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David Tong, Theoretical Physicist: A Collection of Talks and…
www.damtp.cam.ac.uk/user/tong/talks.html17 Jun 2021: PDF (8 Mb). Particle-Vortex Duality PDF (8 Mb). Quantum Hall Matrix Models PDF (20 Mb). -
Eocene Syndrome'
www.damtp.cam.ac.uk/user/mem/eocene-syndrome.html17 Jul 2021: Copyright Michael E. McIntyre 2009. Last updated 20 March 2019. -
How To Compute Spectra With Error Control 2mmOn The Foundations of…
www.damtp.cam.ac.uk/user/mjc249/talks/ICOSAHOM_mjc110 Jul 2021: γ. Im(z). Re(z)-30 -25 -20 -15 -10 -5 5 10. -40. ... 40. -30. -20. -10. 10. 20. 30. 40. γ. Scδ,0. Im(z). -
Hull Vibration Excitation by Propeller Sources: a link between…
www.damtp.cam.ac.uk/user/or100/DISW_Intro.pdf19 Apr 2021: temperature, pressure,. • 20 Hz wave: 75m λ in water17m λ in air. -
1 Classical Field Theory‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S1.html18 Oct 2021: 1. 2. A. ˙. i. 2. The Lagrangian (1.20) has no kinetic term. ... To see that Maxwell’s equations indeed follow from (1.20), we compute. (. -
Diagonalising Infinite-Dimensional Operators 2mmComputing spectral…
www.damtp.cam.ac.uk/user/mjc249/talks/ICOSAHOM_mjc214 Jul 2021: O(log. (1 )). |ρf (x0) µf (x0)| = O( log(1)) and need N 20/. ... 1.29:. 1.28:. 1.27:. 1.26:. 1.25:. 1.24:. 1.23:. 1.22:. 1.21:. 1.20:. 1.19:. -
Computing spectral measures anda programme on the foundations of ...
www.damtp.cam.ac.uk/user/mjc249/talks/spec_meas_IWOTA19 Aug 2021: O(log. (1 )). |ρf (x0) µf (x0)| = O( log(1)) and need N 20/. ... 1.29:. 1.28:. 1.27:. 1.26:. 1.25:. 1.24:. 1.23:. 1.22:. 1.21:. 1.20:. 1.19:. -
Communications inCommun. Math. Phys. 90, 161-173 (1983)…
www.damtp.cam.ac.uk/user/tong/susy/index.pdf19 Apr 2021: 20)Π-£-, (4.7)M α tannxα. where xα's are the skew eigenvalues of the curvature form. ... Σ Π'CotKα )/2), (4.22). Equations (4.20)-(4.23) are the generalized fixed point theorems first derived byAtiyah and Bott [17]. -
Fluid Mechanics of Mosaic Ciliated Tissues
www.damtp.cam.ac.uk/user/gold/pdfs/mosaic.pdf2 Nov 2021: 20 -10 0 10 20-20 -10 0 10 200. 10. 20. ... 30. 40. 50. 0. 10. 20. 30. 40. 50(c) (d). isolated bundle. -
Supplemental Material:Fluid mechanics of mosaic ciliated tissues…
www.damtp.cam.ac.uk/user/gold/pdfs/mosaic_SM.pdf2 Nov 2021: Particle traces fromoverexposed images were obtained by setting the expo-sure time to 20 ms. ... 0.20.40.60.81. 1.2. 0 5 10. 300. 1200. 150. 600300. 12001200. 150. -
Computing semigroups and solutions of time-fractional PDEs with error …
www.damtp.cam.ac.uk/user/mjc249/talks/GSSI_mjc_final1 Dec 2021: 0 10 20 30 40 5010. -15. 10-10. 10-5. 100. t. ... 40. -30. -20. -10. 10. 20. 30. 40. γ. δ@@R. Im(z). -
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: Recall that we built the state by integrating over momentum modes in the window (2.20). ... Figure 10: Harmonic oscillator wavefunctions for the. 20. th. excited state on the left, and the. -
Turing’s diffusive threshold in random reaction-diffusion systems—…
www.damtp.cam.ac.uk/user/gold/pdfs/turing_SM.pdf9 Jun 2021: Onremoving zero roots, this discriminant of a discriminant isfound to be a polynomial of degree 20 in 3D or 3E, respec-tively; complicated expressions for its coefficients in terms ofthe ... 5, 15, 17.5, 20}.For # = 3, we ran both a search for general, -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/SIAM_2021_mjc23 Jul 2021: n = 20 106 K = 60.0000030 0.0000015 n = 30 106 K = 6. ... 0 10 20 30 40 50 60. 10-4. 10-3. 10-2. 10-1. -
Oldroyd B, and not A?
