Velocity distribution reconstruction

The flow resistance behavior of the reconstructed medium can now be examined by performing 3D flow simulations with the Lattice Boltzmann method (Chen and Doolen, 1998), and obtaining the permeability of the material (Konstandopoulos, 2003). Figure 8(a) depicts a visualization of 3D flow tubes and flow velocity distributions at different cross sections in a reconstructed filter material. Figure 8(b) shows the comparison of computer simulated and experimental permeabilities obtained with the experimental protocol described in Konstandopoulos (2003). 

The inverse problem consists in reconstructing the velocity distribution from the observed pressure field ... 

The moment-transport equations discussed above become more and more complicated as the order increases. Moreover, these equations are not closed. In quadrature-based moment methods, the velocity-distribution function is reconstructed from a finite set of moments, thereby providing a closure. In this section, we illustrate how the closure hypothesis is applied to solve the moment-transport equations with hard-sphere collisions. For clarity, we will consider the monodisperse case governed by Eq. (6.131). Formally, we can re-express this equation in conservative form ... 

The quadrature-based closure of Eqs. (6.176) and (6.177) then proceeds as follows. Let / (f, X, v) denote the velocity-distribution function reconstructed from the transported moments (Eq. 6.173), and define the negative- and positive-integer moments for... 

Figure 7 TOF spectrum of trimethylgallium (TMG) from the (2 X 4)-reconstructed QaAs(IOO) surface at 638 K when a pulsed TMG beam is supplied to the surface. The spectrum is well reproduced by convolution of the incident and scattered velocity distributions as well as a surface residence time of 0.9 ns. (Reproduced with permission from Sasaki M and Yoshida S (1996) Scattering of pulsed trimethylgallium beam from GaAs(IOO), -(110), and -(111) B surfaces. Surface Science 356 233-246 Elsevier.)...

In this paper a method is described to measure accurately the three-dimensional geometry of the isolated, working canine heart during the cardiac cycle. Times of flight of ultrasonic pulses are measured with high accuracy for many directions through the object under study. These transmissions times are then used to reconstruct the ultrasound velocity distribution in the plane of measurement. 

With ultrasound velocity tomography the local speed of ultrasound in a cross section of the subject under study is computed from a large set of ultrasound transmission times. These calculations (reconstructions) are based upon a model that describes the propagation of ultrasound in a medium. In its simplest form the ultrasonic pulses are supposed to travel along straight pathways from transmitter to receiver. The measured transmission times depends on the velocity distribution v(jc, y) in the plane of reconstruction ... 

More quantitative information can be obtained from the images when the full three-dimensional speed and angular distributions are reconstructed using mathematical transformations of the crushed two-dimensional images, or alternatively by using forward convolution simulation techniques. If the initial three-dimensional distribution has cylindrical symmetry, a unique transformation - the inverse Abel transform - can be used to reconstruct the initial three-dimensional velocity distribution. As the photolysis laser vector defines automatically an axis of cylindrical symmetry, the inverse Abel transformation can usually be used, as long as the plane of the position-sensitive detector is placed parallel to the laser polarization vector. 

Greenleaf, J.F. Johnson S.A. Samayoa, W.F. and Duck, F.A. (1975). Algebraic reconstruction of spatial distributions of acoustic velocities in tissue from their time-of-flight profiles. In Acoustical Holography, Vol. 6, Ed. N. Booth, Plenum Press, 71-90. 

Fig. 17.14. Separation principle in MECC. A compound (neutral or charged) is partitioned between the micellar and aqueous phase. A fully solubilized neutral compound migrates with the velocity of the micelles. A neutral compound with no affinity for the micelles migrates with the velocity of the EOF. A neutral compound with an affinity for both the micellar and the aqueous phase migrates with an intermediate velocity. (A) Schematic overview of the partitioning of compound (N the EOF moves toward the cathode and the typical SDS micelles toward the anode. (B) Diagram of the zone distribution within the capillary. (C) Reconstructed typical electropherogram.

The atmospheric transport of heavy metals, oil hydrocarbons, and radionuclides is described by many models (Phillips et al., 1997 Payne et al., 1991 Sportisse, 2000). Application of these models to the reconstruction of the pollution distribution over Q makes it possible to estimate optimal values of Atp, AA and time steps At. The present level of the database for the Arctic Basin provides for use of a single-level Euler model with At = 10 days, A

pollution sources can be located at the Arctic Basin boundary. Detailed distributions of these pollution sources are given as SSMAE input. The transport of pollutants to the Arctic Basin and the formation of their spatial distribution are realized in conformity with the wind velocity field, which is considered as given (Krapivin and Phillips, 2001a, b). 

Figure 8.6 Temispack reconstruction of the present-day distribution of overpressures induced by compaction disequilibrium for two assumed conditions of fault permeability a. faults are assumed to be permeable b. faults are assumed to be impermeable (arrows Darcy velocity) (from Burrus et al., 1991, Geological Society Special Publication no. 59, Fig. 7, p. 97. Reprinted by permission).

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