Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.Comment: 23 page

Estimation of Wind Hazard over Canada and Reliability-based Assignment of Design Wind Load

The current National Building Code of Canada (NBCC) recommends a wind load factor of 1.4 and the nominal wind velocity pressure corresponding to 50-year return period value of the annual maximum hourly-mean wind speed, VAH. This study is focused on mapping wind hazard for Canada and on calibrating the required design wind load to improve reliability consistency of the designed structures. Extreme value analysis of VAH was carried out by considering surface wind observations from approximately 1300 stations. The results indicate that the spatial trends of the estimated mean of VAH are similar whether the data from stations with at least 20 or 10 years’ useable wind observations are considered, but the small sample size affects the spatial variations of the coefficient of variation (cov) of VAH. The estimated 50-year return period values of VAH based on the at-site analysis differ from those inferred from two previous versions of the NBCC, and the differences persist if the estimates were obtained by using the region of influence approach. Potential reasons for the discrepancy were elaborated. It was shown that an improved reliability consistency can be achieved if a wind load factor of 1.0 is employed and the nominal wind velocity pressure is assigned using 500-year return period value of VAH. It is also shown that a further improvement on the reliability consistency can be achieved if a variable return period as a function of cov of VAH is used to assign the nominal wind velocity pressure