www.damtp.cam.ac.uk/user/hinch/talks/OldroydTalk4.pdf9 Sep 2021: τ. (〈rr〉 r. 20. 3I. ),. Note upper-convected time-derivative. And bulk stress, with number density of polymers n,. ... where A = 3〈rr〉/r 20 and L =. 3Nb/r0. 2c. Chilcott and Rallison (1988) suggested FENE-CR, with a constant shear viscosity,. -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/INI_MDL_mjc26 Oct 2021: n = 20 106 K = 60.0000030 0.0000015 n = 30 106 K = 6. ... 0 10 20 30 40 50 60. 10-4. 10-3. 10-2. 10-1. -
February 2021 EPL, 133 (2021) 44002 www.epljournal.orgdoi:…
www.damtp.cam.ac.uk/user/lauga/papers/188.pdf8 Jul 2021: In order to address the stability of a line of swimmers,we place 20 equally distant squirmers along a vertical line,i.e., the x-direction, as shown in fig. ... M., Science, 339 (2013) 936. [20] Dombrowski C., Cisneros L., Chatkaew S., Gold-stein R. -
Direct measurement of unsteady microscale Stokes flow using optically …
www.damtp.cam.ac.uk/user/gold/pdfs/unsteady.pdf27 May 2021: 20. 3. ], (12a). B(r ) = 3α02ρ3. [3 3α0 α20 (3 3ρ ρ2 )eα0ρ. ], ... 20) and (22) can be written thescaling forms for the phase and amplitude,. -
Purely viscous acoustic propulsion of bimetallic rods
www.damtp.cam.ac.uk/user/lauga/papers/202.pdf12 Sep 2021: Rods moving in the nodal plane(movie S2 [43]) were recorded for 5 s at 20 frames per second (FPS) (100 frames) and tracked usingMOSAICSUITE with CLIJ GPU acceleration [44,45] ... 20] B. Dai, J. Wang, Z. Xiong, X. Zhan, W. Dai, C. -
Front-back asymmetry controls the impact of viscoelasticity on…
www.damtp.cam.ac.uk/user/lauga/papers/191.pdf8 Jul 2021: experiments (from below 1 to above 20), a cleartrend is not apparent in the data. ... 12) with values ξs = 20 (solid line), 40 (dashed line), and 80(dash-dotted line). -
Capillary-Induced Motion of Particles Bridging Interfaces of a…
www.damtp.cam.ac.uk/user/hinch/publications/PhysRevLett.122.098001.pdf25 Oct 2021: Received 4 July 2018; revised manuscript received 20 December 2018; published 5 March 2019). ... Leja, Trans. Faraday Soc. 50, 598. (1954).[20] D. E. Tambe and M. -
1 Geodesics in Spacetime‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S1.html16 Oct 2021: Rediscovering Electromagnetism. Rather than jumping straight into the reparameterisation invariant action (1.14), we instead start by modifying the action (1.20). ... This time we consider the generalisation of (1.20) given by the action. -
Non-linear Forchheimer corrections in acoustic scattering Matthew…
www.damtp.cam.ac.uk/user/mjc249/pdfs/AIAA_mjc_2021_b.pdf31 Jul 2021: Constant. 10-2. 10-1. 100. 101. 102. -50. -40. -30. -20. -10. ... 20. 25. 30. 35. 40. Case 2. surface roughness. 10-2. 10-1. -
Vol. 44 (2013) ACTA PHYSICA POLONICA B No 12 ...
