Flatness of tracer density profile produced by a point source in turbulence

The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness (kurtosis) is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation from a Gaussian profile at time t of the order of five times the velocity correlation time, with a t–1 decay to the Gaussian value at large times. Monotonically decaying forms of the velocity time correlation function are shown to yield negative values for the first order excess flatness, but positive values can result when the correlation function has an oscillatory tail

On the spectrum of a stretched spiral vortex

Corrections are found to the k^–5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]0[infinity]k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^–5/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(–B1k2) and an exp(–B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show –log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation

On the anomalous dynamics of capillary rise in porous media

The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago (Delker et al., Phys. Rev. Lett. 76 (1996) 2902) is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode and (iii) interface de-pinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process

Nucleation of colloids and macromolecules: does the nucleation pathway matter?

A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially-extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing \emph{any} proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented for the nucleation of high-concentration bubbles in a low-concentration solution of globular proteins and it is found that the relative probabilities (new theory compared to classical result) for reaching a critical nucleus containing $N_c$ molecules scales as $e^{-N_c/3}$ thus indicating that for all but the smallest nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure

Reflexive obstacle avoidance for kinematically-redundant manipulators

Dexterous telerobots incorporating 17 or more degrees of freedom operating under coordinated, sensor-driven computer control will play important roles in future space operations. They will also be used on Earth in assignments like fire fighting, construction and battlefield support. A real time, reflexive obstacle avoidance system, seen as a functional requirement for such massively redundant manipulators, was developed using arm-mounted proximity sensors to control manipulator pose. The project involved a review and analysis of alternative proximity sensor technologies for space applications, the development of a general-purpose algorithm for synthesizing sensor inputs, and the implementation of a prototypical system for demonstration and testing. A 7 degree of freedom Robotics Research K-2107HR manipulator was outfitted with ultrasonic proximity sensors as a testbed, and Robotics Research's standard redundant motion control algorithm was modified such that an object detected by sensor arrays located at the elbow effectively applies a force to the manipulator elbow, normal to the axis. The arm is repelled by objects detected by the sensors, causing the robot to steer around objects in the workspace automatically while continuing to move its tool along the commanded path without interruption. The mathematical approach formulated for synthesizing sensor inputs can be employed for redundant robots of any kinematic configuration

Infrared spectrum and stability of a π-type hydrogen-bonded complex between the OH and C2H2 reactants

A hydrogen-bonded complex between the hydroxyl radical and acetylene has been stabilized in the reactant channel well leading to the addition reaction and characterized by infrared action spectroscopy in the OH overtone region. Analysis of the rotational band structure associated with the a-type transition observed at 6885.53(1) cm−1 (origin) reveals a T-shaped structure with a 3.327(5) Å separation between the centers of mass of the monomer constituents. The OH (v = 1) product states populated following vibrational predissociation show that dissociation proceeds by two mechanisms: intramolecular vibrational to rotational energy transfer and intermolecular vibrational energy transfer. The highest observed OH product state establishes an upper limit of 956 cm−1 for the stability of the π-type hydrogen-bonded complex. The experimental results are in good accord with the intermolecular distance and well depth at the T-shaped minimum energy configuration obtained from complementary ab initio calculations, which were carried out at the restricted coupled cluster singles, doubles, noniterative triples level of theory with extrapolation to the complete basis set limit