Solid modeling primitives

Fig. 9. Eqiulibrium stress-strain behavior of entangled networks in uniaxial extensicm and compression. The solid lines (p = 0.5, 0.75,1.00) were calculated for the primitive segment model (. 62 and II-5). The short-dash line is the Doi-Edwards model (Eq. 40 and 11-11). The long-dash line is the affine Gaussian network model (Eq. 41 and n-12) adjusted to have the same initial modulus...

Figure flf. Potential of mean force between the Na" " and Cl ions in ambient water at infinite dilution. Results following from the 3D-RISM/HNC and 3D-RISM/KH approach (solid and short-dashed hnes, respectively), and from the ion-ion radial distribution function obtained by the site-site DRISM/HNC theory (dash dotted Une). Molecular simulation data [115] (open squares). Prediction of the primitive continuum model of solvent (long dashed line). 

Solid modeler-based CWE calculation methods can overcome the limitations introduced by discrete methods since the cutter and the work-piece can be modeled using geometric primitives or complex geometric shapes. 

A solid primitive is prepared for combination with other solid primitives or a more complex solid model under construction. It is created in its final position or repositioned after creation somewhere in the model space. Values of its dimensions are set and the solid primitive is ready for one of the element combination operations. The shapes of primitives are predefined for the modeling system or defined by engineers at application of the modeling system. Users apply one of the available solid generation rules starting from contours, sections, and curves as input entities. Primitives with predefined shape are called canonical. They are the cuboid, wedge, cylinder, cone, sphere, and torus (Figure 4-11). Inclusion of shapes other than canonical as predefined shapes is rare because application oriented shape definitions are better to define as form features. 

The shape of a mechanical part can be divided into a well-defined set of solid primitives. A purposeful sequence of combination operations with the primitives can be applied to form the shape of the part. Constructive solid geometry (CSG) is based on this recognition. CSG was the traditional way of solid modeling. The construction method is also applied in advanced part modeling. While the traditional method applied CSG data structure, present modeling methods generate boundary representation. This difference often causes misunderstanding around CSG. 

For round 1 evaluations, we focus on auto surfacing and the software stability. In roimd 2, we focus on parametric solid modeling, we look for primitive feature recognition (such as cylinder, cone, etc.), parametric modeling, and model exporting to CAD packages. 

Solid modeling capabilities in the context of reverse engineering for the four selected software are listed in Table 5, based on the first glance. Among these four. Geomagic, Rapidform, and SolidWorks are able to recognize basic primitives, such as plane, cylinder. 

An explicit rigorous solution for an ion at a solution—solid interface does not exist at present. Explicit solutions for the electrostatic potential experienced by an ion at a solution—solid interface can be obtained only for model interfaces. For the following treatment, the primitive interfacial model [31 ] will be used. The primitive interface is composed of three parts (1) a semi-infinite continuum dielectric solid, (2) a semi-infinite solution containing solute molecules in a continuum dielectric solvent, and (3) a Stem layer of ions lying between the two semi-infinite phases, as shown in Fig. 2. 

The semi-infinite continuum solid has a dielectric strength, 8g. The semi-in-finite solution is identical to that used in the Debye—Hiickel model, consisting of a continuum solvent with dielectric strength, e, and solute ions, Y y, with ionic diameter, ay- Hence, the primitive interfacial model can be considered to be at about the same level of electrostatic sophistication as the Debye—Hiickel model for electrolyte solutions. 

Flowever, in real systems, activity coefficients may play a small role in nonionic surface complexation reactions. In order for the cancellation to occur in Eqs (186)—(188) requires that the activity coefficient of the surface site and the nonionic complexed surface are the same. For the primitive interfacial model they are the same so the activity coefficient quotient reduces to unity. For nonionic—surface site complexes in real solid—solution interfacial systems the activity coefficients... 

A CONSTRUCT is an entity that has a scope. The data structure of a construct represents a three-dimensional geometrical shape. Certain domains of this shape may have material properties associated with them. A construct is not an elementary solid model but defines a function which -when evaluated- will produce a solid. The function operators are BOOLEAN, the operands are of type BOOL OPERAND. The elementary operands which are called PRIMITIVE entities exist in the scope of the CONSTRUCT only. However, POLYHEDRON models and B REP entities may exist in the construct scope and may be used as operands to boolean operations (if the CAD system provides this capability). The attribute result is an instance of the BOOLEAN which represents the root of the boolean tree or simply of a PRIMITIVE, B REP, POLYHEDRON, or another CONSTRUCT. 

Thanks to their speed and relatively low computational cost, M D and MC simulations can be used for studying the physical properties of large systems. This is extremely useful in heterogeneous catalysis, e.g., for modeling the structure and the properties of the bulk and the surface of a solid catalyst, or the properties of the bulk and interface of liquid/liquid biphasic systems. However, since the number of particles modeled is still very small compared to real materials, the models are susceptible to wall effects. One neat trick for avoiding this problem is to apply periodic boundary conditions The volume containing the model is treated as the primitive cell of an... 

Abstract In this chapter, we review the general properties of protoplanetary disks and how the gaseous and solid components contained within evolve. We focus on the models that are currently used to describe them while highlighting the successes that these models have had in explaining the properties of disks and primitive materials in our Solar System. We close with a discussion of the open issues that must be addressed by future research in order to develop fully our understanding of protoplanetary disk structures. 

We have given this primitive modelling of the density to stress the importance of finding localized descriptions of the electron density in a molecule (or solid, especially amorphous materials, e.g. Si, where the periodicity that is so helpful in a crystalline solid no longer is present). 

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