Elliott Waters Montroll

Elliott Waters Montroll's AcademicInfluence.com Rankings

Physics

#2841

Historical Rank

physics Degrees

Elliott Waters Montroll

Mathematics

#4415

Historical Rank

Probability Theory

#50

Historical Rank

Measure Theory

#448

Historical Rank

mathematics Degrees

Download Badge

Physics
Mathematics

Why Is Elliott Waters Montroll Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Elliott Waters Montroll was an American scientist and mathematician. Education Elliott Montroll was born on May 4, 1916, in Pittsburgh, Pennsylvania, and received his elementary and high school education at the Dormont Public Schools. In 1933 he entered the University of Pittsburgh and in 1937 he received a BS degree in Chemistry. From 1937 until 1939 he was a graduate assistant in the Mathematics Department of the University of Pittsburgh, and during the first semester of the school year 1939–1940 he carried out research in the Chemistry Department of Columbia University. He was awarded a Ph.D in mathematics at the University of Pittsburgh in 1939, with a thesis Some Notes and Applications of the Characteristic Value Theory of Integral Equations in which he applied integral equations to the study of imperfect gases. A paper published jointly with Joseph E. Mayer in 1941 Statistical mechanics of imperfect gases also examined ideas developing out of his thesis.

(See a Problem?)

