Enhanced drainage and coarsening in aqueous foams

Experiments are presented elucidating how the evolution of foam microstructure by gas diffusion from high to low pressure bubbles can significantly speed up the rate of gravitational drainage, and vice versa. This includes detailed data on the liquid-fraction dependence of the coarsening rate, and on the liquid-fraction and the bubble-size profiles across a sample. These results can be described by a "coarsening equation" for the increase of bubble growth rate for drier foams. Spatial variation of the average bubble size and liquid fraction can also affect the growth and drainage rates.     

EPR detection of [Cu(mnt)X2]2−—A possible halogenide stabilized intermediate in ligand exchange reactions

During the reaction of [Cu(mnt)₂]^2? with CuX₂ (X = Cl, Br) [Cu(mnt)X₂]^2? species are formed and characterized EPR spectroscopically supporting a dissociative mechanism for ligand exchange reactions between [Cu(mnt)₂]^2? and other Cu(II), Ni(II) and Pd(II) complexes which contain unsaturated dichalcogeno ligands.     

Comparison between ocean-acoustic fluctuations in parabolic-equation simulations and estimates from integral approximations

Line-integral approximations to the acoustic path integral have been used to estimate the magnitude of the fluctuations in an acoustic signal traveling through an ocean filled with internal waves. These approximations for the root-mean-square (rms) fluctuation and the bias of travel time, rms fluctuation in a vertical arrival angle, and the spreading of the acoustic pulse are compared here to estimates from simulations that use the parabolic equation (PE). PE propagations at 250 Hz with a maximum range of 1000 km were performed. The model environment consisted of one of two sound-speed profiles perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model with strengths of 0.5, 1, and 2 times the GM reference energy level. Integral-approximation (IA) estimates of rms travel-time fluctuations were within statistical uncertainty at 1000 km for the SLICE89 profile, and in disagreement by between 20% and 60% for the Canonical profile. Bias estimates were accurate for the first few hundred kilometers of propagation, but became a strong function of time front ID beyond, with some agreeing with the PE results and others very much larger. The IA structure functions of travel time with depth are predicted to be quadratic with the form theta(2)vc0(-2)deltaz(2), where deltaz is vertical separation, c0 is a reference sound speed, and thetav is the rms fluctuation in an arrival angle. At 1000 km, the PE results were close to quadratic at small deltaz, with values of thetav in disagreement with those of the integral approximation by factors of order 2. Pulse spreads in the PE results were much smaller than predicted by the IA estimates. Results imply that acoustic tomography of internal waves at ranges up to 1000 km can use the IA estimate of travel-time variance with reasonable reliability.     

An Adaptive Algorithm for Vector Partitioning

The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output.     

On Hadamard Inequality for Log-Concave Functions

Some improvements and generalizations of Finks results about Hadamards inequality for log-concave functions are given.AMS Subject Classification: 26D07, 26D15, 26A51.     

Vorticity-velocity-pressure formulation for Stokes problem

We propose a three-field formulation for efficiently solving a two-dimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.