Asymptotic-preserving projective integration schemes for kinetic equations in the diffusion limit

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on the diffusion time scale. We show that, with an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the diffusion equation, whereas the required number of inner steps does not depend on the mean free path. We also provide a consistency result. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the diffusion equation in the limit of vanishing mean free path. The analysis is illustrated with numerical results, and we present an application to the Su-Olson test

Relative affinity constants by electrospray ionization and Fourier transform ion cyclotron resonance mass spectrometry: calmodulin binding to peptide analogs of myosin light chain kinase

Synthetic RS20 peptide and a set of its point-mutated peptide analogs have been used to analyze the interactions between calmodulin (CaM) and the CaM-binding sequence of smooth-muscle myosin light chain kinase both in the presence and the absence of Ca2+. Particular peptides, which were expected to have different binding strengths, were chosen to address the effects of electrostatic and bulky mutations on the binding affinity of the RS20 sequence. Relative affinity constants for protein/ligand interactions have been determined using electrospray ionization and Fourier transform ion cyclotron resonance mass spectrometry. The results evidence the importance of electrostatic forces in interactions between CaM and targets, particularly in the presence of Ca2+, and the role of hydrophobic forces in contributing additional stability to the complexes both in the presence and the absence of Ca2+

Gravity tests with INPOP planetary ephemerides

In this paper, we present several gravity tests made in using the last INPOP08 planetary ephemerides. We first propose two methods to estimate the PPN parameter $\beta$ and its correlated value, the Sun J2 and we discuss the correlation between the Sun J2 and the mass of the asteroid ring. We estimate possible advance in the planet perihelia. In the end we show that no constant acceleration larger than 1/4 the Pioneer anomaly can affect the planets of our solar system.Comment: 11 pages. submitted to proceedings of IAU symposium 264 "Relativity in Fundamental Astronomy: Dynamics, Reference Frames and Data analysis

A geometric optics method for high-frequency electromagnetic fields computations near fold caustics—Part II. The energy

AbstractWe present the computation of the amplitudes needed to evaluate the energy deposited by the laser wave in a plasma when a fold caustic forms. We first recall the Eulerian method designed in Benamou et al. (J. Comput. Appl. Math. 156 (2003) 93) to compute the caustic location and the phases associated to the two ray branches on its illuminated side. We then turn to the computation of the amplitudes needed to evaluate the energy. We use the classical geometrical form of the amplitudes to avoid the blow up problem at the caustic. As our proposed method is Eulerian we have to consider transport equations for these geometrical quantities where the advection field depends on the ray flow. The associated vector field structurally vanishes like the square root of the distance to the caustic when approaching the caustic. This introduces an additional difficulty as traditional finite difference scheme do not retain their accuracy for such advection fields. We propose a new scheme which remains of order 1 at the caustic and present a partial theoretical analysis as well as a numerical validation. We also test the capability of our Eulerian geometrical algorithm to produce numerical solution of the Helmholtz equation and attempt to check their frequency asymptotic accuracy

Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

Time-Varying Gravitomagnetism

Time-varying gravitomagnetic fields are considered within the linear post-Newtonian approach to general relativity. A simple model is developed in which the gravitomagnetic field of a localized mass-energy current varies linearly with time. The implications of this temporal variation of the source for the precession of test gyroscopes and the motion of null rays are briefly discussed.Comment: 10 pages; v2: slightly expanded version accepted for publication in Class. Quantum Gra

General post-Minkowskian expansion of time transfer functions

Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant $G$ (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.Comment: 10 pages. Minor modifications. Accepted in Classical and Quantum Gravit

Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Gra