www.damtp.cam.ac.uk/user/tong/talks/zakopane.pdf15 Apr 2021: In this notation, Ohm’s law reads. j(ω) = σ(ω) E(ω). (20). ... The definition (20) then tells us the conductivity:it is. σ(ω) =σ0. -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justtwo.pdf7 Apr 2021: 1.0 -0.5 0.0 0.5 1.0. 0.0. 0.5. 1.0. 1.5. Figure 20:. -
3 Structure Formation‣ Cosmology by David Tong
www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S3.html18 Oct 2021: 3 Structure Formation. 3 Structure Formation. Until now, we have discussed a universe which is perfectly homogeneous and isotropic. But that is not the universe we live in. Instead, our universe contains interesting objects which clump together, -
Rechargeable self-assembled droplet microswimmers driven by surface…
www.damtp.cam.ac.uk/user/lauga/papers/198.pdf10 Sep 2021: Scale bars, 20 μm. NaTuRE PhySiCS | VOL 17 | SEPTEMBER 2021 | 1050–1055 | www.nature.com/naturephysics1052. ... 90. 80. 700 0. 0. 80. 60. 40. 20. 100 100 150 20050200 300 400. -
Modelling chordwise-varying porosity to reduceaerofoil-turbulence…
www.damtp.cam.ac.uk/user/mjc249/pdfs/AIAA_mjc_2021_a.pdf31 Jul 2021: 100. 101. -60. -50. -40. -30. -20. -10. 0. Fig. 5 Effect of varying 𝛼𝐿 on trailing-edge noise over a range of frequencies. ... 906, 2021. [20] Graham,R.R., “The silent flight of owls,” Aeronaut. J, Vol. -
4 A Quantum Particle in Three Dimensions‣ Quantum Mechanics by David…
www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S4.html18 Oct 2021: Figure 20: The (un-normalised) wavefunctions for fixed. n. =. 4. with angular momentum varying from. ... 0. node. In Figure 20 we’ve fixed the energy level to. -
Cilia density and flow velocity affect alignment of motile cilia from …
www.damtp.cam.ac.uk/user/lauga/papers/184.pdf17 Jan 2021: w (x). X. Transwell chipchannel (top view). Fluid flow –0.55 10 15 20. ... For each tapered channel (Transwell chip), we acquired 20–25 fields of view (FOVs). -
Oldroyd B, and not A? John Hincha, Oliver Harlenb,∗ ...
www.damtp.cam.ac.uk/user/hinch/publications/Oldroyd12b.pdf25 Oct 2021: 20] showed that spheroids (ellipsoids with an axis of symmetry) rotate in a. ... σ = pI µ(u uT ) GfA, (19)5A=. 1. τ(fA I) , (20). -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/two.pdf12 Jun 2021: E = r. Q. 40r. =. Q. 40. r̂. r2(2.20). where r2 = x x. ... 20 = k/m is the frequency of the undamped harmonic oscillator and = /2m. -
Hydrodynamics and direction change of tumbling bacteria
www.damtp.cam.ac.uk/user/lauga/papers/199.pdf20 Jul 2021: PLOS ONE. PLOS ONE | https://doi.org/10.1371/journal.pone.0254551 July 20, 2021 1 / 26. ... PLOS ONE | https://doi.org/10.1371/journal.pone.0254551 July 20, 2021 9 / 26. -
5 When Gravity is Weak‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S5.html16 Oct 2021: h. 10. -. 20. These are small numbers. Nonetheless, as we mentioned previously, this is the sensitivity that has been achieved by gravitational wave detectors. -
Computational Projects Lecture 8 part 1 : Project Information ...
