Convex Sobolev inequalities and spectral gap

This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities with constants which are uniformly bounded in the limit approaching the logarithmic Sobolev inequalities. We recover the case of the logarithmic Sobolev inequalities as a special case

Analysis of Scarp Profiles: Evaluation of Errors in Morphologic Dating

Morphologic analysis of scarp degradation can be used quantitatively to determine relative ages of different scarps formed in cohesionless materials, under the same climatic conditions. Scarps of tectonic origin as well as wavecut or rivercut terraces can be treated as topographic impulses that are attenuated by surface erosional processes. This morphological evolution can be modelled as the convolution of the initial shape with erosion (or degradation) function whose width increases with time. Such modeling applies well to scarps less than 10m high, formed in unconsolidated fanglomerates. To a good approximation, the degradation function is Gaussian with a variance measuring the degree of rounding of the initial shape. This geometric parameter can be called the degradation coefficient. A synthetic experiment shows that the degradation coefficient can be obtained by least squares fitting of profiles levelled perpendicular to the scarp. Gravitational collapse of the free face is accounted for by assuming initial scarp slopes at the angle of repose of the cohesionless materials (30°–35°). Uncertainties in the measured profiles result in an uncertainty in degradation coefficient that can be evaluated graphically. Because the degradation coefficient is sensitive to the regional slope and to three-dimensional processes (gullying, loess accumulation, stream incision, etc.), a reliable and accurate determination of degradation coefficient requires several long profiles across the same scarp. The linear diffusion model of scarp degradation is a Gaussian model in which the degradation coefficient is proportional to numerical age. In that case, absolute dating requires only determination of the propotionality constant, called the mass diffusivity constant. For Holocene scarps a few meters high, in loose alluvium under arid climatic conditions, mass diffusivity constants generally range between 1 and 6 m^2/kyr. Morphologic analysis is a reliable method to compare ages of different scarps in a given area, and it can provide approximate absolute ages of Holocene scarplike landforms

Stark quenching of rovibrational states of H2+ due to motion in a magnetic field

The motional electric field experienced by an H2+ ion moving in a magnetic field induces an electric dipole, so that one-photon dipole transitions between rovibrational states become allowed. Field induced spontaneous decay rates are calculated for a wide range of states. For an ion stored in a high-field (B ~ 10 T) Penning trap, it is shown that the lifetimes of excited rovibrational states can be shortened by typically 1-3 orders of magnitude by placing the ion in a large cyclotron orbit. This can greatly facilitate recently proposed [E. G. Myers, Phys. Rev. A 98, 010101 (2018)] high-precision spectroscopic measurements on H2+ and its antimatter counterpart for tests of CPT symmetry

On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity

Field theories whose full action is Lorentz invariant (or diffeomorphism invariant) can exhibit superluminal behaviors through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagations is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories, and we stress the role played by the Cauchy problem and the notions of chronology and time arrow. We show that superluminal behavior threaten causality only if a prior chronology on spacetime is chosen. In the case where superluminal propagations occur, however, there is at least two non conformally related metrics on spacetime and thus two available notions of chronology. These two chronologies are on equal footing and it would thus be misleading to choose \textit{ab initio} one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. We actually show that superluminal propagations do not threaten causality. As an illustration of these conceptual issues, we consider two field theories, namely k-essences scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, MOND-like theories of gravity and varying speed of light theories.Comment: 15 pages, 2 figures; minor changes, references added, submitted to Phys.Rev.

Modeling of the multiwavelength emission of M87 with H.E.S.S. observations

M87 is the first extragalactic source detected in the TeV range that is not a blazar. The large scale jet of M87 is not aligned with the line of sight. Modification of standard emission models of TeV blazars appears necessary to account for the gamma-ray observations made by H.E.S.S. despite this misalignment. We present a new multi-blob synchrotron self-Compton model that deals explicitly with large viewing angles and moderate values of the Lorentz factor inferred from MHD simulations of jet formation.Comment: 4 pages, 4 figures; to appear in "SF2A 2007 proceedings", eds. J. Bouvier, A. Chalabaev and C. Charbonne

Variation of the constants in the late and early universe

Recent key observational results on the variation of fine structure constant, the proton to electron mass ratio and the gravitational constant are reviewed. The necessity to substantiate the dark sector of cosmology and to test gravity on astrophysical scales is also emphasized.Comment: 19 pages, 6 figures, Invited talk at the conference "The Quest for Cosmological Scalar Fields", Porto, 8-10 July 200