Subfactor realisation of modular invariants

We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D_5^(1). In particular for the double of S_3, 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors

Coupling the solar surface and the corona: coronal rotation, Alfv\'en wave-driven polar plumes

The dynamical response of the solar corona to surface and sub-surface perturbations depends on the chromospheric stratification, and specifically on how efficiently these layers reflect or transmit incoming Alfv\'en waves. While it would be desirable to include the chromospheric layers in the numerical simulations used to study such phenomena, that is most often not feasible. We defined and tested a simple approximation allowing the study of coronal phenomena while taking into account a parametrised chromospheric reflectivity. We addressed the problems of the transmission of the surface rotation to the corona and that of the generation of polar plumes by Alfv\'en waves (Pinto et al., 2010, 2011). We found that a high (yet partial) effective chromospheric reflectivity is required to properly describe the angular momentum balance in the corona and the way the surface differential rotation is transmitted upwards. Alfv\'en wave-driven polar plumes maintain their properties for a wide range of values for the reflectivity, but they become bursty (and eventually disrupt) when the limit of total reflection is attained.Comment: Solar Wind 13: Proceedings of the Thirteenth International Solar Wind Conferenc

The Phase Structure of the Weakly Coupled Lattice Schwinger Model

The weak coupling expansion is applied to the single flavour Schwinger model with Wilson fermions on a symmetric toroidal lattice of finite extent. We develop a new analytic method which permits the expression of the partition function as a product of pure gauge expectation values whose zeroes are the Lee-Yang zeroes of the model. Application of standard finite-size scaling techniques to these zeroes recovers previous numerical results for the small and moderate lattice sizes to which those studies were restricted. Our techniques, employable for arbitrarily large lattices, reveal the absence of accumulation of these zeroes on the real hopping parameter axis at constant weak gauge coupling. The consequence of this previously unobserved behaviour is the absence of a zero fermion mass phase transition in the Schwinger model with single flavour Wilson fermions at constant weak gauge coupling.Comment: 8 pages, 2 figures, insert to figure 2 include

Monitoring thermal ablation via microwave tomography. An ex vivo experimental assessment

Thermal ablation treatments are gaining a lot of attention in the clinics thanks to their reduced invasiveness and their capability of treating non-surgical patients. The effectiveness of these treatments and their impact in the hospital's routine would significantly increase if paired with a monitoring technique able to control the evolution of the treated area in real-time. This is particularly relevant in microwave thermal ablation, wherein the capability of treating larger tumors in a shorter time needs proper monitoring. Current diagnostic imaging techniques do not provide effective solutions to this issue for a number of reasons, including economical sustainability and safety. Hence, the development of alternative modalities is of interest. Microwave tomography, which aims at imaging the electromagnetic properties of a target under test, has been recently proposed for this scope, given the significant temperature-dependent changes of the dielectric properties of human tissues induced by thermal ablation. In this paper, the outcomes of the first ex vivo experimental study, performed to assess the expected potentialities of microwave tomography, are presented. The paper describes the validation study dealing with the imaging of the changes occurring in thermal ablation treatments. The experimental test was carried out on two ex vivo bovine liver samples and the reported results show the capability of microwave tomography of imaging the transition between ablated and untreated tissue. Moreover, the discussion section provides some guidelines to follow in order to improve the achievable performances

The Structure of the Aoki Phase at Weak Coupling

A new method to determine the phase diagram of certain lattice fermionic field theories in the weakly coupled regime is presented. This method involves a new type of weak coupling expansion which is multiplicative rather than additive in nature and allows perturbative calculation of partition function zeroes. Application of the method to the single flavour Gross-Neveu model gives a phase diagram consistent with the parity symmetry breaking scenario of Aoki and provides new quantitative information on the width of the Aoki phase in the weakly coupled sector.Comment: 9 pages, 1 figure (minor changes) To be published in Phys. Lett.

Orbit Representations from Linear mod 1 Transformations

We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta,\alpha}(x)=\beta x +\alpha$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{\beta,\alpha}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $\alpha\in [0,1[$ and $\beta\geq 1$