Finite difference methods for time dependent, linear differential algebraic equations

AbstractRecently the authors developed a global reduction procedure for linear, time-dependent DAE that transforms their solutions of smaller systems of ODE's. Here it is shown that this reduction allows for the construction of simple, convergent finite difference schemes for such equations

Domain wall roughening in dipolar films in the presence of disorder

We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain wall in a thin film with in-plane magnetization, where we consider the contribution of the long-range dipolar interaction beyond the quadratic approximation. We show that such a Hamiltonian is analogous to the Hamiltonian of a one-dimensional polaron in an external random potential. We use a replica variational method to compute the roughening exponent of the domain wall for the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and references 1,2 and 12 were added to conform with the referee's repor

History and Actuality of Galician Emigrants: A Galicia (Spain) Shared between Latin America and Europe

Despite the significant advances in path planning methods, problems involving highly constrained spaces are still challenging. In particular, in many situations the configuration space is a non-parametrizable variety implicitly defined by constraints, which complicates the successful generalization of sampling-based path planners. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. It builds on recently developed tools for Higher-dimensional Continuation, which provide numerical procedures to describe an implicitly defined variety using a set of local charts. We propose to extend these methods to obtain an efficient path planner on varieties, handling highly constrained problems. The advantage of this planner comes from that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do.Postprint (author’s final draft

Geometric notes on optimization with equality constraints

AbstractFor minimization problems with nonlinear equality constraints, various numerical tools are shown to become available when the constraint set has a manifold structure. In appropriate local coordinate systems these tools permit the computation, e.g., of the gradient and Hessian of the transformed (unconstrained) objective function. This opens up a new view on the computational solution of the minimization problem which—while leading to algorithms similar in concept and performance to the well-known “reduced Hessian” methods—provides a different theoretical basis for these methods

On smoothness and invariance properties of the gauss-newton method

Beyn W-J. On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization. 1993;14(5-6):503-514.We consider systems of m nonlinear equations in m + p unknowns which have p-dimensional solution manifolds. It is well-known that the Gauss-Newton method converges locally and quadratically to regular points on this manifold. We investigate in detail the mapping which transfers the starting point to its limit on the manifold. This mapping is shown to be smooth of one order less than the given system. Moreover, we find that the Gauss-Newton method induces a foliation of the neighborhood of the manifold into smooth submanifolds. These submanifolds are of dimension m, they are invariant under the Gauss-Newton iteration, and they have orthogonal intersections with the solution manifold