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Demographic characteristics of nuclear power station sites in the UK and US
Published in Stan Openshaw, Nuclear Power, 2019
An approximate rule of thumb that can be applied to Table 7.5 is to look for a ‘significant’ discontinuity in the within cluster sum of squares function. A major jump occurs between 5 and 6 types suggesting that perhaps 6 is the most parsimonious choice. The reader who is interested further in the taxonomic method that was used should refer to the CCP package program which is described in Openshaw (1982).
Applications of Radiation Energy Transfer
Published in John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel, Thermal Radiation Heat Transfer, 2020
John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel
19.4A radiator is planned to reject excess heat from a nuclear power plant that provides electrical power for a lunar outpost. The radiator is horizontal on the lunar surface, and condensing working fluid in the power cycle will maintain the surface temperature of the radiator at a uniform temperature of 800 K. The radiator is shielded from the nearby lunar outpost by a 1.5 m high vertical plate (see diagram). The width of the radiator is limited to 2 m. The radiator has a diffuse-gray emissivity of 0.92, while the shield has a diffuse-gray emissivity of 0.37. The shield is made of a material with thermal conductivity of k = 300 W/m·K and has a thickness of 2 cm. It is backed with a layer of very good insulation. It is expected that the radiator will be quite long. A solar flux of 1360 W/m2 is incident on the radiator/shield system at an angle of 30° to the normal of the radiator. Set up the equations for finding the heat flux distribution on the radiator, q1(x), and the temperature distribution on the shield, T2(y). Note any assumptions.Solve the equations for q1(x) and T2(y). Compare your solution to the results for the non-conducting case with and without solar energy input. Generate a contour plot of the weighted sum-of-squares function over the ranges τL ∈ [1, 5] and Ω∈ [0, 1], and overlay the solutions obtained from part (b).If the total heat rejection from the radiator is required to be 1 MW, what must be the length of the radiator (m)?If the radiator itself has a thickness of 1 cm and a thermal conductivity of 287 W/m·K, how would your solution change?
Process Modeling and Identification
Published in F. Joseph Schurk, Pradeep B. Deshpande, Kenneth W. leffew, Vikas M. Nadkarni, Control of Polymerization Reactors, 2017
Schurk F. Joseph, Deshpande Pradeep B.
For stochastic estimation, the effect of transients can be minimized by starting at t = u + 1, where u is the larger of rand s + b. Thus, the conditional sum of squares function takes on the expression
An alternative sensitivity method for a two-dimensional inverse heat conduction-radiation problem based on transient hot-wire measurements
Published in Numerical Heat Transfer, Part B: Fundamentals, 2018
The LMM is an iterative procedure based on the minimization of a sum of squares function expressed as the quadratic difference between the model predictions and the experimental measurements. The parameters considered to be inversely estimated are put in a vector of unknowns P = (k, β, ω) and the sum of squares function is written as:
Consensus analysis of multi-agent systems with general linear dynamics and switching topologies by non-monotonically decreasing Lyapunov function
Published in Systems Science & Control Engineering, 2019
Xieyan Zhang, Linfeng Chen, Yan Chen
Consensus problems with time-dependent communication links have been considered for MASs without self-dynamics (Moreau, 2004, 2005; Olfati-Saber & Murray, 2004). In Moreau (2004), an intrinsic limitation has been pointed out that balance conditions in terms of constraints on the column sums of the coupling matrix need to be imposed when the sum of squares function is considered as a candidate-Lyapunov function, and a generalized conclusion of consensus has been obtained by contraction analysis with the aid of the Lyapunov function . For general linear MASs including unstable dynamics, consensus problems under switching-disconnected topologies are much more complex, because convergence analyses depend on the stability of isolated agents and the connectivity of network topologies. Regardless of the intrinsic limitation, the difficulty of applying Lyapunov method is that each switched sub-system may not be a convergent one. With non-increasing Lyapunov function, several sufficient conditions of consensus for marginally stable agents have been obtained by Ni and Cheng (2010), Qin, Yu, and Gao (2014), Su and Huang (2012a, 2012b), Huang (2017) and Meng, Yang, Li, Ren, and Wu (2018). However, the condition, derivatives of Lyapunov functions are negative semidefinite along the solutions of dynamics, cannot be satisfied in the case of exponentially unstable dynamics and switching-disconnected topologies. As an extension of classic Lyapunov function method, non-monotonically decreasing Lyapunov function method (NMDLF method) (Aeyels & Peuteman, 1999; Zhou, 2016) is applicable to complex time-varying dynamics, especially for fast time-varying systems. It is worth noting that, in the works of Li, Liao, Lei, Huang, and Zhu (2013; Li, Liao, Huang, Zhu, & Liu, 2015) and Ni, Wang, and Xiong (2012), consensus and leader-following consensus problems of general linear MASs have been considered by their averaged systems with the help of NMDLF method. However, conditions under which NMDLF is feasible have not been discussed thoroughly.