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fluids
www.damtp.cam.ac.uk/user/tong/fluids/fluids5.pdf16 Sep 2022: bit hole. First we’ll sort out some of the terms in (6.24), and then return to the 3-point. ... Our equation (6.24) for the correlation function has now. become. @Cij(r; t). -
Preprint typeset in JHEP style - HYPER VERSION F́ısica ...
www.damtp.cam.ac.uk/user/tong/statphys/fisest.pdf25 Aug 2022: Preprint typeset in JHEP style - HYPER VERSION. F́ısica Estad́ıstica. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences. Wilberforce Road,. Cambridge, CB3 OBA, UK. -
fluids
www.damtp.cam.ac.uk/user/tong/fluids/fluids2.pdf16 Sep 2022: u = Ga and P =x a. 4r3(3.24). – 78 –. where G is the matrix. Gij =1. 8µ. ijr. xixjr3. The tensor G is known as the Stokeslet. ... right. Proof: First, we’ll check that the solution (3.24) obeys µr2u = rP everywhere. -
Mathematical Tripos Part IB Electromagnetism Harvey Reall…
www.damtp.cam.ac.uk/user/hsr1000/electromagnetism_lectures.pdf28 Feb 2022: E 2E = µ0J. t 1c22E. t2(1.24). Finally use (M1) and rearrange to obtain. ... Φ2(x) =q1. 4π0|x x1|. q24π0|x x2|. (2.24). We now repeat with the third particle and so on, obtaining (2.21) by induction (the. -
IMA Journal of Applied Mathematics (2020) 85,…
www.damtp.cam.ac.uk/user/mjc249/pdfs/scattering_porous_mcolbrook.pdf21 Jul 2022: Received on 29 August 2019; revised on 10 April 2020; accepted on 24 June 2020]. -
Day et al. eLife 2022;11:e72707. DOI: https:// doi. org/ ...
www.damtp.cam.ac.uk/user/gold/pdfs/cellorg.pdf21 Feb 2022: Day et al. eLife 2022;11:e72707. DOI: https:// doi. org/ 10. 7554/ eLife. 72707 1 of 28. Cellular organization in lab- evolved and extant multicellular species obeys a maximum entropy lawThomas C Day1, Stephanie S Höhn2, Seyed A Zamani- Dahaj1,3,4 -
Stabilization of microbial communities by responsive phenotypic…
www.damtp.cam.ac.uk/user/gold/pdfs/switching.pdf19 Sep 2022: PHYSICAL REVIEW RESEARCH 4, 033224 (2022). Stabilization of microbial communities by responsive phenotypic switching. Pierre A. Haas ,1,2,3, Maria A. Gutierrez ,4 Nuno M. Oliveira ,4,5,† and Raymond E. Goldstein 4,‡1Max Planck Institute for the -
electro
www.damtp.cam.ac.uk/user/tong/em/el6.pdf3 Dec 2022: n1 sinI = n2 sinT (7.24). This is the law of refraction, known as Snell’s law. – ... Let’s return to Snell’s law (7.24) that tells us the angle of refraction,. -
fluids
www.damtp.cam.ac.uk/user/tong/fluids/fluids3.pdf28 Nov 2022: 2 = gk(1 l2ck2) tanh(kH) (4.24). while the phase velocity is. -
The difficulty of computing stable and accurate neural networks: On…
www.damtp.cam.ac.uk/user/mjc249/pdfs/PNAS_Stable_Accurate_NN.pdf16 Mar 2022: 1 for an example of AI-generated hallucinations.There is a growing awareness of this problem in high-stakesapplications and society as a whole (20, 23, 24), and instabilityseems to be
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