Quantum groups in the higgs phase

In the Higgs phase we may be left with a residual finite symmetry groupH of the condensate. The topological interactions between the magnetic and electric excitations in these so-called discreteH gauge theories are completely described by the Hopf algebra or quantum groupD(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebraD(H) into the quasi-Hopf algebraD (H) by means of a 3-cocycle onH. Consequently, the finite number of physically inequivalent discreteH gauge theories obtained in this way are labelled by the elements of the cohomology groupH ³(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 509–523, March, 1994     

Geometry of coset spaces and massless modes of the squashed seven-sphere in supergravity

We derive some general results for Killing vectors on arbitrary coset manifolds and explicitly exhibit the squashed seven-sphere as the coset space Sp₄×Sp₂/Sp₂×Sp₂. Using these results, we then analyze the zero-mass sector of supergravity of the squashed S⁷ and argue that it is not interpretable as a spontaneously broken version of N=8 supergravity. We also point out the existence of a new solution which combines squashing and torsion.     

Composite vector fields and tumbling gauge theories

In non-abelian gauge theories with a non-real fermion content it is possible that vector channels become more attractive than the most attractive scalar channel. It is speculated that the appearance of a vector condensate may signal the presence of massless composite vector fields which gauge a flavour symmetry of the underlying model, as is suggested by earlier work on non-linear spinor models.     

Adaptation of dynamical properties of time series data and its applications in deep brain stimulation

Nonlinear Dynamics - The chaotic nature of the brain can be observed by electroencephalogram signals. This chaotic behavior can be affected by the progressive nature of neurodegenerative disorders...     

Configurations of SO(3) monopoles with multiple magnetic charge

In this paper we consider configurations of monopoles with multiple magnetic charge in nonabelian gauge theory. Explicit gauge transformations are constructed which eliminate the string singularities for single monopoles of multiple magnetic charge, and for an arbitrary number of monopoles lying along a line. The question of finding nonsingular solutions is discussed.     

Skin Cancer Risks Avoided by the Montreal Protocol—Worldwide Modeling Integrating Coupled Climate‐Chemistry Models with a Risk Model for UV

The assessment model for ultraviolet radiation and risk “AMOUR” is applied to output from two chemistry‐climate models (CCMs). Results from the UK Chemistry and Aerosols CCM are used to quantify the worldwide skin cancer risk avoided by the Montreal Protocol and its amendments: by the year 2030, two million cases of skin cancer have been prevented yearly, which is 14% fewer skin cancer cases per year. In the “World Avoided,” excess skin cancer incidence will continue to grow dramatically after 2030. Results from the CCM E39C‐A are used to estimate skin cancer risk that had already been inevitably committed once ozone depletion was recognized: excess incidence will peak mid 21st century and then recover or even super‐recover at the end of the century. When compared with a “No Depletion” scenario, with ozone undepleted and cloud characteristics as in the 1960s throughout, excess incidence (extra yearly cases skin cancer per million people) of the “Full Compliance with Montreal Protocol” scenario is in the ranges: New Zealand: 100–150, Congo: ?10–0, Patagonia: 20–50, Western Europe: 30–40, China: 90–120, South‐West USA: 80–110, Mediterranean: 90–100 and North‐East Australia: 170–200. This is up to 4% of total local incidence in the Full Compliance scenario in the peak year.     

On the algebraic structure of self-dual gauge fields and sigma models

An extensive and detailed analysis of self-dual gauge fields, in particular with axial symmetry, is presented, culminating in a purely algebraic procedure to generate solutions. The method which is particularly suited for the construction of multimonopole solutions for a theory with arbitrary G, is also applicable to a wide class of non-linear sigma models.The relevant symmetries as well as the associated linear problems which underly the exact solubility of the problem, are constructed and discussed in detail.