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

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

Radioscience simulations in General Relativity and in alternative theories of gravity

In this communication, we focus on the possibility to test GR with radioscience experiments. We present a new software that in a first step simulates the Range/Doppler signals directly from the space time metric (thus in GR and in alternative theories of gravity). In a second step, a least-squares fit of the involved parameters is performed in GR. This software allows one to get the order of magnitude and the signature of the modifications induced by an alternative theory of gravity on radioscience signals. As examples, we present some simulations for the Cassini mission in Post-Einsteinian gravity and with the MOND External Field Effect.Comment: 4 pages; Proceedings of "Les Rencontres de Moriond 2011 - Gravitation session

Normal transport properties for a classical particle coupled to a non-Ohmic bath

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility over macroscopic time scales of order exp(-c/F). The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties

Testing special relativity with geodetic VLBI

Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay in the barycentric reference frame. As the Earth is orbiting around the Solar system barycentre with the velocity $V$ of 30 km/s, VLBI proves to be a handy tool to detect the subtle effects of the special and general relativity theory with a magnitude of $(V/\textrm{c})^2$. The theoretical correction for the second order terms reaches up to 300~ps, and it is implemented in the geodetic VLBI group delay model. The total contribution of the second order terms splits into two effects - the variation of the Earth scale, and the deflection of the apparent position of the radio source. The Robertson-Mansouri-Sexl (RMS) generalization of the Lorenz transformation is used for many modern tests of the special relativity theory. We develop an alteration of the RMS formalism to probe the Lorenz invariance with the geodetic VLBI data. The kinematic approach implies three parameters (as a function of the moving reference frame velocity) and the standard Einstein synchronisation. A generalised relativistic model of geodetic VLBI data includes all three parameters that could be estimated. Though, since the modern laboratory Michelson-Morley and Kennedy-Thorndike experiments are more accurate than VLBI technique, the presented equations may be used to test the VLBI group delay model itself.Comment: Proceedings of the IAG 2017 Scientific Meeting, Kobe, Japa

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.

Head to head comparisons of two modalities of perfusion adenosine stress echocardiography with simultaneous SPECT

<p>Abstract</p> <p>Background</p> <p>Real-time perfusion (RTP) contrast echocardiography can be used during adenosine stress echocardiography (ASE) to evaluate myocardial ischemia. We compared two different types of RTP power modulation techniques, angiomode (AM) and high-resolution grayscale (HR), with ^99mTc-tetrofosmin single-photon emission computed tomography (SPECT) for the detection of myocardial ischemia.</p> <p>Methods</p> <p>Patients with known or suspected coronary artery disease (CAD), admitted to SPECT, were prospectively invited to participate. Patients underwent RTP imaging (SONOS 5500) using AM and HR during Sonovue^®infusion, before and throughout the adenosine stress, also used for SPECT. Analysis of myocardial perfusion and wall motion by RTP-ASE were done for AM and HR at different time points, blinded to one another and to SPECT. Each segment was attributed to one of the three main coronary vessel areas of interest.</p> <p>Results</p> <p>In 50 patients, 150 coronary areas were analyzed by SPECT and RTP-ASE AM and HR. SPECT showed evidence of ischemia in 13 out of 50 patients. There was no significant difference between AM and HR in detecting ischemia (p = 0.08). The agreement for AM and HR, compared to SPECT, was 93% and 96%, with Kappa values of 0.67 and 0.75, respectively (p < 0.001).</p> <p>Conclusion</p> <p>There was no significant difference between AM and HR in correctly detecting myocardial ischemia as judged by SPECT. This suggests that different types of RTP modalities give comparable data during RTP-ASE in patients with known or suspected CAD.</p