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1. Justino, Júlia Maria da Rocha Vilaverde. Nonstandard linear algebra with error analysis.

Degree: 2013, Universidade de Évora

Neste trabalho consideramos sistemas de equações lineares exíveis, sistemas de equações lineares cujos coe cientes têm incertezas de tipo o (:) ou O (:). Este tipo de incertezas irá ser analisado, à luz da análise não standard, como conjuntos de in nitesimais conhecidos como neutrizes. Em sistemas de equações lineares exíveis nem sempre existe uma solução exata. No entanto, neste trabalho apresentam-se condições que garantem a existência de pelo menos uma solução admissível, no sentido de inclusão, e as condições que garantem a existência de solução maximal nesse tipo de sistemas. Tais condições são restrições àcerca da ordem de grandeza do tipo de incertezas existentes, tanto na matriz dos coe cientes do sistema como na respetiva matriz dos termos independentes. Utilizando a regra de Cramer sob essas condições é possível produzir, pelo menos, uma solução admissível do sistema. No caso em que se garante a obtenção da solução maximal do sistema pela re- gra de Cramer, prova-se que essa solução corresponde à solução obtida pelo método de eliminação de Gauss; ABSTRACT: Systems of linear equations, called exible systems, with coe¢ cients having uncertain- ties of type o (:) or O (:) are studied from the point of view of nonstandard analysis. Then uncertainties of the afore-mentioned kind will be given in the form of so-called neutrices, for instance the set of all in nitesimals. In some cases an exact solution of a exible system may not exist. In this work conditions are presented that guarantee the existence of an admissible solution, in terms of inclusion, and also conditions that guarantee the existence of a maximal solution. These conditions concern restrictions on the size of the uncertainties appearing in the matrix of coe¢ cients and in the constant term vector of the system. Applying Cramer s rule under these conditions, one obtains, at least, an admis- sible solution of the system. In the case a maximal solution is produced by Cramer s rule, one proves that it is the same solution produced by Gauss-Jordan elimination. Advisors/Committee Members: Berg, Imme van den.

Subjects/Keywords: Regra de Cramer; Método de eliminação de Gauss; Neutrizes; Números externos; Análise não standard; Cramer´s rule; Gauss-Jordan elimination; Neutrices; External numbers; Nonstandard analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Justino, J. M. d. R. V. (2013). Nonstandard linear algebra with error analysis. (Thesis). Universidade de Évora. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:dspace.uevora.pt:10174/16316

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Justino, Júlia Maria da Rocha Vilaverde. “Nonstandard linear algebra with error analysis.” 2013. Thesis, Universidade de Évora. Accessed November 20, 2019. http://www.rcaap.pt/detail.jsp?id=oai:dspace.uevora.pt:10174/16316.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Justino, Júlia Maria da Rocha Vilaverde. “Nonstandard linear algebra with error analysis.” 2013. Web. 20 Nov 2019.

Vancouver:

Justino JMdRV. Nonstandard linear algebra with error analysis. [Internet] [Thesis]. Universidade de Évora; 2013. [cited 2019 Nov 20]. Available from: http://www.rcaap.pt/detail.jsp?id=oai:dspace.uevora.pt:10174/16316.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Justino JMdRV. Nonstandard linear algebra with error analysis. [Thesis]. Universidade de Évora; 2013. Available from: http://www.rcaap.pt/detail.jsp?id=oai:dspace.uevora.pt:10174/16316

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of Southern California

2. Yang, Shanling. Boundary layer and separation control on wings at low Reynolds numbers.

Degree: PhD, Aerospace Engineering, 2013, University of Southern California

In the transitional chord-based Reynolds number regime for aeronautics, 10⁴ ≤ Re ≤ 10⁵, fluid flow over a surface is prone to separation followed by possible reattachment and transition to turbulence. The amplification of disturbances in the boundary layer promotes transition to turbulence, so boundary layer and separation control methods are especially favorable in this transitional Re regime. The use of sound to control flow separation at transitional and moderate Re for various smooth airfoils has been experimentally studied in the literature. Optimum excitation frequencies are reported to match the frequency or sub harmonics of the naturally occurring instabilities in the shear layer, and correlations between optimum frequencies for external acoustic forcing and tunnel anti-resonances have been observed. However, reported optimum frequency values based on the Strouhal number scaling St/Re^(1/2) are not in complete agreement among the different reported studies. Little attention has been given to distinguish the effects of standing waves from traveling sound waves. Mathematical and experimental studies of sound and boundary layer instability interactions have also yielded mixed results, suggesting that there still lacks a full understanding about the mechanism by which acoustic waves affect boundary layer flows. ❧ Results on boundary layer and separation control through acoustic excitation at low Re numbers are reported. The Eppler 387 profile is specifically chosen because of its pre-stall hysteresis and bi-stable state behavior in the transitional Re regime, which is a result of flow separation and reattachment. External acoustic forcing on the wing yields large improvements (more than 70%) in lift-to-drag ratio and flow reattachment at forcing frequencies that correlate with the measured anti-resonances in the wind tunnel. The optimum St/Re^(1/2) range for Re = 60,000 matches the proposed optimum range in the literature, but there is less agreement for Re = 40,000, which suggests that correct St scaling has not been determined. The correlation of aerodynamic improvements to wind tunnel resonances implies that external acoustic forcing is facility-dependent, which inhibits practical application. Therefore, internal acoustic excitation for the same wing profile is also pursued. ❧ Internal acoustic forcing is designed to be accomplished by embedding small speakers inside a custom-designed wing that contains many internal cavities and small holes in the suction surface. However, initial testing of this semi-porous wing model shows that the presence of the small holes in the suction surface completely transforms the aerodynamic performance by changing the mean chordwise separation location and causing an originally separated, low-lift state flow to reattach into a high-lift state. The aerodynamic improvements are not caused by the geometry of the small holes themselves, but rather by Helmholtz resonance that occurs in the cavities, which generate tones that closely match the intrinsic flow instabilities.… Advisors/Committee Members: Spedding, Geoffrey R. (Committee Chair), Redekopp, Larry G. (Committee Member), Eliasson, Veronica (Committee Member), Bickers, Gene (Committee Member), Radovich, Charles (Committee Member).

Subjects/Keywords: low Reynolds numbers; separation control; acoustic excitation; active separation control; passive separation control; boundary layers; fluid dynamics; aerodynamics; Helmholtz resonance; local acoustic forcing; external acoustic excitation; internal excitation; flow control

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Yang, S. (2013). Boundary layer and separation control on wings at low Reynolds numbers. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/337675/rec/1155

Chicago Manual of Style (16th Edition):

Yang, Shanling. “Boundary layer and separation control on wings at low Reynolds numbers.” 2013. Doctoral Dissertation, University of Southern California. Accessed November 20, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/337675/rec/1155.

MLA Handbook (7th Edition):

Yang, Shanling. “Boundary layer and separation control on wings at low Reynolds numbers.” 2013. Web. 20 Nov 2019.

Vancouver:

Yang S. Boundary layer and separation control on wings at low Reynolds numbers. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2019 Nov 20]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/337675/rec/1155.

Council of Science Editors:

Yang S. Boundary layer and separation control on wings at low Reynolds numbers. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/337675/rec/1155

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