Quasi-steady spreading of a thin ridge of fluid with temperature-dependent surface tension on a heated or cooled substrate

We investigate theoretically the problem of the quasi-steady spreading or contraction of a thin two-dimensional sessile or pendent ridge of viscous fluid with temperature-dependent surface tension on a planar horizontal substrate that is uniformly heated or cooled relative to the atmosphere. We derive an implicit solution of the leading-order thin-film equation for the free-surface profile of the ridge and use this to examine the quasi-steady evolution of the ridge, the dynamics of the moving contact lines being modelled by a 'Tanner law' relating the velocity of the contact line to the contact angle; in particular, we obtain a complete description of the possible forms that the evolution may take. In both the case of a (sessile or pendent) ridge on a heated substrate and the case of a pendent ridge on a cooled substrate when gravitational effects are relatively weak, there is one stable final state to which the ridge may evolve. In the case of a pendent ridge on a cooled substrate when gravitational effects are stronger, there may be one or two stable final states; moreover, the contact angles may vary non-monotonically with time during the evolution to one of these states. In the case of a pendent ridge on a cooled substrate when gravitational effects are even stronger, there may be up to three stable final states with qualitatively different solutions; moreover, the ridge may evolve via an intermediate state from which quasi-steady motion cannot persist, and so there will be a transient non-quasi-steady adjustment (in which the contact angles change rapidly, with the positions of the contact lines unaffected), after which quasi-steady motion is resumed. Lastly, we consider the behaviour of the ridge in the asymptotic limits of strong heating or cooling of the substrate and of strong or weak gravitational effects

Hurricane risk analysis: A review on the physically-based approach

This paper reviews recent studies that take a physically-based approach to better assess and manage hurricane risk. Such a methodology includes three components: modeling the storm climatology (which defines TC risk in terms of the upper tail of the storm statistics); modeling landfalling hazards; and characterizing damage and losses

Further restrictions on the topology of stationary black holes in five dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.Comment: LaTex, 22 pages, 9 figure

Barrier effects on the collective excitations of split Bose-Einstein condensates

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure

On quantum teleportation with beam-splitter-generated entanglement

Following the lead of Cochrane, Milburn, and Munro [Phys. Rev. A {\bf 62}, 062307 (2000)], we investigate theoretically quantum teleportation by means of the number-sum and phase-difference variables. We study Fock-state entanglement generated by a beam splitter and show that two-mode Fock-state inputs can be entangled by a beam splitter into close approximations of maximally entangled eigenstates of the phase difference and the photon-number sum (Einstein-Podolsky-Rosen -- EPR -- states). Such states could be experimentally feasible with on-demand single-photon sources. We show that the teleportation fidelity can reach near unity when such ``quasi-EPR'' states are used as the quantum channel.Comment: 7 pages (two-column), 7 figures, submitted to Phys. Rev. A. Text unmodified, postscript error correcte

Phenotypic Diversity for Seed Mineral Concentration in North American Dry Bean Germplasm of Middle American Ancestry

Dry bean (Phaseolus vulgaris L.) seeds are a major protein, carbohydrate, and mineral source in the human diet of peoples in multiple regions of the world. Seed mineral biofortification is an ongoing objective to improve this important food source. The objective of this research was to assess the seed mineral concentration of five macroelements and eight microelements in a large panel (n = 277) of modern race Durango and race Mesoamerica genotypes to determine if variability existed that could be exploited for targeted seed biofortification. Varieties that derive from these races are found in many diets throughout the world. The panel was grown in replicated trials under typical production conditions in the major bean growing regions of the United States, and a subset of the panel was also grown in replicated trials at three locations under control and terminal drought conditions. Except for K, seed mineral concentrations were higher for race Mesoamerica genotypes. Significantly higher seed concentrations for the majority of the minerals were observed for white-seeded genotypes and race Durango genotypes with the now preferred indeterminate, upright growth habit. Modern genotypes (since 1997) had equal or increased mineral concentrations compared with older genotypes. Drought affected mineral content differentially, having no effect on the microelement content but increased Co, Fe, and Ni concentrations. The correlation of Ca and Mn concentrations suggests that these elements may share seed deposition mechanisms. The high heritability for seed mineral concentration implies that breeding progress can be achieved by parental selection from this panel

The Kuiper Belt and Other Debris Disks

We discuss the current knowledge of the Solar system, focusing on bodies in the outer regions, on the information they provide concerning Solar system formation, and on the possible relationships that may exist between our system and the debris disks of other stars. Beyond the domains of the Terrestrial and giant planets, the comets in the Kuiper belt and the Oort cloud preserve some of our most pristine materials. The Kuiper belt, in particular, is a collisional dust source and a scientific bridge to the dusty "debris disks" observed around many nearby main-sequence stars. Study of the Solar system provides a level of detail that we cannot discern in the distant disks while observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book "Astrophysics in the Next Decade

The torsion of a finite quasigroup quandle is annihilated by its order

We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the torsion of its homology. It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. From the very beginning of the rack homology (between 1990 and 1995) the analogous result was suspected. The first general results in this direction were obtained independently about 2001 by R.A.Litherland and S.Nelson, and P.Etingof and M.Grana. In Litherland-Nelson paper it is proven that if (Q;*) is a finite homogeneous rack (this includes quasigroup racks) then the torsion of homology is annihilated by |Q|^n. In Etingof-Grana paper it is proven that if (X;A) is a finite rack and N=|G^0_Q| is the order of a group of inner automorphisms of Q, then only primes which can appear in the torsion of homology are those dividing N (the case of connected Alexander quandles was proven before by T.Mochizuki). The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki and in particular, they prove that the torsion part of the homology of the dihedral quandle R_3 is annihilated by 3. In Niebrzydowski-Przytycki paper it is conjectured that for a finite quasigroup quandle, torsion of its homology is annihilated by the order of the quandle. The conjecture is proved by T.Nosaka for finite Alexander quasigroup quandles. In this paper we prove the conjecture in full generality. For this version, we rewrote the Section 3 totally and introduced the concept of the precubic homotopy. In Section 2, the main addition is Corollary 2.2 which summarizes identities observed in the proof of the main theorem as we use it later in Section 3.Comment: 13 pages, 1 figure; accepted for publication in Journal of Pure and Applied Algebr