Eigenfunctions for Liouville Operators, Classical Collision Operators, and Collision Bracket Integrals in Kinetic Theory

In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit the eigenvalue problem of the Liouville operator and re-examine the method previously reported[Chem. Phys. 20, 93(1977)]. Then we apply the notion and concept of the eigenfunctions of the Liouville operator and knowledge acquired in the study of the eigenfunctions to obtain alternative forms for collision integrals. One of the alternative forms is given in the form of time correlation function. This form, on an additional approximation, assumes a form reminiscent of the Chapman-Enskog collision bracket integral for dilute gases. It indeed gives rise to the latter in the case of two particles. The alternative forms obtained are more readily amenable to numerical simulation methods than the collision bracket integras expressed in terms of a classical collision operator, which requires solution of classical Lippmann-Schwinger integral equations. This way, the aforementioned kinetic theory of dense fluids is made more accessible by numerical computation/simulation methods than before.Comment: 34 pages, no figure, original pape

The product in the Hochschild cohomology ring of preprojective algebras of Dynkin quivers

In this paper, we compute the product structure of the Hochschild cohomology of preprojective algebras of quivers of type D and E over a field of characteristic zero.Comment: 55 page

Future research priorities of Organic Agriculture. Policy paper of the IFOAM EU Group

This policy paper presents the main research priorities for organic farming agreed by the IFOAM EU Group. It identifies the main clusters both in a table format and with a more detailed explanation of the individual priorities. The paper was discussed at the board meeting of 13th March 2004, amended by additional input from national farmers’ associations and various research institutes from all EU members, revised with a priorisation exercise at the board meeting of 26th June in Lednice (Czech Rep) and finally was reviewed and approved at the board meeting in Bonn the 3rd September

Book Review: Islamic Finance Principles and Practice, by Hans Visser, Cheltenham: Edward Elgar, 2009, 184 pp.

- book review