Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function modulo 2 and 3.Comment: 19 page

Verrucous venous malformation

Verrucous venous malformation, also known as verrucous hemangioma, is a superficial vascular malformation with a variable degree of hyperkeratosis that is composed of capillaries and veins in the dermis and sometimes subcutaneous tissue. We describe a 53-year-old man who presented with a large hyperkeratotic plaque of the left dorsal and plantar foot. Biopsy revealed verrucous acanthosis of the epidermis and a proliferation of thin-walled vessels in the dermis. We provide a brief review of the clinical and histopathologic presentation, differential diagnosis, and management of this rare entity

An alternative approach to field-aligned coordinates for plasma turbulence simulations

Turbulence simulation codes can exploit the flute-like nature of plasma turbulence to reduce the effective number of degrees of freedom necessary to represent fluctuations. This can be achieved by employing magnetic coordinates of which one is aligned along the magnetic field. This work presents an approach in which the position along the field lines is identified by the toroidal angle, rather than the most commonly used poloidal angle. It will be shown that this approach has several advantages. Among these, periodicity in both angles is retained. This property allows moving to an equivalent representation in Fourier space with a reduced number of toroidal components. It will be shown how this duality can be exploited to transform conventional codes that use a spectral representation on the magnetic surface into codes with a field-aligned coordinate. It is also shown that the new approach can be generalised to get rid of magnetic coordinates in the poloidal plane altogether, for a large class of models. Tests are carried out by comparing the new approach with the conventional approach employing a uniform grid, for a basic ion temperature gradient (ITG) turbulence model implemented by the two corresponding versions of the ETAI3D code. These tests uncover an unexpected property of the model, that localized large parallel gradients can intermittently appear in the turbulent regime. This leaves open the question whether this is a general property of plasma turbulence, which may lead one to reconsider some of the usual assumptions on micro-turbulence dynamics.Comment: 19 pages (once in pdf format). 1 LaTeX file and 10 eps figures in the zip folde

Effective Potential Theory: A Practical Way to Extend Plasma Transport Theory to Strong Coupling

The effective potential theory is a physically motivated method for extending traditional plasma transport theories to stronger coupling. It is practical in the sense that it is easily incorporated within the framework of the Chapman-Enskog or Grad methods that are commonly applied in plasma physics and it is computationally efficient to evaluate. The extension is to treat binary scatterers as interacting through the potential of mean force, rather than the bare Coulomb or Debye-screened Coulomb potential. This allows for aspects of many-body correlations to be included in the transport coefficients. Recent work has shown that this method accurately extends plasma theory to orders of magnitude stronger coupling when applied to the classical one-component plasma model. The present work shows that similar accuracy is realized for the Yukawa one-component plasma model and it provides a comparison with other approaches.Comment: 6 pages, 3 figures, Proceedings of the Strongly Coupled Coulomb Systems conference 201

Transition to High-Speed Networks — SuperJANET Experience

For the time being, trials to establish the Information Superhighway are booming. In Britain, JANET has provided wide-area computer communication, and has recently been upgraded to SuperJANET, increasing the throughput by a factor of five to 10 Mb/s, with some sites having PDH access at n × 34 Mb/s. In this paper, the technological changes seen from a user perspective are addressed. A multimedia communication-based distance learning project on SuperJANET is introduced and the network performance measurements for this project are presented. These measurements suggest the employment of reservation protocol and packet scheduling. We also provide a mechanism for on-the-fly playback of continuous media