Differential-difference evolution equations. II (Darboux transformation for the Toda lattice)

Toda lattice equation is represented in the form of the condition of compatibility of the system of linear equations corresponding to a non-Hermitian Lax representation. The Darboux invariance of this linear system is defined and proved in the text, and enables us to construct some new formulas for the solutions of the Toda lattice equation. These formulas involving determinants are applicable to an arbitrary initial solution of the Toda equation for example to a solution growing at infinity.Physique Mathématique et Théorique, Equipe de recherche associée au CNRS.This work has been done as part of the program Recherche Cooperative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses.Leningrad State University, U.S.S.R.     

In memoriam: Boris Dubrovin

Letters in Mathematical Physics -     

Investigation of limits of applicability of the pBRDF model for active polarimeters

The polarimetric bidirectional reflectance distribution function is modeled for active polarimeters. The applicability boundaries of the model are determined based on the comparison of the simulated and experimental data.     

Numerical modeling of wave processes in coupled magnonic crystals with periods shifted relative to each other

A calculation model has been developed to describe the propagation of magnetostatic waves in a periodic structure consisting of two one-dimensional magnonic crystals, the periods of which are shifted relative to each other in the wave propagation direction. It is shown that, depending on the shift between the magnonic crystals, up to three bandgaps can be formed in this structure in the first Bragg resonance.     

Molecular mobility of counterion functional groups in ionic liquid 1-ethyl-3-methylimidazolium acetate according to 1H and 13C NMR relaxation data

1-Ethyl-3-methylimidazolium acetate was studied by NMR relaxation. The temperature dependences of the spin-lattice relaxation rates (1/T ₁) for ¹H and ¹³C were obtained. The curves with maxima were observed for the majority of the temperature dependences 1/T ₁, which provided a reliable temperature dependence of the correlation times (τ_c). In the low-temperature range, the proton relaxation rates tend to an asymptotic value, which is related, most likely, to spin diffusion manifested in the studied samples. The values of correlation times τ_c calculated for ¹H and ¹³C of the same functional group almost coincide at high temperatures, which confirms that the used approach is adequate for the determination of characteristic times of rotational reorientation of counterions in the studied ionic liquid.     

Theory of the stopping of fast heavy highly charged structured ions in their collisions with complex atoms

We have developed a nonperturbative theory of the energy losses by fast heavy structured ions in their collisions with neutral complex atoms by taking into account all of the possible, including multiple, excitations and ionizations of both projectile and target. We have been able to achieve a significant simplification of the problem by considering multielectron targets and by restricting our analysis to highly charged structured ions with charges much larger than unity, when the characteristic size of the electron coat of the projectile ion is much smaller than that of the neutral target atom. The errors in the approximations used and in the calculations of inelastic cross sections are estimated. We have derived formulas for the effective stopping similar to the well-known Bethe-Bloch formulas. To illustrate the contribution from multielectron excitations of the ion coat to the effective stopping, we make a comparison with the calculations based on the perturbation theory. The energy losses of U ^q+ (10 ≤ q ≤ 70) ions in their collisions with argon atoms and the energy losses of Pb and Bi ions on several targets have been calculated. A comparison with experiment is made.     

Study of the reaction π–<Emphasis Type="Italic">A</Emphasis> π<Superscript>+</Superscript>π<Superscript>–</Superscript>π<Superscript>–</Superscript><Emphasis Type="Italic">A</Emphasis> at large statistics with VES setup

Partial wave analysis of the π–A π⁺π^–π^– system produced by 29 GeV/cπ^– beam on a beryllium target is presented. About 30 × 10⁶ |events in the wide t′|range 0–0.8 GeV²/c ² are collected with upgraded VES setup. The size of the data sample is 2.5 times larger than one previously analyzed by VES. Data are analyzed using formalism of the density matrix with unlimited rank. We discuss status of the a ₁(1420) a ₂(1700) a ₃(1875) states and a structure of exotic ρ(770)π P-wave with J ^PC = 1^-+. Parameters of a ₃(1875) are estimated as M = 1985 ± 20 MeV/c ², Γ = 200 ± 50 MeV/c ² (preliminary).     

Reconstruction of the blood flow velocity vector as an additional mode of ultrasonic tomograph

The possibility of simultaneous reconstruction of the blood flow velocity vector and spatial distributions of the speed of sound and absorption coefficient in a medical ultrasonic tomograph is discussed. The operating capacity of the proposed spatial-correlation method for determining the blood flow velocity vector is confirmed by experiments on a tomograph prototype.