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2 A Quantum Particle in One Dimension‣ Quantum Mechanics by David Tong
www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S2.html18 Oct 2021: and. -. 𝑑. x. x. e. -. a. x. 2. =. 0. (2.24). where the second equality follows because the integrand is odd (and suitably well behaved at infinity). ... σ. ). exp. (. -. x. 2. σ. |. α. |. 2. ). =. k. 0. where, to get the final equality, we did the -
Biofilm Growth Under Elastic Confinement: Supplementary Material…
www.damtp.cam.ac.uk/user/gold/pdfs/Fortune_etal_SM021221.pdf2 Dec 2021: 2/x0 0 24 6/x4 2/x2. -
1 Classical Field Theory‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S1.html18 Oct 2021: ϕ. (. y. ). (1.24). A priori, there’s no reason for this. -
Vol. 44 (2013) ACTA PHYSICA POLONICA B No 12 ...
www.damtp.cam.ac.uk/user/tong/talks/zakopane.pdf15 Apr 2021: ds2 =L2. r2. (f(r)dt2 dr. 2. f(r) ηµνdx. µdxν). (24). and. ... This is the Reissner–Nordström black hole solution. Itagain has metric (24), now with the function f(r) taking the form. -
2 Free Fields‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S2.html18 Oct 2021: 24. d. 𝒪. (. a. 2. ). where, in the last line, we’ve used the fact that. ... π. 24. (. 1. d. 1. L. -. d. ). 𝒪. (. a. 2. ). (2.113). This is still infinite in the limit. -
Part III MathematicsFluid Dynamics of Climate (PHH part) Michaelmas…
www.damtp.cam.ac.uk/user/phh/atmosocean/notes2020-21_lectures11-15_19-24.pdf16 Sep 2021: equations. Lectures 16-18 JRT 11 Fronts, 12 Internal wavesand instability inside fronts: Lectures 19-24 PHH, 13 Wave mean-flow interaction, 14Mean meridional circulations, 15 Equatorial waves.These notes include -
5 Phase Transitions‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S5.html18 Oct 2021: 5 Phase Transitions. 5 Phase Transitions. A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein condensation. In that case, we -
Preprint typeset in JHEP style - HYPER VERSION Lent ...
www.damtp.cam.ac.uk/user/tong/aqm/solidstate.pdf7 Apr 2021: qg = 2πn with n Z (1.24). This is the famous Dirac quantisation condition. ... qg = 2πn with n Z. This, of course, is the Dirac quantisation condition (1.24). -
Stabilizing viscous extensional flows using reinforcement learning
www.damtp.cam.ac.uk/user/lauga/papers/205.pdf1 Dec 2021: Biological and bioinspired appli-cations at high Reynolds numbers include control and energyoptimization in fish swimming [24–26], gliding and perching[27], and locomotion in potential flows [28]. ... Dt 1 = Dt βt δt Qt. (24)To ensure convergence, it -
5 When Gravity is Weak‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S5.html16 Oct 2021: 5 When Gravity is Weak. 5 When Gravity is Weak. The elegance of the Einstein field equations ensures that they hold a special place in the hearts of many physicists. However, any fondness you may feel for these equations will be severely tested if
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