Radial velocity method

The Doppler shift or radial velocity method The transit method... 

Current extrasolar planets are all much larger than the Earth. The total count at present (9 September 2005) is 168 found in 144 planetary systems, of which 18 contain multiple planets. The first to be discovered was 51-Pegasi in the constellation of Pegasus by the radial velocity method. It is about 0.45 Mjupiter and has an orbital period around the star of about 4.5 days. Of the 168 planets found so far only nine are present within a habitable zone around their star. The survey of the star catalogue for planets has only just started and we have found a large number of planets very quickly - solar systems, at least, are not special. 

The masses of the planets so far discovered vary between about 0.02 and 18 Jupiter masses. There are also very large variations in the values of the semi-major axis of the planetary orbits. If the first two methods for the discovery of extrasolar planets are compared (Doppler and transit methods), Doyle et al. (2000) point out the following facts around 40,000 photons are required to determine the transit of an extrasolar planet across the star HD 209548 using a photometer. But detection of the same system using variations in radial velocity requires 10 million photons. 

Thus, we have demonstrated, in the form of a diagram, the crosstalk between transverse velocity and a radial velocity measured by red shift. As we shall se in Section XII, the crosstalk between the radial velocity and the apparent transverse velocity is demonstrated by the use of another but similar diagram. By adding those two diagrams together we will finally find a method of evaluating the true velocity of the light source. 

Formulation of multi-component emulsions and mixtures are of interest in chemical and industrial processes (Vilar, 2008 Vilar et al., 2008). Standard stirred tank reactors (STR) and oscillatory baffled reactors (OBR) are traditional methods for the formulation of liquid-liquid mixtures and liquid-solid emulsions. Compared with STR, oscillatory baffled reactors provide more homogeneous conditions and uniform mixing with a relatively lower shear rate (Gaidhani et al., 2005 Harrison and Mackley, 1992 Ni et al., 2000). Figure 17 is a sketch of a typical oscillatory baffled reactor. It consists of the reactor vessel, orifice plate baffles, and an oscillatory movement part. The orifice plate baffles play an important role in the OBR for the vertex generation in the flow vessels as well as the radial velocities of the emulsions and mixtures. They are equally spaced in the vessel with a free area in the center of each baffle... 

Lapple and Shepherd (1940) have given the general equations for motion of particles in a cyclone. These equations cannot be solved except by the method of approximations. If the tangential and radial accelerations are neglected, the radial velocity of the particle is given by the equation... 

Statistical methods based on measuring energy or radial velocity in the liquid in the cavitation field thermal methods, acoustic output, and measurement of velocity associated with bubble oscillation. 

Collision efficiency was calculated by the method proposed for the first time by Dukhin Derjaguin (1958). To calculate the integral in Eq. (10.25) it is necessary to know the distribution of the radial velocity of particles whose centre are located at a distance equal to their radius from the bubble surface. The latter is presented as superposition of the rate of particle sedimentation on a bubble surface and radial components of liquid velocity calculated for the position of particle centres. Such an approximation is possibly true for moderate Reynolds numbers until the boundary hydrodynamic layer arises. At a particle size commensurable with the hydrodynamic layer thickness, the differential of the radial liquid velocity at a distance equal to the particle diameter is a double liquid velocity which corresponds to the position of the particle centre. Such a situation radically differs from the situation at Reynolds numbers of the order of unity and less when the velocity in the hydrodynamic field of a bubble varies at a distance of the order ab ap. At a distance of the order of the particle diameter it varies by less than about 10%. Just for such conditions the identification of particle velocity and liquid local velocity was proposed and seems to be sufficiently exact. In situations of commensurability of the size of particle and hydrodynamic boundary layer thickness at strongly retarded surface such identification leads to an error and nothing is known about its magnitude. 

An approximate value for the transit time can be obtained by the method suggested by Bruckenstein and Feldman (24). The radial velocity near the electrode surface is given by (9.3.10), which can be written... 

Axial dispersion and wall effects in narrow fixed beds with aspect ratios < 10 were investigated, both by classical methods and by NMR imaging." The residence time distribution (RTD) in the center and at the wall was measured by using water/NaCl-soln. as tracer, and subsequently compared with radial velocity profiles based on NMR imaging. The effects of the aspect ratio and particle Reynolds number on dispersion and on the degree of nonuniformity of the velocity profile were studied. The NMR results are consistent with the RTD and also with literature data of numerical simulations. For low aspect ratios, dispersion/wall effects have a strong effect on the reactor behavior, above all, in cases where a low effluent concentration is essential, as proven by breakthrough experiments with the reaction of H2S with ZnO. 

At first we tried to solve the problem in study by a simultaneous numerical analysis of the Navier-Stokes equations and the mass transport equation. Since by this method serious numerical instabilities were encountered we choose an alternative procedure. This consists of calculating first, at each grid point in the tube, the axial and radial velocities, after which these values are used to solve the mass transport equation. In solving this equation care is taken that the grid used is identical to that for solving the velocity field. 

Radial velocity or Doppler method as we have seen above, a star will move under the gravitational attraction of a planet. This motion about the center of gravity of the system can be detected by small Doppler shifts of the star s spectral lines (see Fig. 6.2). Note that only the radial velocity component, that is the velocity that is directed toward (or away) from the observer causes a Doppler shift which varies periodically. This method has been so far the most promising one and most of the extrasolar planets detected so far were found from these Doppler shifts. The inclination / of the orbital plane with the sky is unknown, therefore, we measure the velocity... 

The wall boundary condition applies to a solid tube without transpiration. The centerline boundary condition assumes S5anmetry in the radial direction. It is consistent with the assumption of an axis5Tnmetric velocity profile without concentration or temperature gradients in the 0-direction. This boundary condition is by no means inevitable since gradients in the 0-direction can arise from natural convection. However, it is desirable to avoid 0-dependency since appropriate design methods are generally lacking. 

The dimensionless velocity component in the axial direction,, = V,/u, is calculated using the method of Example 8.8. The component in the radial direction, L/R) Wr, is calculated using a dimensionless version of Equation (8.70) ... 

So far, some researchers have analyzed particle fluidization behaviors in a RFB, however, they have not well studied yet, since particle fluidization behaviors are very complicated. In this study, fundamental particle fluidization behaviors of Geldart s group B particle in a RFB were numerically analyzed by using a Discrete Element Method (DEM)- Computational Fluid Dynamics (CFD) coupling model [3]. First of all, visualization of particle fluidization behaviors in a RFB was conducted. Relationship between bed pressure drop and gas velocity was also investigated by the numerical simulation. In addition, fluctuations of bed pressure drop and particle mixing behaviors of radial direction were numerically analyzed. 

Electroimmunoassay (rocket electrophoresis) and radial immunodiffusion (A5) lack sensitivity at low Lp(a) concentrations, and the response is influenced by the size of the apo(a) isoforms (A5, K28). Differences in migration velocity in the agarose gel lead to an underestimation of the samples with large apo(a) isoforms and to an overestimation of samples with small apo(a) isoforms. Moreover, the detection limit lies around 0.07-0.08 g/liter Lp(a), so that this method is better suited for screening and detection of individuals with elevated Lp(a) levels than for the exact measurement of the plasma Lp(a) concentration. 

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