www.damtp.cam.ac.uk/user/rlj22/catam/L8-details-2021.pdf16 May 2021: Many students will find that CATAM contributes 20% to their total mark. -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/four.pdf12 Jun 2021: attractive or repulsive). – 63 –. bb. Figure 20:. Firstly, by energy conservation, the speed of the particle at the end of its trajectory. ... negligible. But, from (4.20), we see that, regardless of the initial velocity v, if you fire. -
Fluid flow in the sarcomere
www.damtp.cam.ac.uk/user/lauga/papers/197.pdf8 Jul 2021: demonstrated that, during cyclic contraction, bulk fluidmovement augments substrate transport [20] over diffusion alone. ... 20 25%, indicating that 5 10%of the volume is composed of bound cytoplasm [7]. -
1 The Fundamentals of Statistical Mechanics‣ Statistical Physics by…
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S1.html18 Oct 2021: 1. k. B. T. (1.20). And the normalization factor that sits in the denominator of the probability is written,. -
Turing’s Diffusive Threshold in Random Reaction-Diffusion Systems
www.damtp.cam.ac.uk/user/gold/pdfs/turing.pdf9 Jun 2021: 1(a)] if itexceeds the diffusivity difference D 1 of the physicalsystem: D 1 for similarly sized molecules in solution,but, e.g., D 20 for the stochastic Turing instabilityobserved in ... Rev. E 80,030902(R) (2009). [20] T. Biancalani, D. Fanelli, and F. -
1 The Expanding Universe‣ Cosmology by David Tong
www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S1.html18 Oct 2021: 1.20). This is intuitive: the light is stretched by the expansion of space as it travels through it so that the observed wavelength is longer than the emitted wavelength. ... If they are emitted with frequency. ν. 1. then, from (1.20), they arrive with -
solidstate
www.damtp.cam.ac.uk/user/tong/aqm/solid4.pdf7 Apr 2021: 2 =2µ. k2 (4.20). Meanwhile, transverse waves have k = 0 and dispersion! ... tudinal. The frequencies! s(k) correspond to either (4.20) or (4.21) depending on the. -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justfive.pdf7 Apr 2021: 2 =2µ. k2 (5.20). Meanwhile, transverse waves have k = 0 and dispersion! ... tudinal. The frequencies! s(k) correspond to either (5.20) or (5.21) depending on the. -
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: m.2. 020. 1112. G.T. Fortune and others. (b)(a). 1 mm 20 cm. ... 2 θ. 23ϕ0. r2θ. ). O(3)|r=c = 0. (4.20). ϕ0. r+. ( -
3 Introducing Riemannian Geometry‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S3.html16 Oct 2021: 3 Introducing Riemannian Geometry. 3 Introducing Riemannian Geometry. We have yet to meet the star of the show. There is one object that we can place on a manifold whose importance dwarfs all others, at least when it comes to understanding gravity. -
J. Fluid Mech. (2021), vol. 914, A20, doi:10.1017/jfm.2020.1112 The…
www.damtp.cam.ac.uk/user/gold/pdfs/worms.pdf5 Mar 2021: 20. 12 5τ0. 8(1 τ20 )2 log. (τ0 1τ0 1. ) , (3.11)i.e. ... 2 θ. 23ϕ0. r2θ. ). O(3)|r=c = 0. (4.20). ϕ0. r+. ( -
An “occlusive thrombosis-on-a-chip” microfluidic device for…
www.damtp.cam.ac.uk/user/gold/pdfs/thrombosis.pdf29 Oct 2021: In these experiments, the time it takes for an artery to occludeafter thrombosis is triggered is monitored.20,21 If pre-treatment with a compound delays or prevents occlusion, thecompound is ... Coated wafers aresoft-baked using a 65 C heat pad for 5 -
3 Interacting Fields‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S3.html18 Oct 2021: 3 Interacting Fields. 3 Interacting Fields. The free field theories that we’ve discussed so far are very special: we can determine their spectrum, but nothing interesting then happens. They have particle excitations, but these particles don’t -
Hydrodynamic synchronization in strong confinement
www.damtp.cam.ac.uk/user/lauga/papers/187.pdf8 Jul 2021: Note that, in some unicellular organisms, synchroniza-tion is mediated by intracellular (basal) coupling [20]. ... 1. 250. 1. i. 20 0tω/2π. [(χn π) mod 2π]/π(b). FIG. -
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 -
Convex optimization and quantum information theory
www.damtp.cam.ac.uk/user/hf323/qip2021_tutorial_cvxqi.pdf22 Apr 2021: Slow convergence/stallat low-medium accuracy. 20/82. Polynomial optimization, sums of squares. 21/82. ... 5 10 15 20. -1. 1. 2. 3. Log. m=3. Improve approximation by bringing x closer to 1 and usinglog(x) = 1h log(x.
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