The superstring Hagedorn temperature in a pp-wave background

The thermodynamics of type IIB superstring theory in the maximally supersymmetric plane wave background is studied. We compute the thermodynamic partition function for non-interacting strings exactly and the result differs slightly from previous computations. We clarify some of the issues related to the Hagedorn temperature in the limits of small and large constant RR 5-form. We study the thermodynamic behavior of strings in the case of $AdS_3 \times S^3 \times T^4$ geometries in the presence of NS-NS and RR 3-form backgrounds. We also comment on the relationship of string thermodynamics and the thermodynamic behavior of the sector of Yang-Mills theory which is the holographic dual of the string theory.Comment: 22 pages, JHEP style, minor misprints corrected, some comments adde

Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field

A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation function is described by an infinite family of scaling exponents, which satisfy exact transcendental equations derived explicitly in d dimensions. The exponents are organized in a hierarchical order according to their degree of anisotropy, with the spectrum unbounded from above and the leading exponent coming from the isotropic sector. For the higher-order structure functions, the anomalous scaling behavior is a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators, whose negative critical dimensions determine the exponents. A close formal resemblance of the model with the stirred NS equation reveals itself in the mixing of operators. Using the RG, the anomalous exponents are calculated in the one-loop approximation for the even structure functions up to the twelfth order.Comment: 37 pages, 4 figures, REVTe

Overcritical states of a superconductor strip in a magnetic environment

A current-carrying superconducting strip partly penetrated by magnetic flux and surrounded by a bulk magnet of high permeability is considered. Two types of samples are studied: those with critical current controlled by an edge barrier dominating over the pinning, and those with high pinning-mediated critical current masking the edge barrier.It is shown for both cases that the current distribution in a central flux-free part of the strip is strongly affected by the actual shape of the magnetic surroundings. Explicit analytical solutions for the sheet current and self-field distributions are obtained which show that, depending on the geometry, the effect may suppress the total loss-free transport current of the strip or enhance it by orders of magnitude. The effect depends strongly on the shape of the magnet and its distance to the superconductor but only weakly on the magnetic permeability.Comment: 20 pages, 20 figure

Influence of UV-radiation on structure and properties of diamond-like a-C:N films

Study results on effect of a low power (up to 1 W/cm²) UV and visible radiation on the structure and properties of diamond-like carbon nitride (α-C:N) films during their growth have been presented. The UV irradiation of the growing film surface has been found to be effective for the graphite phase etching and to result in an improved structure ordering of the film and enhanced quality thereof.Представлены результаты исследования воздействия УФ- и видимого излучения невысокой мощности (до 1 Вт/см² на структуру и свойства алмазоподобных пленок нитрида углерода α-C:N в процессе их роста. Обнаружено, что УФ-облучение ростовой поверхности пленок эффективно для травления графитной фазы, ведет к росту структурной упорядоченности пленок и улучшает их качество.Представлено результати досліджєння впливу УФ- i видимого випромінювання невисокої потужності (до 1 Вт/см²) на структуру і властивості алмазоподібних плівок нітриду вуглецю α-C:N у процесі їхнього росту. Виявлено, що УФ-опромінення ростової поверхні плівок ефективно для травлення графітної фази, веде до росту структурної упорядкованості плівок і поліпшує їхню якість

Structure and magnetic properties of Ni-N nanofilms

All range of nanostructured films of nickel nitrides is synthesized by the method of magnetron sputtering (from the phase of Ni and up to the phase of Ni₂N) and was investigated the change in the magnetic properties. We found out the globular structure of paramagnetic phases of Ni₃N and Ni₂N, and also the ferromagnetic behavior of Ni₄N phase is confirmed

Structure defects and properties of fianites

X-ray structure examination and spectroscopy, as well as hydrostatic method and fluorescence have been used to investigate single crystals of fianites differing in colors, doped with yttrium and rare earth ions. The crystal lattice defects, microhardness, absorption spectra and fluorescence of those fianites have been determined. It is shown that mechanical (density, hardness) and optical (color, absorption, fluorescence) properties of fianites depend on rare-earth microimpurities (Ce, Eu) and structure defects.Рентгеновскими структурным и спектральным, гидростатическим и флюоресцентным методами исследованы легированные иттрием и редкоземельными ионами фиани-товые монокристаллы, отличающиеся цветом. Определена дефектность кристаллической решетки этих фианитов, их микротвердость, спектры поглощения и флюоресценции. Показано, что механические (плотность, твердость) и оптические (цвет, поглощение, флюоресценция) свойства фианитов зависят от редкоземельных микропримесей (Ce, Eu) и дефектности структуры.Рентгенівськими структурним i спектральним, гідростатичним i флюоресцентним методами досліджено леговані ітрієм і рідкісноземельними іонами фіанітові монокристали, які відрізнялися кольором. Визначено дефектність кристалічної гратки цих фіанітів, їх мікротвердість, спектри поглинання та флюоресценції. Показано, що механічні (густина, твердість) та оптичні (колір, поглинання, флюоресценція) властивості фіанітів залежать від рідкісноземельних мікродомішок (Ce, Eu) і дефектності структури