"... In PAGE 1: ... Notation Key This section provides convenient lists of the notational conventions used throughout this chapter. Table1 lists the notation used for various physical and geometrical quantities, Table 2 details the usage of Greek symbols, and Table 3 summarizes the conventions for superscripts and subscripts. 1 Introduction In the following, we shall present the formulation for tracing particles from surfaces to surfaces inside an enclosure.... In PAGE 3: ...3 Table1 : Physical and Geometrical Quantities (cont.) R = random number, from a uniform distribution between 0 and 1 R = speedup ratio of scalar to vector execution times RD = di usely re ected photon RS = specularly re ected photon r = radius (m) S = arc length (m) S1, S2 = square of distance between the rst or second end point of a surface and the intersection point, X(1or2) ? XI 2 (m2) S12 = square of distance between end points of a surface, jX1 ? X2j2 (m2) S = scalar execution rate (MFLOP apos;s) s = path length (m) T = absolute temperature ( K) V = vector execution rate (MFLOP apos;s) X = vector point, fX; Y; Zg (m) XE = point of emission (m) XI = point of intersection (m) X; Y; Z = point in global Cartesian coordinates (m) Table 2: Greek Symbols = absorbance XL; YL = di erence in the X or Y direction between the end points of surface L (m) quot; = emittance = cone angle = re ectance = Stefan Boltzmann constant (W m?2 K?4) = azimuthal angle !... ..."

"... In PAGE 7: ... Statistical comparisons of the results were made using ANOVA and relationships between soil parameters were evaluated by correlation analysis. RESULTS AND DISCUSSION Physical properties The textural class ( Table2 ) determined using particle size distribution, varied from silty clay to silty clay loam at Dhamrai and silty clay to clay at Daulatpur. In Bogra, both Gabtali and Shibganj had a similar silty clay texture.... In PAGE 7: ... This suggests that fields within each area, except Daulatpur, were located on the same land type. The ecological fields at Daulatpur ( Table2 ) tended to have higher clay contents than the conventional fields. Probably because the ecological farmed fields were situated in the centre of a basin.... In PAGE 7: ... Probably because the ecological farmed fields were situated in the centre of a basin. The soils were alluvial containing higher clay fractions ( Table2 ) following the accumulation of soil particles removed from higher elevations and their deposition in low lying areas. Bulk density was significantly lower (P lt;0.... ..."

"... In PAGE 7: ... Our robots will be unusual in that they are capable of changing shape over time if the dynamics demand this of them. Before we embark on a discussion of object-oriented physical design for robots within spaces, we present Table1 to illustrate how, through mappings from one discipline to another, di erent areas t into this general scenario scheme. 4 Model Engineering Our basis for physical modeling begins with object-oriented design concepts as described in textbooks [5, 45] as well as object-oriented modeling as applied speci cally for simulation of discrete event systems [57].... ..."

"... In PAGE 7: ... Our robots will be unusual in that they are capable of changing shape over time if the dynamics demand this of them. Before we embark on a discussion of object-oriented physical design for robots within spaces, we present Table1 to illustrate how, through mappings from one discipline to another, di erent areas t into this general scenario scheme. 4 Model Engineering Our basis for physical modeling begins with object-oriented design concepts as described in textbooks [5, 45] as well as object-oriented modeling as applied speci cally for simulation of discrete event systems [57].... ..."

"... In PAGE 18: ... Since now the Poincar e invariant S has been enrolled as a canonical variable, the adaptation to the Poincar e group is complete. Table4 summarizes the typical form of the Poincar e realization, di- splaying the same distinctions made before between gauge and physical variables as well as between center of mass and relative variables. Note that the vectors ~ S; ~ R; ~ S ^ ~ R de ne a right-handed orthogonal reference frame (see Figure 1) and satisfy the following peculiar algebraic relations: Si ; Sj = ijkSk ; Ri ; Rj = 0 ; Si ; Rj = ijkRk ; n(~ S ^ ~ R)i ; Sjo = ijk(~ S ^ ~ R)k ; n(~ S ^ ~ R)i ; (~ S ^ ~ R)jo = ? R2 ijkSk n(~ S ^ ~ R)i ; Rjo = RiRj ? R2 ij : (47) 6 The system of three particles as a canonical realization of the Euclidean group E(3) The simplest model in which both the constraint and the Poincar e group structu- res are substantially exploited, and the Euclidean second-rank group plays an e ective instrumental role, is provided by a system of three particles.... ..."

"... In PAGE 19: ....1. Optical Properties of Each Aerosol Species [58] Aerosol optical properties (extinction cross section, single-scattering albedo, and asymmetry parameter) are cal- culated by Mie theory based on wavelength-dependent refractive indices and aerosol size distributions. The effective dry radius and density, as well as optical properties of dry particles at l = 550 nm, are listed in Table6 for each aerosol class. The particle size distributions for black carbon, organic carbon, and sulfate aerosol that is not associated with dust and sea salt particles are assumed to obey the standard gamma distribution, with an area-weighted effective variance of 0.... In PAGE 19: ... [1991] are used for OC. [59] Sea salt and mineral dust aerosol optical properties are calculated over each size bin, based on the parameters listed in Table6 . Then the overall extinction cross section s, single- scattering albedo w, and asymmetry parameter g of sea salt (or dust) are calculated by assuming sea salt (or dust) particles from different size bins are externally mixed.... In PAGE 20: ...those of sulfate aerosol (see Table6 ), based on the urban measurements of Lestari et al. [2003].... In PAGE 20: ... Over the oceans, sulfate, nitrate, OC, BC, sea salt, and aerosol water are assumed to be internally mixed within each sea salt size bin. Sulfate, OC, and BC are distributed into each sea salt bin according to their specified size distributions (see Table6 ). Predicted nitrate associated with sea salt particles is distributed into each size bin as described in section 6.... In PAGE 26: ... BC has high positive forcing at TOA and strong negative forcing at the surface because of its absorbing character and large mass extinction efficiency of 12.5 m2 gC01 ( Table6 ). TOA BC forcing exceeds +2 W mC02 over areas with high BC concentrations from fossil consumption and biomass burning, and over areas with high surface albedo.... ..."

"... In PAGE 14: ...Table1 ) around the Sun. We integrated a sample particle, having radius of 1 mm and the same density of the central bodies, for 7000 days, i.... ..."

"... In PAGE 24: ... 11 quot;) , including both physics modes and background processes, nominal means lost-particle interactions were overlayed with a probability scale factor of one, while 10 means lost-particle interactions were overlayed with a probability scale factor of 10. Table8 shows e ciencies and rates for these scenarios. The open trigger rates exceed the 2000Hz limit by an order of magnitude.... ..."

"... In PAGE 24: ... 11 quot;) , including both physics modes and background processes, nominal means lost-particle interactions were overlayed with a probability scale factor of one, while 10 means lost-particle interactions were overlayed with a probability scale factor of 10. Table8 shows e ciencies and rates for these scenarios. The open trigger rates exceed the 2000Hz limit by an order of magnitude.... ..."

"... In PAGE 24: ... 11 quot;) , including both physics modes and background processes, nominal means lost-particle interactions were overlayed with a probability scale factor of one, while 10 means lost-particle interactions were overlayed with a probability scale factor of 10. Table8 shows e ciencies and rates for these scenarios. The open trigger rates exceed the 2000Hz limit by an order of magnitude.... ..."