Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0_0

Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.Comment: 30 page

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

A new parametrization of the 3-metric allows to find explicitly a York map in canonical ADM tetrad gravity, the two pairs of physical tidal degrees of freedom and 14 gauge variables. These gauge quantities (generalized inertial effects) are all configurational except the trace ${}^3K(\tau ,\vec \sigma)$ of the extrinsic curvature of the instantaneous 3-spaces $\Sigma_{\tau}$ (clock synchronization convention) of a non-inertial frame. The Dirac hamiltonian is the sum of the weak ADM energy $E_{ADM} = \int d^3\sigma {\cal E}_{ADM}(\tau ,\vec \sigma)$ (whose density is coordinate-dependent due to the inertial potentials) and of the first-class constraints. Then: i) The explicit form of the Hamilton equations for the two tidal degrees of freedom in an arbitrary gauge: a deterministic evolution can be defined only in a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A general solution of the super-momentum constraints, which shows the existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: a) the explicit form of the weak ADM energy and of the super-momentum constraint; b) the determination of the shift functions and then of the lapse one. iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger time gauge, upon the gauge variable ${}^3K(\tau ,\vec \sigma)$, determining the convention of clock synchronization. Therefore it should be possible (for instance in the weak field limit but with relativistic motion) to try to check whether in Einstein's theory the {\it dark matter} is a gauge relativistic inertial effect induced by ${}^3K(\tau ,\vec \sigma)$.Comment: 90 page

Elastic interactions of active cells with soft materials

Anchorage-dependent cells collect information on the mechanical properties of the environment through their contractile machineries and use this information to position and orient themselves. Since the probing process is anisotropic, cellular force patterns during active mechanosensing can be modelled as anisotropic force contraction dipoles. Their build-up depends on the mechanical properties of the environment, including elastic rigidity and prestrain. In a finite sized sample, it also depends on sample geometry and boundary conditions through image strain fields. We discuss the interactions of active cells with an elastic environment and compare it to the case of physical force dipoles. Despite marked differences, both cases can be described in the same theoretical framework. We exactly solve the elastic equations for anisotropic force contraction dipoles in different geometries (full space, halfspace and sphere) and with different boundary conditions. These results are then used to predict optimal position and orientation of mechanosensing cells in soft material.Comment: Revtex, 38 pages, 8 Postscript files included; revised version, accepted for publication in Phys. Rev.

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

International audienceThis chapter proposes a framework for dealing with two problems related to the analysis of shapes: the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [8], we consider the characteristic functions of the subsets of ℝ2 and their distance functions. The L 2 norm of the difference of characteristic functions and the L∞ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular that induced by the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ℝ2 of positive reach in the sense of Federer [12], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem. We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational de.nitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples

Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.Comment: 20 pages, Review paper to appear in EPJ

Discovery of a gamma-ray black widow pulsar by GPU-accelerated Einstein@Home

We report the discovery of 1.97 ms period gamma-ray pulsations from the 75 minute orbital-period binary pulsar now named PSR J1653−0158. The associated Fermi Large Area Telescope gamma-ray source 4FGL J1653.6−0158 has long been expected to harbor a binary millisecond pulsar. Despite the pulsar-like gamma-ray spectrum and candidate optical/X-ray associations—whose periodic brightness modulations suggested an orbit—no radio pulsations had been found in many searches. The pulsar was discovered by directly searching the gamma-ray data using the GPU-accelerated Einstein@Home distributed volunteer computing system. The multidimensional parameter space was bounded by positional and orbital constraints obtained from the optical counterpart. More sensitive analyses of archival and new radio data using knowledge of the pulsar timing solution yield very stringent upper limits on radio emission. Any radio emission is thus either exceptionally weak, or eclipsed for a large fraction of the time. The pulsar has one of the three lowest inferred surface magnetic-field strengths of any known pulsar with B surf ≈ 4 × 107 G. The resulting mass function, combined with models of the companion star's optical light curve and spectra, suggests a pulsar mass gsim2 M ⊙. The companion is lightweight with mass ~0.01 M ⊙, and the orbital period is the shortest known for any rotation-powered binary pulsar. This discovery demonstrates the Fermi Large Area Telescope's potential to discover extreme pulsars that would otherwise remain undetected

Heat sterilization of archaeal-liposomes

Peer reviewed: YesNRC publication: Ye

Ribose biosynthesis in methanogenic bacteria

Peer reviewed: YesNRC publication: Ye