Brownian theory of 2D turbulence and generalized thermodynamics

We propose a new parametrization of 2D turbulence based on generalized thermodynamics and Brownian theory. Explicit relaxation equations are obtained that should be easily implementable in numerical simulations for three typical types of turbulent flows. Our parametrization is related to previous ones but it removes their defects and offers attractive new perspectives.Comment: Submitted to Phys. Rev. Let

Statistical mechanics of two-dimensional vortices and stellar systems

The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002

Financial restrictions in optimizing dynamic input-output model

Note: 716

Financial restrictions in optimizing dynamic input-output model (Rep. to the conf. on input-output models, Lodz, Poland, December, 1985)

Note: 715

1,2,3,4-Tetrafluorobiphenylene: A Prototype Janus-Headed Scaffold for Ambipolar Materials.

The title compound was synthesized by Ullmann cross-coupling in low yield as first representative of [n]phenylene containing hydrocarbon and fluorocarbon rings. Stille / Suzuki-Miyaura cross-coupling reactions, as well as substitution of fluorine in suitable starting compounds, failed to give the same product. The geometric and electronic structures of the title compound were studied by X-ray diffraction, cyclic voltammetry and density functional theory calculations, together with Hirshfeld surface and reduced density gradient analyses. The crystal structure features head-to-tail π-stacking and other fluorine-related secondary bonding interactions. From the nucleus-independent chemical shifts (NICS) descriptor, the four-membered ring of the title compound is antiaromatic, and the six-membered rings are aromatic. The Janus molecule is highly polarized; and the six-membered fluoro- and hydrocarbon rings are Lewis π-acidic and π-basic, respectively. The electrochemically-generated radical cation of the title compound is long-lived as characterized by electron paramagnetic resonance, whereas the radical anion is unstable in solution. The title compound reveals electrical properties of an insulator. On expanding its molecular scaffold towards partially fluorinated [n]phenylenes (n ≥ 2), the properties presumably can be transformed into those of semiconductors. In this context, the title compound is suggested as a prototype scaffold for ambipolar materials for organic electronics and spintronics