Transition to chaos in the presence of noise is an important problem in nonlinear and statistical physics. Recently, a scaling law has been theoretically predicted which relates the Lyapunov exponent to the noise variation near the transition. Here we present experimental observation of noise-induced chaos in an electronic circuit and obtain the fundamental scaling law characterizing the transition. The experimentally obtained scaling exponent agrees very well with that predicted by theory.

Long wave evolution on free falling viscous films is described using a new evolution equation. The scaling proposed here brings in the viscous and pressure correction terms that are missing in the existing long-wave equations. Small amplitude expansion of the equation gives a dissipative form of the Kuromoto-Sivashinsky equation. Improved accuracy of the new equation over existing equations is demonstrated by comparison of neutral curves with Orr-Sommerfeld equations and experimental data.

“Simple limiter control” of chaotic systems is analytically and numerically investigated, proceeding from the one-dimensional case to higher dimensions. The properties of the control method are fully described by the one-parameter one-dimensional flat-top map family, implying that orbits are stabilized in exponential time, independent of the periodicity and without the need for targeting. Fine-tuning of the control is limited by superexponential scaling in the control space, where orbits of the uncontrolled system are obtained for a set of zero Lebesgue measure. In higher dimensions, simple limiter control is a highly efficient control method, provided that the proper limiter form and placement are chosen.

We show that wetting properties crucially control the patterns in two-phase flows of immiscible fluids in microchannels. Ordered patterns, continuously entrained by the flow, are obtained when one phase completely wets the walls, while disordered patterns, intermittently adhering to the channel walls, are unavoidably produced when wetting is partial. A lower limit for the channel sizes capable of generating well structured objects (drops, pears, pearl necklaces, $\dots$) is presented.

Apparent mass ($M_{\mathrm{a}\mathrm{p}\mathrm{p}}$) measurements at the bottom of granular packings inside a vertical tube in relative motion are reported. They demonstrate that Janssen’s model is valid over a broad range of velocities $v$. The variability of the measurements is lower than for static packings and the theoretical exponential increase of $M_{\mathrm{a}\mathrm{p}\mathrm{p}}$ with the height of the packing is precisely followed (the corresponding characteristic screening length is of the order of the tube diameter). The limiting apparent mass at large heights is independent of $v$ and significantly lower than the static value.

The standard hydrodynamic description does not apply to the rapid flow regime of inelastic grains in the dense limit. Emphasizing the role of inelastic loss and collapse, we propose a new approach relying on a nonlocal dissipation scheme. Our model succeeds in accounting qualitatively and quantitatively for the linear profile of velocity found in experiments on dense gravity-driven flows.

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast, $c=({\mu }_1-{\mu }_2)/({\mu }_1+{\mu }_2)$, in a model porous medium defined as a Hele-Shaw cell with random gap $b_0+\delta b$. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, nonconserved, and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number Ca as ${\ell }_1\sim b_0(c\mathrm{C}\mathrm{a}{)}^{-1/2}$ and ${\ell }_2\sim b_0{\mathrm{C}\mathrm{a}}^{-1}$. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.

We report on a new class of electromagnetically driven fluid interface instability. Using the optical radiation pressure of a cw laser to bend a very soft near-critical liquid-liquid interface, we show that it becomes unstable for sufficiently large beam power $P$, leading to the formation of a stationary beam-centered liquid microjet. We explore the behavior of the instability onset by tuning the interface softness with temperature and varying the size of the exciting beam. The instability mechanism is experimentally demonstrated. It simply relies on total reflection of light at the deformed interface whose condition provides the universal scaling relation for the onset $P_S$ of the instability.

The influence of surface roughness on the boundary condition for the flow of a Newtonian fluid near a hard wall has been investigated by measurement of the hydrodynamic drainage force. The degree of slip is found to increase with surface roughness. This leads to the conclusion that in most practical situations boundary slip takes place, leading to a reduction of the drainage force.

We present a simple analytical model for the forces that determine jet diameter during electrospinning as a function of surface tension, flow rate, and electric current in the jet. The model predicts the existence of a terminal jet diameter, beyond which further thinning of the jet due to growth of the whipping instability does not occur. Experimental data for various electrospun fibers attest to the accuracy of the model.

