Non-diffusive transport in plasma turbulence: a fractional diffusion approach

Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time, that incorporate in a unified way space-time non-locality (non-Fickian transport), non-Gaussianity, and non-diffusive scaling. The fractional diffusion model reproduces the shape, and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed super-diffusive scaling

Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations

Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of L\'evy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the L\'evy index $\alpha$. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.Comment: 5 pages, 5 figures. Accepted as a letter in Physics of Plasma

A Synthetic Single-Site Fe Nitrogenase: High Turnover, Freeze-Quench ^(57)Fe Mössbauer Data, and a Hydride Resting State

The mechanisms of the few known molecular nitrogen-fixing systems, including nitrogenase enzymes, are of much interest but are not fully understood. We recently reported that Fe–N_2 complexes of tetradentate P_3^E ligands (E = B, C) generate catalytic yields of NH_3 under an atmosphere of N_2 with acid and reductant at low temperatures. Here we show that these Fe catalysts are unexpectedly robust and retain activity after multiple reloadings. Nearly an order of magnitude improvement in yield of NH_3 for each Fe catalyst has been realized (up to 64 equiv of NH_3 produced per Fe for P_3^B and up to 47 equiv for P_3^C) by increasing acid/reductant loading with highly purified acid. Cyclic voltammetry shows the apparent onset of catalysis at the P_3^BFe–N_2/P_3^BFe–N_2– couple and controlled-potential electrolysis of P_3^BFe^+ at −45 °C demonstrates that electrolytic N_2 reduction to NH_3 is feasible. Kinetic studies reveal first-order rate dependence on Fe catalyst concentration (P_3^B), consistent with a single-site catalyst model. An isostructural system (P_3^(Si)) is shown to be appreciably more selective for hydrogen evolution. In situ freeze-quench Mössbauer spectroscopy during turnover reveals an iron–borohydrido–hydride complex as a likely resting state of the P_3^BFe catalyst system. We postulate that hydrogen-evolving reaction activity may prevent iron hydride formation from poisoning the P_3^BFe system. This idea may be important to consider in the design of synthetic nitrogenases and may also have broader significance given that intermediate metal hydrides and hydrogen evolution may play a key role in biological nitrogen fixation

Separatrix Reconnections in Chaotic Regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand abrupt jumps of diffusive-like processes in the relevant phase-space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998

On the Quantum Mechanics for One Photon

This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation, respectively. These other two representations are relevant to some current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 1/2.Comment: 15 pages, typos corrected, references added, corrections and improvements made owing to the anonymous referee's responsible and helpful remarks, accepted for publication in Journal of Mathematical Physics:

Geometrothermodynamics

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy