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  2. University of Cambridge, DAMTP: Goldstein Lab

    www.damtp.cam.ac.uk/user/gold/press.html
    16 May 2022: Department of Applied Mathematics. and Theoretical Physics. Goldstein Lab. Recent Press. 2006-2015 Department of Applied Mathematics and Theoretical Physics, University of Cambridge. Information provided by R.E.Goldstein@damtp.cam.ac.uk.
  3. Classical Dynamics University of Cambridge Part II Mathematical…

    www.damtp.cam.ac.uk/user/tong/dynamics/dynhtml/dyn.html
    27 Mar 2022: If you're not using speech conversion software then you will likely be better served by the lecture notes inGenerated on Thu Mar 24 09:29:54 2022 by LaTeXML..
  4. Classical Dynamics by David Tong

    www.damtp.cam.ac.uk/user/tong/dynamics/dynhtml/S1.html
    27 Mar 2022: i. j. 𝑑. 𝐫. i. (1.24). Like before, we need to consider conservative forces to get energy conservation. ... Generated on Thu Mar 24 09:29:54 2022 by LaTeXML..
  5. Proving Existence Is Not Enough_ Mathem...al Networks in Artificial…

    www.damtp.cam.ac.uk/user/mjc249/pdfs/ProvingExistenceIsNotEnough.pdf
    2 May 2022: CF4@QSR9O4<.C2,-CC0,>2/.C24@01?4/=2A;C1=-022A-A-0/24@,.;-/=E010,01FC=CQTR9UA-10E54@/4<.C2,-CC0,>2/.C2=,VP=CA-,E-2A-VEA=11-CWA--14@ ... 4-CXY1-0>24.,C20<1-;-2A4>C0,>VP_?-,-/02->A011.E=,02=4,CH-B-,=,CE-,0/=4C3A-/-3-E0,D/4B-2A02C20<1-0,>0EE./02-77C-Z=C2IG./;
  6. PowerPoint Presentation

    www.damtp.cam.ac.uk/user/mjc249/talks/CMStats.pdf
    18 Dec 2022: Slide 24. Slide 25. Slide 26. Slide 27.
  7. 11 Jun 2022: the integral representationlog(x) =. 10(x1)/(t(x1) 1)dt [24, Remark 2.10]. We. omit the details because of limitations on space. ... 2, no. 1, pp. 1–24, 2020. [8] O. Ordentlich and Y.
  8. Biofilm Growth under Elastic Confinement

    www.damtp.cam.ac.uk/user/gold/pdfs/biofilms.pdf
    29 Apr 2022: Rev. 24, 661 (2000). [5] A. van Leeuwenhoek, An abstract of a letter from Mr.Anthony Leewenhoeck at Delft, dated Sep. ... Fluid Mech.778, 335 (2015). [24] R. E. Gibson, R. L. Schiffman, and S.
  9. 25 Aug 2022: 24. Conclusions: mechanisms. I Visco-elastic Oldroyd-B predicts a reduction in pressure drop compared with a Newtonian.
  10. 3 The Motion of Rigid Bodies�

    www.damtp.cam.ac.uk/user/tong/dynamics/dynhtml/S3.html
    27 Mar 2022: moves with the body. Figure 24: The fixed space frame and the moving body frame.
  11. Residual Dynamic Mode Decomposition Rigorous data-driven computation…

    www.damtp.cam.ac.uk/user/mjc249/talks/ResDMD_VT_mjc.pdf
    9 Nov 2022: 24:. 25:. 26:. 27:. 28:. 29:. 30:. 31:. 32:. 33:. 34:.
  12. The Unified Transform: A Spectral Collocation Methodfor Acoustic…

    www.damtp.cam.ac.uk/user/mjc249/pdfs/AIAA2019_mjc.pdf
    22 Jul 2022: S̃l(λ) =. 0. eiλtSl(t)dt. (24). B. Collocation points and basis choice.
  13. electro

    www.damtp.cam.ac.uk/user/tong/em/el5.pdf
    3 Dec 2022: 162r2c3|m̈|2 sin2 ẑ (6.24). – 150 –. Integrating over all space gives us the power emitted,.
  14. susy

    www.damtp.cam.ac.uk/user/tong/susy/susy5.pdf
    13 Jun 2022: ei ̃i (5.24). The subscript B stands for “baryon” since this is the vector-like symmetry under which. ... transformation (5.24) can be thought of as shifting the theta angle.
  15. 2 The Lagrangian Formalism

    www.damtp.cam.ac.uk/user/tong/dynamics/dynhtml/S2.html
    27 Mar 2022: 2 The Lagrangian Formalism. 2 The Lagrangian Formalism. When I was in high school, my physics teacher called me down one day after class and said, “You look bored, I want to tell you something interesting”. Then he told me something I have
  16. Preprint typeset in JHEP style - HYPER VERSION Michaelmas ...

    www.damtp.cam.ac.uk/user/tong/sft/one.pdf
    21 Feb 2022: 1.3.1 The Landau-Ginzburg Free Energy 24. 1.3.2 The Saddle Point and Domain Walls 26.
  17. 1 Raymond Ethan Goldstein FRS Researcher ID: F-2932-2011; ORCID: ...

    www.damtp.cam.ac.uk/user/gold/pdfs/CV_REGoldstein290522.pdf
    29 May 2022: 2017 Schlumberger Chair for Mathematical Sciences, IHES, Bures-sur-Yvette, France SUPERVISION OF GRADUATE STUDENTS AND POSTDOCTORAL FELLOWS 1991 – 2020 24 PhD Students Completed (3 Princeton, 6 Arizona, 15 Cambridge): 5 ... 24. Geometrical and
  18. susy

    www.damtp.cam.ac.uk/user/tong/susy/susy4.pdf
    13 Jun 2022: i! eii and ̃i! eĩi (4.24). We started with 2N fields and ̃. ... The ei has been taken to coincide with the gauge action (4.24), so that.
  19. electro

    www.damtp.cam.ac.uk/user/tong/em/el1.pdf
    3 Dec 2022: 2.2.3 General Charge Distributions 20. 2.2.4 Field Lines 23. 2.2.5 Electrostatic Equilibrium 24.
  20. On the Barriers of Deep Learning, Approximate Sharpness, and…

    www.damtp.cam.ac.uk/user/mjc249/talks/OWOS_mjc
    21 Feb 2022: σs,M(x)1 = inf{‖x z‖1 : z Σs,M}. 24/38. The robust nullspace property.
  21. Instability of an active fluid jet

    www.damtp.cam.ac.uk/user/lauga/papers/212.pdf
    9 Nov 2022: III and IV. The setup of downward jets is relevant to range of biological situations,including a falling plume of a cell suspension, i.e., bioconvection [22–24]. ... Pedley, Bioconvection, Fluid Dyn. Res. 37, 1 (2005).[24] M. A. Bees, Advances in
  22. Smale’s 18th Problem and the Barriers of Deep Learning-4mm

    www.damtp.cam.ac.uk/user/mjc249/talks/OWML_mjc
    11 May 2022: 23/40. The world of neural networks. 24/40. Need: Classification theory saying what can/cannot be done.
  23. fluids

    www.damtp.cam.ac.uk/user/tong/fluids/fluids4.pdf
    28 Nov 2022: capillary waves. (See the large k limit of (4.24).) This is to be expected: waves with. ... t+ u r! =. 1. 2r rP! ru r2u (5.24).
  24. Residual Dynamic Mode Decomposition Rigorous data-driven computation…

    www.damtp.cam.ac.uk/user/mjc249/talks/mpEDMD_talk.pdf
    18 Nov 2022: mpEDMD: First convergent Galerkin method! 24/34. Numerical examples. 25/34. Lorenz system: scalar-valued spec measሶ𝑥1 = 10 𝑥2 𝑥1 , ሶ𝑥2 = 𝑥1 28 𝑥3 𝑥2, ሶ𝑥3 = 𝑥1𝑥2.
  25. J. Fluid Mech. (2018), vol. 856, pp. 921–957. c© ...

