{'fraction_non_alphanumeric': 0.0242603550295858, 'fraction_numerical': 0.0029585798816568047, 'mean_word_length': 5.149090909090909, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Vacuum System Design using Symbolic Numeric Processors

The widespread availability of symbolic numeric processor environments for the personal computer (such as MathCAD [1], Maple [2], Mathematica [3], Macsyma [4], etc.) now provides a convenient framework to support the design of large and complicated vacuum systems. The mathematical model introduced below provides a framework for using symbolic processors to design both simple and complex vacuum systems. The widespread availability of software for the personal computer (Maple, MathCAD, Mathematica, etc.) provides a convenient means of analyzing the design of vacuum systems for large and small facilities. The overall vacuum system is easily expressed as a matrix equation that includes surface outgassing and vacuum pumping rates and can include such effects as opening and closing of valves. Once the matrix equation has been defined, it is a simple matter to derive pressure solutions as a function of the different variables and to determine the effects of opening or closing valves. Thus one can derive the vacuum pressure in each section of the entire system as a function of these variables and quickly optimize the overall vacuum system design. 2. MATHEMATICAL FRAMEWORK All vacuum systems can be modeled as a series of chambers or segments comprised of outgassing surfaces with mutual conductances between adjacent segments. In each segment, n, the mass flow of gas, Q n(Torrliters/sec) is equal to the outgassing from the surfaces of that segment, R n, plus the gas conducted in from the adjacent segments minus the gas conducted out into the adjacent segments and minus any vacuum pumping, V, connected to that segment: