Spin strings

We shall use roulette wheel selection. Spinning the virtual wheel ten times gives us ten strings as the starting point for the new population (Table 2). We note that the fitter strings are indeed now more numerous than before, as we would expect, although, as there is a stochastic element in the choice of parents, repeated runs on the same problem can be expected to generate different results. 

Garrahan and Chandler [230] have recently attempted to rationalize the string-like motion in supercooled liquids based on a completely different concept of dynamic facilitation, derived from the study of magnetic spin models originally developed by Fredrickson and Anderson [231]. Although these spin models seem to exhibit dynamic heterogeneity of some kind and slow relaxation processes, the slowing down of the dynamics in these models is entirely decoupled from the spin model s thermodynamics [116, 230]. In view... 

A GMCSC configuration can be viewed as a linear combination, with adjustable coefficients, of f(Ne,S) structures with a common orbital string , each of them analogous to a classic-VB structure except for orbital optimization and for the use of YK spin functions. Note the latter is not actually a limitation inasmuch as all of them are included, since they span the full spin space for Ne electrons with given values of S and M. One should perhaps note that for Nc=l the wavefunction in Eq. (1) reduces to a single-configuration spin-coupled wavefiinction [3]-[6], and d then becomes simply a normalization constant. 

Man is. . . related inextricably to all reality, known and unknowable. .. plankton, a shimmering phosphorescence on the sea and the spinning planets and an expanding universe, all bound together by the elastic string of time. It is advisable to look from the tidal pool to the stars and then back to the tide pool again. 

TOCSY (total correlation spectroscopy) is an extension of the COSY experiment, in which the coherence transfer is not limited to a single jump from one proton to another via a J coupling. Instead, coherence is spread out over an entire spin system of coupled protons via multiple /-coupled jumps. For example, in a string of carbons CHa-CHb-CHc-CHd, coherence can be transferred by the TOCSY mixing sequence from Ha to Hc or from Ha to Hj. Thus, crosspeaks will be observed at F% = va and I = i b, vc or (Fig. B.5). 

The HF wavefunction takes the form of a single Slater determinant, constructed of spin-orbitals, the spatial parts of which are molecular orbitals (MOs). Each MO is a linear combination of atomic orbitals (LCAOs), contributed by all atoms in the molecule. The wavefunction in classical VB theory is a linear combination of covalent and ionic configurations (or structures), each of which can be represented as an antis5nnmetrised product of a string of atomic orbitals (AOs) and a spin eigenfunction. The covalent structures recreate the different ways in which the electrons in the AOs on the atoms in the molecule can be engaged in bonding or lone pairs. An ionic structure contains one or more doubly-occupied AOs. Each of the structures within the classical VB wavefunction can be expanded in terms of several Slater determinants constructed from atomic spin orbitals. 

In order to search for an interpretation of the error threshold relation by analogy to the spin system, we shall be more specific and consider binary sequences replicating with uniform error rates. Individual sequences are identified with the rows of a two-dimensional spin lattice. A genealogy corresponds to an entire, two-dimensional array of spins. We assign spin values (s= +1) to the digits (0,1). A sequence of v digits is identified with a string of spin values ... 

Flow properties. Slugging tendency of a fluidized bed increases with increased Stormer viscosity (207). The modified Stormer viscometer used ill this work is provided with a paddle that is rotated in the fluidized bed (by means of a weight attached to a string passing over a system of pulleys). Viscosity is measured by determining the weight required to spin the paddle at 200 r.p.m. Stormer viscosity of the bed increases with decreased gas velocity and with increased size and density of particles. Viscosity of coarse catalyst is decreased, within limits, by addition of fines. 

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