The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of a Newtonian fluid at a smooth surface. A rigorous analysis of slip-dependent damping for the oscillator is presented. Initially, the phenomenon of finite surface slip and the slip length are considered for a half space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are reconsidered and clarified in light of inconsistencies in the literature. We point out that, in general oscillating flows, Navier’s slip length $b$ is a complex number. An intuitive velocity discontinuity parameter of unrestricted phase is used to describe the effect of slip on measurement of viscous shear damping. The analysis is applied to the composite oscillator, and preliminary experimental work for a 40 kHz oscillator is presented. The nonslip boundary condition has been verified for a hydrophobic surface in water to within $\sim 60\text{nm}$ of $\left|b\right|=0\text{nm}$. Experiments were carried out at shear rate amplitudes between 230 and $6800{\text{s}}^{-1}$, corresponding to linear displacement amplitudes between 3.2 and 96 nm.

The flow structuration of silicon oil (Prandtl number of 10.3) in a open cylindrical pool heated from the center of the surface is investigated numerically. Our purpose is to perform the numerical simulation of experimental results obtained by Favre et al. [Phys. Fluids 9, 1473 (1997)] who observed transitions between steady and axisymmetric flows at sufficiently low values of the Marangoni number (Ma) and various types of instability depending on the height of the fluid. The hydrothermal wave regime has been obtained at critical values of Ma which depend on the Bond number and on the aspect ratio. The numerical results are in good agreement with the experimental ones.

Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Öttinger, Phys. Rev. Lett. 94, 080602 (2005)]—the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin’s artificial compressibility method. A comparison of the two methods for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers shows that the results from both methods are in good agreement with each other. However, in the transient flow, it is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, unlike the artificial compressibility method.

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the“granular droplet”) and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.

In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the $J_1\text{−}{J}_2$ model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the $J_1\text{−}{J}_2$ model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.

Mechanically generated weakly breaking waves were studied experimentally in clean water and water with a soluble surfactant whose bulk concentration was above the critical micelle concentration (CMC). For the surfactant case, the breaker, which forms a surface-tension-dominated spilling breaker in clean water [wave frequencies 1.42 to $1.15\mathrm{Hz}$, see Duncan et al., J. Fluid Mech. 379, 191 (1999)], ranges from a spiller at the highest frequency to an overturning wave with a plunging microjet at the lowest frequency. It is shown that this behavior is consistent with that of a wave in a pure liquid with a lower surface tension than water rather than water with a surfactant monolayer. The analysis of the geometrical characteristics of the breaking surface generated by the jet impact on the front face of the wave crest indicates a patch of more violent turbulence suggesting an increase of air-sea transfer compared to the clean water case.

We present the results of a computer simulation study of thermodynamical properties of TIP4P water confined in a hydrophobic disordered matrix of soft spheres upon supercooling. The hydrogen-bond network of water appears preserved in this hydrophobic confinement. Nonetheless a reduction in the average number of hydrogen bonds due to the geometrical constraints is observed. The liquid branch of the spinodal line is calculated from 350 K down to 210 K. The same thermodynamic scenario of the bulk is found: the spinodal curve is monotonically decreasing. The line of maximum density bends avoiding a crossing of the spinodal. There is, however, a shift both of the line of maximum density and of the spinodal toward higher pressures and lower temperatures with respect to bulk.

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix $\mathbf{B}$; some key properties of the eigenspectrum of $\mathbf{B}$ are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.

A model of an artery consisting of a thin-walled flexible tube filled with a Newtonian incompressible liquid and surrounded by an external viscoelastic tissue is studied. The dispersion relations and attenuation lengths are determined for the lowest axially symmetric propagation modes: the Young, Lamb, and torsional modes. The numerical calculations confirm a low attenuation of the Young mode and a relatively weak dependence of its phase velocity on the elastic parameters of the surrounding medium. The Lamb and torsional modes show a nonzero frequency (a gap) at zero wave vector except for the limiting case of the absence of surroundings. The attenuation of the Lamb mode at zero frequency and the gap frequency turns out to be particularly sensitive to the elastic parameters of the surroundings. However, the spatial attenuation of the Lamb mode extends over a length of the order of $10\mathrm{cm}$ at the viscoelastic parameters corresponding to human tissues. Such lengths are comparable to the size of human organs. Three kinds of local axially symmetric perturbations have been studied, and the corresponding amplitude ratios of the Lamb to the Young mode calculated. The amplitude of the Lamb mode turns out to exceed that of the Young mode by a factor of ten at some frequencies with perturbations involving axial motions. Physiological consequences of this effect are discussed.

We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns (“oblique” and “straight” ones). Unlike them, compact “crater-shaped” vortices are unstable, transforming themselves into randomly walking fundamental beams.

We show how to generalize the lattice-switch Monte Carlo method to calculate the phase diagram of a binary system. A global coordinate transformation is combined with a modification of particle diameters, enabling the multicomponent system in question to be explored and directly compared to a suitable reference state in a single Monte Carlo simulation. We use the method to evaluate the free energies of binary hard-sphere crystals. Calculations at moderate size ratios $\alpha =0.58$ and 0.73 are in agreement with previous results, and confirm $AB2$ and $AB13$ as stable structures. We also find that the $AB\left(\mathrm{Cs}\mathrm{Cl}\right)$ structure is not entropically stable at the size ratio and volume where it has been reported experimentally, and therefore that those observations cannot be explained by packing effects alone.

