Biographical Memoirs Volume 63 (1994) / Chapter Skim
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14. Elliott Waters Montroll
14. Elliott Waters Montroll
Pages 364-381
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From page 365... ...
These tools were to prove the cornerstone to a signif~cant portion of Elliot's future work. Following the receipt of his doctorate, Elliott spent three years as a postdoctoral fellow working for a year at Columbia with Joseph Mayer, followecl by a year as a Sterling fellow at Yale with Lars Onsager, and finally spending a year with John Kirkwooc3 at Cornell.
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From page 366... ...
as a source of techniques that he later cleveloped and applied in other scientific fields. Following the war Elliott briefly held teaching and research positions at Brooklyn Polytechnic Institute en cl the University of Pittsburgh.
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From page 367... ...
Elliott's scientific style was extremely elegant, producing insight into often cliff~cult physical problems usually by means of very simple calculations. One of his earliest pieces of work resulted in the publication, together with Joseph Mayer, of a technique for the summation of the contribution of the class of ring diagrams in the diagrammatic analysis of the theory of imperfect gases.2 This seminal contribution proved to be the forerunner of a powerful technique subsequently adapted by many investigators to analyze a variety of problems in both equilibrium anc!
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From page 368... ...
consisted of some work first publishecl in the journal of Chemical Physics in the context of the Tsing model.4 After the mathematical icleas had been distilled from this work Elliot publishecl an elegant extension of it in the Annals of Mathematical Statistics.5 This later paper contained a general and easily applicable formalism for calculating the probability distribution of functions definec3 on a Markov chain or a continuous Markov process. The technique will be recognized as starting from the analog of a partition function but proved valuable in making .
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From page 369... ...
Blackman's work suggested that one could not neglect the lattice structure of the solid and suggested that the proper starting point for investigating thermodynamic properties of solids was the Born-von Karman moclel, which pictures! the solicl as a lattice of cliscrete atoms connected by springs that obeyed Hooke's law.
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From page 370... ...
for Elliott's combination of techniques and talents for over twenty-five years dating from his initial contribution to this area of physics. As an example of this, Elliott and Renfrew Potts tackled the problem of calculating thermoclynamic properties of lattices, particularly lattices with defects.~3 ~4 This involves computing sums of the form S = I,g(°i)
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From page 371... ...
to his coauthorship of Lattice Dynamics in the Harmonic Approximation with Alex Maradudin and myself.~5 Somewhat characteristically, the book was originally supposed to have been a review article for Advances in Solid State Physics, which Elliott put off writing until there was so much material available that it could only fit into a book. Aside from the analysis of lattice dynamic problems suggested by applications in solid state physics, Elliott, together with Peter Mazur, studied the properties of Poincare cycles for an assembly of harmonic oscillators as a simple model for irreversibility in statistical mechanics.
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From page 372... ...
While engaged in this work on lattice dynamics, Elliott also made fundamental contributions to the theory of unimolecular relaxation as a consultant to the National Bureau of Standards, in collaboration with Kurt Shuler.~7 ~8 The investigators managed to shed considerable light on an important f~elcl through the study of a simple physical model as well as to initiate lines of research in the study of chemical kinetics that have been pursued to the present time. Although the original work consisted of a study of the relaxation and dissociation of a weakly interacting system of harmonic oscillators, the formalism developed has been shown to apply to many other systems.
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From page 373... ...
A unifying thread throughout his many papers on this subject is the use of many of the same elegant mathematical tools he developed in his analyses of lattice dynamics. In one of his first papers on the subject, he tried to stucly the excluclec3-volume problem in polymer physics by analyzing properties of random walks with exclusions that only ranged over a fixecI number of steps.
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From page 374... ...
In adctition, in this early work Elliott showed that Tauberian theorems for power series and I~aplace transforms greatly simplif~ecl the calculation of many asymptotic properties of random walks. This work was taken up and extencled somewhat later in Elliott's most cited paper.23 A number of results scattered in the mathematical literature were derived in a unified manner by using Tauberian methocls, but also a significant new model of lattice random walks was suggested in this paper allowing the notion of such walks in continuous time.
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From page 375... ...
continuous-time random walk allowed for quite general distributions of interjump times. Development of the theory of the continuous-time ranclom walk was a purely theoretical one in Elliot's most frequently cited paper.23 In another paper,25 Harvey Scher and Elliott clemonstrated some of the potentialities inherent in the formalism of the continuous-time random walk by applying it to anomalous dispersion arising in the transport of charge in amorphous solicts.
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From page 376... ...
Using this greatly oversimplified moclel, which assumes that changes occur onlY in reaction to differences in relative speed, Elliott r and his collaborators were able to show that for certain ranges in the two parameters, ~ and T a sufficiently long stream of traffic wouic!
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From page 377... ...
This brief account of some of Elliott's work harcIly begins to do justice to his wicle-ranging interests, which incluclect not only the physical sciences but also all aspects of the world around him. For example, Elliott, together with Robert Herman, wrote a paper on statistical properties of the prices found in Sears Roebuck catalogs over a periocl of years.30 His interests in the history of science were legenclary, ant!
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From page 378... ...
H Weiss, Lattice Dynamics in the Harmonic Approximation (Academic Press, New York, 1963~; 2nd ed.
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From page 379... ...
W Montroll, "Markoff Chains and Excluded Volume Effect in Polymer Chains," Journal of Chemical Physics, 18~1950~:734.
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From page 380... ...
E Shuler, "Dynamics of Technological Evolution: Random Walk Model for the Research Enterprise," Proc.
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