Elliott Waters Montroll's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Anomalous transit-time dispersion in amorphous solids (1975) (2378)
Random Walks on Lattices. II (1965) (2082)
Traffic Dynamics: Studies in Car Following (1958) (1337)
Traffic Dynamics: Analysis of Stability in Car Following (1959) (706)
Random walks on lattices (1969) (682)
Lectures in statistical mechanics (1963) (472)
Random Walks on Lattices. III. Calculation of First‐Passage Times with Application to Exciton Trapping on Photosynthetic Units (1969) (434)
On the Theory of the Ising Model of Ferromagnetism (1953) (359)
On 1/f noise and other distributions with long tails. (1982) (351)
Nonlinear Population Dynamics. (Book Reviews: On the Volterra and Other Nonlinear Models of Interacting Populations) (1971) (336)
Generalized master equations for continuous-time random walks (1973) (306)
STUDIES IN NONEQUILIBRIUM RATE PROCESSES. I. THE RELAXATION OF A SYSTEM OF HARMONIC OSCILLATORS (1957) (296)
Effect of Defects on Lattice Vibrations (1955) (294)
Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries (1973) (291)
Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails (1983) (285)
On the Williams-Watts function of dielectric relaxation. (1984) (268)
Correlations and Spontaneous Magnetization of the Two‐Dimensional Ising Model (1963) (256)
On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation (1984) (242)
VI – Diversity and Stability in Ecological Systems (1971) (229)
Theory of Depolymerization of Long Chain Molecules (1940) (205)
The Liquid state of matter : fluids, simple and complex (1982) (194)
Quantum Theory of Anharmonic Oscillators: Energy Levels of a Single and a Pair of Coupled Oscillators with Quartic Coupling (1978) (190)
CHAPTER 2 – On an Enriched Collection of Stochastic Processes* (1979) (182)
Quantum theory of anharmonic oscillators. I. Energy levels of oscillators with positive quartic anharmonicity (1975) (169)
Introduction to Quantitative Aspects of Social Phenomena (1975) (149)
Quantum Statistics of Interacting Particles; General Theory and Some Remarks on Properties of an Electron Gas (1958) (145)
Random walks with self-similar clusters. (1981) (133)
Random Walks in Multidimensional Spaces, Especially on Periodic Lattices (1956) (119)
Poincaré Cycles, Ergodicity, and Irreversibility in Assemblies of Coupled Harmonic Oscillators (1960) (115)
Nonequilibrium phenomena. II - From stochastics to hydrodynamics (1984) (114)
Statistical Mechanics of Nearest Neighbor Systems (1941) (107)
Frequency Spectrum of Crystalline Solids (1942) (96)
Quantum theory of anharmonic oscillators. II. Energy levels of oscillators with x2alpha anharmonicity (1976) (92)
Markoff Chains and Excluded Volume Effect in Polymer Chains (1950) (92)
Statistical Mechanics of Imperfect Gases (1941) (91)
Remarks on the Vibrations of Diatomic Lattices (1958) (86)
Effect of Defects on Lattice Vibrations: Interaction of Defects and an Analogy with Meson Pair Theory (1956) (85)
Size Effect in Low Temperature Heat Capacities (1950) (80)
Nonequilibrium phenomena I - The Boltzmann equation (1983) (77)
Quantum Theory on a Network. I. A Solvable Model Whose Wavefunctions Are Elementary Functions (1970) (74)
Social dynamics and the quantifying of social forces. (1978) (74)
Markoff chains, Wiener integrals, and quantum theory (1952) (73)
A Note on the Theory of Diffusion Controlled Reactions with Application to the Quenching of Fluorescence (1946) (72)
Vibration Frequency Spectra of Disordered Lattices. I. Moments of the Spectra for Disordered Linear Chains (1959) (60)
Random walks and generalized master equations with internal degrees of freedom. (1977) (60)
Fractal random walks (1982) (59)
Vibration Frequency Spectra of Disordered Lattices. II. Spectra of Disordered One-Dimensional Lattices (1959) (57)
Dynamics of a Square Lattice I. Frequency Spectrum (1947) (56)
Denaturation and renaturation of DNA. I. Equilibrium statistics of copolymeric DNA (1966) (53)
Studies in Nonequilibrium Rate Processes. III. The Vibrational Relaxation of a System of Anharmonic Oscillators (1958) (50)
Erratum: Frequency Spectrum of Crystalline Solids. II. General Theory and Applications to Simple Cubic Lattices (1943) (48)
Thermodynamic treatment of nonphysical systems: Formalism and an example (Single-lane traffic) (1986) (40)
On the Scattering of Plane Waves by Soft Obstacles. I. Spherical Obstacles (1951) (40)
Lectures in statistical physics (1971) (39)
Adsorption on heterogeneous surfaces. I. Evaluation of the energy distribution function via the Wiener and Hopf method (1976) (37)
On a convergent nonlinear perturbation theory without small denominators or secular terms (1976) (36)
Frequency Spectrum of Crystalline Solids. III. Body‐Centered Cubic Lattices (1944) (35)
Molecular Size Distributions and Depolymerization Reactions in Polydisperse Systems (1941) (34)
Free Radical Statistics (1958) (33)
A manner of characterizing the development of countries. (1972) (32)
A note on the ground state energy of an assembly of interacting electrons. (1971) (32)
On a nonlinear perturbation theory without secular terms: I. Classical coupled anharmonic oscillators (1974) (32)
Scattering of Plane Waves by Soft Obstacles. II. Scattering by Cylinders, Spheroids, and Disks (1951) (31)
On the Theory of Markoff Chains (1947) (25)
On the dynamics and evolution of some sociotechnical systems (1987) (24)
SCATTERING OF PLANE WAVES BY SOFT OBSTACLES. III. SCATTERING BY OBSTACLES WITH SPHERICAL AND CIRCULAR CYLINDRICAL SYMMETRY (1952) (24)
Field-induced trapping as a probe of dimensionality in molecular crystals. (1980) (24)
Quantum statistics of interacting particles II. Cluster integral development of transport coefficients (1959) (24)
From stochastics to hydrodynamics (1984) (22)
Statistical Mechanics of Nearest Neighbor Systems II. General Theory and Application to Two‐Dimensional Ferromagnets (1942) (21)
On coupled rate equations with quadratic nonlinearities. (1972) (20)
Quantum Theory on a Network. II. A Solvable Model Which May Have Several Bound States per Node Point (1970) (19)
Motion of Clusters on Surfaces (1977) (19)
Denaturation and renaturation of DNA. II. Possible use of synthetic periodic copolymers to establish model and parameters (1968) (19)
