925 research outputs found
Surface group representations in with finite mapping class orbits
Given an oriented surface of positive genus with finitely many punctures, we
classify the finite orbits of the mapping class group action on the moduli
space of semisimple complex special linear two dimensional representations of
the fundamental group of the surface. For surfaces of genus at least two, such
orbits correspond to homomorphisms with finite image. For genus one, they
correspond to the finite or special dihedral representations. We also obtain an
analogous result for bounded orbits in the moduli space.Comment: 30 pages, 5 figures, accepted for publication in Geometry & Topolog
Analysis of the Three-dimensional Superradiance Problem and Some Generalizations
We study the integral equation related to the three and higher dimensional
superradiance problem. Collective radiation phenomena has attracted the attention
of many physicists and chemists since the pioneering work of R. H. Dicke in 1954.
We first consider the three-dimensional superradiance problem and find a differential
operator that commutes with the integral operator related to the problem. We
find all the eigenfunctions of the differential operator and obtain a complete set of
eigensolutions for the three-dimensional superradiance problem. Generalization of
the three-dimensional superradiance integral equation is provided. A commuting differential
operator is found for this generalized problem. For the three dimensional
superradiance problem, an alternative set of complete eigenfunctions is also provided.
The kernel for the superradiance problem when restricted to one-dimension is the
same as appeared in the works of Slepian, Landau and Pollak. The uniqueness of the
differential operator commuting with that kernel is indicated. Finally, a concentration
problem for the signals which are bandlimited in disjoint frequency-intervals is
considered. The problem is to determine which bandlimited signals lose the smallest
fraction of their energy when restricted in a given time interval. A numerical
algorithm for solution and convergence theorems are given. Orthogonality properties
of analytically extended eigenfunctions over L2(−∞,∞) are also proved. Numerical
computations are carried out in support of the theory
Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PI{\lambda}D{\mu} Controllers to Handle a Class of Fractional Order Systems
A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and
Integral of Squared Controller Output (ISCO) minimization based time domain
optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is
proposed in this paper with a Linear Quadratic Regulator (LQR) based technique
that minimizes the change in trajectories of the state variables and the
control signal. A class of fractional order systems having single non-integer
order element which show highly sluggish and oscillatory open loop responses
have been tuned with an LQR based FOPID controller. The proposed controller
design methodology is compared with the existing time domain optimal tuning
techniques with respect to change in the trajectory of state variables,
tracking performance for change in set-point, magnitude of control signal and
also the capability of load disturbance suppression. A real coded genetic
algorithm (GA) has been used for the optimal choice of weighting matrices while
designing the quadratic regulator by minimizing the time domain integral
performance index. Credible simulation studies have been presented to justify
the proposition.Comment: 6 pages, 5 figure
Embedded Network Test-Bed for Validating Real-Time Control Algorithms to Ensure Optimal Time Domain Performance
The paper presents a Stateflow based network test-bed to validate real-time
optimal control algorithms. Genetic Algorithm (GA) based time domain
performance index minimization is attempted for tuning of PI controller to
handle a balanced lag and delay type First Order Plus Time Delay (FOPTD)
process over network. The tuning performance is validated on a real-time
communication network with artificially simulated stochastic delay, packet loss
and out-of order packets characterizing the network.Comment: 6 pages, 12 figure
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