719 research outputs found
RTCC requirements for mission G - Trajectory computers for TLI and MCC processors, part 1 Final report
Functional properties of trajectory computers for translunar injection and midcourse correction procedures on lunar orbit
Abelian gauge theories on compact manifolds and the Gribov ambiguity
We study the quantization of abelian gauge theories of principal torus
bundles over compact manifolds with and without boundary. It is shown that
these gauge theories suffer from a Gribov ambiguity originating in the
non-triviality of the bundle of connections whose geometrical structure will be
analyzed in detail. Motivated by the stochastic quantization approach we
propose a modified functional integral measure on the space of connections that
takes the Gribov problem into account. This functional integral measure is used
to calculate the partition function, the Greens functions and the field
strength correlating functions in any dimension using the fact that the space
of inequivalent connections itself admits the structure of a bundle over a
finite dimensional torus. The Greens functions are shown to be affected by the
non-trivial topology, giving rise to non-vanishing vacuum expectation values
for the gauge fields.Comment: 33 page
On unbounded bodies with finite mass: asymptotic behaviour
There is introduced a class of barotropic equations of state (EOS) which
become polytropic of index at low pressure. One then studies
asymptotically flat solutions of the static Einstein equations coupled to
perfect fluids having such an EOS. It is shown that such solutions, in the same
manner as the vacuum ones, are conformally smooth or analytic at infinity, when
the EOS is smooth or analytic, respectively.Comment: 6 page
Analytic structure of solutions to multiconfiguration equations
We study the regularity at the positions of the (fixed) nuclei of solutions
to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of
Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution
to the rank--M multiconfiguration equations for a molecule with L fixed nuclei
at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there
exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k},
phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) =
phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar
result holds for the corresponding electron density. The proof uses the
Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the
study of the eigenfunctions of the Schr"odinger operator of atoms and molecules
near two-particle coalescence points.Comment: 15 page
Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
We study curvature functionals for immersed 2-spheres in a compact,
three-dimensional Riemannian manifold M. Under the assumption that the
sectional curvature of M is strictly positive, we prove the existence of a
smoothly immersed sphere minimizing the L^{2} integral of the second
fundamental form. Assuming instead that the sectional curvature is less than or
equal to 2, and that there exists a point in M with scalar curvature bigger
than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1,
where H is the mean curvature vector
Analysis of optical flow models in the framework of calculus of variations
In image sequence analysis, variational optical flow computations require the solution of a parameter dependent optimization problem with a data term and a regularizer. In this paper we study existence and uniqueness of the optimizers. Our studies rely on quasiconvex functionals on the spaces W¹,P(Ω, IRd), with p > 1, BV(Ω, IRd), BD(&Omeag;). The methods that are covered by our results include several existing techniques. Experiments are presented that illustrate the behavior of these approaches
General existence proof for rest frame systems in asymptotically flat space-time
We report a new result on the nice section construction used in the
definition of rest frame systems in general relativity. This construction is
needed in the study of non trivial gravitational radiating systems. We prove
existence, regularity and non-self-crossing property of solutions of the nice
section equation for general asymptotically flat space times. This proves a
conjecture enunciated in a previous work.Comment: 14 pages, no figures, LaTeX 2
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
What is the optimal shape of a pipe?
We consider an incompressible fluid in a three-dimensional pipe, following
the Navier-Stokes system with classical boundary conditions. We are interested
in the following question: is there any optimal shape for the criterion "energy
dissipated by the fluid"? Moreover, is the cylinder the optimal shape? We prove
that there exists an optimal shape in a reasonable class of admissible domains,
but the cylinder is not optimal. For that purpose, we explicit the first order
optimality condition, thanks to adjoint state and we prove that it is
impossible that the adjoint state be a solution of this over-determined system
when the domain is the cylinder. At last, we show some numerical simulations
for that problem
Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold
(M,g). In this paper we study the restrictions on the topology and geometry of
the fibres (the level sets) of the solutions f to (P1). We give a technique
based on certain remarkable property of the fibres (the analytic representation
property) for going from the initial PDE to a global analytical
characterization of the fibres (the equilibrium partition condition). We study
this analytical characterization and obtain several topological and geometrical
properties that the fibres of the solutions must possess, depending on the
topology of M and the metric tensor g. We apply these results to the classical
problem in physics of classifying the equilibrium shapes of both Newtonian and
relativistic static self-gravitating fluids. We also suggest a relationship
with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis
is proved. Please address all correspondence to D. Peralta-Sala
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