Randomized k-server algorithms for growth-rate bounded graphs

The k-server problem is a fundamental online problem where k mobile servers should be scheduled to answer a sequence of requests for points in a metric space as to minimize the total movement cost. While the deterministic competitive ratio is at least k, randomized k-server algorithms have the potential of reaching o(k)-competitive ratios. Prior to this work only few specific cases of this problem were solved. For arbitrary metric spaces, this goal may be approached by using probabilistic metric approximation techniques. This paper gives the first results in this direction, obtaining o(k)-competitive ratio for a natural class of metric spaces, including d-dimensional grids, and wide range of k.     

Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.     

Dynamic forces between bubbles and surfaces and hydrodynamic boundary conditions

A bubble attached to the end of an atomic force microscope cantilever and driven toward or away from a flat mica surface across an aqueous film is used to characterize the dynamic force that arises from hydrodynamic drainage and electrical double layer interactions across the nanometer thick intervening aqueous film. The hydrodynamic response of the air/water interface can range from a classical fully immobile, no-slip surface in the presence of added surfactants to a partially mobile interface in an electrolyte solution without added surfactants. A model that includes the convection and diffusion of trace surface contaminants can account for the observed behavior presented. This model predicts quantitatively different interfacial dynamics to the Navier slip model that can also be used to fit dynamic force data with a post hoc choice of a slip length.     

Nonvacuum taub-type cosmological model

The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S ³ topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.     

Some applications of Ball's extension theorem

We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice , equipped with the metric, in any -uniformly convex Banach space is of order .

     

Metallophilic and Inter-Ligand Interactions in Diargentous Compounds Bound by a Geometrically Flexible Macrocycle

A series of mono- and di-nuclear Ag^I complexes supported by a flexible macrocyclic ligand are reported. The geometric flexibility of the ligand was found to allow for a range of Ag−Ag interactions in the disilver complexes, depending on the identities of both the ancillary ligand and the counterion. Studies of the solution-phase dynamic exchange processes for these latter complexes found rapid interconversion through a mechanism that retained the multi-nuclearity. Quantum Theory of Atoms in Molecules (QTAIM) and Independent Gradient Model based on Hirshfeld partition (IGMH) analyses are used to evaluate the d¹⁰-d¹⁰ interactions between silver centers in the various geometries observed for the solid-state structures of these complexes, revealing nearly identical Ag−Ag interactions, regardless of the relative geometries of the Ag centers. Instead, a weak, but non-negligible, inter-ligand interaction between two isocyanide units may contribute to the folded-ligand geometry observed in the solid state.     

Particle Network Self-Assembly of Similar Size Sub-Micron Calcium Alginate and Polystyrene Particles Atop Glass

Particle-mediated self-assembly, such as nanocomposites, microstructure formation in materials, and core-shell coating of biological particles, offers precise control over the properties of biological materials for applications in drug delivery, tissue engineering, and biosensing. The assembly of similar-sized calcium alginate (CAG) and polystyrene sub-micron particles is studied in an aqueous sodium nitrate solution as a model for particle-mediated self-assembly of biological and synthetic mixed particle species. The objective is to reinforce biological matrices by incorporating synthetic particles to form hybrid particulate networks with tailored properties. By varying the ionic strength of the suspension, the authors alter the energy barriers for particle attachment to each other and to a glass substrate that result from colloidal surface forces. The particles do not show monotonic adsorption trend to glass with ionic strength. Hence, apart from DLVO theory—van der Waals and electrostatic interactions—the authors further consider solvation and bridging interactions in the analysis of the particulate adsorption-coagulation system. CAG particles, which support lower energy barriers to attachment relative to their counterpart polystyrene particles, accumulate as dense aggregates on the glass substrate. Polystyrene particles adsorb simultaneously as detached particles. At high electrolyte concentrations, where electrostatic repulsion is largely screened, the mixture of particles covers most of the glass substrate; the CAG particles form a continuous network throughout the glass substrate with pockets of polystyrene particles. The particulate structure is correlated with the adjustable energy barriers for particle attachment in the suspension.     

Effect of non-homogeneous surface viscosity on the Marangoni migration of a droplet in viscous fluid

Marangoni migration of a single droplet in an unbounded viscous fluid under the additional effect of variable surface viscosity is studied. The surface tension and the surface viscosity depend on concentration of dissolved species. Cases of the motion induced by the presence of a point source and by a given constant concentration gradient are considered. The dependence of the migration velocity on the governing parameters is computed under quasi-stationary approximation. The effect of weak advective transport is studied making use of singular perturbations in the Peclet number, Pe. It is shown that, when the source is time dependent a Basset-type history term appears in the expansion of the concentration and, as a result, the leading order correction to the flow and to the migration velocity is of O(Pe(1/2)). If the source of active substance driving the flow is steady, the effect of convective transport on the migration is weaker.     

Magnetic Field Directed Rare-Earth Separations

The separation of rare-earth ions from one another is challenging due to their chemical and physical similarities. Nearly all rare-earth separations rely upon small changes in ionic radii to direct speciation or reactivity. Herein, we show that the intrinsic magnetic properties of the rare-earth ions impact the separations of light/heavy and selected heavy/heavy binary mixtures. Using TriNOx³⁻ ([{(2-^tBuNO)C₆H₄CH₂}₃N]³⁻) rare-earth complexes, we efficiently and selectively crystallized heavy rare earths (Tb–Yb) from a mixture with light rare earths (La and Nd) in the presence of an external Fe₁₄Nd₂B magnet, concomitant with the introduction of a concentration gradient (decrease in temperature). The optimal separation was observed for an equimolar mixture of La:Dy, which gave an enrichment factor of EF_La:Dy=297±31 for the solid fraction, compared to EF_La:Dy=159±22 in the absence of the field, and achieving a 99.7 % pure Dy sample in one step. These results indicate that the application of a magnetic field can improve performance in a molecular separation system for paramagnetic rare-earth cations.