Self-Field Effects in Magneto-Thermal Instabilities for Nb-Sn Strands

Recent advancements in the critical current density (Jc) of Nb$_{3}$Sn conductors, coupled with a large effective filament size, have drawn attention to the problem of magnetothermal instabilities. At low magnetic fields, the quench current of such high Jc Nb$_{3}$Sn strands is significantly lower than their critical current because of the above-mentioned instabilities. An adiabatic model to calculate the minimum current at which a strand can quench due to magneto-thermal instabilities is developed. The model is based on an 'integral' approach already used elsewhere [1]. The main difference with respect to the previous model is the addition of the self-field effect that allows to describe premature quenches of non-magnetized Nb$_{3}$Sn strands and to better calculate the quench current of strongly magnetized strands. The model is in good agreement with experimental results at 4.2 K obtained at Fermilab using virgin Modified Jelly Roll (MJR) strands with a low Residual Resistivity Ratio (RRR) of the stabilizing copper. The prediction of the model at 1.9 K and the results of the tests carried out at CERN, at 4.2 K and 1.9 K, on a 0.8 mm Rod Re-Stack Process (RRP) strand with a low RRR value are discussed. At 1.9 K the test revealed an unexpected strand performance at low fields that might be a sign of a new stability regime

Special Values of Generalized Polylogarithms

We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear space generated by values of generalized polylogarithms.Comment: 32 page

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

Development of the Multi-Analyte Test for Immune-Chromatographic Detection of Botulinum Toxins

Designed is the multi-analyte test for simultaneous immune chromatographic detection of A & B type botulinum neurotoxins (BT), using colloid gold nanoparticles. It is meant for food and environmental samples' analysis. The sensitivity of simultaneous BT detection of the A (30 ng/ml) and B (10 ng/ml) types is as high as that of mono-analytical tests, designed for one type BT detection. The test is demonstrated to be a specific one and can be used for BT detection in food stuffs

Construction of Immune-Chromatographic Indicator Elements for Burnet Rickettsia Detection

mc/ml, and the elapsed time – 20 minutes. The IE is specific to other members of the family Ricketsiaceae, for instance to R. prowazekii , to antigen complexes of R. prowazekii and R. sibirika , as well as to vaccinia virus (L-IVP strain). The IE engineered can be used for rapid indication of Burnet Rickettsia at different stages of laboratory investigation. Span time reduction, lack of necessity to perform any accessory technological operations, visual and (or) automatic registration of the results build up premises to observe immune-chromatographic method for Burnet Rickettsia detection as one of the alternatives for identification of these microorganisms under field conditions when monitoring ambient environment objects

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added