General properties of the light and heavy quark propagators have been investigated in the context of string tension interaction. Confinement, chiral symmetry breaking, spectral properties of the propagator are analytically studied and numerically validated. We show that the propagator is analytic in the infrared region even for massless quarks with a non zero radius of convergence. Emergence of more than one mass scale is exemplified. Massless limit of the quark propagator does exhibit critical behaviour.

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A systematic method of analysing Bethe-Salpeter equation using spectral representation for the relativistic bound state wave function is given. This has been explicitly applied in the context of perturbative QCD with string tension in the 1 N expansion. We show that there are only a few stable bound state mesons due to the small "threshold mass"(constituent mass) of quarks. The asymptotic properties of the bound states are analytically analysed. The spectrum is derived analytically and compared phenomenologically. Chiral symmetry breaking and PCAC results are demonstrated. We make a simple minded observation to determine the size of the bound states as a function of the energy of the boundstate.

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Abstract. The one-dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take-up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non-stationary equations the effect of viscoelasticity on the stability of the spinning process was studied.