Air bubbles created in many viscous liquids rise up to the liquid-air interface and stay there for a while before exploding and disappearing. The lifetimes of such bubbles are governed by the thinning dynamics of the hemispherical liquid film separating the bubble from bulk air. Here, the lifetime of bubbles confined by two separated wetting plates is experimentally studied as the distance apart, viscosity, and bubble size are changed. Although the film is not hemispherical but takes a nontrivial shape, a relatively simple hydrodynamic model accounts for the observations.

In this work we investigate the phase behavior of a family of continuous bidimensional $n$-vector models (with $n=2$, 3, and 4) using Monte Carlo simulation. In all cases we detect the presence of a defect mediated order-disorder transition of the Berezinskii-Kosterlitz-Thouless type with critical temperatures that decrease with the spin dimensionality. Coupled with the order-disorder transition a gas-liquid equilibrium is found at low temperatures. Here one observes that the stability region of the liquid phase shrinks with the growing spin dimensionality, in parallel with a decrease in magnitude of the angular averaged spin-spin interaction.

We present a statistical mechanical study of stiff polymers, motivated by experiments on actin filaments and the considerable current interest in polymer networks. We obtain simple, approximate analytical forms for the force-extension relations and compare these with numerical treatments. We note the important role of boundary conditions in determining force-extension relations. The theoretical predictions presented here can be tested against single molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules. Our work is motivated by the buckling of the cytoskeleton of a cell under compression, a phenomenon of interest to biology.

We investigate the possibility to suppress noise-induced intensity pulsations (relaxation oscillations) in semiconductor lasers by means of a time-delayed feedback control scheme. This idea is first studied in a generic normal-form model, where we derive an analytic expression for the mean amplitude of the oscillations and demonstrate that it can be strongly modulated by varying the delay time. We then investigate the control scheme analytically and numerically in a laser model of Lang-Kobayashi type and show that relaxation oscillations excited by noise can be very efficiently suppressed via feedback from a Fabry-Perot resonator.

Chaotic mixing, induced by breakup and reformation of a magnetic chain under the influence of a rotating magnetic field, is studied. A direct simulation method combining the Maxwell stress tensor and a fictitious domain method is employed to solve flows with suspended magnetic particles. The motion of the chain is significantly dependent on the Mason number (Ma), the ratio of viscous force to magnetic force. The degree of chaos is characterized by the maximum Lyapunov exponents. We also track the interface of two fluids in time and calculate the rate of stretching as it is affected by the Mason number. The progress of mixing is visualized via a tracer particle-tracking method and is characterized by the discrete intensity of segregation. Within a limited range of Mason number, a magnetic chain rotates and breaks into smaller chains, and the detached chains connect again to form a single chain. The repeating topological changes of the chain lead to the most efficient way of chaotic mixing by stretching at chain breakup and folding due to rotational flows.

Ultrashort broadband terahertz pulses are applied to probe the electron dynamics of gaseous Ar and ${\mathrm{O}}_2$ following ionization by an intense femtosecond laser pulse. The conductivity in the plasma center is extracted by a modified Wentzel-Kramers-Brillouin approach. It exhibits a nearly perfect Drude-like spectral shape and yields the temporal evolution of the free-electron density and collision rate. While the electron density in the Ar plasma remains nearly constant during the first $200\mathrm{ps}$ after generation, it decays much faster in ${\mathrm{O}}_2$ due to dissociative recombination which is only possible in molecular plasmas. Adding a small amount of the electron scavenger ${\mathrm{SF}}_6$ to Ar reduces the electron lifetime in the plasma dramatically and allows us to determine the electron temperature to about $20000\mathrm{K}$. Furthermore, anomalously high, metal-like electron collision rates of up to $25\mathrm{THz}$ are found. Kinetic plasma theory substantially underestimates these rates pointing towards additional and more complex processes randomizing the total electronic momentum. Our results are relevant to both lightning control and generation of terahertz radiation by intense laser pulses in gases.

We study the soliton ratchets in the damped sine-Gordon equation with periodic nonsinusoidal, additive, and parametric driving forces. By means of symmetry analysis of this system we show that the net motion of the kink is not possible if the frequencies of both forces satisfy a certain relationship. Using a collective coordinate theory with two degrees of freedom, we show that the ratchet motion of kinks appears as a consequence of a resonance between the oscillations of the momentum and the width of the kink. We show that the equations of motion that fulfill these collective coordinates follow from the corresponding symmetry properties of the original systems. As a further application of the collective coordinate technique we obtain another relationship between the frequencies of the parametric and additive drivers that suppresses the ratchetlike motion of the kink. We check all these results by means of numerical simulations of the original system and the numerical solutions of the collective coordinate equations.

We consider the problem of the soliton dynamics in anharmonic chains with nearest-neighbor interactions and negative group velocity. By using the quasicontinuum approach we derive analytic expressions for envelope solitons. We observe that these solitons are stable under collisions and, moreover, in the absence of losses they can propagate with nearly any desired velocity. Energy loss effects are discussed by considering the presence of Stokes and hydrodynamical damping. Numerical simulations are performed showing a good agreement with the theory.

We explore in detail the creation of stable localized structures in the form of localized energy distributions that arise from general initial conditions in the Peyrard-Bishop (PB) model. By means of a method based on the inverse scattering transform we study the solutions of PB model equations obtained in the form of planar waves whose amplitudes are described by the nonlinear Schrödinger equation (NLS). For localized initial conditions different from the pure $N$-soliton shape, we have obtained analytical results that predict and control the number, amplitude, and velocity of the NLS solitary waves. To verify the validity of these results we have carried out numerical simulations of the PB model with the use of realistic values of parameters and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the NLS. In the simulations we have found that $N$ localized structures arise in agreement with the prediction of the analytical results obtained in the NLS.