Linear-Parallel

Identifying specific quantified building ventilation rates can be difficult due to the number of non-linear parallel paths that may have to be simultaneously considered. 

FIGURE 2.4 Examples of four types of deperi(fency. In the bottom left-hand graph the 2 groups of points might represent males and females, for example, including random, linear, parallel, and curvilinear relationships. 

For linear parallel polarizations of the writing beams at 0) and 2(0 frequencies and uniaxial (rod-like) molecules, the distribution N( 2) depends only on the polar angle 0. So the eigensolutions of the diffusion equation are the Legendre polynomials, with eigenvalues -/( +l). Therefore, the different order parameters... 

SMBR - equilibrium transport A + BjiC + D Linear Parallel reactions Kawase et al. 2001... 

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

For the parallel recording of EEL spectra in STEM, linear arrays of semiconductor detectors are used. Such detectors convert the incident electrons mto photons, using additional fluorescent coatings or scintillators in the very same way as the TEM detectors described above. 

The diffraction of low-energy electrons (and any other particles, like x-rays and neutrons) is governed by the translational syimnetry of the surface, i.e. the surface lattice. In particular, the directions of emergence of the diffracted beams are detemiined by conservation of the linear momentum parallel to the surface, bk,. Here k... 

Alternatively, the electron can exchange parallel momentum with the lattice, but only in well defined amounts given by vectors that belong to the reciprocal lattice of the surface. That is, the vector is a linear combination of two reciprocal lattice vectors a and b, with integer coefficients. Thus, g = ha + kb, with arbitrary integers h and k (note that all the vectors a,b, a, b and g are parallel to the surface). The reciprocal lattice vectors a and are related to tire direct-space lattice vectors a and b through the following non-transparent definitions, which also use a vector n that is perpendicular to the surface plane, as well as vectorial dot and cross products ... 

Watson S C and Carter E A 2000 Linear-scaling parallel algorithms for the first principles treatment of metals Comp. Pbys. Common. 128 67-92... 

The skeletal LN procedure is a dual timestep scheme, At, Atm, of two practical tasks (a) constructing the Hessian H in system (17) every Atm interval, and (b) solving system (17), where R is given by eq. (3), at the timestep At by procedure (23) outlined for LIN above. When a force-splitting procedure is also applied to LN, a value At > Atm is used to update the slow forces less often than the linearized model. A suitable frequency for the linearization is 1-3 fs (the smaller value is used for water systems), and the appropriate inner timestep is 0.5 fs, as in LIN. This inner timestep parallels the update frequency of the fast motions in force splitting approaches, and the linearization frequency Atm) is analogous to the medium timestep used in such three-class schemes (see below). 

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