Robust control of chaos in Chua’s circuit based on internal model principle

The paper treats the question of robust control of chaos in Chua’s circuit based on the internal model principle. The Chua’s diode has polynomial non-linearity and it is assumed that the parameters of the circuit are not known. A robust control law for the asymptotic regulation of the output (node voltage) along constant and sinusoidal reference trajectories is derived. For the derivation of the control law, the non-linear regulator equations are solved to obtain a manifold in the state space on which the output error is zero and an internal model of the k-fold exosystem (k = 3 here) is constructed. Then a feedback control law using the optimal control theory or pole placement technique for the stabilization of the augmented system including the Chua’s circuit and the internal model is derived. In the closed-loop system, robust output node voltage trajectory tracking of sinusoidal and constant reference trajectories are accomplished and in the steady state, the remaining state variables converge to periodic and constant trajectories, respectively. Simulation results are presented which show that in the closed-loop system, asymptotic trajectory control, disturbance rejection and suppression of chaotic motion in spite of uncertainties in the system are accomplished.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Intranuclear cascading at ultrahigh energy in heavy-ion interactions

Intranuclear cascading mechanism one of the important non-linear effects in high energy nucleusnucleus collisions is investigated. The data on multiplicity (n _s ) and pseudorapidity (η) distributions of shower particles produced by³²S and¹⁶O at 200A GeV,¹⁶O at 60A GeV,²⁸Si at 14.5A GeV and He at ≈140A GeV are presented and compared with the string model VENUS, which takes into account the cascade interactions of secondary particles. The effect of the intranuclear collisions on the distributions of <η> versus <n _s > is discussed for all the beams.     

High spin states in120Xe

High spin states in ¹²⁰Xe, populated via¹⁰⁷Ag(¹⁶O, p2n) and¹⁰⁸Pd(¹⁶O, 4n)reactions have been studied using γ-ray spectroscopic techniques. 21 new transitions have been added to extend the level scheme. Two S-bands are extended upto 26⁺ and 22⁺;these bands are found to cross the g. s band at hΩ=0. 39 and 0. 47 MeV. The band structures have been discussed within the framework of CSM.     

Hyperfine structure and isotope shift studies of rhenium by laser optogalvanic spectroscopy

Doppler-limited high resolution laser optogalvanic spectra of six transitions of rhenium lying in the range 560–620 nm have been recorded. Isotope shifts between the two natural isotopes of rhenium,¹⁸⁵Re and¹⁸⁷Re, have been calculated in all the six transitions. Hyperfine coupling constants for eight levels belonging to the configurations 5d ⁵6s ², 5d ⁶6s, 5d ⁴6s ²6p and 5d ⁵6s6p are reported. Wherever possible our constants are compared with those given by others.     

Electrical properties of the Ag2SO4-Na2SO4 binary system

A systematic investigation of the Ag₂SO₄-Na₂SO₄ binary system which forms a complete solid solution in the entire compositional range reveals the mobility of Ag⁺ as well as Na⁺. This is concluded on the basis of the appearance of two overlapping semicircles in the complex impedance plane. Transport number measurements using Tubandt and dc polarisation methods support the mobility of both ions. Further, the maximum conductivity for 30 Ag₂SO₄-70 Na₂SO₄ is due to optimum percolating paths resulting from lattice expansion. The decrease in conductivity beyond this, is caused by the increased interaction of Ag⁺ and Na⁺.     

Certain fractional derivative formulae involving the product of a general class of polynomials and the multivariableH-function

In the present paper, we obtain three unified fractional derivative formulae (FDF). The first involves the product of a general class of polynomials and the multivariableH-function. The second involves the product of a general class of polynomials and two multivariableH-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives. The last FDF also involves the product of a general class of polynomials and the multivariableH-function but it is obtained by the application of the first FDF twice and it involves two independent variables instead of one. The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the typex ^ρ Π _i=1 ^s (x ^t _i +α _i ) ^σ _i are quite general in nature. These formulae, besides being of very general character have been put in a compact form avoiding the occurrence of infinite series and thus making them useful in applications. Our findings provide interesting unifications and extensions of a number of (new and known) results. For the sake of illustration, we give here exact references to the results (in essence) of five research papers [2, 3,10, 12, 13] that follow as particular cases of our findings. In the end, we record a new fractional derivative formula involving the product of the Hermite polynomials, the Laguerre polynomials and the product ofr different Whittaker functions as a simple special case of our first formula.