The average persistent current 〈I〉 of diffusive electrons in the Hartree-Fock approximation is derived in a simple non-diagrammatic picture. The Fourier expansion directly reflects the winding number decomposition of the diffusive motion around the ring. One recovers the results of Ambegaokar and Eckern, and Schmid. Moreover one finds an expression for 〈I〉 which is valid beyond the diffusive re...

Abstract Fluxes of the magnetic helicity density play an important role in large-scale turbulent dynamos, allowing growth fields while overcoming catastrophic quenching. We show here, analytically, how several types fluxes can arise from terms involving triple correlators fluctuating evolution equation. For this, we assume incompressibility and weak inhomogeneity, use a quasi-normal closure app...

When liquids are confined into a nanometer-scale slit, the induced layering-like film structure allows liquid to sustain non-isotropic stresses and thus be load-bearing. Such anisotropic characteristics of under confinement arise naturally from liquids’ wavenumber dependent compressibility, which does not need solidification take place as prerequisite. In other words, can still retain fluidity ...

Gaseous neurotransmitters such as nitric oxide (NO) provide a unique and often overlooked mechanism for neurons to communicate through diffusion within a network, independent of synaptic connectivity. NO provides homeostatic control of intrinsic excitability. Here we conduct a theoretical investigation of the distinguishing roles of NO-mediated diffusive homeostasis in comparison with canonical...

Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence, consistency, and stability are defined through truncated Hilbert expansions. In this setting it is shown that consistency and stability imply convergence. Monotone...

This article presents a new approach so-called 'diffusive pseudo invariant' with application on the robust control of a DC motor with uncertain parameters. The fundamental property of this approach is to preserve as much as possible, in the uncertainty domain, the dynamic characteristics of the system. The controllers obtained are of fractional nature and can be achieved in a non-hereditary way...