Fluctuating fluxes on a complex network lead to load fluctuations at the vertices, which may cause them to become overloaded and to induce a cascading failure. A characterization of the one-point load fluctuations is presented, revealing their dependence on the nature of the flux fluctuations and on the underlying network structure. Based on these findings, an alternate robustness layout of the network is proposed. Taking load correlations between the vertices into account, an analytical prediction of the probability for the network to remain fully efficient is confirmed by simulations. Compared to previously proposed mean-flux layouts, the alternate layout comes with significantly less investment costs in the high-confidence limit.

We consider the nodal points (NPs) $u=0$ and $v=0$ of the in-plane vectorial displacements $\mathbf{u}=\left(u,v\right)$ which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.

We analyze the stability of the plane Couette flow of a Newtonian fluid past an incompressible deformable solid in the creeping flow limit where the viscous stresses in the fluid (of the order ${\eta }_{f}V∕R$) are comparable with the elastic stresses in the solid (of the order $G$). Here, ${\eta }_f$ is the fluid viscosity, $V$ is the top-plate velocity, $R$ is the channel width, and $G$ is the shear modulus of the elastic solid. For $({\eta }_{f}V∕GR)=O\left(1\right)$, the flexible solid undergoes finite deformations and is, therefore, appropriately modeled as a neo-Hookean solid of finite thickness which is grafted to a rigid plate at the bottom. Both linear as well as weakly nonlinear stability analyses are carried out to investigate the viscous instability and the effect of nonlinear rheology of solid on the instability. Previous linear stability studies have predicted an instability as the dimensionless shear rate $\Gamma =({\eta }_{f}V∕GR)$ is increased beyond the critical value ${\Gamma }_c$. The role of viscous dissipation in the solid medium on the stability behavior is examined. The effect of solid-to-fluid viscosity ratio ${\eta }_r$ on the critical shear rate ${\Gamma }_c$ for the neo-Hookean model is very different from that for the linear viscoelastic model. Whereas the linear elastic model predicts that there is no instability for $H<\sqrt{{\eta }_r}$, the neo-Hookean model predicts an instability for all values of ${\eta }_r$ and $H$. The value of ${\Gamma }_c$ increases upon increasing ${\eta }_r$ from zero up to $\sqrt{{\eta }_r}∕H\approx 1$, at which point the value of ${\Gamma }_c$ attains a peak and any further increase in ${\eta }_r$ results in a decrease in ${\Gamma }_c$. The weakly nonlinear analysis indicated that the bifurcation is subcritical for most values of $H$ when ${\eta }_r=0$. However, upon increasing ${\eta }_r$, there is a crossover from subcritical to supercritical bifurcation for $\sqrt{{\eta }_r}∕H\approx 1$. Another crossover is observed as the bifurcation again becomes subcritical at large values of ${\eta }_r$. A plot in $H$ versus $\sqrt{{\eta }_r}∕H$ space is constructed to mark the regions where the bifurcation is subcritical and supercritical. The equilibrium amplitude and some physical quantities of interest, such as the total strain energy of the disturbance in the solid, have been calculated, and the effect of parameters $H$, ${\eta }_r$, and interfacial tension on these quantities are analyzed.

Steady two-layer thin-film planar flow under gravity is investigated theoretically in this study. The film is assumed to emerge out of a channel and flow over a straight plate. The interplay among inertia, viscous and surface or interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, film thickness ratio at inception, and surface-to-interfacial tension ratio. In the absence of surface and interfacial tension, the profiles of the film layers vary monotonically streamwise. The surface tension effect leads to waviness in layer profiles, with increasing wave number as the surface tension effect is reduced.

We have characterized the plasma produced by a picosecond laser pulse using x-ray spectroscopy. High-resolution high-sensitivity spectra of $K$-shell emission from a Ti plasma have been obtained, showing a strong contribution from multiply ionized ions. Hydrodynamic and collisional-radiative codes are used to extract the plasma temperature and density from these measurements. We show that our measurements can provide benchmarks for particle-in-cell (PIC) simulations of preplasma conditions in ultraintense laser-matter interactions.