Statistical Mechanics of Transport and Nonequilibrium Processes (1954) (18)
A Note on Bessel Functions of Purely Imaginary Argument (1946) (17)
The Wonderful world of stochastics : a tribute to Elliott W. Montroll (1985) (17)
Lectures on nonlinear rate equations, especially those with quadratic nonlinearities (1968) (17)
Continuum models of cooperative phenomenon (1949) (16)
Age-specific, deterministic model of predator-prey populations: application to Isle royale (1973) (16)
Theory of the Vibration of Simple Cubic Lattices with Nearest Neighbor Interactions (1956) (15)
On the entropy function in sociotechnical systems. (1981) (14)
Random walks on lattices containing traps (1969) (13)
On the dynamics of the Ising model of cooperative phenomena. (1981) (13)
On nonlinear processes involving population growth and diffusion (1967) (13)
Fractal and lacunary stochastic processes (1983) (13)
Errata: Studies in Nonequilibrium Rate Processes. III. The Vibrational Relaxation of a System of Anharmonic Oscillators (1958) (13)
Dynamics of technological evolution: Random walk model for the research enterprise. (1979) (13)
The vibration spectra of disordered lattices (1959) (12)
CAR FOLLOWING AND ACCELERATION NOISE (1964) (11)
Unsteady‐State Separation Performance of Cascades. I (1952) (11)
Quantum statistics of interacting particles (1958) (11)
Models of Population Growth, Diffusion, Competition and Rearrangement (1973) (11)
Application of a novel interpolative perturbation scheme to the determination of anharmonic oscillator wavefunctions (1978) (9)
Two‐level radiative systems and perturbation theory (1975) (8)
Phase transition versus disorder: A criterion derived from a two-dimensional dynamic ferromagnetic model. (1981) (8)
Frequency Spectrum of Vibrations of a Crystal Lattice (1954) (7)
Surface properties of a network model of electrons in solids (1973) (7)
Two-component ising chain with nearest-neighbor interaction (1973) (7)
On the wedding of certain dynamical processes in disordered complex materials to the theory of stable (Lévy) distribution functions (1983) (6)
ON SOME MATHEMATICAL MODELS OF SOCIAL PHENOMENA (1978) (6)
Scattering of waves by irregularities in periodic discrete lattice spaces. I. Reduction of problem to quadratures on a discrete model of the Schrödinger equation (1975) (6)
Fractal stochastic processes: Clusters and intermittancies (1983) (6)
On the Quantum Analogue of the Levy Distribution (1974) (5)
Averages over normal modes of coupled oscillators with application to theory of specific heats (1947) (5)
LECTURES IN STATISTICAL MECHANICS; WITH AN APPENDIX ON QUANTUM STATISTICS OF INTERACTING PARTICLES (1961) (4)
Kinetics of adsorption on stepped surfaces and the determination of surface diffusion constants (1983) (3)
An analytical approach to the ising problem (1951) (2)
On the mapping of chains of first order chemical reactions on random walks. (1977) (2)
Phenomenological Theory of Emulsion Polymerization (1945) (2)
Topics in the theory of the solid state (1952) (1)
Mathematical Properties of Several Population Dynamics Models@@@On the Volterra and Other Models of Interacting Populations (1972) (1)
Some Statistical Observations from a 75 Year Run of Sears Roebuck Catalogues (1977) (1)
Some remarks on turbulence (1969) (1)
Propagation of waves in discrete media. harmonic, anharmonic, and defective (1974) (1)
Scattering of waves by irregularities in periodic discrete lattice spaces. 2. Calculations. Interim report (1983) (1)
Analysis of Assemblies with Large Defect Concentrations with Special Application to Theory of Denaturation of Copolymeric DNA (1968) (1)
II – Volterra Model (1971) (1)
3. On the Dynamics of Technological Evolutions: Phase Transitions (1982) (0)
VIII – Population Growth as Birth and Death Processes (1971) (0)
V – Time-Dependent Fluctuations in Population (1971) (0)
Topics in statistical mechanics of interacting particles (1951) (0)
Network Model of Electronic States of Thin Films, Solid Interfaces, and Planar Defects (1975) (0)
Random Walks and Generalized Master Equations with Internal Degrees of Freedom (Stochastic Processes/Transport Phenomena), (1976) (0)
III – A Primitive Statistical Model of Population Growth (1971) (0)
Network Models of Crystals (1974) (0)
Erratum: "Some Historical Remarks on the Catalytic Process and on Stochastic Models of Chemical Kinetics" [AIP Conference Proceedings 61, 1 (1980)] (1980) (0)
Joseph E. Mayer (1984) (0)
VII – Volterra Equations with Random Rate Constants (1971) (0)
D1 – INFLUENCE OF DEFECTS ON LATTICE VIBRATIONS (1965) (0)
Random walks and generalized master equations with internal degrees (0)
Randomwalksandgeneralized master equations withinternal degrees offreedom (1977) (0)
Dynamicsoftechnological evolution: Randomwalkmodelforthe research enterprise (dimensionless constants/scaling) (1979) (0)
On the cluster integral development of pair distribution functions (1958) (0)
III. The Science Curriculum (1967) (0)
On Coupled Rate Equations with Quadratic Nonlinearities ( population growth and competition ) (0)
IX – Time Lags in Population (1971) (0)
Introduction to Quantitative Aspects of Social Phenomena.@@@Measurement in Social Sciences. Theories and Strategies. (1975) (0)
IV – Equilibrium Theory (1971) (0)
X – Generalization of Volterra Equations (1971) (0)
Some Historical Remarks on the Catalytic Process and on Stochastic Models of Chemical Kinetics (1980) (0)
Effect of Defects on the Vibration of Crystal Lattices (1963) (0)
XI – Experimental Verification of Volterra's Model (1971) (0)
Theory of nonlinear processes (1975) (0)

This paper list is powered by the following services:

Other Resources About Elliott Waters Montroll

en.wikipedia.org

What Schools Are Affiliated With Elliott Waters Montroll?

Elliott Waters Montroll is affiliated with the following schools:

Elliott Waters Montroll's Academic­Influence.com Rankings

Why Is Elliott Waters Montroll Influential?

Elliott Waters Montroll's Published Works

Published Works

Other Resources About Elliott Waters Montroll

What Schools Are Affiliated With Elliott Waters Montroll?

Image Attributions

Elliott Waters Montroll's AcademicInfluence.com Rankings