Noncommutative space-time models

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N=5 part of them are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.Comment: 8 pages; talk given at XIV International Colloquium of Integrable Systems, Prague, June 16-18, 200

On the Fermionic Frequencies of Circular Strings

We revisit the semiclassical computation of the fluctuation spectrum around different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from the Green-Schwarz action. It has been known that the results for these frequencies obtained from the algebraic curve and from the worldsheet computations sometimes do not agree. In particular, different methods give different results for the half-integer shifts in the mode numbers of the frequencies. We find that these discrepancies can be removed if one carefully takes into account the transition matrices in the spin bundle over the target space.Comment: 13 pages, 1 figur

Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio

Quark--anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion. Moreover, we study analytically the generalized quark--anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton

The main peculiarities of the processes of the deformation and destruction of lunar soil

The main results of study of the physical and mechanical properties of lunar soil, obtained by laboratory study of samples returned from the moon by Luna 16 and Luna 20, as well as by operation of the self-propelled Lunokhod 1 and Lunokhod 2 on the surface of the moon, are analyzed in the report. All studies were carried out by single methods and by means of unified instruments, allowing a confident comparison of the results obtained. The investigations conducted allowed the following values of the main physical-mechanical properties of lunar soil to be determined: in the natural condition the solid density corresponds to the porosity of 0.8; the modal value of the carrying capacity is 0.4 kg/square cm; adhesion is 0.04 to 0.06 kg/square cm; and the internal angle of friction is 20 to 25 degree. The main mechanisms of deformation and destruction of the soil are analyzed in the report, and the relationships between the mechanical properties and physical parameters of the soil are presented

Degradation of structure and properties of rail surface layer at long-term operation

The microstructure evolution and properties variation of the surface layer of rail steel after passed 500 and 1000 million tons of gross weight (MTGW) have been investigated. The wear rate increases to 3 and 3.4 times after passed 500 and 1000 MTGW, respectively. The corresponding friction coefficient decreases by 1.4 and 1.1 times. The cementite plates were destroyed and formed the cementite particles of around 10-50 nm in size after passed 500 MTGW. The early stage dynamical recrystallization was observed after passed 1000 MTGW. The mechanisms for these have been suggested. The large number of bend extinction contours is revealed in the surface layer. The internal stress field is evaluated

Fractography of Fatigue Fracture Surface in Silumin Subjected to Electron-Beam Processing

The surface modification of the eutectic silumin with high-intensity pulsed electron beam has been carried out. Multi-cycle fatigue tests were performed and irradiation mode made possible the increase in the silumin fatigue life more than 3.5 times was determined. Studies of the structure of the surface irradiation and surface fatigue fracture of silumin in the initial (unirradiated) state and after modification with intense pulsed electron beam were carried out by methods of scanning electron microscopy. It has been shown, that in mode of partial melting of the irradiation surface the modification process of silicon plates is accompanied by the formation of numerous large micropores along the boundary plate/matrix and microcracks located in the silicon plates. A multi-modal structure (grain size within 30-50 μm with silicon particles up to 10 [mu]m located on the boundaries) is formed in stable melting mode, as well as subgrain structure in the form of crystallization cells from 100 to 250 [mu]m in size). Formation of a multi-modal, multi-phase, submicro- and nanosize structure assisting to a significant increase in the critical length of the crack, the safety coefficient and decrease in step of cracks for loading cycle was the main cause for the increase in silumin fatigue life

On the Derivation of the Exact Slope Function

In this note we give a simple derivation of the exact slope function conjectured by Basso for the anomalous dimensions of Wilson operators in the sl2 sector of planar N=4 Super-Yang-Mills theory. We also discuss generalizations of this result for higher charges and other sectors.Comment: 8pages. v2: minor corrections, JHEP versio