The Lorentz gas model describes a cloud of noninteracting point particles in an infinitely extended array of spherical scatterers with centers in a given locally finite point set of uniform density. In the classical case of identical scatterers, Marklof and Strömbergsson have recently developed a general framework that derives the macroscopic transport equations of this gas for a large class of such point sets. This master's thesis is part of a forthcoming paper by the author that generalizes this framework so as to allow non-identical scatterers. Under certain conditions on the point set and on the distribution of scatterer types, we prove a limit theorem for the free path length and the parameters of the first collision. We also establish bounds on the probability of grazing a scatterer, and sketch how this knowledge gives control of the flight process in the macroscopic limit. As an application, we show that our hypotheses hold for finite unions of affine lattices with one scatterer type per lattice, generalizing a recent result of Palmer and Strömbergsson.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-533282 |
| Date | January 2024 |
| Creators | Avelin, Erik |
| Publisher | Uppsala universitet, Dynamiska system och talteori |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2024:11 |
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