Relativistic minimal surfaces

We find classical solutions to the equations of motion of an M-dimensional surface moving in a higher-dimensional embedding space-time for arbitrary M. In the case of closed membranes, solutions exist for any topological type (genus)

Isotopic and Micro-Raman investigation of Interplanetary Dust Particles Collected during 2003 Earth passage through Comet Grigg-Skjellerup Dust Stream

We report microscale H and N isotopic and Raman spectral data for IDPs collected in April 2003. The samples show extreme D and 15N enrichments carried by very primitive organic matter. A high abundance of D anomalies might indicate a cometary origin

Problems on electrorheological fluid flows

We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field strength, and on the angle between the vectors of velocity and electric field. We study general problems on the flow of such fluids at nonhomogeneous mixed boundary conditions, wherein values of velocities and surface forces are given on different parts of the boundary. We consider the cases where the viscosity function is continuous and singular, equal to infinity, when the second invariant of the rate of strain tensor is equal to zero. In the second case the problem is reduced to a variational inequality. By using the methods of a fixed point, monotonicity, and compactness, we prove existence results for the problems under consideration. Some efficient methods for numerical solution of the problems are examined.Comment: Presented to the journal "Discrete and Continuous Dynamical Systems, Series

Curved Space (Matrix) Membranes

Hamiltonian formulations of M-branes moving in curved backgrounds are given

A C0 interior penalty discontinuous galerkin method and an equilibrated a posteriori error estimator for a nonlinear fourth order elliptic boundary value problem of p-biharmonic type

We consider a C$^0$ Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of a nonlinear fourth order elliptic boundary value problem of p-harmonic type and an equilibrated a posteriori error estimator. The C0IPDG method can be derived from a discretization of the corresponding minimization problem involving a suitably defined reconstruction operator. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken $W^{2,p}$ norm in terms of the associated primal and dual energy functionals. It requires the construction of an equilibrated flux and an equilibrated moment tensor based on a three-field formulation of the C0IPDG approximation. The relationship with a residual-type a posteriori error estimated is studied as well. Numerical results illustrate the performance of the suggested approach

Path-following primal-dual interior-point methods for shape optimization of stationary flow problems

We consider shape optimization of Stokes flow in channels where the objective is to design the lateral walls of the channel in such a way that a desired velocity profile is achieved. This amounts to the solution of a PDE constrained optimization problem with the state equation given by the Stokes system and the design variables being the control points of a Bézier curve representation of the lateral walls subject to bilateral constraints. Using a finite element discretization of the problem by Taylor-Hood elements, the shape optimization problem is solved numerically by a path-following primal-dual interior-point method applied to the parameter dependent nonlinear system representing the optimality conditions. The method is an all-at-once approach featuring an adaptive choice of the continuation parameter, inexact Newton solves by means of right-transforming iterations, and a monotonicity test for convergence monitoring. The performance of the adaptive continuation process is illustrated by several numerical examples

Extensive microscale N isotopic heterogeneity in chondritic organic matter

Introduction: H and N isotopic anomalies (mainly excesses of D and 15N) in organic matter from primitive meteorites and IDPs suggest preservation of presolar molecular cloud material [1-3]. However, there have been very few spatially correlated H and N studies for either chondrites or IDPs [4, 5]. We report C and N isotopic imaging data for organic matter from four meteorites and three IDPs. D/H imaging data for many of the same samples are presented in [6, 7] and bulk organic isotope data in [8]