Self-diffusion in a non-uniform one dimensional system of point particles with collisions

Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle converges, as A , to a Brownian motion W _D (t) with diffusion constant , where is the average density, is the mean absolute velocity and ^–1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e. , then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.Dedicated to Frank Spitzer on the occasion of his 60th birthdayWork supported in part by NSF Grants No. PHY 8201708 and No. DMR 81-14726Heisenberg-fellowAlso Department of Physics     

Direct separation of the enantiomers of cetirizine and related compounds by reversed-phase chiral HPLC

Summary Direct separations of the enantiomers of cetirizine and related compounds have been achieved by reversed-phase HPLC on the Chiralcel OD-R, a polysaccharide-derived chiral stationary phase; the mobile phase was usually perchlorate solution supplemented with acetonitrile. Resolution of the enantiomers of cetirizine and related compounds was good. The effect of the acetonitrile content of the mobile phase was investigated, and the effect of the structure of the chiral compounds on their behavior on the Chiralcel OD-R column is discussed.     

A graph-theoretic approach to quantitative structure—activity/reactivity studies

Characterization of molecular species based on the use of suitable graph invariants (graph paths, in particular) can provide a quantitative means of encoding structure; the technique is complementary to commoner approaches to studies of quantitative structure— activity relationships. Graph path encoding is here applied to quantitative studies of relationships between molecular structures and biological activity; the examples are the rates of various substrate reactions with hexoldnase, and the potential opiate-like activity of enkephalin analogs.     

Reactivity of singlet oxygen toward strained substrates and a novel non-photochemical method for determination of quenching constants of singlet oxygen.

Rate constants for quenching of ¹O₂ by a number of strained molecules have been determined by the competitive rubrene photooxidation method; the rate constant for quenching by Q may be evaluated by adaption of a kinetic analysis already in the literature for the rubrene photooxidation method.