Spatial partitioning

Figure 1. Global Environment Cycles and Spatial Partitions.

Figure 6 Illustration of the spatial partitioning in the ParTAD method, (a) Lattice and sublattice (SL) partitioning in the SL method on which ParTAD is built. Patches are indicated by numbers, subpatches by letters, (b) Setup for TAD dynamics on one subpatch. Reprinted, with permission, from ref. 34. Copyright 2007 by the American Physical Society, http // link.aps.org/doi/10.1103/PhysRevB.71.125432...

Equation (4.15) is important, it offers an atom-by-atom partitioning of the molecular binding energy. The nice thing about (4.15) is that it does not imply any spatial partitioning of the molecule. Equation (4.13) is instrumental in the theory of bond energies. AE is convenient for comparisons with experimental results. 

R. F. W. Bader and P. M. Beddall, /. Chem. Phys., 56, 3320 (1972). Virial Field Relationship for Molecular Charge Distributions and the Spatial Partitioning of Molecular Properties. 

Leroux X., Bariac T., and Mariotti A. (1995) Spatial partitioning of the soil-water resource between grass and shrub components in a West-African humid Savanna. Oecologia 104(2), 147-155. 

K. E. Laidig,/. Phys. Ghent. 97, 12760 (1993). General Expression for the Spatial Partitioning of the Moments and Multipole Moments of Molecular Charge Distributions. 

Equation (6.52) expresses the simple but important result that each particle s share of the potential energy is given by the virial of the force exerted on it by the other. The virial operator r F,( is like a projection operator in that it projects from V, that part of the potential energy operator belonging to particle k. In this elementary case, each share of the potential energy is dependent upon the choice of origin used in the definition of the vectors Tj and Fj. This does not turn out to be the case when this idea is used to spatially partition the potential energy of a many-electron system. If one denotes by Yjc complete set of virial operators in eqn (6.50), one has... 

Temporal partition is assurance that two components do not interfere with each other s allocated timeslots. Spatial partition is assurance that two components do not interfere with each other s resources (i.e., memory, processing, etc.). 

In the NPP investigated, five buildings of the entire plant (cf. Table 1) were found to be representative to be analyzed within the Fire PSA (see Rowekamp et al. 2006 and Rowekamp et al. 2007). The spatial partitioning was principally based on the plant specific identification system of the entire NPP exceptional cases there were, e.g., the sub-division of the huge... 

Table 1. Exemplary spatial partitioning of different buildings of a German BWR built to earlier standards.

I Quantum Coupling The self-consistent determination of the interaction energy at a QM level is the hallmark of the quantum coupling approach. The spatial partition of the entire system is shown in Figure 8.2. In specific, the total energy can be expressed as ... 

Actually, Harbury s approach exploits DNA templating in a different way. Strictly speaking, the library is not synthesized by templated reactions. DNA templates are not used to bring reactants in proximity to boost the effective molarity instead DNA templating is the mean to spatially partition the templates into sub-pools. The advantage of this approach is mostly that chemical building blocks can be directly used without the need to couple to a DNA strand and no cleavable linkers are needed second, the chemical reactions take place on solid support (DEAE Sepharose column), therefore potentially more chemical reactions can be applied to create libraries with more diverse structures. However, so far there has been no report of library synthesis other than peptidic structures. 

Bader RFW, Beddall PM (1972) Virial field relationship for molecular charge distributions and spatial partitioning of molecular properties. J Chem Phys 56 3320-3329... 

IMA is based upon two fundamental principles spatial partitioning and temporal partitioning. This partitioning ensures that the individual applications do not interfere or affect each other, either inadvertently or deliberately. The enforcement of these principles is achieved through the specific implementation of the IMA software architecture (timeslot scheduling in the case of ARINC 653) and MMU-enforced separation of partitions (for details of an example implementation of an ARINC 653 architecture, see (ARINC 2003)). 

ToF-SIMS is also useful in revealing surface degradation products [827] and in morphological studies of multiphase systems to determine the distribution (spatial partitioning) of additives within polymer blends. ToF-SIMS is equally capable of simultaneously providing quantitative trace metal element, monomer (ENB content, C2/C3 ratio) and oxidation analysis from microscopic polymer domains, such as full compositional analysis of EPDM gels [828]. 

A convenient formulation of hybrid potentials for spatially partitioned sys-... 

Time and space partitioning is a way to ease the composable development of software applications, as well as to improve the overall safety of the system. Spatial partitioning ensures that a task in one partition is unable to change private data of another task in another partition. Temporal partitioning, on the other hand, guarantees that the timing characteristics of tasks, such as their worst-case execution times, are not affected by the execution of other tasks in other partitions. Consequently, time and space partitioning enforces two important features ... 

Furthermore, each computing resource (implemented according to the ARINC 653 API) must provide an efficient temporal and spatial partitioning so that it can host applications with different levels of criticality. 

---