On Blowup for Gain-Term-Only classical and relativistic Boltzmann equations

We show that deletion of the loss part of the collision term in all physically relevant versions of the Boltzmann equation, including the relativistic case, will in general lead to blowup in finite time of a solution and hence prevent global existence. Our result corrects an error in the proof given in Ref. [12], where the result was announced for the classical hard sphere case; here we give a simpler proof which applies much more generally.Comment: 10 pages, 2 figure

A model for generating circadian rhythm by coupling ultradian oscillators

BACKGROUND: Organisms ranging from humans to cyanobacteria undergo circadian rhythm, that is, variations in behavior that cycle over a period about 24 hours in length. A fundamental property of circadian rhythm is that it is free-running, and continues with a period close to 24 hours in the absence of light cycles or other external cues. Regulatory networks involving feedback inhibition and feedforward stimulation of mRNA transcription and translation are thought to be critical for many circadian mechanisms, and genes coding for essential components of circadian rhythm have been identified in several organisms. However, it is not clear how such components are organized to generate a circadian oscillation. RESULTS: We propose a model in which two independent transcriptional-translational oscillators with periods much shorter than 24 hours are coupled to drive a forced oscillator that has a circadian period, using mechanisms and parameters of conventional molecular biology. Furthermore, the resulting circadian oscillator can be entrained by an external light-dark cycle through known mechanisms. We rationalize the mathematical basis for the observed behavior of the model, and show that the behavior is not dependent on the details of the component ultradian oscillators but occurs even if quite generalized basic oscillators are used. CONCLUSION: We conclude that coupled, independent, transcriptional-translational oscillators with relatively short periods can be the basis for circadian oscillators. The resulting circadian oscillator can be entrained by 24-hour light-dark cycles, and the model suggests a mechanism for its evolution

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

Hydroformylation of 1-Dodecene in Microemulsions: Operation and Validation of Lab Results in a Miniplant

A method of hydroformylation to convert long- chained olefins, using tunable microemulsion systems, tests were conducted on a mini-plant at the center InPROMPT/TRR 63. Surfactant allowing a quasi-homogeneous reaction of olefin in aqueous Rhodium catalyst solution

The Broadwell Model in a Box: Strong L1-Convergence to Equilibrium

The global solution of the one-dimensional Broadwell model in the interval [1,0], with reflecting boundary conditions at 0, is shown to converge strongly in L1[0,1] to the constant equilibrium solution

Marketing on Random Networks

Non UBCUnreviewedAuthor affiliation: University of VictoriaFacult