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Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry
KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
2016 (English)In: PHYSICAL REVIEW E, ISSN 2470-0045, Vol. 93, no 6, 062147Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

We consider coupled diffusions in n-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multiscale analysis. As an example, we consider coupled diffusions in three-dimensional space and on the group manifold SO(3) of proper rotations, generalizing results obtained by H. Brenner [J. Colloid Interface Sci. 80, 548 (1981)]. We show in detail how the analysis can be conveniently carried out using local charts and invariance arguments. As a further example, we consider coupled diffusions in two-dimensional complex space and on the group manifold SU(2). We show that although the local operators may be the same as for SO(3), due to the global nature of the solvability conditions the resulting diffusion will differ and generally be more isotropic.

Place, publisher, year, edition, pages
2016. Vol. 93, no 6, 062147
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-190673DOI: 10.1103/PhysRevE.93.062147ISI: 000378875200005Scopus ID: 2-s2.0-84977083523OAI: oai:DiVA.org:kth-190673DiVA: diva2:953009
Note

QC 20160816

Available from: 2016-08-16 Created: 2016-08-12 Last updated: 2017-05-12Bibliographically approved
In thesis
1. Dynamics and Thermodynamics of Translational and Rotational Diffusion Processes Driven out of Equilibrium
Open this publication in new window or tab >>Dynamics and Thermodynamics of Translational and Rotational Diffusion Processes Driven out of Equilibrium
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Diffusion processes play an important role in describing systems in many fields of science, as in physics, biology, finance and social science. One of the most famous examples of the diffusion process is the Brownian motion. 

 

At mesoscopic scale, the Brownian theory describes the very irregular and animated motion of a particle suspended in a fluid. In this thesis, the dynamics and thermodynamics of diffusion processes driven out of equilibrium, at mesoscopic scale, are investigated. 

 

For dynamics, the theory of Brownian motion for a particle which is able to rotate and translate in three dimensions is presented. 

Moreover, it is presented how to treat diffusion process on n-dimensional Riemann manifolds defining the Kolmogorov forward equation on such manifold.

 

For thermodynamics, this thesis describes how to define thermodynamics quantities at mesoscopic scale using the tools of Brownian theory. The theory

of stochastic energetics and how to compute entropy production along a trajectory are presented introducing the new field of stochastic thermodynamics.

Moreover, the "anomalous entropy production" is introduced. This anomaly in the entropy production arises when diffusion processes are driven out of equilibrium by space dependent temperature field. The presence of this term expresses the fallacy of the overdamped approximation in computing thermodynamic quantities. 

 

In the first part of the thesis the translational and rotational motion of an ellipsoidal particle in a heterogeneous thermal environment, with a space-dependent temperature field, is analyzed from the point of view of stochastic thermodynamics. 

 

In the final part of the thesis, the motion of a Brownian rigid body three-dimensional space in a homogeneous thermal environment under the presence of an external force field is analyzed, using multiscale method and homogenization. 

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. 97 p.
Series
TRITA-CSC-A, ISSN 1653-5723 ; 2017:13
Keyword
Translational and Rotational Diffusion Processes, Brownian
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-207039 (URN)978-91-7729-405-4 (ISBN)
Public defence
2017-06-15, FD5, D5:3008,, 5th floor, Roslagstullsbacken 12, AlbaNova, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20170515

Available from: 2017-05-15 Created: 2017-05-12 Last updated: 2017-05-22Bibliographically approved

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