Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn

Seminar

Speaker: Robert Niven, School of Engineering and Information Technology, The University of New South Wales, Canberra, Australia

Title: Maximum Entropy Analysis of Flow Systems and Networks * Colloquium on Complex and Biological Systems

Time: Fri, May 14, 2013, 14:15am

Place: bldg 28, room 2.123

Abstract:
The concept of a 'network' - a set of nodes connected by flow paths - unites many seemingly disparate disciplines, including electrical circuit, communications, water distribution, vehicular transport, chemical reaction and ecological systems, and is now a popular representation for human financial, political and social systems. Historically, the state of a flow network has been analysed by conservation and potential difference (Kirchhoff's) laws or network mappings (e.g. Tellegen's theorem), and more recently by various optimisation methods and dynamical simulation. A relatively unexplored approach, however, is the use of Jaynes' maximum entropy (MaxEnt) method [1]. This method is founded on the generic concept of 'entropy', representing the uncertainty associated with a system. When maximised, this gives the most uncertain or most probable state of the system, and so can be used to infer its state.

Recently, the author presented a new formulation of non-equilibrium thermodynamics for the analysis of infinitesimal flow systems, based on a direct application of MaxEnt [2,3]. The analysis invokes an entropy over the set of instantaneous flow and reaction states, giving a potential function (analogous to the Planck potential) which is minimised at steady-state flow. The analysis provides a steady-state analog of the MaxEnt formulation of equilibrium thermodynamics [4]. In this seminar, the formulation of this MaxEnt framework and its implications are presented in detail. The framework is then extended to enable the MaxEnt analysis of generalised networks of any type of flows. The analysis is sufficiently general to allow the inclusion of multiple connections between nodes, sources/sinks at each node, multiple species flows, and frictional and capacity constraints.

This project has received funding from the DAAD (Germany) and Go8 (Australia).

[1] E.T. Jaynes (G.L. Bretthorst, ed.) Probability Theory: The Logic of Science, Cambridge U.P., Cambridge, 2003.
[2] R.K. Niven, Physical Review E 80(2): 021113 (2009).
[3] R.K. Niven, Philosophical Transactions B, 365: 1323-1331 (2010).
[4] H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed., John Wiley, NY, 1985.

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Past NLD Seminars (1994-2007) & (2008 ...)

Students' seminar: Theoretical Physics, PIK, Modeling & TSA Berlin-Potsdam-Colloquia: PhysGesellschaft Berlin, TU Berlin, Pro Physik, AIP, AEI, MPI-KGF, GFZ, HMI, PIK, AWI, Max Planck Institute for the History of Science, Mathematik, DPG Disputationen, & Vorschau UP

Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
Phone: (+49-331) 977-1658, Fax : (+49-331) 977-1045

Email: Udo.Schwarz AT uni-potsdam.de

DFG SFB 1294

DFG Sonderforschungsbereich 1294 Data assimilation

DFG SPP 1488

DFG Schwerpunktprogramm 1488 Planetmag


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