36,717 research outputs found
Quadratic metric-affine gravity
We consider spacetime to be a connected real 4-manifold equipped with a
Lorentzian metric and an affine connection. The 10 independent components of
the (symmetric) metric tensor and the 64 connection coefficients are the
unknowns of our theory. We introduce an action which is quadratic in curvature
and study the resulting system of Euler-Lagrange equations. In the first part
of the paper we look for Riemannian solutions, i.e. solutions whose connection
is Levi-Civita. We find two classes of Riemannian solutions: 1) Einstein
spaces, and 2) spacetimes with metric of a pp-wave and parallel Ricci
curvature. We prove that for a generic quadratic action these are the only
Riemannian solutions. In the second part of the paper we look for
non-Riemannian solutions. We define the notion of a "Weyl pseudoinstanton"
(metric compatible spacetime whose curvature is purely Weyl) and prove that a
Weyl pseudoinstanton is a solution of our field equations. Using the
pseudoinstanton approach we construct explicitly a non-Riemannian solution
which is a wave of torsion in Minkowski space. We discuss the possibility of
using this non-Riemannian solution as a mathematical model for the graviton or
the neutrino.Comment: 25 pages, LaTeX2
A variational method for second order shape derivatives
We consider shape functionals obtained as minima on Sobolev spaces of
classical integrals having smooth and convex densities, under mixed
Dirichlet-Neumann boundary conditions. We propose a new approach for the
computation of the second order shape derivative of such functionals, yielding
a general existence and representation theorem. In particular, we consider the
p-torsional rigidity functional for p grater than or equal to 2.Comment: Submitted paper. 29 page
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions
We study the finite-horizon optimal control problem with quadratic
functionals for an established fluid-structure interaction model. The coupled
PDE system under investigation comprises a parabolic (the fluid) and a
hyperbolic (the solid) dynamics; the coupling occurs at the interface between
the regions occupied by the fluid and the solid. We establish several trace
regularity results for the fluid component of the system, which are then
applied to show well-posedness of the Differential Riccati Equations arising in
the optimization problem. This yields the feedback synthesis of the unique
optimal control, under a very weak constraint on the observation operator; in
particular, the present analysis allows general functionals, such as the
integral of the natural energy of the physical system. Furthermore, this work
confirms that the theory developed in Acquistapace et al. [Adv. Differential
Equations, 2005] -- crucially utilized here -- encompasses widely differing PDE
problems, from thermoelastic systems to models of acoustic-structure and, now,
fluid-structure interactions.Comment: 22 pages, submitted; v2: misprints corrected, a remark added in
section
Universal Features of Holographic Anomalies
We study the mechanism by which gravitational actions reproduce the trace
anomalies of the holographically related conformal field theories. Two
universal features emerge: a) the ratios of type B trace anomalies in any even
dimension are independent of the gravitational action, being uniquely
determined by the underlying algebraic structure b) the normalization of the
type A and the overall normalization of the type B anomalies are given by
action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma
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