    www.damtp.cam.ac.uk/user/mt599/papers/2018-jfm.pdf
    10 May 2022: 2.24). Notably, this expression can be simplified into. s0 =sb(rc) r s(.
  26. A programme for computational analysis in the age of data

    www.damtp.cam.ac.uk/user/mjc249/talks/SCI_computer_assisted%20proofs.pdf
    12 Sep 2022: 23/36. What went wrong? 24/36. What went wrong? 24/36. Recall complexity of Karmarkar’s algorithm: 𝑂(𝑛3.5𝐿2 log 𝐿 log log 𝐿 ). Question: What happens with 𝐿 =?
  27. Pseudoergodic operators and periodic boundary conditions

    www.damtp.cam.ac.uk/user/mjc249/pdfs/Pseudoergodic_BCs.pdf
    22 Jul 2022: In particular, we refer the reader to work by Böttcher [14,24],Böttcher and Silbermann [22], Lindner [59, 61], Marletta [62], and Marletta andScheichl [63].
  28. Order and information in the patterns of spinning magnetic…

    www.damtp.cam.ac.uk/user/lauga/papers/208.pdf
    29 Jan 2022: Wang et al., Sci. Adv. 8, eabk0685 (2022) 14 January 2022. S C I E N C E A D V A N C E S | R E S E A R C H A R T I C L E. 1 of 14. C O N D E N S E D M A T T E R P H Y S I C S. Order and information in the patterns of spinning magnetic micro-disks at
  29. Elastohydrodynamic Synchronization of Rotating Bacterial Flagella

    www.damtp.cam.ac.uk/user/lauga/papers/210.pdf
    18 May 2022: Niedermayer, B. Eckhardt, and P. Lenz, Chaos 18,. 037128 (2008).[24] D.
  30. Preprint typeset in JHEP style - HYPER VERSION Michaelmas ...

    www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf
    21 Oct 2022: 2.4.1 Noether’s Theorem 24. 2.5 Applications 26. 2.5.1 Bead on a Rotating Hoop 26. ... kinetic energy,. T(t2) T(t1) =i. Fexti dri. i 6=j. Fij dri (1.24).
  31. 4 Feb 2022: 24/34. Fractional beam equations. x. u = y = displacement F (x,t) = forcing. ... ρ = 1, F (x,t) = cos(πt)(24 π2(1 x2)2), y(x, 0) = (1 x2)2, yt.
  32. Collapse of a hemicatenoid bounded by a solid wall: instability and…

    www.damtp.cam.ac.uk/user/gold/pdfs/hemicatenoid.pdf
    7 Jul 2022: Eng. Sci.,1976, 31, 901–911. 24 S. Engelnkemper, M. Wilczek, S. V. ... Tcholakova, M. Vethamuthuand A. Lips, Surfactant Mixtures for Control of Bubble SurfaceMobility in Foam Studies, Langmuir, 2008, 24, 9956–9961.
  33. electro

    www.damtp.cam.ac.uk/user/tong/em/el2.pdf
    3 Dec 2022: 2. Zd3r0 r0 J(r0) (3.24). Just as in the electric case, the multipole expansion continues to higher terms. ... 3.24),. B(r) =µ04. 3(m1 r̂)r̂ m1. r3. (3.30). Now we’ll consider how this aects the second dipole m = m2.
  34. 4 The Hamiltonian Formalism

    www.damtp.cam.ac.uk/user/tong/dynamics/dynhtml/S4.html
    27 Mar 2022: Expand out all 24 terms and watch them cancel one by one.
  35. 16 Jun 2022: Û(t) = exp(itĤ) (24). which is sensibly called the time evolution operator.
  36. PNAS202212078_proof

    www.damtp.cam.ac.uk/user/lauga/papers/213.pdf
    9 Nov 2022: Newtonian fluids, includingboth short-range and long-range hydrodynamic interactions,direct collisions, and Brownian motion (24, 28, 29, 31, 32,43, 44). ... 24) forNewtonian fluids to predict the size of the radius of curvatureusing the distribution of
  37. GENERALISED HARDNESS OF APPROXIMATION AND THE SCI HIERARCHY– ON ...

