Abstract/Details

Controlling molecular-scale motion: Exact predictions for driven stochastic systems


2010 2010

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Abstract (summary)

Despite inherent randomness and thermal fluctuations, controllable molecular devices or molecular machines are currently being synthesized around the world. Many of these molecular complexes are non-autonomous in that they are manipulated by external stimuli. As these devices become more sophisticated, the need for a theoretical framework to describe them becomes more important. Many non-autonomous molecular machines are modeled as stochastic pumps: stochastic systems that are driven by time-dependent perturbations. A number of exact theoretical predictions have been made recently describing how stochastic pumps respond to arbitrary driving. This work investigates one such prediction, the current decomposition formula, and its consequences.

The current decomposition formula is a theoretical formula that describes how stochastic systems respond to non-adiabatic time-dependent perturbations. This formula is derived for discrete stochastic pumps modeled as continuous-time Markov chains, as well as continuous stochastic pumps described as one-dimensional diffusions.

In addition, a number of interesting consequences following from the current decomposition formula are reported. For stochastic pumps driven adiabatically (slowly), their response can be given a purely geometric interpretation. The geometric nature of adiabatic pumping is then exploited to develop a method for controlling non-autonomous molecular machines. As a second consequence of the current decomposition formula, a no-pumping theorem is proved which provides conditions for which stochastic pumps with detailed balance exhibit no net directed motion in response to non-adiabatic cyclic driving. This no-pumping theorem provides an explanation of experimental observations made on 2- and 3-catenanes.

Indexing (details)


Subject
Physics;
Theoretical physics
Classification
0605: Physics
0753: Theoretical physics
Identifier / keyword
Pure sciences; Brownian motion; Geometric phases; Molecular machines; Stochastic systems
Title
Controlling molecular-scale motion: Exact predictions for driven stochastic systems
Author
Horowitz, Jordan Michael Abel
Number of pages
102
Publication year
2010
Degree date
2010
School code
0117
Source
DAI-B 71/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781124072548
Advisor
Jarzynski, Christopher
Committee member
Alexander, Millard; Dorfman, J. Robert; Fisher, Michael E.; Hu, Bei-Lok
University/institution
University of Maryland, College Park
Department
Physics
University location
United States -- Maryland
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3409592
ProQuest document ID
722544356
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/722544356
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