Stochastic mechanics

Mischke, C. R. 1992 Fitting Weibull Strength Data and Applying it to Stochastic Mechanical Design. Journal of Mechanical Design, 114, 35-41. 

To obtain a large transfer area between raffinate and extract phases, one of the two liquids must be dispersed into drops. Figure 9.2 demonstrates this process schematically at a single nozzle. Similar to a dripping water tap, individual drops periodically leave the nozzle when the volumetric flow rate of the dispersed phase is low. When the flow rate is higher, however, the liquid forms a continuous jet from the nozzle that breaks into droplets. Because of stochastic mechanisms, uniform droplets are not formed. If the polydispersed droplet swarm is characterized by a suitable mean drop... 

A. Naess and S. Krenk (eds.) IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. Proceedings of the IUTAM Symposium held in Trondheim, Norway. 1996... 

H.H. McAdams, A. Arkin, Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94(3), 814-819 (1997)... 

If we are again moving with the velocity v, then a Gaufi distribution will arise that broadens in time. Often this behavior is addressed that the particle flows away or melts in time. Thus, we are finding in the stochastic mechanics a very similar situation to that in comparison to the quantum mechanics. The concepts of the position and the momentum must be revisited and replaced by a new concept. In stochastic mechanics, we can reasonably justify that a particle never can be observed in an isolated manner. Here an interaction with other particles in the neighborhood appears. This interaction cannot be described by a deterministic method. Therefore, we chose a statistic description of the motion. Quantum mechanics starts with certain postulates that cannot be justified in detail. The success of the method defends it, even when the vividness suffers. 

The similarity of stochastic mechanics with quantum mechanics has been pointed out and used by several authors [7-9]. The relationship goes back to Nelson [10, 11], who published in the mid-1960s a stochastic theory that eventually led to SchrPdinger s equation. At that time. Nelson s theory did not become very popular, because it did not explain the origin of the stochastic noise, which is essential for this theory. However, nowadays this theory seems to have been rediscovered [12]. 

Durran, R., Neate, A., Truman, A. The divine clockwork Bohr s correspondence principle and Nelson s stochastic mechanics for the atomic elliptic state. J. Math. Phys. 49,1 2 (2008). [electronic] URL http //arxiv.org/abs/0711.0157 http //arxiv.org/abs/0711.0157... 

Beck, J.L. 6c Katafygiotis, L.S. 1991. Updating of a model and its uncertainties utilizing dynamic test data, 1st International Conference on Computational Stochastic Mechanics, Corfu, Greece. 

McAdams, H.H., and A. Arldn. 1997. Stochastic mechanisms in gene expression. Proceedings of the National Academy of Sciences 94(3) 814-819. 

As in failures analysis this process consists of two main steps (i) inference of reliability quantities that explain the stochastic mechanism that originate the accident/recovery process such as accidents and recovery rates and (ii) characterization of accidental behavior by applying stochastic process analysis methods (e.g. Markov process). 

Several important theoretical aspects also were not reviewed here, most notably those pertaining to systems with fluctuating barriers and boundaries [97, 189,190], anomalous diffusion [55, 95, 191] and Hamiltonian methods for large fluctuations [52, 185]. Finally, in this review we focused entirely on the analytical approaches. Simulation techniques that complement analytical approaches have played a crucial role in revealing the stochastic mechanisms of cells and molecules. We direct the reader to Refs. 51, 181, and 192 as starting points for further inquiry. 

Department of Mechanical Aeronautical Engineering, Stochastic Mechanical Systems and Automation (SMSA) Laboratory, University of Patras, Patras, Greece... 

Schueller G (1997) A state-of-the-art report on computational stochastic mechanics. Probabilist Eng Mech 12(4) 197-321... 

Cacciola P, Colajanni P, Muscolino G (2004) Combination of modal responses consistent with seismic input representation. J Struct Eng 130 47-55 Crandal SH (1979) Random vibration of one- and two-dimensiRandom vibration of discrete and continuous systems, hi Schiehlen W, Wedig W (eds) Analysis and estimation of stochastic mechanical systems. International centre for mechanical sciences - CISM, courses and lectures no. 303. Springer, Berlin Eurocode 8 (2004) Design of structures for earthquake resistance - part 1 general rules, seismic actions and rules for buildings. European Committee for Standardization (CEN), Bruxelles... 

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