Recent experimental studies on the instability of capillary jets have revealed the suitability of a linear spatiotemporal instability analysis to ascertain the parametrical conditions for specific flow regimes such as steady jetting or dripping. In this work, an extensive analytical, numerical, and experimental description of confined capillary jets is provided, leading to an integrated picture both in terms of data and interpretation. We propose an extended, accurate analytic model in the low Reynolds number limit, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show remarkable accuracy when compared with the extensive experimental mapping.

With the equations of fluid mechanics, the proper boundary conditions, and the gas properties, we simulate the processes of single-bubble sonoluminescence. The calculation demonstrates the process of the evolution of the radiation energy spectrum with time for bright sonoluminescing bubbles, which clearly shows how the prominence of the OH line near $310\mathrm{nm}$ gradually merges into the continuous spectral background as the radiation power increases and finally disappears in the spectrum. For the dim bubble, the spectral line of OH radicals or the sodium line near $589\mathrm{nm}$ is prominent on the spectrum.

A numerical simulation using the multiple relaxation time lattice-Boltzmann method is carried out for the purpose of investigating fluid flow over two vibrating side-by-side circular cylinders and the effect of moving the cylinders on the wake characteristics. As a benchmark problem to assess the validity and efficiency of the model, the calculation was carried out at Reynolds number of 200 and four pitch ratios ($T∕D$, where $D$ is the cylinder diameter while $T$ is the center-to-center spacing between the two cylinders) of 1.2, 1.6, 2.2, and 3.2, respectively. The calculated results indicate that the vibration of the cylinder pair has significant influence on the wake patterns. When the amplitude of vibration is big enough, the vibration locks up the vortex shedding and formation. For each cylinder vibration frequency, there exists a threshold of vibration amplitude for the lock-up phenomenon. With the vibration frequency is increased, the threshold of vibration amplitude decreases.

We present the results of an experimental investigation of the temporal evolution of plasmas produced by high power laser irradiation of various types of target materials (at intensities $I_L⩽{10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$). We obtained interferometric data on the evolution of the plasma profile, which can directly be compared to analytical models and numerical simulations. For aluminum and plastic targets, the agreement with 1D simulations done with the hydrocode MULTI is excellent, at least for large times $(t⩾400\mathrm{ps})$. In this case, simulations also show that the effect of radiation transport is negligible. The situation is quite different for gold targets for which, in order to get a fair agreement, radiation transport must be taken into account.

A potential buildup in front of a magnetized cascaded arc hydrogen plasma source is explored via $\vec{E}\times \vec{B}$ rotation and plate potential measurements. Plasma rotation approaches thermal speeds with maximum velocities of $10\mathrm{km}∕\mathrm{s}$. The diagnostic for plasma rotation is optical emission spectroscopy on the Balmer-$\beta$ line. Asymmetric spectra are observed. A detailed consideration is given on the interpretation of such spectra with a two distribution model. This consideration includes radial dependence of emission determined by Abel inversion of the lateral intensity profile. Spectrum analysis is performed considering Doppler shift, Doppler broadening, Stark broadening, and Stark splitting.

Terahertz (THz) radiation from the interaction of ultrashort laser pulses with gases is studied both by theoretical analysis and particle-in-cell (PIC) simulations. A one-dimensional THz generation model based on the transient ionization electric current mechanism is given, which explains the results of one-dimensional PIC simulations. At the same time the relation between the final THz field and the initial transient ionization current is shown. One- and two-dimensional simulations show that for the THz generation the contribution of the electric current due to ionization is much larger than the one driven by the usual ponderomotive force. Ionization current generated by different laser pulses and gases is also studied numerically. Based on the numerical results we explain the scaling laws for THz emission observed in the recent experiments performed by Xie et al. [Phys. Rev. Lett. 96, 075005 (2006)]. We also study the effective parameter region for the carrier envelop phase measurement by the use of THz generation.

