Two-dimensional random walk description of fluid flow in the presence of a wall: The origin of stick versus slip boundary conditions in the continuum limit

It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1) specular reflection, 2) diffuse reflection and 3) trapping at the surface. The steady state is solved exactly. In the continuum limit the case of stick versus slip boundary conditions is explained in its relation to the interplay of bulk and boundary processes.     

On the functional integral representation of general continuous markov processes

The unambiguous continuous functional integral representation of general diffusion processes will be derived by means of a transformation invariant Fourier series analysis of the alternate paths between specified endpoints. Previous results from Stratonovich, Horsthemke and Bach, and Graham will be confirmed, while deeper insight is gained into the limit of continuity in functional integration.     

On the theory of activation: Kramers' reaction rate in bistable systems

Kramers' model for equilibrium via noise activated escape over a potential barrier is considered as an eigenvalue problem. Using Rayleigh's identity for the pertinent eigenvalue, the escape rate is obtained for a bistable system with a smooth parabolic barrier.     

PHOTOCHEMICAL HYDROXYLATION OF 7,8-DIMETHYLALLOXAZINE (LUMICHROME)-A FLASH PHOTOLYSIS STUDY

Abstract— Flash photolysis experiments on the hydroxylation of lumichrome (L) in aqueous 0.5 M H₂SO₄ solution in the presence of O₂ or Ni²⁺ as triplet quenchers and quantum yield measurements confirm the assignment of the photoreactive species to the protonated form of the excited singlet state. A mechamism concerning the photochemical step is proposed, accounting for the formation of protonated 9-hydroxy-5,10-dihydrolumichrome (LOH₃⁺). This primary stable photoproduct was characterized by spectral and kinetic data. The dark reactions originating from LOH₃⁺ were investigated, and data regarding the successive steps are presented. The reaction LOH₃⁺ L→ LO + LH₃⁺ is demonstrated to be a two-electron reduction. The rate constant for the reaction of LH₂⁺ with O₂ is much larger than that for the oxidation of LH₃⁺ by oxygen.     

Ultrafast laser written active devices

Direct‐write optical waveguide device fabrication is probably the most widely studied application of femtosecond laser micromachining in transparent dielectrics at the present time. Devices such as buried waveguides, power splitters, couplers, gratings, optical amplifiers and laser oscillators have all been demonstrated. This paper reviews the application of the femtosecond laser direct‐write technique to the fabrication of active waveguide devices in bulk glass materials.