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

Studies of high-field sections of a muon helical cooling channel with coil separation

The Helical Cooling Channel (HCC) was proposed for 6D cooling of muon beams required for muon collider and some other applications. HCC uses a continuous absorber inside superconducting magnets which produce solenoidal field superimposed with transverse helical dipole and helical gradient fields. HCC is usually divided into several sections each with progressively stronger fields, smaller aperture and shorter helix period to achieve the optimal muon cooling rate. This paper presents the design issues of the high field section of HCC with coil separation. The effect of coil spacing on the longitudinal and transverse field components is presented and its impact on the muon cooling discussed. The paper also describes methods for field corrections and their practical limits. The magnetic performance of the helical solenoid with coil separation was discussed in this work. The separation could be done in three different ways and the performances could be very different which is important and should be carefully described during the beam cooling simulations. The design that is currently being considered is the one that has the poorest magnetic performance because it presents ripples in all three components, in particular in the helical gradient which could be quite large. Moreover, the average gradient could be off, which could affect the cooling performance. This work summarized methods to tune the gradient regarding the average value and the ripple. The coil longitudinal thickness and the helix period can be used to tune G. Thinner coils tend to reduce the ripples and also bring G to its target value. However, this technique reduces dramatically the operational margin. Wider coils can also reduce the ripple (not as much as thinner coils) and also tune the gradient to its target value. Longer helix periods reduce ripple and correct the gradient to the target value

Superconducting magnet system for muon beam cooling

A helical cooling channel has been proposed to quickly reduce the six-dimensional phase space of muon beams for muon colliders, neutrino factories, and intense muon sources. A novel superconducting magnet system for a muon beam cooling experiment is being designed at Fermilab. The inner volume of the cooling channel is filled with liquid helium where passing muon beam can be decelerated and cooled in a process of ionization energy loss. The magnet parameters are optimized to match the momentum of the beam as it slows down. The results of 3D magnetic analysis for two designs of magnet system, mechanical and quench protection considerations are discussed

MANX, a 6-D Muon Beam Cooling Experiment for RAL

MANX is a six-dimensional muon ionization cooling demonstration experiment based on the concept of a helical cooling channel in which a beam of muons loses energy in a continuous helium or hydrogen absorber while passing through a special superconducting magnet called a helical solenoid. The goals of the experiment include tests of the theory of the helical cooling channel and the helical solenoid implementation of it, verification of the simulation programs, and a demonstration of effective six-dimensional cooling of a muon beam. We report the status of the experiment and in particular, the proposal to have MANX follow MICE at the Rutherford-Appleton Laboratory (RAL) as an extension of the MICE experimental program. We describe the economies of such an approach which allow the MICE beam line and much of the MICE apparatus and expertise to be reused

The COMPASS Experiment at CERN

The COMPASS experiment makes use of the CERN SPS high-intensitymuon and hadron beams for the investigation of the nucleon spin structure and the spectroscopy of hadrons. One or more outgoing particles are detected in coincidence with the incoming muon or hadron. A large polarized target inside a superconducting solenoid is used for the measurements with the muon beam. Outgoing particles are detected by a two-stage, large angle and large momentum range spectrometer. The setup is built using several types of tracking detectors, according to the expected incident rate, required space resolution and the solid angle to be covered. Particle identification is achieved using a RICH counter and both hadron and electromagnetic calorimeters. The setup has been successfully operated from 2002 onwards using a muon beam. Data with a hadron beam were also collected in 2004. This article describes the main features and performances of the spectrometer in 2004; a short summary of the 2006 upgrade is also given.Comment: 84 papes, 74 figure

Characteristics of genetic and phenotypic properties of tick-borne encephalitis virus strains isolated from various source on the territory of Eastern Siberia

Since ixodid ticks and their feeders (vertebrates) form the basis of the tick-borne encephalitis virus (TBEV) population, it was interesting to obtain a genetic characteristic of strains isolated from various sources in the territory of Eastern Siberia. In our study, it was found that the circulation of TBEV of genotypes 1, 2, 3, 5 and "polytypic" strains in the territory of Eastern Siberia is maintained both by the main vectors (I. persulcatus ticks) and by their feeders (small and large mammals, birds). The distribution of genotypes in strains groups from ixodid ticks and vertebrates varied. TBEV strains of genotypes 1 and 2 were significantly more often isolated from rodents, and genotype 3 from ixodid ticks (p < 0.05). Isolates of genotype 3 (85.5 %) prevailed in the group of strains isolated from ixodid ticks, of which 29.6 % belonged to "Vasilchenko", and 25.6 % to "Zausaev"subgenotypes. Genotypes 1 and 2 were represented by single isolates (3.3 % and 1.3 %, respectively). Among strains isolated from warm-blooded hosts, the proportion of genotype 1 was 35.3 %, genotype 2 -11.8 %, genotype 3 - 35.3 %. More than half of genotype 3 strains (58.3 %) were related to "Vasilchenko" subgenotype, and the strains of "Zausaev" subgenotype were not detected. The obtained data suggest that ixodid ticks and warm-blooded animals are amplifiers of TBEV of genotypes 3 and 1, respectively. The certain differences in the phenotypic characteristics of strains isolated from ticks and warm-blooded animals have been revealed. It has been found that strains isolated from ticks are more homogeneous in their antigenic characteristics, less heterogeneous in S-feature than strains isolated from warm-blooded sources. The strains isolated from warm-blooded animals demonstrate somewhat greater resistance to warming but reducing the reproduction of the virus at 42 °C, and have greater virulence compared to strains isolated from ticks

