Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained

Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity

We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated

High-power ultrasonic synthesis and magnetic-field-assisted arrangement of nanosized crystallites of cobalt-containing layered double hydroxideu

High-quality stoichiometric Co2Al–NO3 and Co2Al–CO3 layered double hydroxides (LDHs) have been obtained by precipitation followed by anion exchange, both high-power sonication assisted. Application of high-power ultrasound has been demonstrated to result in a considerable acceleration of the crystallization process and the anion-exchange reaction. Two independent approaches were used to form bulk and 2-D samples of Co2Al–NO3 with the oriented crystallites, namely uniaxial pressing of deposits from sonicated LDH slurries and magnetic field assisted arrangement of LDH crystallites precipitating on glass substrates. A convenient way of preparation of semi-transparent compacts with relatively big blocks of oriented crystallites have been demonstrated. Thin dense transparent films of highly-ordered crystallites of Co2Al–NO3 LDH have been produced and characterized.publishe

Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity

We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated

Anomalous Evolution of Strength and Microstructure of High‐Entropy Alloy CoCrFeNiMn after High‐Pressure Torsion at 300 and 77 K

Ultrafine and nanocrystalline states of equiatomic face‐centered cubic (fcc) high‐entropy alloy (HEA) CoCrFeNiMn (“Cantor” alloy) are achieved by high‐pressure torsion (HPT) at 300 K (room temperature, RT) and 77 K (cryo). Although the hardness after RT‐HPT reaches exceptionally high values, those from cryo‐HPT are distinctly lower, at least when the torsional strain lies beyond γ = 25. The values are stable even during long‐time storage at ambient temperature. A similar paradoxal result is reflected by torque data measured in situ during HPT processing. The reasons for this paradox are attributed to the enhanced hydrostatic pressure, cryogenic temperature, and especially large shear strains achieved by the cryo‐HPT. At these conditions, selected area electron diffraction (SAD) patterns indicate that a partial local phase change from fcc to hexagonal close‐packed (hcp) structure occurs, which results in a highly heterogeneous structure. This heterogeneity is accompanied by both an increase in average grain size and especially a strong decrease in average dislocation density, which is estimated to mainly cause the paradox low strength.© 2019 The Author