temperature field is simpler than that in all existing models. Thanks to its intrinsic features, the present model is more efficient, more stable, and much simpler than the existing models. In this paper, several kinds of nontrivial thermal buoyancy-driven flows in vertical cylinders, which are of interest from the standpoint of both basic fluid dynamics and practical applications, are simulated by the present model.

We present a theoretical and experimental study of the role of hydrodynamic interactions on the motion and dispersion of metal rodlike particles in the presence of an externally applied electric field. In these systems, the electric field polarizes the particles and induces an electroosmotic flow relative to the surface of each particle. The simulations include the effect of the gravitational body force, buoyancy, far-field hydrodynamic interactions, and near-field lubrication forces. The particles in the simulations and experiments were observed to experience repeated pairing interactions in which they come together axially with their ends approaching each other, slide past one another until their centers approach, and then push apart. These interactions were confirmed in measurements of particle orientations and velocities, pair distribution functions, and net dispersion of the suspension. For large electric fields, the pair distribution functions show accumulation and depletion regions consistent with many pairing events. For particle concentrations of ${10}^8\text{particles}∕\mathrm{mL}$ and higher, dispersion within the suspension dramatically increases with increased field strength.

We consider noise-assisted spike propagation in myelinated axons within a multicompartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagation from node to node and (ii) there exists an optimum number of ion channels which allows for the most efficient signal propagation and it corresponds to the actual physiological values.

This study examines the large time asymptotic behavior for the family of reactions of the form $nA+mB\to C$ when the reactants $A$ and $B$ are initially separated. Once the reactants are brought into contact they are assumed to react with a kinetic rate proportional to $A^n{B}^m$. A planar reaction front forms and usually moves away from its initial position to invade one of the reactant solutions. The position of the reaction front relative to the initial position where the reactants were put in contact $x_f$ for large times $t$, is found theoretically to satisfy the expansion $x_f=2\sqrt{t}[\alpha +{\alpha }_2{t}^{-2\sigma }+{\alpha }_3{t}^{-3\sigma }+O\left(t^{-4\sigma }\right)]$, where $\sigma =1∕(n+m+1)$ and $\alpha$, ${\alpha }_2$, and ${\alpha }_3$ are constants. This expansion is valid provided that $n$ and $m$ are positive constants less than or equal to 3. The implication of this is that when $n+m\ne 3$, $x_f$ either tends to zero or infinity, while if $n+m=3$ then there exists the possibility of $x_f$ tending to a finite nonzero constant. For fractional order kinetics, $n$ and $m$ are arbitrary positive constants, however, for simple reactions $n$ and $m$ are positive integers. Hence, the reaction $A+2B\to C$ is the only reaction of the form $nA+mB\to C$ with $n$ and $m$ being positive integers less than 4 in an infinite domain that can lead to a reaction front approaching at a finite but nonzero distance from the position at which the two liquids first met.

We consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology—i.e., identify the time evolution of the couplings between the network nodes. To this aim, we present an adaptive strategy that, based on a potential that the network systems seek to minimize in order to maintain synchronization, can be successfully applied to identify the time evolution of the network from limited information. This strategy takes advantage of the properties of synchronism of chaos and of the presence of different communication delays over the network links. As a motivating example, we consider a network of sensors surveying an area, in which information regarding the time evolution of the network connections can be used, e.g., to detect changes taking place within the area. We propose two different setups for our strategy. In the first one, synchronization has to be achieved at each node (as well as the identification of the couplings over the network links), based solely on a single scalar signal representing a superposition of signals from the other nodes in the network. In the second one, we incorporate an additional node, termed the maestro, having the function of maintaining network synchronization. We will see that when such an arrangement is realized, it will become possible to effectively identify the time evolution of networks that are much larger than would be possible in the absence of a maestro.

Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies.