Opto-electronic strain meter

A new opto-electronic strain meter is described. This instrument can be used to record tensile load-extension and elastic aftereffect diagrams for film microspecimens at a maximum elongation rate of 1 mm/sec and a resolution of 1.5µ.Moscow Branch, Institute of Chemical Physics, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, No. 6, pp. 1110–1111, November–December, 1969.     

Elliptic solutions of the semidiscrete B-version of the Kadomtsev–Petviashvili equation

Theoretical and Mathematical Physics - We study elliptic solutions of the semidiscrete B-version of the Kadomtsev–Petviashvili equation and derive the equations of motion of their poles. The...     

Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit

We show that the dispersionless limits of the Pfaff–KP (also known as the DKP or Pfaff lattice) and the Pfaff–Toda hierarchies admit a reformulation in terms of elliptic functions. In the elliptic form, they look like natural elliptic deformations of the respective dispersionless KP and two-dimensional Toda hierarchies.     

Features of rubber swelling in transformer oil,according to NMR data

NMR spectroscopy, NMR relaxation, and NMR with a pulsed magnetic field gradient methods are used to study the swelling of the elastomers based on ethylene-propylene rubber, butadiene-nitrile rubber, and fluororubber SKF-26 in transformer oil. Components corresponding to the fractions of oil and polymer network are identified. It is shown that the affinity of the polymers toward transformer oil displays an increase in the orderly sequence of ethylene-propylene rubber, fluororubber, and butadiene-nitrile rubber; the stability of the polymers towards carbon tetrachloride falls in the same sequence. Based on an analysis of the spin–spin relaxation time depending on the degree of swelling, it is found that fluororubber elastomers are characterized by the formation of a polymer network that prevents further sorption, In contrast, elastomer based on ethylene-propylene rubber gives no indication of the formation of a rigid polymer network.     

Multi-cut solutions of Laplacian growth

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hele-Shaw cells. Integrals of motion for the multi-cut LG solutions in terms of singularities of the Schwarz function are found, and the dynamics of densities (jumps) on the cuts are derived. The subclass of these solutions with linear Cauchy densities on the cuts of the Schwarz function is of particular interest, because in this case the integral equation for the conformal map becomes linear. These solutions can also be of physical importance by representing oil/air interfaces, which form oil fjords with a constant opening angle, in accordance with recent experiments in a Hele-shaw cell.     

Higher harmonics of azimuthal anisotropy in relativistic heavy-ion collisions in HYDJET++ model

The LHC data on azimuthal anisotropy harmonics from PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted in the framework of the HYDJET++ model. The cross-talk of elliptic $v_2$ and triangular $v_3$ flow in the model generates both even and odd harmonics of higher order. Comparison with the experimental data shows that this mechanism is able to reproduce the $p_\mathrm{T}$ and centrality dependencies of quadrangular flow $v_4$ , and also the basic trends for pentagonal $v_5$ and hexagonal $v_6$ flows.     

The spectral problem for theq-Knizhnik-Zamolodchikov equation and continuousq-Jacobi polynomials

The spectral problem for theq-Knizhnik-Zamolodchikov equations for at arbitrary non-negative levelk is considered. The case of two-point functions in the fundamental representation is studied in detail. The scattering states are given explicitly in terms of continuousq-Jacobi polynomials, and theS-matrix is derived from their asymptotic behavior. The level zeroS-matrix is closely connected with the kink-antikinkS-matrix for the spin- XXZ antiferromagnet. An interpretation of the latter in terms of scattering on (quantum) symmetric spaces is discussed. In the limit of infinite level we observe connections with harmonic analysis onp-adic groups with the primep given byp=q ^–2.Work supported in part by the NSF: PHY-91-23780     

Gluon shadowing and unitarity effects

New data from HERA experiment on deep inelastic scattering have been used to parametrize nucleon and Pomeron structure functions. Within the Gribov theory, the parameterizations were employed to calculate gluon shadowing for various heavy ions. The latter was compared with predictions from other models. Calculations of multiplicity reduction due to gluon shadowing for d+Au collisions at forward rapidities at √s _NN =200 GeV are in good agreement with BRAHMS data on the nuclear modification factor.     

Conformal Maps and Integrable Hierarchies

We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as “string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the domain out of a set of its harmonic moments. This is the same solution which is known to describe 2D gravity coupled to c= matter. We also introduce a concept of the τ-function for analytic curves. Received: 20 December 1999/ Accepted: 2 March 2000     

Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and demonstrate the role of Bäcklund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. We show that the nested Bethe ansatz technique is equivalent to a chain of successive Bäcklund transformations “undressing” the original problem to a trivial one.