Motion and shape of an axisymmetric viscoplastic drop slowly falling through a viscous fluid

Slow sedimentation of a deformable drop of Bingham fluid in an unbounded Newtonian medium is studied using a variation of the integral equation method (Toose et al., J Eng Math 30:131–150, 1996, Int J Numer Methods Fluids 30:653–674, 1999). The Green function for the Stokes equation is used, and the non-Newtonian stress is treated as a source term. The computations are performed for a range of physical parameters of the system. It is demonstrated that initially deformed drop similar to Newtonian ones breaks up for high capillary number, Ca, and stabilizes to steady shapes at low Ca. Estimations of critical capillary number for specific initial deformations demonstrated its growth (increase in the stability of the drop) with the yield stress magnitude both for prolate and oblate initial shapes. Prolate initial shapes become more stable with the increase of the plastic viscosity. In contrast to this, for low yield stress, oblate shapes are destabilized with the growth of the plastic viscosity. This effect is similar to the effect of the viscosity of a Newtonian drop on its stability. However, at higher yield stress, the effect of plastic viscosity is reversed.     

A geometrical problem arising in a signal restoration algorithm

Let ℤ_2N={0, ..., 2N-1} denote the group of integers modulo 2N, and let L be the space of all real functions of ℤ_2N which are supported on {0,...N−1}. The spectral phase of a function f:ℤ_2N→ℝ is given by φ_f(k)=arg for k ∈ ℤ_2N, where denotes the discrete Fourier transforms of f. For a fixed s∈L let K_s denote the cone of all f:ℤ_2N→ℝ which satisfy φ_f ≡ φ_s and let M_s be its linear span. The angle α_s between M_s and L determines the convergence rate of the signal restoration from phase algorithm of Levi and Stark [3]. Here we prove the following conjectures of Urieli et al. [7] who verified them for the N≤3 case:

Dynamic ionization of water under extreme conditions

Raman spectroscopy in a laser heated diamond anvil cell and first principles molecular dynamics simulations have been used to study water in the temperature range 300 to 1500 K and at pressures to 56 GPa. We find a substantial decrease in the intensity of the O-H stretch mode in the liquid phase with pressure, and a change in slope of the melting line at 47 GPa and 1000 K. Consistent with these observations, theoretical calculations show that water beyond 50 GPa is "dynamically ionized" in that it consists of very short-lived (<10 fs) H2O, H3O+, and OH- species, and also that the mobility of the oxygen ions decreases abruptly with pressure, while hydrogen ions remain very mobile. We suggest that this regime corresponds to a superionic state.     

Thermal image encryption obtained with a SiO2 space-variant subwavelength grating supporting surface phonon-polaritons

Space-variant partially polarized thermal emission is investigated. We show that by coupling surface phonon-polaritons to a propagating field, large anisotropy of the emissivity is obtained within a narrow spectral range. We experimentally demonstrate this effect by fabricating a space-variant subwavelength grating on a SiO2 substrate to encrypt an image in the polarization state of a thermal radiation field.     

(1, 2)-Symplectic Metrics, Flag Manifolds and Tournaments

It has recently been shown by Mo and Negreiros that a necessarycondition for an invariant almost complex structure on the complexfull flag manifold F(n) to admit a (1, 2)-symplectic invariantmetric is that its associated tournament be cone-free. In thispaper, a canonical stair-shaped form is given for such tournaments,and this is applied to show that the condition is also sufficient;in the process, all the associated (1, 2)-symplectic metricsare described. 2000 Mathematics Subject Classification 53C55,05C20, 58E20.     

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.     

Cosmic ray diffusion from the galactic spiral arms,iron meteorites,and a possible climatic connection

We construct a Galactic cosmic ray (CR) diffusion model. The CR flux reaching the Solar System should periodically increase each crossing of a Galactic spiral arm. We confirm this prediction in the CR exposure age record of iron meteorites. We find that although the geological evidence for the occurrence of iceage epochs in the past eon is not unequivocal, it appears to have a nontrivial correlation with the spiral arm crossings-agreeing in period and phase.     

Van der Waals interactions between surfaces of biological interest

Microscopic and macroscopic approaches to calculations of long-range Van der Waals interactions between bodies are reviewed. Expressions are presented for various geometries, including planar-layered structures, sheathed spheres and rods. Retardation effects are shown to reduce dispersion interactions in a similar fashion in both approaches. Pair summation procedure gives 10–25% greater values of dispersion interactions than the macroscopic approach. Orientation effects, previously neglected in microscopic approaches are strongly dependent on many-body effects. When orientation effects are included in a pair summation procedure, its calculated values are close to those calculated with the macroscopic approach.Experimentally determined force values are in agreement with calculated ones for distances of separation above 15 Å in vacuum. In general, the theory is insufficient for yielding forces at distances of separation below 20 Å in water.Determination of Van der Waals parameters from refractive indices of pure liquids and solutions is described. Within 5%, dispersion coefficients are independent of concentration of solution, and isotropic electronic polarizabilities agree with those obtained by the addition of bond polarizabilities. Van der Waals parameters of several major components of cellular surfaces and intercellular media are arranged according to an ascending sequence: water<alkanes<phospholipids<proteins and cholesterol<sugars.Variations in compositions, distances of separation, and layer thicknesses are considered in the calculation of the interactions between cellular surfaces, both in planar and spherical systems, including phospholipid vesicles. In planar-cellular systems, Hamaker coefficients vary between 4 x 10^-15 and 6 x 10^-14 erg; at 50 Å distance of separation the free energies and forces are 210 to 1600 kT/μm², and 4 x 10^-5 to 3 x 10^-4 dynes/μm² respectively. The total potential curve, including electrostatic interactions, is calculated and the questions of cellular adhesion and fusion of phospholipid vesicles are discussed.