tailieunhanh - The MEMS Handbook (1st Ed) - M. Gad el Hak Part 2

Tham khảo tài liệu 'the mems handbook (1st ed) - m. gad el hak part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Molecular-Based Models In the continuum models discussed thus far the macroscopic fluid properties are the dependent variables while the independent variables are the three spatial coordinates and time. The molecular models recognize the fluid as a myriad of discrete particles molecules atoms ions and electrons. The goal here is to determine the position velocity and state of all particles at all times. The molecular approach is either deterministic or probabilistic refer to Figure . Provided that there is a sufficient number of microscopic particles within the smallest significant volume of a flow the macroscopic properties at any location in the flow can then be computed from the discrete-particle information by a suitable averaging or weighted averaging process. This section discusses molecular-based models and their relation to the continuum models previously considered. The most fundamental of the molecular models is a deterministic one. The motion of the molecules is governed by the laws of classical mechanics although at the expense of greatly complicating the problem the laws of quantum mechanics can also be considered in special circumstances. The modern molecular dynamics MD computer simulations have been pioneered by Alder and Wainwright 1957 1958 1970 and reviewed by Ciccotti and Hoover 1986 Allen and Tildesley 1987 Haile 1993 and Koplik and Banavar 1995 . The simulation begins with a set of N molecules in a region of space each assigned a random velocity corresponding to a Boltzmann distribution at the temperature of interest. The interaction between the particles is prescribed typically in the form of a two-body potential energy and the time evolution of the molecular positions is determined by integrating Newton s equations of motion. Because MD is based on the most basic set of equations it is valid in principle for any flow extent and any range of parameters. The method is straightforward in principle but has two hurdles choosing a proper .