Transverse motion

Heuberger M, Drummond C and Israelaohvili J N 1998 Coupling of normal and transverse motions during friotional sliding J. Phys. Chem. B 102 5038-41... 

Example The equation for the unsteady transverse motion of a uniform beam clamped at the ends is... 

FIGURE 9.6 The fluid mosaic model of membrane structure proposed by S. J. Singer and G. L. Nicolsou. In this model, the lipids and proteins are assumed to be mobile, so that they can move rapidly and laterally in the plane of the membrane. Transverse motion may also occur, but it is much slower. 

Quer-achse, /. transverse axis, -arm, m. cross arm, cross bar. -balken, m. cross beam, cross bar. -beweguug, /. transverse motion. 

Nevertheless, encouraging results have been obtained in recent years (see reviews(Bonetto et al, 1961) and the references therein). For example it is now known that in one dimensional systems of the Fermi-Pasta-Ulam (FPU) type (Lepri et al, 1998), heat conduction is anomalous and the coefficient of thermal conductivity k diverges with the system size L as k L2/5 (when the transverse motion is considered n L1/3... 

Numerical experiments have shown that in many one dimensional systems with total momentum conservation, the heat conduction does not obey the Fourier law and the heat conductivity depends on the system size. For example, in the so-called FPU model, k IP, with (3 = 2/5, and if the transverse motion is introduced, / = 1/3. Moreover, in the billiard gas channels (with conserved total momentum), the value of P differs from model to model(Li and Wang, 2003). The question is whether one can relate / to the dynamical and statistical properties of the system. 

The friction factor per base pair y for rotation of DNA around its symmetry axis was determined from FPA studies of restriction fragments containing N+ 1 =43 and 69 bp.(109) Both fragments are sufficiently short that a substantial amplitude of C (t), and also F (t), resides in their Uniform Mode Zones. Particular values of certain parameters were assumed, namely, the rise per base pair h = 3.4 A, the hydrodynamic radius b = 12 A for transverse motion in Eqs. (4.43)-(4.47) (which are quite insensitive to b), and D, = 1.8 x 106 s-1 for 43 bp and D = 4.8 x 105 s for 69 bp. The latter values were extrapolated or interpolated from the data of Elias and Eden using an inverse cubic relation between DL and L. They are close to the values calculated using the theory of Tirado and Garcia de la Torre.(129)... 

Oldham discovered that there are actually two kinds of seismic vibrations, one called P (or "primary," because it travels faster and arrives first) and the other called S (or "secondary," because of its later arrival at the same station). The compressional motion of the P waves can be transmitted through most substances, although the speed at which the wave moves decreases as the stiffness of the medium decreases. In contrast, the transverse motion of S waves cannot be transmitted through a liquid, because the loosely bonded molecules in a liquid slip past each other too easily. S waves are observed to disappear at the top of the core. Then, at a depth of approximately 5100 km, the P wave velocity abruptly increases and there is a hint of the reappearance of an S wave. From such observations, Danish geophysicist Inge Lehman hypothesized in 1936 that the core was stratified, with an outer liquid portion and an inner solid portion. The existence of molten metal at core pressures requires some light element to act as antifreeze. 

Since the phospholipids have cis-unsaturated fatty acid components there is a certain amount of fluidity to the bilayer. You can picture a sea of lipids moving in a transverse motion across the inside and outside faces. Note that the exterior of the membrane is composed of the polar portions of the biolipids while the interior of the membrane is highly nonpolar. 

Rigid fixtures which simulate the mounting of the fuze in service shall be used to mount the fuze to the vibration machine. The control accelerometer or accelerometers shall be mounted as close as possible to the fuze mounting point. The fixture shall be designed such that the trans-missibility at any point on the fixture shall be less than two (2). The transverse motion of the input monitoring points shall be less than 100 percent of the input motion. The transmissi-bility and transverse motion of the fixture, loaded with fuzes or dummy equivalents, shall be evaluated thru the ratnge of test frequencies... 

The lifetime of the transition state over a saddle point near the top of the barrier is the most probable time for the system to stay near this configuration. It is simply expressed, for a one-dimensional reaction coordinate (frequency ) near the top of the barrier, as r = l/ . For values of ha from 50 to 500 cm"1, t ranges from 100 to 10 fs. In addition to this motion, one must consider the transverse motion perpendicular to the reaction coordinate, with possible vibrational resonances, as discussed below. 

An ejected photoion can have nonzero transversal velocity, Autr, if a part of the excitation energy is converted to kinetic energy during the photodetachment from the surface. It is assumed that the average kinetic energy of the transverse motion of a photoion equals kin- Then, in a way similar to the above procedure, it is possible to estimate the spatial resolution due to this effect. To achieve the spatial resolution Ax of 3-5 A at Fmax = 0.2 eV/A and r - 103 A, it is necessary to realize a very precise MPI of the chro-mophore on the cooled tip with excess of transversal kinetic energy of only = 10-3 eV. 

A typical photoelectron image (PEI) of a UF-F2 needle tip is presented in Fig. 5. The laser intensity was varied in the range 4 x 103—8 x 103W/cm2, determined by the dynamic range of the registration system used. Since the photoemitted electrons possess some nonzero transverse motion kinetic energy E m, each photoelectron must be imaged as a spot with a diameter defined by the expression... 

Figure 5-2. Phonon in a crysial, schematic. Transversal motion of a linear atomic chain, described by two different waves with wavelength >2a and wavelength <2a, a = (average) distance of atoms.

J. Mellmann, The transverse motion of solids in rotating cylinders— forms of motion and transition behavior, Powder Technol. 118 (2001) 251-270. 

Further increases in elasticity lead to the next limit of the minimum velocity for a perfectly elastic surface film. Here, the mode coupling leads to the case when the transverse motion is favored at the expense of lateral motion that is now practically stopped. Treating this case as a departure from the infinite lateral modulus case, Limit V, expressions for co0 and a are given as follows. 

Figure 12 (a) Temperature dependence of the longitudinal resistivity of (TMTSF)2PF6 obtained with the clamped contact technique. (From W. Kang, private communication, and O. Traetteberg, Thesis, Univ. Orsay, 1993.) (b) The conductivity anisotropy is temperature independent as long as the transverse motion remains incoherent. Data for (TMTSF)2PF6 under 12 kbar. (After Ref. 6.)... 

Figure 7b. Scattering of sound by transverse motion of an air microbubble. Both longitudinal (solid line) and shear (dashed line) waves are generated.

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