Corner cutting

To make cut stars, the damp mixture is spread out in a shallow pan, pressed down evenly, cut into cubes, say to % inch on the side, allowed to dry, and broken apart. Because of their corners, cut stars take fire very readily and are well suited for use in rockets and small aerial bombshells. Cylindrical stars are preferred for Roman candles. 

The cross indicates the saddle point. One possible corner-cutting trajectory is shown (schematic). The unbound initial state corresponds to a gas-phase reaction. (From Ovchinnikova [1979].)... 

The deformation of crystal seems to be more enhanced in the corner-cut crystal than in the cubic one within the same dissolution period. 

It is assumed that each crystal is surrounded completely by gas at a uniform concentration, which means that direct transfer between crystals is neglected and that all the crystal surface is accessible to the gas. The 2 assumptions are self-compensating, but one could expect serious errors if there is significant crystal-binder agglomeration. It is assumed further that all the crystals are uniformly-sized spheres, mainly for mathematical simplicity. Of course, 5A crystals are in fact cubic, but with the corners cut off, so that the spherical approximation is not unreasonable. The uniform size is a more drastic assumption, which is discussed below. The diffusion processes in both crystals and pores are assumed to be governed by Pick s law. For the pores, an effective diffusivity Dp) is used, which can be related to the bulk gas diffusivity Dq) by the relation ... 

C. de Boor Local corner cutting and the smoothness of the limiting curve. CAGD 7(5), pp389-398, 1990... 

M. Paluszny, H.Prautzsch and M.Schafer A geometric look at corner cutting. CAGD 14(5), pp421-448 1997... 

G.Aumann Corner cutting curves and a new characterization of Bezier and B-spline curves. CAGD 14(5), pp449-474, 1997... 

E. Mainar and J.M.Pena Corner cutting algorithms associated with optimal shape preserving representations. CAGD 16(9), pp883-906, 1999... 

The molecule has the symmetry of the regular tetrahedron—four threefold rotation axes, three twofold rotation axes, and some symmetry planes. The four nitrogen atoms lie at the corners of a regular tetrahedron and the six carbon atoms lie at the corners of a regular octahedron. The polyhedron defined by the twelve hydrogen atoms is the truncated tetrahedron, a tetrahedron with each corner cut off by a plane parallel to the opposite face. 

When 2Qpv/cob < 1, we are in the fast-flip , or sudden approximation , or corner-cutting , or large curvature limit, where the reaction coordinate follows theMEP, but before it reaches the saddle point it tunnels along the s coordinate in a time that is short compared to the timescale of the Q vibration. 

Promoting Vibrations - Corner Cutting and the Masking of KIEs... 

Reaction path curvature is actually a vector with 3N — 7 components [80]. Each component is associated with a particular generalized normal mode, and it measures the extent to which the system curves into a particular direction as it progresses along the MEP. Corner-cutting tunneling involves a coupled motion involving the reaction coordinate and all the generalized normal modes that are associated with nonzero curvature components [81]. 

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