In this review we discuss cosmologicalN-body codes with a special emphasis on particle mesh codes. We present the mathematical model for each component ofN-body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined to reduce the overall errors inN-body codes.

In this communication, we investigate the behavior of the derivatives of invariants for Hamiltonian systems, using information derived from an analysis of the Liapunov exponents of the system. We show that under certain conditions on the analyticity properties of the solutions of the equations of motion, it is possible to construct 2n invariants of motion which are guaranteed to beC^∞ as functions of phase space and time in a suitably defined domainD.

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary orderp can also be rewritten in terms ofp supercharges (i.e. all of which obeyQ_i²=0). However, the Hamiltonian cannot be expressed in a simple form in terms of thep supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, thep supercharges, thep conformal supercharges along with HamiltonianH, conformal generatorK and dilatation generatorD form a closed algebra.

FRW models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe.

We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.

We study high energy photon production from a quark-gluon plasma at finite baryon density. We find that the photon production spectrum from the quark-gluon plasma maintained at constant temperature is only mildly dependent on the quark chemical potential.

We have studied some of the two body nonleptonic decays ofB meson in the context of heavy quark effective theory using factorization hypothesis. Treatinga₁ as a free parameter, we have obtained its value asa₁=0.822±0.045, by correlating the experimental and predicted branching ratio for$$\bar B^0 \to D^ + \pi ^ - $$ process. With this value ofa₁ the branching ratios obtained for other decay channels are in good agreement with the experiment. The decay constant ofD meson is extracted to be 280.82 MeV. Heavy quark spin symmetry has also been tested.

In the optical model (OM) approach for fusion, absorption of flux occuring beyond the barrier position is presented in detail at low energies. It has been shown that the OM transmission can be well approximated as a sum of the WKB transmission and a long range absorption (LRA) contribution. Owing to absence of LRA, the fusion predictions of coupled channel codes based on transmission approach like the CCFUS code, do not agree with the predictions of complete coupled reaction channel (CRC) calculations based on OM approach using the code FRESCO. The CCFUS code with a modified transmission which includes LRA contribution is shown to be consistent with the CRC results using FRESCO. The static deformation of the colliding nuclei strongly influences the fusion imaginary potential and therefore the deep sub-barrier fusion cross sections.

Cross-sections for the reactions with product nuclei²⁴Na,²²Na,⁶⁸Ga and⁶⁷Ga were investigated over the energy range of 30 to 75 MeV for alpha particle induced reactions on natural aluminium and copper, using stacked-foil activation technique. The measured excitation functions were analysed with special reference to their suitability for monitoring beam energy and intensity. The experimental results were compared with the predictions of hybrid model of Blann. The assumption of initial exciton numbern₀=4(4p0h) best satisfies the measured excitation functions in the present work.