On perturbation problems associated with finite boundaries

Wassermann, Günter; Mott, N. F.

doi:10.1017/s030500410002421x

Cited by 11 publications

(2 citation statements)

References 11 publications

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“…We now assume that the outer boundary is displaced by a small amount such that the new surface point nr is a unit vector from the unperturbed surface pointing outwards. Using the method detailed by (Wassermann, 1948) and (Hinch, 1991) we expand the solution to Eqn. (1b) using perturbation theory.…”

Section: Expansion Of Perturbed Surfaces In Transport Theorymentioning

confidence: 99%

Methods of studying the effect of rough surfaces on reactivity in two-dimensional reactor physics problems

Williams

Eaton

2019

Annals of Nuclear Energy

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Rough and perturbed surfaces are examined in the field of reactor physics using homotopy, homogenisation and the Feinberg-Galanin method. The homotopy method allows a problem with a perturbed interface to be represented as an unperturbed problem with a modified boundary condition. Perturbation theory was applied to this method and the results were studied for the neutron transport equation, the neutron diffusion approximation and a hybrid ABH-diffusion approximation. The homogenisation of surface roughness in the fuelmoderator interface was also examined and compared to the homotopy approach. Finally, the effect of larger-scale geometric uncertainties was studied using the Feinberg-Galanin approach. The effectiveness of the methods is determined by examining the change in effective multiplication factor keff examined both directly and via the six-factor formula. Analytic solutions to approximations of perturbation theory differentials were capable of accurately predicting the change in keff when compared to numerical solutions. Examining a change in fuel pin radius of 20 µm, we find that for water moderated systems the overall change in eff k is close to 70 pcm and for graphite systems it is 18 pcm. This shows that water and graphite moderated cores are sensitive to small changes in geometry.

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Section: Expansion Of Perturbed Surfaces In Transport Theorymentioning

confidence: 99%

Methods of studying the effect of rough surfaces on reactivity in two-dimensional reactor physics problems

Williams

Eaton

2019

Annals of Nuclear Energy

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“…When these effects are caused by an underlying elastic deformation field u (as defined in section 2.2.1), a coupling between the cavity electromagnetic field and the elastodynamic field results, which we compute now. Following the work of Bethe and Schwinger [181] (see also [182]), we consider the two configurations shown in fig. 2.10, depicting a cavity perturbed in shape, i.e.…”

Section: Photon-phonon Coupling In a Cavitymentioning

confidence: 99%

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sudhir

2018

Springer Theses

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PAR Vivishek SUDHIR JOSEPH CONRAD, Heart of DarknessExperimental physics demands a certain degree of manual dexterity, the patience to tolerate the mundane, and an inexhaustible supply of optimism. Tobias hired me to work on an immensely sophisticated experiment despite any proof of my possessing these qualities; I am indebted to him for the belief he has placed in me. I would also like to acknowledge his dedication to fostering an environment where the pursuit of science is unencumbered by other worldly concerns. Stefan, Ewold and Samuel bore the brunt of a theorist trying to perform delicate experiments; the stern, yet encouraging, stewardship of this trio ensured that I enjoyed the culture shock. Dal Wilson was more than a colleague and a post-doc; his pragmatic approach to physics provided the ideal counter-point in our attempts to forge a deeper understanding of things ranging from vibration isolation to the subtleties of quantum mechanics. Without the patient efforts of Amir, Ryan and Hendrik in designing, fabricating, and testing of devices, none of the results reported here would have been possible. I hope I have been able to bequeath a better vision of the future of our experiment to Sergey. Conversations with Alexey, Daniel and Nathan have enabled me to vicariously learn how to measure microwave "photons". John Jost once taught me how to decorate a Christmas tree; since then he has imparted some wisdom on frequency metrology, and some on atomic physics. Together with Dal, Victor and Caroline have probably spent the most time with me outside the lab; it was fun to exercise an air of social normalcy with this bunch. Christophe has been an amazing sparring partner on every subject capable of being brought under scientific scrutiny.The personal space required for the pursuit of science comes through the sacrifice of many people. My family back home in India -parents, sister, grand-parents -have had to patiently wait for the brief interludes when I go home. No words can do justice to this and the very many other pleasures they have surrendered over the years for my sake. Before physics attracted me, I was charmed by someone else; I am lucky to have married her. Long time friends, mentorsAjith and Subeesh -have played pivotal roles in my being able to engage in physics; I hope to repay this enormous debt, some day.It was a privilege to have learnt from a few great teachers during my formative years. Their vision of an indelible unity in nature continues to motivate my study of physics. vii AbstractThe precision measurement of position has a long-standing tradition in physics. Cavendish's verification of the universal law of gravitation using a torsion pendulum, Perrin's confirmation of the atomic hypothesis via the precise measurement of the Brownian motion, and, the verification of the mechanical effect of electromagnetic radiation, all belong to this classical heritage. Quantum mechanics posits that the measurement of position results in an uncertain momentum; an idea developed to full maturity within the ...

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Photon-Phonon Coupling: Cavity Optomechanics

Sudhir

2017

Springer Theses

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On perturbation problems associated with finite boundaries

Cited by 11 publications

References 11 publications

Methods of studying the effect of rough surfaces on reactivity in two-dimensional reactor physics problems

Methods of studying the effect of rough surfaces on reactivity in two-dimensional reactor physics problems

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Photon-Phonon Coupling: Cavity Optomechanics

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