    www.damtp.cam.ac.uk/research/afha/anders/GHA.pdf
    23 Sep 2022: work in [24, 29, 42, 48, 49,66, 67].
  38. 29 Jan 2022: Thesis, University of. Kaiserslautern, Kaiserslautern, Germany, 2000.[24] L. Koens and E.
  39. An Experimental Investigation of the Circumstances Which Determine…

    www.damtp.cam.ac.uk/user/tong/fluids/Reynolds.pdf
    23 Mar 2022: 24 , 20 No. 3. 11 220 1 967 2 34242 0 14525 0 29392 1 66300. ... 23 ,- 11 116 2 004 2-33445 0 14525 0 30189 1P65503 25 ,, 24. ,
  40. susy

    www.damtp.cam.ac.uk/user/tong/susy/susy2.pdf
    24 Jul 2022: walls, but somewhat beyond the scope of these lectures.). – 24 –. 2.2.1 R-Symmetry. We started this section by noting that all internal symmetries must commute with the. ... e. iQ̄̇ (2.24). This U(1) symmetry is known as an R-symmetry and is
  41. Asymptotic theory of hydrodynamic interactions between slender…

    www.damtp.cam.ac.uk/user/mt599/papers/2021-prf.pdf
    10 May 2022: 3. using a bispherical coordinate system [24–26]. These classical analytical results were later. ... Yamakawa kernel and matched asymptotics uses a larger prefactor of e3/24 [61].
  42. Geometrical Constraints on the Tangling of Bacterial Flagellar…

    www.damtp.cam.ac.uk/user/mt599/papers/2020-scirep.pdf
    10 May 2022: the proximal to the distal end of the filament13,24,41. ... Phys. Rev. E 98,. 042419, https://doi.org/10.1103/PhysRevE.98.042419 (2018). 24. Lee, W., Kim, Y., Griffith, B.
  43. 18 May 2022: Rev. Fluid Mech. 24, 313–358 (1992). 8R. E. Goldstein, “Green algae as model organisms for biological fluid dynami-cs,” Annu. ... Miller, “Roles for motility in bacterial–host inter-actions,” Mol. Microbiol. 24, 1109–1117 (1997).
  44. WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for…

    www.damtp.cam.ac.uk/user/mjc249/pdfs/WARPd_mjc.pdf
    17 Sep 2022: to 1. 93.5. 2.24. 28. by M. atth. ew C. olbr. ... 93.5. 2.24. 28. by M. atth. ew C. olbr. ook. (mjc.
  45. Preprint typeset in JHEP style - HYPER VERSION Michaelmas ...

    www.damtp.cam.ac.uk/user/dt281/dynamics/clas.pdf
    21 Oct 2022: 2.4.1 Noether’s Theorem 24. 2.5 Applications 26. 2.5.1 Bead on a Rotating Hoop 26. ... kinetic energy,. T(t2) T(t1) =i. Fexti dri. i 6=j. Fij dri (1.24).
  46. fluids

    www.damtp.cam.ac.uk/user/tong/fluids/fluids5.pdf
    16 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).
  47. Preprint typeset in JHEP style - HYPER VERSION F́ısica ...

    www.damtp.cam.ac.uk/user/tong/statphys/fisest.pdf
    25 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.
  48. fluids

    www.damtp.cam.ac.uk/user/tong/fluids/fluids2.pdf
    16 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.
  49. IMA Journal of Applied Mathematics (2020) 85,…

    www.damtp.cam.ac.uk/user/mjc249/pdfs/scattering_porous_mcolbrook.pdf
    21 Jul 2022: Received on 29 August 2019; revised on 10 April 2020; accepted on 24 June 2020].
  50. Mathematical Tripos Part IB Electromagnetism Harvey Reall…

    www.damtp.cam.ac.uk/user/hsr1000/electromagnetism_lectures.pdf
    28 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.
  51. Day et al. eLife 2022;11:e72707. DOI: https:// doi. org/ ...

    www.damtp.cam.ac.uk/user/gold/pdfs/cellorg.pdf
    21 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

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