The distribution of tick-borne encephalitis virus genotypes in different types of landscapes of Eastern Siberia

To find out what is the role of some environmental factors in the formation of a heterogeneous viral population, the analysis of the distribution of tick-borne encephalitis virus (TBEV) genotypes in different types of landscapes of Eastern Siberia has been carried out. In our study, it was shown that TBEV area in all investigated landscapes of Eastern Siberia is represented not only by TBEV of genotype 3, absolute dominance of which is noted in the studied regions, regardless the landscapes where the foci are located, but also by strains of other genotypes. The relationship between genotypes 1,3 and "polytypic" strains with a certain type of landscape and the degree of their development by man has not been established. The prevailing number of strains of TBEV genotype 5 is isolated from the material collected in the Transbaikalia, in the landscapes of the mountain taiga. They, as well as the strain of genotype 4, are found in the foci, where joint circulation of several TBEV genotypes is noted. The strains of TBEV genotype 2 were revealed in the landscapes of plains and plateaus taiga and insular steppes and forest steppes of the southern part of the Baikal region. Moreover, the detection of RNA of TBEV genotype 2 in the "polytipic" 763-87 and 765-87 strains isolated in the floodplain and forest-steppe landscapes of the Barguzin hollow does not exclude the possibility of circulation of TBEV genotype 2 in the Transbaikalian foci. The greatest genetic heterogeneity of TBEV is observed in natural foci located along Lake Baikal and in the southeastern part of Transbaikalia

Characteristics of round and extracted strands of Nb3Al Rutherford cable

Long Nb{sub 3}Al strands with copper stabilizer are promising for future high field accelerator magnets. A 1.2 kilometer Nb{sub 3}Al strand with Cu stabilizer was fabricated at the National Institute for Materials Science in Japan. Using this strand a 30 meter Cu stabilized Nb{sub 3}Al Rutherford cable was made for the first time by a collaboration of NIMS and Fermilab. The Nb{sub 3}Al strands extracted from cable with a relatively low packing factor showed almost no J{sub c} degradation. But the extracted strands from the highly compacted cable showed some degradation in both J{sub c} and n value, which may be caused by local separation of the copper stabilizer. Still, its J{sub c} degradation is lower than that of typical Nb{sub 3}Sn strands. The current limit due to magnetic instability in low field is about 500 A at 4.2 K. The magnetization of the strands, which was measured with balanced coils at 4.2 K, showed large flux jumps, usually around 1.5 T. This value is much larger than the B{sub c2} (4.2 K) of the Nb matrix, which is around 0.4 Tesla. The magnetic instability of the Nb{sub 3}Al strand at low field is not completely understood, but it might be explained by the superconducting coupling current through the Nb matrix

CHARACTERISTICS OF THE BAIKAL SUBTYPE OF TICK-BORNE ENCEPHALITIS VIRUS CIRCULATING IN EASTERN SIBERIA

Background. During the study of the genetic variability of the tick-borne encephalitis virus (TBEV) in Eastern Siberia, a group of 22  strains with a unique genetic structure significantly different from all  known TBEV subtypes was identified. This TBEV variant was  tentatively called “group 886”. Therefore, for this original TBEV  variant it was necessary to study the genetic, biological properties of the “group 886” strains, clarify its TBEV taxonomic status, its range, evolutionary history, etc.Aim. The generalization of the currently available data on genetic and biological properties of TBEV “886” group.Materials and methods. The genetic structure of “group 886” strains was studied by the complex of molecular-genetic methods (MHNA, sequencing of fragments or the complete genome).Results. It was shown that “group 886” strains form a separate cluster on phylogenetic tree, and the level of genetic differences  from other genotypes is more than 12 %. It was defined that this  TBEV variant has its own area (Irkutsk region, Republic of Buryatia,  Trans-Baikal region, Northern Mongolia). Its ecological connection  with all links of the transmissive chain (ixodid ticks, small mammals,  human), participation in human pathology, stability and duration of  circulation in the Baikal region, individual evolutionary history  were proved. Some phenotypic characteristics of the “group 886” strains were considered.Conclusion. The presented data testify to the validity of the “886 group” isolation as an independent genetic type. Taking into account  the geographical distribution of this TBEV genotype, we propose to assign it the name “Baikal genotype/subtype”