Boundary Conditions
The atoms in our system can have different degrees of freedom. For example, in case of a tube suspended over two supports, we need to fix certain number of atoms N* at the tube ends during the calculation. In this case, it is enough not to move these N* atoms in the step 4 or 8 in Figure 3, but we still calculate their interaction with other atoms in the steps 2 and 5. i.e. from mathematical point of view, we change the total number of variables in the energy function from 3N to 3N-3N*using the boundary condition, by which the values of these 3N* unknown variables are taken as known constants. Note that one can even fix atoms in only one or two directions in this way.
Moreover, one can equally adding other boundary conditions to the minimized energy function, such as adding external forces or external electric fields to the system. In these cases, the terms in potential energy function will be changed but the number of variables remains constant.
Here an example of the application of the energy minimization method in molecular modeling in nanoscience is shown in Figure 4.
Further information about the application of this method in nanoscience and Computational Codes programmed in Fortran for students is available in the following external links.
Read more about this topic: Energy Minimization
Famous quotes containing the words boundary conditions, boundary and/or conditions:
“The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
—Willard Van Orman Quine (b. 1908)
“If you meet a sectary, or a hostile partisan, never recognize the dividing lines; but meet on what common ground remains,—if only that the sun shines, and the rain rains for both; the area will widen very fast, and ere you know it the boundary mountains, on which the eye had fastened, have melted into air.”
—Ralph Waldo Emerson (1803–1882)
“The Settlement ... is an experimental effort to aid in the solution of the social and industrial problems which are engendered by the modern conditions of life in a great city. It insists that these problems are not confined to any one portion of the city. It is an attempt to relieve, at the same time, the overaccumulation at one end of society and the destitution at the other ...”
—Jane Addams (1860–1935)