Scatter operation

According to the Feshbach s formalism (Feshbach, 1958 Feshbach, 1962) the scattering operator T(z) develops the pole at z = z where z is the solution of the following equation... 

In order to complete the calculation of the strong energy-level shift, one has to match at the accuracy 0(a) the particular combination of the non-relativistic coupling d d- Therefore we consider the scattering operator... 

In the scattering operator Tr(z), all kinematical insertions contained in Hr are summed up in the external lines (see (Antonelli et al, 2001) for details). We calculate the matrix element of the scattering operator Tr(z) between the ir d states at 0(a). After removing the CM momentum, the spin-nonflip part of this matrix element on energy shell is equal to... 

In the case of positive electron energy, the scattering operator... 

In the frame of the simplest Hartry-Fock s approximation, the variation calculation of the scattering operator t E, 8) for a few atoms has been made in the articles [12-14]. However, the variation scheme permits taking into account the different configurations in the wave function of the united system of electron and the scatterer. The general form of the scattering operator t(E, 8 Q) is [9,13,14]... 

The single-site matrix t corresponds to a scattering operator t defined by t yi = iupL for any primitive basis orbital (pi in a given atomic cell. Here Xl = (Pl — fr GoV(pL = Jl Cl<,l From this definition it follows that tJi = v The t-matrix is... 

As we have seen on the CRAY the ability to gather data together is essential. Memory speed must be commensurate with floating point speed. When nearest neighbor tables are used fast scatter operations are also needed. The two essential random memory operations needed are ... 

Except for the above gather-scatter operations, simulations are easily vectorizable as defined by the CRAY FORTRAN or the CYBER 200 FORTRAN. Typical vectors have 50 to 500 elements each. 

It has recently been pointed out that the indistinguishability of identical particles has also another consequence for neutron scattering. The scattering processes are spin-dependent, which is expressed by writing the scattering lengths bi (see the scattering operators above) on the form b., Bi I. sn... 

The cross-section is here (and in the following) expressed in units of the scattering of a free electron, i.e., the Thomson cross-section, i//r is the electronic wave function for n electrons, and L is the scattering operator... 

Our interest in Brillouin-Wigner perturbation theory was stimulated by our finding [44] that this theoretical tool proved very useful in the scattering theory. The fundamental equation, known in the scattering theory as Lippmann-Schwinger equation, expresses the scattering operator as... 

Therefore, it may be difficult to obtain a dependable supply of wood from a particular geographic area. Also, most private forest holdings are small and the most efficient total tree harvest-systems cannot operate economically in such situations. When conducting conventional roundwood harvests, the removal of logging residue from small, widely scattered operations poses a difficult problem. 

When introducing the neutron scattering operator, 0 = baCxp (iq-Ra)+ bpexp(iq-Rp), the spatial parts of the matrix elements < I f 0 I i > turn out to have the two forms [12]... 

An alternative broadcast algorithm, performing the broadcast as a scatter operation followed by an all-to-all broadcast, can be modeled as follows ... 

A number of the most widely used collective communication operations provided by MPI are listed in Table A.3. The collective operations have been grouped into operations for data movement only (broadcast, scatter, and gather operations), operations that both move data and perform computation on data (reduce operations), and operations whose only function is to synchronize processes. In the one-to-all broadcast, MPl Bcast, data is sent from one process (the root) to all other processes, while in the all-to-all broadcast, MPI A11 gather, data is sent from every process to every other process (one-to-all and all-to-all broadcast operations are discussed in more detail in section 3.2). The one-to-all scatter operation, MPI Scatter, distributes data from the root process to all other processes (sending different data to different processes), and the all-to-one gather, MPI Gather, is the reverse operation, gathering data from all processes onto the root. 

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