Topological Change in Mean Convex Mean Curvature Flow

Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy group of the complementary region can die only if there is a shrinking S^k x R^(n-k) singularity for some k less than or equal to m. We also prove that for each m from 1 to n, there is a nonempty open set of compact, mean convex regions K in R^(n+1) with smooth boundary for which the resulting mean curvature flow has a shrinking S^m x R^(n-m) singularity.Comment: 19 pages. This version includes a new section proving that certain kinds of mean curvature flow singularities persist under arbitrary small perturbations of the initial surface. Newest update (Oct 2013) fixes some bibliographic reference

Difference Methods for Boundary Value Problems in Ordinary Differential Equations

A general theory of difference methods for problems of the form Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0, is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0 are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution

Numerical and experimental studies of particle flow in a high-pressure boundary-layer wind tunnel

The approach was to simulate the surface environment of Venus as closely as practicable and to conduct experiments to determine threshold wind speeds, particle flux, particle velocities, and the characteristics of various aeolian bedforms. The Venus Wind Tunnel (VWT) is described and the experimental procedures that were developed to make the high-pressure wind tunnel measurements are presented. In terrestrial simulations of aeolian activity, it is possible to conduct experiments under pressures and temperatures found in natural environments. Because of the high pressures and temperatures, Venusian simulations are difficult to achieve in this regard. Consequently, extrapolation of results to Venue potentially involves unknown factors. The experimental rationale was developed in the following way: The VWT enables the density of the Venusian atmosphere to be reproduced. Density is the principal atmospheric property for governing saltation threshold, particle flux, and the ballistics of airborne particles (equivalent density maintains dynamic similarity of gas flow). When operated at or near Earth's ambient temperature, VWT achieves Venusian atmospheric density at pressures of about 30 bar, or about one third less than those on Venus, although still maintaining dynamic similarity to Venus

Crystal growth of sulfide materials from alkali polysulfide liquids

The fluids experiment system was designed for low temperature solution growth, nominally aqueous solution growth. The alkali polysulfides, compositions in the systems Na2S-S and K2S-S form liquids in the temperature range of 190 C to 400 C. These can be used as solvents for other important classes of materials such as transition metal and other sulfides which are not soluble in aqueous media. Among these materials are luminescent and electroluminescent crystals whose physical properties are sensitive functions of crystal perfection and which could, therefore, serve as test materials for perfection improvement under microgravity conditions

The impact of charge symmetry and charge independence breaking on the properties of neutrons and protons in isospin-asymmetric nuclear matter

We investigate the effects of charge independence and charge symmetry breaking in neutron-rich matter. We consider neutron and proton properties in isospin-asymmetric matter at normal densities as well as the high-density neutron matter equation of state and the bulk properties of neutron stars. We find charge symmetry and charge independence breaking effects to be very small.Comment: 6 pages, 8 figure

To transduce a zebra finch: interrogating behavioral mechanisms in a model system for speech.

The ability to alter neuronal gene expression, either to affect levels of endogenous molecules or to express exogenous ones, is a powerful tool for linking brain and behavior. Scientists continue to finesse genetic manipulation in mice. Yet mice do not exhibit every behavior of interest. For example, Mus musculus do not readily imitate sounds, a trait known as vocal learning and a feature of speech. In contrast, thousands of bird species exhibit this ability. The circuits and underlying molecular mechanisms appear similar between disparate avian orders and are shared with humans. An advantage of studying vocal learning birds is that the neurons dedicated to this trait are nested within the surrounding brain regions, providing anatomical targets for relating brain and behavior. In songbirds, these nuclei are known as the song control system. Molecular function can be interrogated in non-traditional model organisms by exploiting the ability of viruses to insert genetic material into neurons to drive expression of experimenter-defined genes. To date, the use of viruses in the song control system is limited. Here, we review prior successes and test additional viruses for their capacity to transduce basal ganglia song control neurons. These findings provide a roadmap for troubleshooting the use of viruses in animal champions of fascinating behaviors-nowhere better featured than at the 12th International Congress