Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Coordination driven self-assembly of metallamacrocycles using ambidentate linkers and self-selection of single linkage isomer

Nicotinate-N-oxide and isonicotinate-N-oxide have been employed to synthesize four heterometallic metallamacrocycles (dppf)(2)Pd-2(nicotinate-N-oxide)(2)](OTf)(2) (1), (dppf)(2)Pt-2(nicotinate-N-oxide)(2)](OTf)(2) (2), (dppf) 2Pd2(isonicotinate-N-oxide)(2)](OTf)(2) (3) and (dppf)(2)Pt-2(isonicotinate-N-oxide)(2)](OTf)(2) (4). The complexes represent the first examples of metallamacrocycles driven by solely Pd(II)/Pt(II)-O coordination using carboxylate-N-oxide donor. All the complexes 1-4 are characterized by IR, UV-Vis, multinuclear NMR spectroscopic and ESI-MS studies. The molecular structures of the complexes 1 and 3 are unambiguously determined by single crystal X-ray diffraction analysis. Despite the possibility of formation of several linkage isomers due to ambidentate nature of the donors, exclusive formation of 2 + 2] self-assembled single isomeric metallamacrocycle in each case is interesting observation. (C) 2011 Elsevier B.V. All rights reserved.

Novel correlations in two dimensions: Two-body problem

We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyse in detail the two-body problem which is completely solvable. We show that the solution of the two-body problem reduces to solving a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strengths and the level structure resembles that of the Landau levels. We also clarify the 'ultraviolet' regularization which is needed to define an inverse-square potential properly and discuss its implications for our model.