Atom decomposition methods

Atom decomposition methods are the most straightforward to implement, reflected by their usage in major simulation packages such as CHARMM and GROMOS. Yet their dependence on global communications limits the number of processors that can be effectively used. In the LJ benchmark, communication costs begin to dominate by the time hundreds of processors have been used, since there is little speed-up when the number of processors is doubled. 

FIG. 10 Division of the force matrix among P processors in the atom-decomposition method. 

To learn more about charge decomposition methods for assigning atomic charges, see G. Henkelman, A. Amaldsson, and H. Jonsson, Comp. Mater. Sci. 36... 

While evaporative methods of generating C atoms utilize bulk carbon and a great deal of thermal or photochemical energy, another approach is to use the exother-micity of the decomposition of a suitable precursor to produce C atoms. These methods yield what are called chemically generated carbon atoms and will be outlined below. 

We have seen in Section 4.5 a full classification of (3, 3)gen, (3,4)gen-, and (4, 3)gen-polycycles. We have also seen that, for all other (r, q), there is a continuum of (r, )-poly cycles. The purpose of this chapter is to introduce a decomposition of polycycles into elementary components in an analogous way to decompose the molecules into atoms. This method will prove to be very effective but only in the elliptic case, since, for all other cases, we will show that there is a continuum of such elementary components (see Theorem 7.2.1). The first occurrence of the method is in [DeSt02b], followed by [DDS05b] and [DDS05c]. 

To provide a less ambiguous method for measuring an olefin scavenger/unimolecular decomposition method was devised (143). When a 1 10 mixture of H C0/cis-2-C4H8 is photolyzed at wavelengths near 300 nm, the photolytic H atoms are scavenged by cis-2-butenes to form vibrationally hot sec-butyl radicals. 

The quantum yield of H atoms (4> ) is measured as the quantum yield of C3H6(<1>C3H ) i-n limit of zero pressure where the col-lisional deactivation process (eq. 32) is negligible compared to the unimolecular decomposition process (eq. 31). Therefore, under appropriate experimental conditions, <1 torr, C3H6 acts as a quantum counter of the H atoms formed. The kinetics involved in reactions 30-33 are expected to give a linear Stern-Volmer plot of 1/ c3H6 vs ptotal This butene scavenger/unimolecular decomposition method has been successfully tested. 

Rather than produce an atomic vapor by evaporation from a solid surface, an aerosol may be generated from an aqueous salt solution by an atomization procedure. The aerosol can then be evaporated so that the salt condenses into a particle. This is known as the spray-pyrolysis technique. The flame decomposition method is a modification of this technique, in which the aerosol is introduced into a high-temperature flame (1200-3000 K). The precursor is vaporized and oxidized to form metal-oxide particles. 

In spatial decomposition, or geometric methods,249 tjjg physical simulation domain is subdivided into small three-dimensional boxes, one for each processor. Each processor computes forces on and updates the positions and velocities of all atoms within its box at each time step, with atoms reassigned to new processors as they move through the physical domain. Because a processor can compute forces on its atoms knowing only the positions of atoms in nearby boxes, the communication required in the spatial decomposition is local, in contrast to the global communications required in the atom and force decomposition methods. 

Stringer and Attrep applied the Dean and Rues and the ultra-violet decomposition methods to the determination of organoarsenic compounds in waste water, using either the AgDDC colorimetric procedure described by Kopp or the arsine-atomic... 

Wickbold Decomposition—Cold-Vapor Atomic Absorption Method. 

Except for the direct analysis of arsenic in body fluids by atomic spectroscopic methods or neutron activation analysis, and cold acid solubilization of solid samples (containing mainly inorganic arsenic) followed by hydride AAS (Haswell et al.. 1988), most methods for total arsenic determination require a complete decomposition of all arsenic compounds present. This can be achieved by a number of dry and wet decomposition procedures that are amply described in the literature (see also the Chapter on Sample Treatment of this book). Thus only examples of the most frequently and successfully applied approaches for subsequent arsenic determination are given below. 

MD simulations of polymer systems, in particular, require computation of two kinds of interactions bonded forces (bond length stretching, bond angle bending, torsional) and nonbonded forces (van der Waals and Coulombic). Parallel techniques developed [31-33] include the atom-decomposition (or replicated-datd) method, the force-decomposition method, and the spatial (domain)-decomposition method. The three methods differ only in the way atom coordinates are distributed among the processors to perform the necessary computations. Although all methods scale optimally with respect to computation, their different data layouts incur different interprocessor communication costs which affect the overall performance of each method. 

The reaction path of the enzyme TIM was characterized by energy minimizations using the combined AMl/CHARMM potential.28 >285 in that study, the substrate and the catalytic side chains of His-95 and Glu-165 were treated quantum mechanically, and all other molecules in a stochastic boundary system (a 16-A sphere) were treated by the empirical CHARMM potential. The entire system consisted of 1250 protein atoms and 100 water molecules. An energy decomposition method was used to locate residues important in catalysis. In addition to the large energy contributions from conserved residues, other amino acids make smaller contributions, but their cumulative effect is significant. Interestingly, a number of residues far from the active site also have sizable effects on the enzyme s catalytic ability.284... 

A DPD simulation may involve as few as 1000 particles for siirple equilibrium simulations to several million particles for simulations of complex fluids. Hence, it is important to run DPD codes in a parallel environment. There are several parallelization strategies, such as domain decomposition and force decomposition methods. One method that is appealing because of the particle-based nature of the method is the atom decomposition algorithm in which the computations for the N particles are split among P processors. Further advantage can be taken from the fact that DPD is a short-range method, i. e. each particle does... 

Conventional magnetic metal powders, with a microscopic grain size, are usually obtained by mechanical attrition, atomization, condensation of metal vapor, electrol3dic decomposition from solution, reduction of metal compounds, centrifugal atomization, decomposition of metal hydrides, etc. Hyperfine metals prepared by chemical method which offers the following principal advantageous [35] ... 

Hydride generation readily allows the power of detection of atomic spectrometric methods to be increased for the determination of elements having volatile hydrides. Moreover, it allows matrix-free determinations of these elements. It should, however, be emphasized that the technique, irrespective of the type of hydride generation used, is prone to a number of systematic errors. Firstly, the hydrideforming elements must be present as inorganic compounds in a well-defined valence state. This may require a sample decomposition step prior to analysis. In the case of water analysis, a treatment with H2SO4-H2O2 may be effective [184]. 

A partial wave decomposition provides the frill close-coupling quantal method for treating A-B collisions, electron-atom, electron-ion or atom-molecule collisions. The method [15] is siumnarized here for the inelastic processes... 

Methods of decomposing the nonbonded force evaluation fall into two classes, spatial decomposition [15] in which atoms and their interactions are divided among processors based on their coordinates, and force-matrix decomposition [16] in which the calculation of the interaction between a pair of atoms is assigned to a processor without considering the location of either atom (Fig. 1). Spatial decomposition scales better to large numbers of... 

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