We present a methodology for the finite-element discretization of nanoscaled semiconductor devices with atomic resolution. The meshing strategy is based on the use of patterns to decompose the unit cell of the underlying crystallographic structures producing unstructured tetrahedral meshes. The unit cells of the bulk semiconductors and, more importantly, of the interfaces between the substrate and the gate dielectric have been extracted from classical molecular dynamics and density functional theory simulations. A Monte Carlo approach has been then used to place the dopants in nodes of the crystal, replacing silicon atoms. The thus created “atomistic” meshes are used to simulate an ensemble of microscopically different double-gate Si metal-oxide-semiconductor field-effect transistors and the transition region at the $\text{Si}/{\text{SiO}}_2$ interface. In addition, a methodology to approximate amorphous dielectrics is also presented.

Proteins acting as molecular machines can undergo cyclic internal conformational motions that are coupled to ligand binding and dissociation events. In contrast to their macroscopic counterparts, nanomachines operate in a highly fluctuating environment, which influences their operation. To bridge the gap between detailed microscopic and simple phenomenological descriptions, a mesoscale approach, which combines an elastic network model of a machine with a particle-based mesoscale description of the solvent, is employed. The time scale of the cyclic hinge motions of the machine prototype is strongly affected by hydrodynamical coupling to the solvent.

We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.

The spectrum of a strongly chaotic system consists of discrete complex Ruelle-Pollicott (RP) resonances. We interpret the RP resonances as eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal diffusion term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long-time asymptotic expansion in the deterministic case.

We consider a rotator whose equation of motion for the angle $\theta$ consists of the zeroth and first Fourier modes. Numerical analysis based on the trailing of saddle-node bifurcations is used to locate the $n:1$ Arnold tongues where synchronization occurs. Several of them are wide enough for high-order synchronization to be seen in passive observations. By sweeping the system parameters within a certain range, we find that the stronger the dependence of $\dot{\theta }$ on $\theta$, the wider the regions of synchronization. Use of a synchronization index reveals a vast number of very narrow $n:m$ Arnold tongues. A competition phenomenon among the tongues is observed, in that they “push” and “squeeze” one another: as some tongues widen, others narrow. Two mechanisms for transitions between different $n:m$ synchronization states are considered: slow variation of the driving frequency, and the influence of low-frequency noise on the rotator.

The purpose of this paper is to investigate the physics underlying the controlled self-assembly of microparticles and nanoparticles at a two-fluid interface using an electric field. As shown in recent experiments, under certain conditions an externally applied electric field can cause particles floating at a two-fluid interface to assemble into a virtually defect free monolayer whose lattice spacing can be adjusted by varying the electric field strength. In this work, we assume that both fluids and particles are perfect dielectrics and for this case analyze the (capillary and electrical) forces acting on the particles, deduce an expression for the lattice spacing under equilibrium condition, and study the dependence of the latter upon the various parameters of the system, including the particles’ radius, the dielectric properties of the fluids and particles, the particles’ position within the interface, the particles’ buoyant weight, and the applied voltage. While for relatively large sized particles whose buoyant weight is much larger than the vertical electrostatic force, the equilibrium distance increases with increasing electric field, for submicron sized particles whose buoyant weight is negligible, it decreases with increasing electric field. For intermediate sized particles, the distance first increases and then decreases with increasing electric field strength.