We present a formulation for nonreflecting boundaries in fluctuating hydrodynamics. Nonreflecting boundary conditions are designed to evacuate sound waves out of the computational domain, thus allowing one to deal with open systems and to avoid finite size effects associated with periodic boundaries. Thermodynamic consistency for the fluctuation of the total mass and momentum of the open system is ensured by a fluctuation-dissipation balance which controls the amplitude of the sound waves generated by stress fluctuations near the boundary. We consider equilibrium and out-of-equilibrium situations (forced sound) in liquid water at ambient conditions and argon ranging from gas to liquid densities. Nonreflecting boundaries for fluctuating hydrodynamics make feasible simulations of ultrasound in microfluidic devices.

We consider a procedure for generating clustered networks previously reported by Newman [Phys. Rev. E 68, 026121 (2003)]. In the same study, clustered networks generated according to the proposed model have been reported to have a lower epidemic threshold under susceptible-infective-recovered-type network epidemic dynamics. By rewiring networks generated by this model, such that the degree distribution is conserved, we show that the lower epidemic threshold can be closely reproduced by rewired networks with close to zero clustering. The reported lower epidemic threshold can be explained by different degree distributions observed in the networks corresponding to different levels of clustering. Clustering results in networks with high levels of heterogeneity in node degree, a higher proportion of nodes with zero connectivity, and links concentrated within highly interconnected components of small size. Hence, networks generated by this model differ in both clustering and degree distribution, and the lower epidemic threshold is not explained by clustering alone.

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

A general self-consistency approach allows for a thorough treatment of the corrections to the mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a coarse-graining procedure. We outline and justify our method by some preliminary calculations. Results are given for the critical temperature and the Landau parameters of the ${\varphi }^4$ theory—the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions—the problem for the calculation of the true critical temperature—is considered within the framework of the present approach. A comprehensive description of the ground-state properties of many-body systems is also demonstrated.

In order to further understand the physical characteristics of liquid silicon, the thermophysical properties are required over a broad temperature range. However, its high reactivity brings about great difficulties in the experimental measurement. Here we report the thermophysical properties by molecular dynamics calculation, including density, specific heat, diffusion coefficient, and surface tension. The calculation is performed with a system consisting of 64 000 atoms, and employing the Stillinger-Weber (SW) potential model and the modified embedded atom method (MEAM) potential model. The results show that the density increases as a quadratic function of undercooling, and the value calculated by SW potential model is only 2–4 % smaller than the reported experimental data. The specific heat is obtained to be $30.95\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ by SW potential model and $32.50\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ by MEAM potential model, both of which are constants in the corresponding ranges of temperature. The self-diffusion coefficient is exponentially dependent on the temperature and consistent with the Arrhenius equation. The surface tension increases linearly with the rise of undercooling and agrees well with the reported experimental results. This work provides reasonable data in much wider temperature range, especially for the undercooled metastable state.

Strong shocks in rapid dense granular flows are studied theoretically and analyzed in detail to compare with benchmark experimental data. The experimental data includes particle image velocimetry measurements of dry granular flow following its continuous release from a silo. The rapidly moving material down the chute impinges on an obstruction wall erected perpendicular at the end of a long and steep channel. Impact leads to a sudden change in the flow regime from a fast moving supercritical thin layer to a stagnant thick heap with variable thickness. This flow configuration is particularly interesting because it is analogous to some hydraulic and aerodynamic situations. We present results about the depth and the velocity evolution and their comparisons with theoretical predictions associated with frictional granular flow equations incorporating anisotropic pressure conditions. These flow equations are integrated by implementing high-resolution nonoscillatory central differencing total variation diminishing schemes. The dynamical and geometrical effects of the flow will be discussed in detail. These include geometry evolution and depositions at supercritical and subcritical flows, the impact velocity, shock speed, its position and evolution, choice of numerical limiters, and the influence of friction angles on the dynamics and depositions. An excellent agreement between theoretical predictions and experimental observations will be demonstrated. These results can be applied to estimate impact pressures exerted by avalanches on defense structures or infrastructure along the channel and in the run-out zones, and to study the complex flow dynamics around the obstacles and in depositions when the mass comes suddenly to a standstill. Importantly, these results can form a basis for calibration of numerical simulations when strong shocks occur in granular flows.

