Enhanced Spatial Approximations

An essential factor in the construction of accurate higher order FDTD techniques is the correct stencil manipulation provided by the respective spatial operators. Thus, apart from the most frequently encountered schemes, discussed in the previous chapters, a variety of rigorous approaches have also been developed [24-30]. As an indication of these interesting trends, this section presents three algorithms which, based on different principles, attempt to improve the behavior of higher order spatial sampling and approximation. 

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In the late 1950s, it was found (Wu et al., 1957) that parity was not conserved in weak interaction processes such as nuclear 3 decay. Wu et al. (1957) measured the spatial distribution of the (3 particles emitted in the decay of a set of polarized 60Co nuclei (Fig. 8.6). When the nuclei decay, the intensity of electrons emitted in two directions, 7) and 72, was measured. As shown in Figure 8.6, application of the parity operator will not change the direction of the nuclear spins but will reverse the electron momenta and intensities, 7) and 72. If parity is conserved, we should not be able to tell the difference between the normal and parity reversed situations, that is, 7, = I2. Wu et al. (1957) found that lt 72, that is, that the (3 particles were preferentially emitted along the direction opposite to the 60Co spin. (God is left-handed. ) The effect was approximately a 10-20% enhancement. 

NCs contain approximately 100-10,000 atoms. Because of the strong spatial confinement of electronic wavefunctions and reduced electronic screening, the effects of carrier-carrier Coulomb interactions are greatly enhanced in NCs compared with those in bulk materials. These interactions open a highly efficient decay channel via Auger recombination and just such a strong carrier-carrier interaction in NCs is responsible for carrier multiplication (61)-(63). 

We compute effective thermal transport coefficients for proteins using linear response theory and beginning in the harmonic approximation, with anharmonic contributions included as a correction. The correction can in fact be rather large, as we compute anharmonicity to nearly double the magnitude of the thermal conductivity and thermal diffusivity of myoglobin. We expect that anharmonicity will generally enhance thermal transport in proteins, in contrast, for example, to crystals, where anharmonicity leads to thermal resistance, since most of the harmonic modes of the protein are spatially localized and transport heat only inefficiently. 

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