Interaction effects in assembly of magnetic nanoparticles

A specific absorption rate of a dilute assembly of various random clusters of iron oxide nanoparticles in alternating magnetic field has been calculated using Landau- Lifshitz stochastic equation. This approach simultaneously takes into account both the presence of thermal fluctuations of the nanoparticle magnetic moments, and magneto-dipole interaction between the nanoparticles of the clusters. It is shown that for usual 3D clusters the intensity of magneto- dipole interaction is determined mainly by the cluster packing density eta = Np*V/Vcl, where Np is the average number of the particles in the cluster, V is the nanoparticle volume, and Vcl is the cluster volume. The area of the low frequency hysteresis loop and the assembly specific absorption rate have been found to be considerably reduced when the packing density of the clusters increases in the range of 0.005 < eta < 0.4. The dependence of the specific absorption rate on the mean nanoparticle diameter is retained with increase of eta, but becomes less pronounced. For fractal clusters of nanoparticles, which arise in biological media, in addition to considerable reduction of the absorption rate, the absorption maximum is shifted to smaller particle diameters. It is found also that the specific absorption rate of fractal clusters increases appreciably with increase of the thickness of nonmagnetic shells at the nanoparticle surfaces.Comment: The paper is accepted for Nanoscale Res. Let

Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations

Commutative sets of Jucys-Murphyelements for affine braid groups of $A^{(1)},B^{(1)},C^{(1)},D^{(1)}$ types were defined. Construction of $R$-matrix representations of the affine braid group of type $C^{(1)}$ and its distinguish commutative subgroup generated by the $C^{(1)}$-type Jucys--Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the $C^{(1)}$-type Jucys--Murphy elements. We specify our general construction to the case of the Birman--Murakami--Wenzl algebras. As an application we suggest a baxterization of the Dunkl--Cherednik elements $Y's$ in the double affine Hecke algebra of type $A$

Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

Off-shell two loop QCD vertices

We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MSbar scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off-shell.Comment: 29 latex pages, 32 figures, anc directory contains txt file with electronic version of vertex functions for each of the three 3-point cases in the MSbar scheme and includes the projection matrice

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe