The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Ma\~n\'e action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of $\alpha$. For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on $\alpha$. We also show injectivity and stability for $g$ and $\alpha$ in a generic class $\mathcal{G}$ including real analytic ones. For the nonlinear problem, we show rigidity for real analytic simple $g$, $\alpha$. Also, rigidity holds for metrics in a given conformal class, and locally, near any $(g,\alpha)\in \mathcal{G}$.Comment: This revised version contains a proof that 2D simple magnetic systems are boundary rigid. Some references have been adde

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential

Entropies, volumes, and Einstein metrics

We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov--Hitchin--Thorpe inequality and Sambusetti's obstruction.Comment: This is a substantial revision and expansion of the 2004 preprint, which I prepared in spring of 2010 and which has since been published. The version here is essentially the published one, minus the problems introduced by Springer productio

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Energy transfer in a fast-slow Hamiltonian system

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a non linear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems

Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Teratogenicity of depleted uranium aerosols: A review from an epidemiological perspective

BACKGROUND: Depleted uranium is being used increasingly often as a component of munitions in military conflicts. Military personnel, civilians and the DU munitions producers are being exposed to the DU aerosols that are generated. METHODS: We reviewed toxicological data on both natural and depleted uranium. We included peer reviewed studies and gray literature on birth malformations due to natural and depleted uranium. Our approach was to assess the "weight of evidence" with respect to teratogenicity of depleted uranium. RESULTS: Animal studies firmly support the possibility that DU is a teratogen. While the detailed pathways by which environmental DU can be internalized and reach reproductive cells are not yet fully elucidated, again, the evidence supports plausibility. To date, human epidemiological data include case examples, disease registry records, a case-control study and prospective longitudinal studies. DISCUSSION: The two most significant challenges to establishing a causal pathway between (human) parental DU exposure and the birth of offspring with defects are: i) distinguishing the role of DU from that of exposure to other potential teratogens; ii) documentation on the individual level of extent of parental DU exposure. Studies that use biomarkers, none yet reported, can help address the latter challenge. Thoughtful triangulation of the results of multiple studies (epidemiological and other) of DU teratogenicity contributes to disentangling the roles of various potentially teratogenic parental exposures. This paper is just such an endeavor. CONCLUSION: In aggregate the human epidemiological evidence is consistent with increased risk of birth defects in offspring of persons exposed to DU