Generalized Jack polynomials and the AGT relations for the SU(3)SU(3) group

We find generalized Jack polynomials for the group $SU(3)$ and verify that their Selberg averages for several first levels are given by Nekrasov functions. To compute the averages we derive recurrence relations for the $sl_3$ Selberg integrals.Comment: 6 pages, refs added, typos corrected, published versio

Spreading of Antarctic Bottom Water in the Atlantic Ocean

This paper describes the transport of bottom water from its source region in the Weddell Sea through the abyssal channels of the Atlantic Ocean. The research brings together the recent observations and historical data. A strong flow of Antarctic Bottom Water through the Vema Channel is analyzed. The mean speed of the flow is 30 cm/s. A temperature increase was found in the deep Vema Channel, which has been observed for 30 years already. The flow of bottom water in the northern part of the Brazil Basin splits. Part of the water flows through the Romanche and Chain fracture zones. The other part flows to the North American Basin. Part of the latter flow propagates through the Vema Fracture Zone into the Northeast Atlantic. The properties of bottom water in the Kane Gap and Discovery Gap are also analyzed

Molecular Motors Interacting with Their Own Tracks

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences non-monotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes

Analitic Investigation of the Regularities of Changing Dust Concentration During the Abrasive Decrease of Stone Structures

In the process of repair or restoration of building structures, it is often necessary to strengthen building structures from limestone-shell rock, concrete, reinforced concrete, hard materials-granite, basalt, etc. by cutting or making cuts of the required size with detachable circles of synthetic diamond and cubic boron nitride (CA and CBN)The cutting process is accompanied by considerable dust formation, which can be both harmful and dangerous factor in the work.The aim of the work is studying the process of dust sedimentation and the regularity of the change in dust concentration during the abrasive cutting of concrete and stone materials.Mathematical models have been developed – dust emission from under the wheel, speed of sedimentation of dust particles depending on their material, size and shape, and also depending on temperature, pressure and humidity, the concentration of dust in the working space and the concentration change during the cutting cycle are calculated.It is shown that the velocity of the sedimentation of particles depends significantly on the shape. The higher the sphericity, the higher the sedimentation rate. The ambient temperature has little effect on the sedimentation rate, in the temperature range (-20 → + 40 °C) at which the operation takes place.The sedimentation rate of dust particles generated by cutting the most common building stone materials also differs slightly. Almost the same sedimentation rate has dust particles obtained by cutting basalt and concrete. A bit higher is the sedimentation rate of particles from granite.The sedimentation rate of particles of generated dust is about 600-700 cm/h or 10-11 cm/min for particles measuring 6 μm. This means that at a production height of about 2 m (200 cm) during the operating cycle (about 3 min), the dust will remain at an altitude of about 1.5 m, i.е. practically remains in the working area. This gives grounds to assert about a high concentration of dust during the cutting cycle (about 4.8 108/m3)

(q,t)(q,t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces

We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody $U_q(\widehat{\mathfrak{g}})_k$ to generic quantum toroidal algebras. A nearly exhaustive presentation is given for the two series $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$ and $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_n)$, when screenings do not exist and thus all the correlators are purely algebraic, i.e. do not include additional hypergeometric type integrations/summations. Generalizing the construction of the intertwiner (refined topological vertex) of the Ding-Iohara-Miki (DIM) algebra, we obtain the intertwining operators of the Fock representations of the quantum toroidal algebra of type $A_n$. The correlation functions of these operators satisfy the $(q,t)$-Knizhnik-Zamolodchikov (KZ) equation, which features the ${\cal R}$-matrix. Matching with the Nekrasov function for the instanton counting on the ALE space is worked out explicitly. We also present an important application of the DIM formalism to the study of $6d$ gauge theories described by the double elliptic integrable systems. We show that the modular and periodicity properties of the gauge theories are neatly explained by the network matrix models providing solutions to the elliptic $(q,t)$-KZ equations.Comment: 56 page

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the parallel-perpendicular orientation transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR

Symmetric achromatic low-beta collider interaction region design concept

We present a new symmetry-based concept for an achromatic low-beta collider interaction region design. A specially-designed symmetric Chromaticity Compensation Block (CCB) induces an angle spread in the passing beam such that it cancels the chromatic kick of the final focusing quadrupoles. Two such CCBs placed symmetrically around an interaction point allow simultaneous compensation of the 1st-order chromaticities and chromatic beam smear at the IP without inducing significant 2nd-order aberrations to the particle trajectory. We first develop an analytic description of this approach and explicitly formulate 2nd-order aberration compensation conditions at the interaction point. The concept is next applied to develop an interaction region design for the ion collider ring of an electron-ion collider. We numerically evaluate performance of the design in terms of momentum acceptance and dynamic aperture. The advantages of the new concept are illustrated by comparing it to the conventional distributed-sextupole chromaticity compensation scheme.Comment: 12 pages, 17 figures, to be submitted to Phys. Rev. ST Accel. Beam