Boundary code

Gra03] J. R Graver, The (m,k)-patch boundary code problem, MATCH 48 (2003) 189-196. 

Balaban, following the method first used by Gordon, used the three possible orientations of a planar honeycomb (hexagonal) lattice with some of the bonds in vertical position to define (1) the boundary code of polycyclic aromatic hydrocarbons... 

Over the years several numerical codes have been developed for benzenoids, such as the boundary code (Trinajstic et al. 1983 von Knop et al. 1983), the DAST code (Miiller et al. 1990), but the binary boundary code (Trinajstic et al. 1983 Herndon and Bruce 1987 Klein et al. 1988) appears to be the simplest to use. 

Among the five possible binary botmdary codes of the naphthalene-bihex, the maximum code is selected 1111011110. The binary boundary code is unique since two non-isomorphic polyhexes cannot produce the same code. In Fig. 9.8, we give the binary botmdary code for the given orientation of the dibenzo[I>,g] phenanthrene polyhex. A mirror-image orientation of the dibenzo[f>,g]phenan-threne polyhex produces the maximum binary boundary code for this structure 1111011011010111101000. 

A way to recover a given polyhex from its binary boundary code is shown in Fig. 9.9. 

Fig. 9.7 A bihex representing the carbon skeleton of naphthalene and its five possible binary boundary codes...

Fig. 9.8 The binary boundary code for a given orientation of the dibenzo[i>, glphenanthrene polyhex...

Fig. 9.9 Recovery of dibenzo[e,m]peropyrene from the corresponding hinary houndary code (a) Binary boundary code 11110101100011110011101100110 0, (b) Construction of the polyhex houndary from the given hinary houndary code, (c) Construction of the polyhex hy filling in the inner space restricted hy the boundary, (d) Recovered polyhex...

Reactor Coolant System Pressure Boundary Code Requirements... 

TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

Note MM-i- is derived from the public domain code developed by Dr. Norm an Allinger, referred to as M.M2( 1977), and distributed by the Quantum Chemistry Program Exchange (QCPE). The code for MM-t is not derived from Dr. Allin ger s present version of code, which IS trademarked MM2 . Specifically. QCMPOlO was used as a starting point Ibr HyperChem MM-t code. The code was extensively modified and extended over several years to include molecular dynamics, switching functuins for cubic stretch terms, periodic boundary conditions, superimposed restraints, a default (additional) parameter scheme, and so on. 

In general, the imposition of boundary eonditions is a part of the assembly process. A simple procedure for this is to assign a eode of say 0 for an unknown degree of freedom and 1 to those that are specified as the boundary conditions. Rows and columns corresponding to the degrees of freedom marked by code 1 are eliminated from the assembled set and the other rows that contain them are modified via transfer of the product of the specified value by its corresponding coefficient to the right-hand side. The system of equations obtained after this operation is determinate and its solution yields the required results. 

Lagranglan codes are characterized by moving the mesh with the material motion, u = y, in (9.1)-(9.4), [24]. The convection terms drop out of (9.1)-(9.4) simplifying all the equations. The convection terms are the first terms on the right-hand side of the conservation equations that give rise to fluxes between the elements. Equations (9.1)-(9.2) are satisfied automatically, since the computational mesh moves with the material and, hence, no volume or mass flux occurs across element boundaries. Momentum and energy still flow through the mesh and, therefore, (9.3)-(9.4) must be solved. 

Other cell variables such as sound speed and heat capacities can be calculated using similar techniques. Some codes allow a variety of multimaterial element thermodynamic treatments. For example, CTH allows all materials in an element to have the same or different pressures or temperatures [44], Material interfaces in multimaterial elements do not coincide with element boundaries, as shown in Fig. 9.14 [45]-[49]. The interfaces must be constructed using pattern matching or some other technique. 

For the determination of downdraft risk in the winter case, three-dimensional and transient CFD computauons were performed using the TASC flow code. Boundary conditions were defined from the results of the thermal modeling. 

Determination of high-resolution, accurate flow data providing a basis for boundary conditions used in CFD, for the verification of CFD results, and for improvement in CFD codes... 

The highly resolved velocity profile can be mapped in the vicinity of solid boundaries such as the walls of a room and in the entire enclosure, providing relevant data for CFD boundary conditions. These data form a basis for verification of CFD results and for improvement of CFD codes. 

It is not an easy task to develop computer codes which correctly treat the advancement of a folding interface as a boundary condition to a diffusion or flow field. In addition, the interface between a solid and a liquid, for example, is usually is not absolutely sharp on an atomic scale, but varies over a few lattice constants [32,33]. In these cases, it is sometimes convenient to treat the interface as having a finite non-zero thickness. An order parameter is then introduced, which for example varies from the value zero on one side of the interface to the value one on the other, representing a smooth transition from liquid to solid across the interface. This is called the phase-field... 

Bakke, J. R., and B. H. Hjertager. 1986a. Quasi-laminar/turbulent combustion modeling, real cloud generation and boundary conditions in the FLACS-ICE code. CMI No. 865402-2. Chr. Michelsen Institute, 1986. Also in Bakke s Ph.D. thesis Numerical simulation of gas explosions in two-dimensional geometries. University of Bergen, Bergen, 1986. 

The Car-Parrinello simulations were performed using the MOTECC-90 computer code [13]. All considered systems consist of 64 atoms in a cubic unit cell with a length of 23.4 a.u. and periodic boundary conditions. The plane-wave cut-off was chosen to be 6 Ryd. The atomic cores were described by the pseudopotentials of Bachelet et al. [14]. 

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