... analysis (or stochastic optimization) can couple the generated random samples with the constructed unit operation and process production model. While the computational complexity of the coupled model will increase exponentially, resulting in large-scale strong nonlinear programming problems, and even...

.... , Cafaro , D. C. , and Grossmann , I. E. , “ Stochastic programming models for optimal shale well development and refracturing planning under uncertainty ,” AIChE J.   63 , 4799 – 4813 ( 2017 ). 10.1002/aic.15804 Ehlinger , V. M.  et al., “ Process design and integration...

... – 4898 ( 2022 ). 10.1016/j.egyr.2022.03.175 Wu , Z. , Lu , Z. , Zhang , B. , He , C. , Chen , Q. , Yu , H.   et al. , “ Stochastic bi-objective optimization for closed wet cooling tower systems based on a simplified analytical model ,” Energy   250 , 123703 ( 2022...

.../behavior) Measurement processes  (definition, superposition, collapse, evolution) Heisenberg uncertainty principle Measurement in QM as a process changing suddenly the state of a system in an irreversible way as a consequence of the intrinsic stochasticity (not an instrumental effect...

... stochasticity (not an instrumental effect) Intrinsic limit to the precision of an incompatible observable simultaneous measure Orbital structure of atoms (probability distribution and not electron rotating on orbits) Stability of atoms not explainable in a classical framework  completely defines...

... system reliability evaluation. Several methods have accordingly been proposed to evaluate the reliability of such systems, including the Markov process, Monte Carlo simulation, reliability block diagram, and fault tree analysis. Markov process The stochastic behavior of a PV system can be regarded...

.../j.compchemeng.2018.08.011 Lee , D. , Mohr , A. , Kwon , J. S. I. , Wu , H. J. , and Singla , A. , “ Stochastic modelling of CTB-receptor binding kinetics ,” in Computer Aided Chemical Engineering ( Elsevier , 2018 ), Vol. 44 , pp. 2143 – 2148 . Lee , D. , Singla...

... into deterministic optimization, stochastic optimization, and meta-heuristic optimization. In this way, the large-scale real-world problems that were intractable mathematically in the past can be solved nowadays thanks to the new technological developments in algorithms and computer hardware. The most used...

... ). Goel , V. and Grossmann , I. E. , “ A stochastic programming approach to planning of offshore gas field development under uncertainty in reserves ,” Comput. Chem. Eng.   28 , 1409 – 1429 ( 2004 ). 10.1016/j.compchemeng.2003.10.005 Gu , Q. and Hoo , K. A. , “ Evaluating...

... of the electron gas by a stochastic method ,” Phys. Rev. Lett.   45 , 566 – 569 ( 1980 ). 10.1103/PhysRevLett.45.566 Chanana , A. and Waghmare , U. V. , “ Prediction of coupled electronic and phononic ferroelectricity in strained 2D h-NbN: First-principles theoretical analysis ,” Phys. Rev...

... ( 7774 ), 394 – 397 ( 2019 ). 10.1038/s41586-019-1544-1 Cabral , T. , Filho , O. , Diniz , C. , Martins , H. , Toledo , O. M. , Neto , L. , and de , V. B. M. , “ A stochastic method for stand-alone PV system sizing ,” Sol. Energy   84 , 1628 – 1636 ( 2010...

... mobility, and ζ( r , t) is a random field uncorrelated in space and time added to mimic stochastic processes such as nucleation during first-order phase transition. Electrostatic equilibrium equation (Gauss's law of electrostatics): (6.84) − ϵ 0 ϵ b ∇ 2 ϕ ( r...

... and data science rely on the concepts of statistical mechanics. Hinton (2007) , a forefather of AI, advocated a symmetrically connected network with a stochastic decision node, so called Boltzmann machine. According to this algorithm, the total input, z_i, is calculated where the sum...

.... , “ Kinetic Monte Carlo modeling of multivalent binding of CTB proteins with GM1 receptors ,” Comput. Chem. Eng.   118 , 283 – 295 ( 2018 ). 10.1016/j.compchemeng.2018.08.011 Lee , D. , Mohr , A. , Kwon , J. S. I. , Wu , H. J. , and Singla , A. , “ Stochastic modelling of CTB...

... ,” Nature   573 ( 7774 ), 394 – 397 ( 2019 ). 10.1038/s41586-019-1544-1 Cabral , T. , Filho , O. , Diniz , C. , Martins , H. , Toledo , O. M. , Neto , L. , and de , V. B. M. , “ A stochastic method for stand-alone PV system sizing ,” Sol. Energy   84 , 1628 – 1636...

..., it is well known that solar energy production strongly depends on local weather and climate conditions. Thus, its inherently intermittent and stochastic characteristics of non-dispatchable solar energy can bring instability to the power system. These stability issues, due to the fluctuating features...

..., 2016 ). A further advantage of using geometry might lie in the more pictorial representations which are not as abstract as an algebraic expression. A drawback might lie in the fact that geometry in mathematics education is reduced in teaching compared to stochastics, algebra and calculus. This implies...

... 1000 adults and over 25% said that radioactive waste would “decay within 100 years.” Eijkelhof mentioned that some of the difficulties people face in understanding radioactivity could arise in part because radioactive decay is stochastic in nature ( Eijkelhof, 1990 ), and we have explored this idea...