The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Uniaxial metallo-dielectric metamaterials with scalar positive permeability

The dispersion relation for plane waves in uniaxial metamaterials with indefinite dielectric tensors and scalar positive permeability is theoretically investigated. It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors. As an example a metallodielectric multilayer was considered and the dispersion relations were determined using an effective medium approximation and an analytically exact Bloch wave calculation. The extraordinary waves in this structure are identified as multilayer plasmons and the validity of the effective medium approximation is examined.

Spectroscopic measurements of phase-resolved electron energy distribution functions in RF-excited discharges

The reliable measurement of the electron energy distribution function (EEDF) of plasmas is one of the most important subjects of plasma diagnostics, because this piece of information is the key to understand basic discharge mechanisms. Specific problems arise in the case of RF-excited plasmas, since the properties of electrons are subject to changes on a nanosecond time scale and show pronounced spatial anisotropy. We report on a novel spectroscopic method for phase- and space-resolved measurements of the electron energy distribution function of energetic (> 12 eV) electrons in RF discharges. These electrons dominate excitation and ionization processes and are therefore of particular interest. The technique is based on time-dependent measurements during the RF cycle of excited-state populations of rare gases admixed in small fractions. These measurements yield � in combination with an analytical model � detailed information on the excitation processes. Phase-resolved optical emission spectroscopy allows us to overcome the difficulties connected with the very low densities (107�109 cm�3) and the transient character of the electrons in the sheath region. The EEDF of electrons accelerated in the sheath region can be described by a shifted Maxwellian with a drift velocity component in direction of the electric field. The method yields the high-energy tail of the EEDF on an absolute scale. The applicability of the method is demonstrated at a capacitively coupled RF discharge in hydrogen.

Kit-positive interstitial cells in the rabbit urethra: structural relationships with nerves and smooth muscle.

OBJECTIVE: To identify interstitial cells (ICs) in the wall of the rabbit urethra using antibodies to the Kit receptor, and to examine their location, morphology and relationship with nerves and smooth muscle cells (SMCs), as studies of enzymatically isolated cells from the rabbit urethra have established that there are specialized cells that show spontaneous electrical activity and have morphological properties of ICs. MATERIALS AND METHODS: Urethral tissues from rabbits were fixed, labelled with antibodies and examined with confocal microscopy. Some specimens were embedded in paraffin wax and processed for histology. Histological sections from the most proximal third and mid-third region of rabbit urethra were stained with Masson's Trichrome to show their cellular arrangement. RESULTS: Sections from both regions had outer longitudinal and inner circular layers of SM, and a lamina propria containing connective tissue and blood vessels; the lumen was lined with urothelial cells. The mid-third region had a more developed circular SM layer than the most-proximal samples, and had extensive inner longitudinal SM bundles in the lamina propria. Labelling with anti-Kit revealed immunopositive cells within the wall of the rabbit urethra, in the circular and longitudinal layers of the muscularis. Double-labelling with an antibody to SM myosin showed Kit-positive cells on the boundary of the SM bundles, orientated parallel to the axis of the bundles. Others were in spaces between the bundles and often made contact with each other. Kit-positive cells were either elongated, with several lateral branches, or stellate with branches coming from a central soma. Similar cells could be labelled with vimentin antibodies. Their relationship with intramural nerves was examined by double immunostaining with an anti-neurofilament antibody. There were frequent points of contact between Kit-positive cells and nerves, with similar findings in specimens double-immunostained with anti-neuronal nitric oxide synthase (nNOS). CONCLUSION: Kit-positive ICs were found within the SM layers of the rabbit urethra, in association with nerves, on the edge of SM bundles and in the interbundle spaces. The contact with nNOS-containing neurones might imply participation in the nitrergic inhibitory neurotransmission of the urethra. PMID: 17212607 [PubMed - indexed for MEDLINE]