Probability density functions (PDFs) of scale-dependent energy fluctuations, $P\left[\delta E\left(\ell \right)\right]$, are studied in high-resolution direct numerical simulations of Navier-Stokes and incompressible magnetohydrodynamic (MHD) turbulence. MHD flows with and without a strong mean magnetic field are considered. For all three systems it is found that the PDFs of inertial range energy fluctuations exhibit self-similarity and monoscaling in agreement with recent solar-wind measurements [Hnat et al., Geophys. Res. Lett. 29, 86 (2002)]. Furthermore, the energy PDFs exhibit similarity over all scales of the turbulent system showing no substantial qualitative change of shape as the scale of the fluctuations varies. This is in contrast to the well-known behavior of PDFs of turbulent velocity fluctuations. In all three cases under consideration the $P\left[\delta E\left(\ell \right)\right]$ resemble Lévy-type gamma distributions $\sim {\Delta }^{-1}\text{exp}\left(-\left|\delta E\right|/\Delta \right){\left|\delta E\right|}^{-\gamma }$ The observed gamma distributions exhibit a scale-dependent width $\Delta \left(\ell \right)$ and a system-dependent $\gamma$. The monoscaling property reflects the inertial-range scaling of the Elsässer-field fluctuations due to lacking Galilei invariance of $\delta E$. The appearance of Lévy distributions is made plausible by a simple model of energy transfer.

Relativistic electrons accelerated by laser wakefields can produce x-ray beams from their motion in plasma termed betatron oscillations. Detailed spectral characterization is presented in which the amplitude of the betatron oscillations $r$ is studied by numerical analysis of electron and x-ray spectra measured simultaneously. We find that $r$ reaches as low as $1\mu \text{m}$ in agreement with previous studies of radiation based on coherence and far-field spatial profile.

This paper provides a report of chaos synchronization regimes which may be accessed in both unidirectionally and bidirectionally coupled multiple-time-delay semiconductor lasers. We demonstrate that in bidirectionally coupled multiple-time-delay lasers additional feedback can considerably enhance synchronization quality.

We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temperature becomes well defined and the sampling of the equilibrium ensemble is regained. The procedure is applied to the Potts model in two and three dimensions.

The near-wall dynamics at the top and bottom phases of a phase-separated colloid-polymer mixture were measured by evanescent-wave dynamic light scattering. The short-time dynamics near the wall were found to be liquidlike in both phases, confirming the presence of a liquid wetting layer. The short-time diffusion within the wetting layer was slower than in the bulk liquid phase. Similarly, the near-wall dynamics in both phases of the colloid-polymer mixture were also slower compared to the near-wall colloidal dynamics in a pure concentrated suspension at the same volume fraction. These effects highlight the role of interparticle attractions and specific wall-induced hydrodynamic interactions in slowing down the colloidal motion in confinement.

We demonstrate the microscopic equivalent of a step-stress rheological measurement. An optical torque is applied to a birefringent wax microdisk embedded in gelatin, a highly entangled viscoelastic biopolymer, using circularly polarized laser tweezers. By increasing the laser power and measuring the angular displacement of the disk, we explore the microscopic rheological response of presheared gelatin from the linear to the nonlinear regime and observe yielding at the microscale. The shape of the microscopic torque-angle relationship matches the stress-strain relationship from a macroscopic measurement of presheared gelatin; from this, we extract an applied stress and deduce the effective strain induced by the rotating disk.

In a region in phase space where there is a chaotic saddle, all initial conditions will escape from it after a transient with the exception of a set of points of zero Lebesgue measure. The action of an external noise makes all trajectories escape faster. Attempting to avoid those escapes by applying a control smaller than noise seems to be an impossible task. Here we show, however, that this goal is indeed possible, based on a geometrical property found typically in this situation: the existence of a horseshoe. The horseshoe implies that there exist what we call safe sets, which assures that there is a general strategy that allows one to keep trajectories inside that region with control smaller than noise. We call this type of control partial control of chaos.

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in raindrop statistics and in stirring tank experiments.

The dynamic resistance of a sphere with a general inhomogeneous slip boundary condition is analyzed in Newtonian unbounded uniform flow at low Reynolds number. The boundary condition is treated as a perturbation to a homogeneous sphere, assuming that the slip length magnitude $b$ is much smaller than the sphere radius $a$. To first order, the effect of inhomogeneous slip is the same as that of a radial deformity of magnitude $b$. Full resistance tensors are presented and the dynamics of a hemispherical inhomogeneous sphere, such as a Janus particle, are explicitly calculated.