Derivation of Maximum Entropy Principles in Two-Dimensional Turbulence via Large Deviations

Spatializing Random Measures: Doubly Indexed Processes and the Large Deviation Principle

Here θ is a probability measure on a Polish space , Dr k k = 1 2r is a dyadic partition of (hence the use of 2r summands) satisfying θ Dr k = 1/2r and Lq 1 Lq 2 Lq 2r is an independent, identically distributed sequence of random probability measures on a Polish space such that Lq k q ∈ N satisfies the large deviation principle with a convex rate function. A number of related asymptotic results ...

Maximum entropy states and coherent structures in two-dimensional microtearing turbulence

Is Turbulence a State of Maximum Energy Dissipation?

Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization ...

Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows

Statistical equilibriummodels of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is investigated for these models. The main results show that models in which the global invariants are treated microcanonically give richer families of equilibria than m...

First Principles Derivation of Displacement and Stress Function for Three-Dimensional Elastostatic Problems, and Application to the Flexural Analysis of Thick Circular Plates

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...