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- Laurent Cordier, Bernd R. Noack, Gilles Tissot, Guillaume Lehnasch, Joël Delville, Maciej Balajewicz +2 others
- 2013

A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To… (More)

- R. K. Niven
- 2009

We examine the combinatorial or probabilistic definition (" Boltzmann's principle ") of the en-tropy or cross-entropy function H ∝ ln W or D ∝ − ln P, where W is the statistical weight and P the probability of a given realization of a system. Extremisation of H or D, subject to any constraints, thus selects the " most probable " (MaxProb) realization. If… (More)

1 Abstract This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy… (More)

- Robert K. Niven
- 2009

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the " maximum entropy production " (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimen-sionless potential function φ st for non-equilibrium systems, analogous to the free energy concept of… (More)

- Robert K. Niven
- 2008

The combinatorial basis of entropy, given by Boltzmann, can be written H = N −1 ln W, where H is the dimensionless entropy, N is the number of entities and W is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and… (More)

— Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Pólya Eggenberger urn sampling scheme, giving the Pólya divergence and the Pólya extension to the Maximum Relative Entropy (MaxEnt) method. Pólya MaxEnt includes the standard MaxEnt as a special case. The universality of standard MaxEnt-advocated by an axiomatic… (More)

- Robert K. Niven
- 2006

1 Abstract This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy… (More)