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

Application of redundancy in the Saturn 5 guidance and control system

The Saturn launch vehicle's guidance and control system is so complex that the reliability of a simplex system is not adequate to fulfill mission requirements. Thus, to achieve the desired reliability, redundancy encompassing a wide range of types and levels was employed. At one extreme, the lowest level, basic components (resistors, capacitors, relays, etc.) are employed in series, parallel, or quadruplex arrangements to insure continued system operation in the presence of possible failure conditions. At the other extreme, the highest level, complete subsystem duplication is provided so that a backup subsystem can be employed in case the primary system malfunctions. In between these two extremes, many other redundancy schemes and techniques are employed at various levels. Basic redundancy concepts are covered to gain insight into the advantages obtained with various techniques. Points and methods of application of these techniques are included. The theoretical gain in reliability resulting from redundancy is assessed and compared to a simplex system. Problems and limitations encountered in the practical application of redundancy are discussed as well as techniques verifying proper operation of the redundant channels. As background for the redundancy application discussion, a basic description of the guidance and control system is included