We present experimental results and theoretical analysis of two-photon ionization of He by a superposition of the 7th to the 13th harmonic of a Ti:sapphire laser. Solving the time-dependent Schrödinger equation for He in a coherent polychromatic field, the ${\mathrm{H}\mathrm{e}}^{+}$ yield is calculated. From this yield the number of ${\mathrm{H}\mathrm{e}}^{+}$ ions produced has been estimated and found in reasonable agreement with its measured value. The present results establish the feasibility of a second-order autocorrelation measurement of superposition of harmonics, and thus they represent the precursor towards the direct temporal characterization of attosecond pulse trains.

Helical modes of light can be focused into toroidal optical traps known as optical vortices, which are capable of localizing and applying torques to small volumes of matter. Measurements of optical vortices created with the dynamic holographic optical tweezer technique reveal an unsuspected dependence of their structure and angular momentum flux on their helicity. These measurements also provide evidence for a novel optical ratchet potential in practical optical vortices.

In a model for rotating non-Boussinesq convection with mean flow, we identify a regime of spatiotemporal chaos that is based on a hexagonal planform and is sustained by the induced nucleation of dislocations by penta-hepta defects. The probability distribution function for the number of defects deviates substantially from the usually observed Poisson-type distribution. It implies strong correlations between the defects in the form of density-dependent creation and annihilation rates of defects. We extract these rates from the distribution function and also directly from the defect dynamics.

Experiments with a thin gas-fluidized granular layer revealed a sequence of well-defined transitions as the amplitude and frequency of the gas flow modulation are varied. The observed patterns include subharmonic squares and stripes, quasiperiodic and disordered structures. The wavelength of subharmonic patterns increases with the mean flow rate and decreases with the modulation frequency.

We consider the 3-body problem in relativistic lineal [i.e., ($1+1$)-dimensional] gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly bound orbits of higher frequency compared to their nonrelativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of nonlinearity in the system. We find numerical evidence for mild chaos and a countably infinite class of nonchaotic orbits, yielding a fractal structure in the outer regions of the Poincaré plot.

A theory of a fast binary chemical reaction, $\mathcal{A}+\mathcal{B}\to \mathcal{C}$, in a statistically stationary bounded chaotic flow at large Peclet number Pe and large Damköhler number Da is described. The first stage correspondent to formation of the developed lamellar structure in the bulk part of the flow is terminated by an exponential decay, $\propto \exp (-\lambda t)$ (where $\lambda$ is the Lyapunov exponent of the flow), of the chemicals in the bulk. The second and the third stages are due to the chemicals remaining in the boundary region. During the second stage, the amounts of $\mathcal{A}$ and $\mathcal{B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the third stage is exponential, $\propto \exp (-\gamma t)$, where $\gamma \sim \lambda /\sqrt{\mathrm{P}\mathrm{e}}$.

We demonstrate that superfluorescent scattering of light can occur when laser light is incident on a collection of dielectric Rayleigh particles suspended in a viscous medium. Using a linear stability analysis, an expression for the spatiotemporal evolution of the scattered (probe) field is derived. An approximate condition for the progression of the interaction into the nonlinear regime is deduced and it is shown that, in the nonlinear regime, the scattered field intensity shows the characteristic quadratic dependence on particle density expected from a superfluorescent or superradiant process, once the effects of pump depletion are accounted for.

Local temperature inhomogeneities in systems containing micron and submicron objects can result in unexpected consequences. If the mean free path of the host gas constituents is comparable to a characteristic length of the system, then a net exchange of momentum occurs between the constituents and the involved surfaces. For a given temperature gradient and a given pressure range, this results in the presence of Knudsen and Knudsen-like forces (KF). The pressure dependence of these forces has been studied using a microelectromechanical system composed of a microcantilever near a substrate surface. Nano-Newton scale KF are observed by the bending of the microcantilever as monitored by the charge variation on the microcantilever-substrate assembly in a capacitive mode.

Using a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett. 89, 084101 (2002)]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin.

We propose a discrete Boltzmann model for microfluidics based on the Boltzmann equation with external forces using a single relaxation time collision model. Considering the electrostatic interactions in microfluidics systems, we introduce an equilibrium distribution function that differs from the Maxwell-Boltzmann distribution by an exponential factor to represent the action of an external force field. A statistical mechanical approach is applied to derive the equivalent external acceleration force exerting on the lattice particles based on a mean-field approximation, resulting from the electrostatic potential energy and intermolecular potential energy between fluid-fluid and fluid-substrate interactions.