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Title: Statistical mechanics of self-driven Carnot cycles

Abstract

The spontaneous generation and finite-amplitude saturation of sound, in a traveling-wave thermoacoustic engine, are derived as properties of a second-order phase transition. It has previously been argued that this dynamical phase transition, called {open_quotes}onset,{close_quotes} has an equivalent equilibrium representation, but the saturation mechanism and scaling were not computed. In this work, the sound modes implementing the engine cycle are coarse-grained and statistically averaged, in a partition function derived from microscopic dynamics on criteria of scale invariance. Self-amplification performed by the engine cycle is introduced through higher-order modal interactions. Stationary points and fluctuations of the resulting phenomenological Lagrangian are analyzed and related to background dynamical currents. The scaling of the stable sound amplitude near the critical point is derived and shown to arise universally from the interaction of finite-temperature disorder, with the order induced by self-amplification. {copyright} {ital 1999} {ital The American Physical Society}

Authors:
 [1]
  1. Los Alamos National Laboratory, Earth and Environmental Sciences Division, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
686870
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 60; Journal Issue: 4; Other Information: PBD: Oct 1999
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; CARNOT CYCLE; STATISTICAL MECHANICS; PHASE TRANSFORMATIONS; PARTITION FUNCTIONS; SCALE INVARIANCE

Citation Formats

Smith, E. Statistical mechanics of self-driven Carnot cycles. United States: N. p., 1999. Web. doi:10.1103/PhysRevE.60.3633.
Smith, E. Statistical mechanics of self-driven Carnot cycles. United States. doi:10.1103/PhysRevE.60.3633.
Smith, E. 1999. "Statistical mechanics of self-driven Carnot cycles". United States. doi:10.1103/PhysRevE.60.3633.
@article{osti_686870,
title = {Statistical mechanics of self-driven Carnot cycles},
author = {Smith, E.},
abstractNote = {The spontaneous generation and finite-amplitude saturation of sound, in a traveling-wave thermoacoustic engine, are derived as properties of a second-order phase transition. It has previously been argued that this dynamical phase transition, called {open_quotes}onset,{close_quotes} has an equivalent equilibrium representation, but the saturation mechanism and scaling were not computed. In this work, the sound modes implementing the engine cycle are coarse-grained and statistically averaged, in a partition function derived from microscopic dynamics on criteria of scale invariance. Self-amplification performed by the engine cycle is introduced through higher-order modal interactions. Stationary points and fluctuations of the resulting phenomenological Lagrangian are analyzed and related to background dynamical currents. The scaling of the stable sound amplitude near the critical point is derived and shown to arise universally from the interaction of finite-temperature disorder, with the order induced by self-amplification. {copyright} {ital 1999} {ital The American Physical Society}},
doi = {10.1103/PhysRevE.60.3633},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 4,
volume = 60,
place = {United States},
year = 1999,
month =
}