Numerical Methods with Worked Examples: Matlab Edition

a b s t r a c tThis paper presents a novel solar-powered active Stirling converter with liquid power piston and solid controllable displacer. First, the working principle of the proposed converter is described. Then, finite time thermodynamic approach incorporating heat transfer equations are employed to determine gas temperatures in hot and cold spaces based on the assumption of imperfect regeneration. Accordingly, pressure variation of the gas due to reciprocating motion of the displacer piston is investigated using the obtained gas temperatures and Schmidt theory. Next, total work done by the converter and thermal efficiency are evaluated. Kinematic and dynamic equations governing the pump system are presented and the water flow characteristics in suction and discharge states are investigated. A simulation study is carried out through coupling and simultaneously solving the obtained equations. An optimization scheme is thus conducted to find an optimum frequency of the active converter so that a maximum power is generated. The influences of regenerator efficiency, dead volumes, and water head on the optimum operating frequency and the generated power are investigated. Finally, the proposed converter is constructed and primarily tested. The experimental outcomes clearly reveal the feasibility of pumping water at low temperature difference through the proposed active Stirling pump.

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“…(21) and (22)) is a difficult task. Therefore, NewtoneRaphson method [29] was proposed to iteratively find an approximate solution:…”

Section: Thermal Analysismentioning

confidence: 99%

A novel solar-powered active low temperature differential Stirling pump

Jokar

Tavakolpour-Saleh

2015

Renewable Energy

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“…The procedure is in fact similar to the definition of the Riemann integral or various procedures of numerical integration e.g. [32,33]. Let us approximate time series A and B by a continuous function and in order to avoid absolute value notation assume that a i ≤ b i , additionally let assume that time series A and B are correlated Eq.…”

Section: Power Law Classification Schemementioning

confidence: 99%

Network Analysis of Correlation Strength between the Most Developed Countries

Miśkiewicz

2013

Acta Phys. Pol. A

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A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classication scheme followed by the analysis of the network on the percolation threshold. The algorithm was applied to the analysis of correlations among gross domestic product per capita time series of 19 most developed countries in the periods (1982, 2011), (1992, 2011) and (2002, 2011). The representative countries with respect to strength of correlation, convergence of time series and stability of correlation are distinguished. The results are compared with ultrametric distance matrix analysed by network on the percolation threshold.

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“…We motivate our contribution with examples that model physical processes, taken from [18,4,15]. These examples illustrate the applicability of our techniques and introduce the main features of our library.…”

Section: Contributionsmentioning

confidence: 99%

“…We illustrate the basic features of our library on the following system of three non-linear equations with three unknowns (v, ω, r). An engineer may need to solve such a system to compute the stress on a turbine rotor [18].…”

Section: Contributionsmentioning

confidence: 99%

Certifying Solutions for Numerical Constraints

Darulová

Kunčak

2013

Runtime Verification

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Abstract. A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the use of approximate numerical methods. Much of numerical software uses self-stabilizing iterative algorithms, for example, to find solutions of nonlinear equations.To support such algorithms, we present a runtime verification technique that checks, given a nonlinear equation and a tentative solution, whether this value is indeed a solution to within a specified precision. Our technique combines runtime verification approaches with information about the analytical equation being solved. It is independent of the algorithm used for finding the solution and is therefore applicable to a wide range of problems. We have implemented our technique for the Scala programming language using our affine arithmetic library and the macro facility of Scala 2.10.

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Numerical Methods with Worked Examples: Matlab Edition

Cited by 25 publications

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A novel solar-powered active low temperature differential Stirling pump

A novel solar-powered active low temperature differential Stirling pump

Network Analysis of Correlation Strength between the Most Developed Countries

Certifying Solutions for Numerical Constraints

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