Half systems

MacKay, D. M. and Mackay, V. (1982) Explicit dialogue between left and right half-systems of split brains , Nature 295, 690-1. 

Relaxation in Coupled Spin Systems. - The ability to transfer coherences between different nuclei in homo- and heteronuclear spin systems is one of the cornerstones of NMR. The transfer of polarization from I = (1/2) to enhance the signal of low-gyromagnetic ratio S = (1/2) nuclei has become routine. In solution state the majority of these methods employ free-precession type techniques such as INEPT where polarization transfer from one spin to another is mediated via the scalar coupling. The majority of these techniques are designed for spin-half systems and have shown particular utility in the study of structure and dynamics of biomolecules labeled with C and N. The use of INEPT for achieving polarization transfer in systems of scalar coupled quadrupolar nuclei has also been investigated. ... 

Turning back to the Electrochemical PUm Systems (EFS), we shall see that a similar situation occurs when the macrokinetics of the electrolysis is investigated. No wonder, the EFS is, in fact, a one-half of the whole electrochemical system and must be coupled with the opposite half-system in any real process. The correct question is whether or not we can neglect the coupling effect. Given the electrorefinement of pol3walent metal as an example, we cannot do this anymore. 

The geometric compensation by means of a gradiometric coil is realised by placing the SQUID exactly between the two halfs of the coil, in order to detect only the response of the sample. In both cases we could achieve a reduction of the excitation field at the location of the SQUID of up to 1000. Electronic and geometric compensation together leads to an improvement of six orders of magnitude in the dynamic range, compared to a system without excitation field compensation. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

Stabilizing resonances also occur in other systems. Some well-known ones are the allyl radical and square cyclobutadiene. It has been shown that in these cases, the ground-state wave function is constructed from the out-of-phase combination of the two components [24,30]. In Section HI, it is shown that this is also a necessary result of Pauli s principle and the permutational symmetry of the polyelectronic wave function When the number of electron pairs exchanged in a two-state system is even, the ground state is the out-of-phase combination [28]. Three electrons may be considered as two electron pairs, one of which is half-populated. When both electron pahs are fully populated, an antiaromatic system arises ("Section HI). 

An instability of the impulse MTS method for At slightly less than half the period of a normal mode is confirmed by an analytical study of a linear model problem [7]. For another analysis, see [2]. A special case of this model problem, which gives a more transparent description of the phenomenon, is as follows Consider a two-degree-of-freedom system with Hamiltonian p + 5P2 + + 4( 2 This models a system of two springs con-... 

Table 1 describes the timing results (in seconds) for a system of 4000 atoms on 4, 8 and 16 nodes. The average CPU seconds for 10 time steps per processor is calculated. In the case of the force-stripped row and force-row interleaving algorithms the CPU time is reduced by half each time the number of processors is doubled. This indicates a perfect speedup and efficiency as described in Table 2. Tables 3, refibm table3 and 5 describe the timing results, speedups and efficiencies for larger systems. In particular. Table 4 shows the scaling in the CPU time with increase in the system size. These results are very close to predicted theoretical results.

The era of the Evans and Sutherland computer systems vanished in the first half of the 1980s, when powerful and more economical workstations were introduced. In spite of advances in computer graphics and in CPU power, these workstations dominate the everyday life of molecular modeling even today. 

WFth all semi-empirical methods, IlyperChem can also perform psendo-RIfF calculations for open -shell systems. For a doublet stale, all electrons except one are paired. The electron is formally divided into isvo "half electron s" with paired spins. Each halfelec-... 

---