Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

Algebraic Integration of Sigma Model Field Equations

We prove that the dualization algebra of the symmetric space coset sigma model is a Lie algebra and we show that it generates an appropriate adjoint representation which enables the local integration of the field equations yielding the first-order ones.Comment: 27p

Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics

A theoretical formula for the probability density function (PDF) of velocity derivatives in a fully developed turbulent flow is derived with the multifractal aspect based on the generalized measures of entropy, i.e., the extensive Renyi entropy or the non-extensive Tsallis entropy, and is used, successfully, to analyze the PDF's observed in the direct numerical simulation (DNS) conducted by Gotoh et al.. The minimum length scale r_d/eta in the longitudinal (transverse) inertial range of the DNS is estimated to be r_d^L/eta = 1.716 (r_d^T/eta = 2.180) in the unit of the Kolmogorov scale eta.Comment: 6 pages, 1 figur

Aggregates of rod-coil diblock copolymers adsorbed at a surface

The behaviour of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adsorbs with the rods parallel to the surface the rods shift with respect to each other to allow for the chains to gain entropy. It is shown that this shift decays with increasing distance from the surface. The profile of this decay away from the surface is calculated by minimisation of the total free energy of the system. The stability of such an adsorbed aggregate and other possible configurations are discussed as well.Comment: 10 pages, 11 figure

Single and pair production of heavy leptons in E6E_6 model

We investigate the single and pair production of new heavy leptons via string inspired $E_{6}$ model at future linear colliders. Signal and corresponding backgrounds for these leptons are studied. We have found that single production of heavy leptons is more relevant than that of pair production, as expected. For a maximal mixing value of 0.1, the upper mass limits of 2750 GeV in the single case and 1250 GeV in the pair production case are obtained at $\sqrt{s}=3$ TeV collider option.Comment: 14 pages, 10 figure