2,519 research outputs found
Robust Adaptive Control
Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known
Fermion Number Fractionization
Solitons emerge as non-perturbative solutions of non-linear wave equations in
classical and quantum theories. These are non-dispersive and localised packets
of energy-remarkable properties for solutions of non-linear differential
equations. In presence of such objects, the solutions of Dirac equation lead to
the curious phenomenon of "fractional fermion number", a number which under
normal conditions takes strictly integral values. In this article, we describe
this accidental discovery and its manifestation in polyacetylene chains, which
has lead to the development of organic conductors.Comment: 10 pages, 3 figure
Perturbative Bottom-up Approach for Neutrino Mass Matrix in Light of Large \theta_{13} and Role of Lightest Neutrino Mass
We discuss the role of lightest neutrino mass (m_0) in the neutrino mass
matrix, defined in a flavor basis, through a bottom-up approach using the
current neutrino oscillation data. We find that if m_0 < 10^{-3} eV, then the
deviation \delta M_\nu in the neutrino mass matrix from a tree-level, say
tribimaximal neutrino mass matrix, does not depend on m_0. As a result \delta
M_\nu's are exactly predicted in terms of the experimentally determined
quantities such as solar and atmospheric mass squared differences and the
mixing angles. On the other hand for m_0 \gsim 10^{-3} eV, \delta M_\nu
strongly depends on m_0 and hence can not be determined within the knowledge of
oscillation parameters alone. In this limit, we provide an exponential
parameterization for \delta M_\nu for all values of m_0 such that it can
factorize the m_0 dependency of \delta M_\nu from rest of the oscillation
parameters. This helps us in finding \delta M_\nu as a function of the solar
and atmospheric mass squared differences and the mixing angles for all values
of m_0. We use this information to build up a model of neutrino masses and
mixings in a top-down scenario which can predict large \theta_{13}
perturbatively.Comment: 26 pages, 42 eps figures, revtex (references are added, more
discussions are added in section-III
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