Supercurrent anomaly in non-abelian supersymmetric theories

A method for regularizing the supercurrent, preserving both gauge invariance and supersymmetry is developed, using point-splitting regularization and path-dependent phase factors in superspace. The supercurrent anomaly for general non-abelian supersymmetric theories is obtained on the mass-shell in the one-loop approximation.     

EPR study of the structure of mechanically activated periclase powders

The EPR method has been used to study mechanically activated periclase powders. The Mn²⁺ and Cr³⁺ spectra in MgO depend on the number of defects. The lines broaden to a degree which depends on the nuclear spin; the ratio between the hyperfine components changes; the line shape changes from Lorentzian to a convoluted form; and the relative intensity of the forbidden transitions in the Mn²⁺ changes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 3, pp. 48–52, March, 1969.     

Some prime factorization results for type II<Subscript>1</Subscript> factors

We prove several unique prime factorization results for tensor products of type II₁ factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if is isomorphic to a subfactor in , for some 2r_i,s_j, then mn. Mathematics Subject Classification (2000) Primary 46L10; Secondary 20F67     

Laponite: aging and shear rejuvenation of a colloidal glass

We study the nonlinear rheological behavior and the microscopic particle dynamics for a colloidal glass, to see whether recently developed models for driven glassy systems can be applied to predict the rheology. Qualitatively, all the findings predicted by the models can be retrieved in our system. Notably, the viscosity decreases strongly with the shear rate. Since it is difficult to predict non-Newtonian viscosities of colloidal systems due to long-ranged hydrodynamic interactions, this shows the promise of this approach for predicting flow behavior. In addition, the measurements allow us to relate the microscopic diffusion dynamics to the macroscopic viscosity of the system.     

The Moduli Space of (1,11)-Polarized Abelian Surfaces is Unirational

We prove that the moduli space A ₁₁ ^lev of (1,11)-polarized Abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface in P ⁴ . Therefore, A ₁₁ ^lev is unirational but not rational, and there are no ₁₁-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of A ₉ ^lev .     

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.     

A II1 Factor Approach to the Kadison–Singer Problem

We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra \({\ell^\infty\mathbb{N}\subset \mathcal{B}(\ell^2\mathbb{N})}\) have unique state extensions to \({\mathcal{B}(\ell^2\mathbb{N})}\) , is equivalent to a similar statement in II₁ factor framework, concerning the ultrapower inclusion \({D^\omega \subset R^\omega}\) , where D is the Cartan subalgebra of the hyperfinite II₁ factor R (i.e., a maximal abelian *-subalgebra of R whose normalizer generates R, e.g. \({D=L^\infty([0, 1]^{\mathbb{Z}}) \subset L^\infty([0,1]^{\mathbb{Z}} \rtimes \mathbb{Z} = R)}\) , and ω is a free ultrafilter. Instead, we prove here that if A is any singular maximal abelian *-subalgebra of R (i.e., whose normalizer consists of the unitary group of A, e.g. \({A=L(\mathbb{Z})\subset L^\infty([0,1]^\mathbb{Z})\rtimes \mathbb{Z}=R}\) ), then the inclusion \({A^\omega \subset R^\omega}\) does satisfy the Kadison–Singer property.