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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 -
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 -
Diagonalising Infinite-Dimensional Operators 2mmComputing spectral…
www.damtp.cam.ac.uk/user/mjc249/talks/ICOSAHOM_mjc214 Jul 2021: 1.29:. 1.28:. 1.27:. 1.26:. 1.25:. 1.24:. 1.23:. 1.22:. 1.21:. 1.20:. 1.19:. ... 0.31:. 0.30:. 0.29:. 0.28:. 0.27:. 0.26:. 0.25:. 0.24:. 0.23:. 0.22:. 0.21:. -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/CRUNCH_mjc11 Jun 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM. -
J. Fluid Mech. (2021), vol. 914, A20, doi:10.1017/jfm.2020.1112 The…
www.damtp.cam.ac.uk/user/lauga/papers/186.pdf8 Jul 2021: of Bristol, 24 Tyndall Avenue, Bristol BS8 1TQ, UK. ... uθ = cΩ I1(κr)K1(κ) K1(κr)I1(κ)I1(κc)K1(κ) K1(κc)I1(κ), (4.24)where. α0 = cκΩ. I1(κ)I1(κc)K1(κ) -
Energetics of synchronization for model flagella and cilia
www.damtp.cam.ac.uk/user/lauga/papers/189.pdf8 Jul 2021: For larger ciliatedcells [24], or for multicellular aquatic organisms equippedwith many short flagella [25], the synchronization dynamicstakes the form of metachronal waves, akin to spectator wavesin sport stadiums. ... p = p1 O(2 ), (24). σ = σ1 O(2 ). -
Modelling chordwise-varying porosity to reduceaerofoil-turbulence…
www.damtp.cam.ac.uk/user/mjc249/pdfs/AIAA_mjc_2021_a.pdf31 Jul 2021: tomodel the effects of the porous plate, where 𝜇 = 𝛼𝐻𝐾𝑅/(𝜋𝑟2) is the porosity parameter [23, 24]. ... 723, 2013, pp. 456–479. [24] Howe,M.S., Scott,M. I., andSipcic, S.R., “The influenceof tangentialmeanflowon theRayleigh -
2 Classical Gases‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S2.html18 Oct 2021: 2 Classical Gases. 2 Classical Gases. Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, flying around in a box. Although much of the -
3 Quantum Gases‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S3.html18 Oct 2021: 3 Quantum Gases. 3 Quantum Gases. In this section we will discuss situations where quantum effects are important. We’ll still restrict attention to gases — meaning a bunch of particles moving around and barely interacting — but one of the -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/seven.pdf12 Jun 2021: 7. Special Relativity. Although Newtonian mechanics gives an excellent description of Nature, it is not uni-. versally valid. When we reach extreme conditions — the very small, the very heavy or. the very fast — the Newtonian Universe that
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