Hartmann, C. and Yanao, Tomohiro (2013) The falling cat problem and shape effects in small molecules in a random environment: a case study. Molecular Physics, 111 (2223). pp. 35343545. ISSN 00268976

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Abstract
We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo nontrivial confor mational transitions we consider a planar fouratomic molecule, with underdamped dynamics of Langevintype. In this simplified setting, we can extend the available gauge theory of semi flexible molecules to the stochastic setting which allows us to analyze and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperaturedependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equa tion, i.e. friction coefficient, atomic masses, temperature, and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g. to the overdamped limit or optimal control.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics Other Institutes > Matheon > A  Life Sciences Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  1298 
Deposited By:  Carsten Hartmann 
Deposited On:  01 Jul 2013 13:05 
Last Modified:  03 Mar 2017 14:41 
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