Projections transverse structure

Figure 8.18. Transversal structure of a fiber. The topological information on the structure of a fiber that is related to the 2D projection / 2 ( 12) contains structure information from the representative cross-sectional plane (ri, r2) of the fiber. Size distribution and arrangement of the domain cross-sections are revealed... 

When dealing with the equatorial streak of a fibo- pattmi, it tqtpears suitable to extract the transverse structure /jj (s ). Through Fourier transformation relation this projection is linked to a two-dimensional two-phase system made ftom needle cross sections in a matrix, as indicated in the bottom row of fig 2. 

An adapted method for the evaluation of the transverse structure had to be devel-oped[i]. /jj (sx2) is genaated by a projection process identical to the one carried out by a Kratky camaa. In particular /jj (sn) exhibits Porod s law with the scattering falling off with Small deviations tom the predicted fall off are accounted to the non-ideal structure of the real two-phase system(7,18] and corrected accordingly, leading to the 2D interference function G2 (su) of m ideal two-jAasesystem... 

Considering TPEs under uniaxial load, Bonart [23] has proposed the study of two aspects of the nanostructure, called longitudinal and transverse structure. They can readily be extracted from the scattering pattern by projections [24]. In both cases, the result is a curve and, obviously, curves are analyzed with less computational effort than 2D scattering patterns. 

Figure 19-23 (A) Diagram of a cross-sectional view of the outer portion of a lamellibranch gill cilium. This has the 9+2 axoneme structure as shown in Fig. 1-8 and in (B). The viewing direction is from base to tip. From M. A. Sleigh.329 (B, C) Thin-section electron micrographs of transverse (B) and longitudinal (C) sections of wild-type Chlamydomonas axonemes. In transverse section labels A and B mark A and B subtubules of microtubule doublets oa, ia, outer and inner dynein arms, respectively sp, spokes cpp, central pair projections bk, beaks. From Smith and Sale.329a...

To calculate L(Z) in terms of the structural-dynamical model of water, we introduce the longitudinal and transverse dimensionless projections, q = py /p and = p /p, of a dipole-moment vector p. These projections are directed, respectively, along and across to the local symmetry axis. In our case (see Fig. 56b), the latter coincides with an equilibrium direction of the H-bond. Next, we introduce the longitudinal and transverse spectral functions as... 

A beam is a bar or structural member subjected to transverse loads that tend to bend it. Any structural members act as a beam if external transverse forces induce bending. A simple beam is a horizontal member that rests on two supports at the ends of the beam. All parts between the supports have free movement in a vertical plane under the influence of vertical loads. A fixed beam, constrained beam, or restrained beam is rigidly fixed at both ends or rigidly fixed at one end and simply supported at the other. A continuous beam is a member resting on more than two supports. A cantilever beam is a member with one end projecting beyond the point of support, free to move in a vertical plane under the influence of vertical loads placed between the free end and the support. 

It is useful to regard the momentum basis functions as states onto which one can project the memory function or the phase space density correlation function. By referring to the notations established in Table 1 and (125), we see that Ip I is the number density state, ip2 the longitudinal current (2-component) state, the energy state, iJ/4 and ij/s the two transverse current (jc- and y-component) states, etc. The elements given in Table 1, /f(a /3), a, /3 4, are those which determine the thermodynamics as well as the basic hydrodynamic structure of the fluid system. Notice that in the limit of ka- O these... 

The transverse and longitudinal vdW radii have been also determined experimentally in other gas-phase molecules. Thus, in T-shaped vdW complexes Rg A2 (Rg = He, Ne, Ar, Kr, Xe A = H, O, N or a halogen) the radii of A (perpendicular to the A-A bond line) were calculated from structural data [99] such complexes are rigid and Rt(A) does not depend (within 0.05 A) on the type of Rg. In some (A2)2 dimers the A2 molecules contact side-to-side and thus Ri is equal to one-half of the (experimentally determined) separation between the molecular centers of mass. These Rt values are close to the corresponding radii of A in Rg A2 complexes the former radii exceed the latter by 0.05 A on average, due to different modes of molecular packing projection into hollow in Rg A2 or projection against projection in (A2)2 [121, 122]. 

A) Simplified microscopic model of a quartz crystal lattice B) Longitudinal effect C) Transverse effect Si " and 2 O refer to centers of gravity (circles) for charges associated with the two types of atoms, where the tetrahedral "Si04 structure has been projected onto a plane (as a hexagon)... 

For a straining series of the material Arnitel E2000/60the equatorial scattering has been extracted and projected onto the transverse plane as discussed in the section Evaluation Methods". The resulting curves of /j (sis) are presented in fig 8(a). After proper consideration of the non-ideal two-phase structure of the sample[5] the 2D chord distribution 32 (atiz) is computed by means of eq 6. The corresponding curves are shown in fig 8(b). When such equatorial scattering was first observed [29], it was attributed to... 

Fig. 12.68a,b. Iliopsoas impingement by an acetabular cup. a Transverse oblique 12-5 MHz US image obtained over the anterior hip shows a beak-shaped hyperechoic projection (arrowheads) on the anterior border of the acetabular cup surrounded by an effusion (asterisks). Ac, acetabulum. IPs, iliopsoas muscle, b Correlative transverse CT image demonstrates a hyperdense anterior structure (arrowhead) which impinges on the posterior aspect of the iliopsoas muscle (IPs), representing cement leakage following the hip replacement procedure... 

In this section, we have used the rotational invariance to predict the form of the phase equations. Recently, a lot of effort has been devoted to the development of amplitude equations - or order parameter equations - in a rotationally invariant form [15, 85, 86]. According to Gunaratne [86], supplemental terms introduced in the equations to meet this constraint could account for the stabilization of otherwise unstable states, in particular rhombic patterns which have been observed both in experiments [87] and in numerical simulations [29]. This could also explain the stabilization of the mixed states of Equation (16), also observed in experiments [51] and simulations [30]. Nevertheless, alternative interpretations can be proposed in terms of finite size effects in the numerical simulations, and in terms of three-dimensional effects for the experiments. Mixed states observed in our laboratory more likely correspond to projections of two exactly superposed layers, the first one with striped symmetry, and the second one with hexagonal symmetry. More generally, one expects that the strong transverse gradients present in the experiments can produce an hybridization between otherwise flawless structures. 

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