Spin modes

The expression for the projection of the /th normal mode onto m of the mth rod is presented elsewhere/17 29) Besides these deformational normal modes, there is also a uniform axial spinning mode in which all of the rods rotate in phase like a speedometer cable. The contribution of that mode to is just 2k Tt/(N+ l)y, as expected for diffusion in one dimension with the friction factor (N + 1)7 of the entire filament. 

The SADARM system is thought to be unique because it uses a passive mm wave radiometric sensor in a high spin mode at low altitude — for the first time ever in a munition it uses a vortex ring parachute that maintains a constant spin rate and drop velocity, and is exceptionally stable and it delivers a long-standoff fragment warhead with armor-penetrating capability Ref Anon, ARRADCOM Voice (Oct 17,1977), 7... 

Mass [amn] Spin Mode of decay h/i Decay energy [MeV]... 

If it is accepted that a spinning mode of propagation exists, then an acoustic theory may be applied to predict the spin frequency, the slope of the helical path on the tube wall, and other characteristics of spinning detonations [75]-[76]. For a planar Chapman-Jouguet wave in an infinitely long tube and in a frame of reference in which the burnt gas is at rest, the circumferential velocity of a traveling tangential acoustic wave at the wall... 

In contrast, the spinning tracks were clearly observed in the scribes made in spinning mode (designated as U shape). Spinning left burrs in the scribes and also wider scribes. Since they provided more exposed surface area, the left burrs in the scribe may have a greater chance to initiate the corrosion. 

The oscillograph records in Figure 5 illustrate the spin effects found in ozone detonations. For high ozone concentrations, there was a high-frequency (high modal number), relatively low-amplitude spin in the middle concentration range, there was no spin and at lower concentrations, a fundamental spin mode developed, which increased in amplitude as the concentration was dropped. The behavior of hydrogen mixtures is very similar to this (IS). 

The ability of NMR spectrometers to operate in the cross-polarization/ magic angle spinning mode is a powerful tool for structural elucidation of insoluble materials (556). Natural abundance solid-phase C-NMR spectra could be obtained for synthetic L-dopa eumelanin. The inordinate number of resonance signals, however, prevented definitive assignments of the peaks to specific carbons. Subsequently Chedekel et al. (357) used this technique to study the conversion of specifically labeled L-dopa and... 

Numerical simulations were performed on the planar problem in [83], which showed that the transition to the self-oscillatory combustion occurs when a parameter related to the Zeldovich number is increased. Numerical studies [5, 6, 79] of the one-dimensional problem found transitions to relaxation oscillations and period doublings, and these studies demonstrated two routes to chaotic dynamics as the bifurcation parameter related to the Zeldovich number was increased. Numerical studies [36 1,1,7,4] of the two- and three-dimensional model found spinning modes of propagation as well as standing modes, which describe multiple point propagation, and quasi-periodic modes of propagation. 

V. Ilyashenko and J. Pojman, Single head spin modes in fronted polymerization. Chaos, 8 (1998), pp. 285-289. 

Principles of the spin mode of combustion front propagation. Combust. Explos. 

J. Pojman, V. Ilyashenko, and A. Khan, Spin mode instabilities in propagating fronts of polymerization, Physica D, 84 (1995), pp. 260-268. 

We next consider the spin mode solution branches shown in Figure 1. The first branch we focus on corresponds to 1-headed spin modes which are traveling waves (TWl). These modes require larger radii for stability than the CP modes. Stable CP modes may be able to exist for smaller values of R as they are, in a sense, reinforced by collisions after circuiting only half the cylinder. The TWl modes also appear to enter with nonzero amplitude of the rotating hot spot. The smallest value of R for which we can find a stable TW1 mode is R=1.68. For this value of R the temperature of the hot spot is approximately 1.21. Unstable TWl modes may well exist for smaller values of R. If we decrease R further solutions with TW 1 initial data evolve to CP modes. We note that the mean axial speeds V for the TW 1 modes near onset are below those of the CP modes near onset, probably due to the fact that R is larger. 

Finally, we have investigated 3-headed spin modes. We find that replicated... 

T. P. Ivleva, A. G. Merzhanov, K. G. Shkadinsky, Principles of the Spin Mode of Combustion Front Propagation, Combustion, Explosion and Shock Waves 16 (1980), 133. 

The spin-mode frontal polymerization resulting in a helicoidal structure (18). 

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