We investigate microscale flows of microparticles driven by a laser beam focused near the air-liquid interface of a suspension droplet. Three distinct regimes, convection, a linear flow, and a nonflow, are found by controlling both the position of the beam focus relative to the air-liquid interface and the laser power. They are governed by the most dominant of two effects exerted by a focused laser beam, i.e., local heating and radiation pressure. We find that in the nonflow regime two-dimensional close-packed arrays of microparticles are formed on the air-liquid interface, and spin on the beam axis. We show that micron-sized polystyrene beads can be bonded into a long chain structure by taking advantage of the linear flow.

We show how a nonlocal version of the real Ginzburg-Landau (GL) equation arises in a large-scale recurrent network model of primary visual cortex. We treat cortex as a continuous two-dimensional sheet of cells that signal both the position and orientation of a local visual stimulus. The recurrent circuitry is decomposed into a local part, which contributes primarily to the orientation tuning properties of the cells, and a long-range part that introduces spatial correlations. We assume that (a) the local network exists in a balanced state such that it operates close to a point of instability and (b) the long-range connections are weak and scale with the bifurcation parameter of the dynamical instability generated by the local circuitry. Carrying out a perturbation expansion with respect to the long-range coupling strength then generates a nonlocal coupling term in the GL amplitude equation. We use the nonlocal GL equation to analyze how axonal propagation delays arising from the slow conduction velocities of the long-range connections affect spontaneous pattern formation.

Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e., the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering. The results show that the benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.

We report the dynamical behavior of $\mu \mathrm{m}$-sized phase separation for a homogeneous mixture of ${\mathrm{D}}_2\mathrm{O}$ and 3-methylpyridine (3MP) induced under continuous photon-flux by a focused YAG laser. At a water-rich composition, stable rhythmic oscillation of the emergence-growth escape of a 3MP-rich droplet is generated. In contrast, at a near-critical composition, an emergent droplet exhibits significant nonequilibrium fluctuation. Such dynamic phenomena are interpreted in terms of the effect of a local dielectric field and a dissipative system generated by a focused laser on the binary mixture.

Periodic stripe patterns which form when an electric field is applied to a thin nematic liquid crystal layer with a very low conductivity are discussed. In this case the dielectric electroconvection mode persists down to very low frequencies of the driving voltage. A Lifschitz point, i.e., a transition from normal to oblique rolls is detected in the dielectric regime. A crossover from electroconvection to flexoelectric domains occurs for extremely low frequencies of about $0.1\mathrm{Hz}$. The crossover scenario yields pattern morphologies characteristic for both mechanisms, i.e., electroconvection and flexoelectric domains which appear consecutively within one period of the driving voltage. A theoretical description of the onset characteristics of dielectric convection, which is based on an extended model including flexoelectricity, is also presented.

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other, but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables. Nor does it need to be active for all times for achieving generalized synchronization. The procedure is based on an analogy between a response map subject to an external drive acting with a probability $p$ and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems.

Polymer-induced drag reduction is the phenomenon by which the friction factor of a turbulent flow is reduced by the addition of small amounts of high-molecular-weight linear polymers, which conformation in solution at rest can vary between randomly coiled and rodlike. It is well known that drag reduction is positively correlated to viscous stresses, which are generated by extended polymers. Rodlike polymers always assume this favorable conformation, while randomly coiling chains need to be unraveled by fluid strain rate in order to become effective. The coiling and stretching of flexible polymers in turbulent flow produce an additional elastic component in the polymer stress. The effect of the elastic stresses on drag reduction is unclear. To study this issue, we compare direct numerical simulations of turbulent drag reduction in channel flow using constitutive equations describing solutions of rigid and flexible polymers. When compared at constant $\varphi r^2$, both simulations predict the same amount of drag reduction. Here $\varphi$ is the polymer volume fraction and $r$ is the polymer aspect ratio, which for flexible polymers is based on average polymer extension at the channel wall. This demonstrates that polymer elasticity plays a marginal role in the mechanism for drag reduction.

A boundary condition for lattice Boltzmann methods, based on the movement of information through Euler characteristic directions, is developed. With respect to the similar conditions used in finite-difference or finite-volume implementations, some corrections are needed to compensate the isothermal compressible nature of standard lattice Boltzmann methods for fluid flow. The results show that the proposed method for inlets and outlets is highly nonreflecting, and mass conserving.