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  2. Hydrodynamic synchronization in strong confinement

    www.damtp.cam.ac.uk/user/lauga/papers/187.pdf
    8 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. 3 Quantum Gases‣ Statistical Physics by David Tong

    www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S3.html
    18 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
  4. Convex optimization and quantum information theory

    www.damtp.cam.ac.uk/user/hf323/qip2021_tutorial_cvxqi.pdf
    22 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.
  5. Geometry of catenoidal soap film collapse induced by boundary…

    www.damtp.cam.ac.uk/user/gold/pdfs/CatenoidCollapse.pdf
    8 Sep 2021: 20)[14],. A = th[xc (1 )]{α2c th2[xc (1 )]. }1/2+ α2c sh1. ... u = za, r = ζ. a, (23). MCF in an Eulerian reference frame is given by [20].
  6. solidstate

    www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf
    7 Apr 2021: r? = r (B̂ r) B̂. Integrating (3.20), we find. r?(t) = r?(0) eB. ... dk. |k̇|. We can use (3.20) to relate |k̇| to the perpendicular velocity,.
  7. IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Stratified Sampling Based ...

    www.damtp.cam.ac.uk/research/afha/anders/CSPaper_Loss_Colbrook_Hansen.pdf
    8 Mar 2021: fj 20 Hz.Reconstruction computed for 10% of samples, SRM samplingwith low frequency range K = 10 used. ... 5. 10. 15. 20. acce. lera. tio. n (. ms. -2) Reconstruction of SHM signal.
  8. 5. Discrete Symmetries In this section, we discuss the ...

    www.damtp.cam.ac.uk/user/tong/aqm/aqmfive.pdf
    25 Aug 2021: The. dual state h|A is defined by. (h|A)| i = h|(A| i) (5.20). ... is an anti-linear operator. But if we just repeat the definition (5.20) then it’s simple.
  9. Pure Maths fun crazy mathematical ideas? what good are they…

    www.damtp.cam.ac.uk/user/or100/2019_NewnhamSummerSchool.pdf
    19 Apr 2021: The Chinese (c. 200 BCE), buying& selling, taxes. Diophantus (c. 200-c.284)solution to 4 = 4x 20 is ‘absurd’!
  10. Artificial polariton molecules

    www.damtp.cam.ac.uk/user/ngb23/publications/PhysRevB.103.L060507.pdf
    27 Feb 2021: G. Berloff, New J. Phys. 20, 113023(2018). [11] I. Carusotto and C. ... Nordlander, Science. 302, 419 (2003).[20] K. Liao, X. Hu, T. Gan, Q.
  11. 3 The Strong Force In the middle of the ...

    www.damtp.cam.ac.uk/user/tong/pp/pp3.pdf
    23 Apr 2021: other quarks or anti-quarks. This phenomenon is called confinement. – 73 –. Figure 20. The chromoelectric flux tube between a quark and anti-quark in a meson state,. ... simulation of QCD shown in Figure 20. It’s as if the quark and anti-quark are
  12. 2 My First Path Integral‣ Statistical Field Theory by David Tong

    www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S2.html
    16 Oct 2021: T. T. c. Figure 20:. T. =. T. c. Finally, we can ask what happens when we sit at the critical point. ... T. =. T. c. A typical configuration is shown in Figure 20.
  13. Can stable and accurate neural networks always be computed?

    www.damtp.cam.ac.uk/user/mjc249/talks/CRUNCH_mjc
    11 Jun 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.
  14. February 2021 EPL, 133 (2021) 44002 www.epljournal.orgdoi:…

    www.damtp.cam.ac.uk/user/lauga/papers/188.pdf
    8 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.
  15. Fluid Mechanics of Mosaic Ciliated Tissues

    www.damtp.cam.ac.uk/user/lauga/papers/204.pdf
    29 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.
  16. Preprint typeset in JHEP style - HYPER VERSION Lent ...

    www.damtp.cam.ac.uk/user/tong/aqm/justaqm.pdf
    25 Aug 2021: We can expand (1.20) in 1/U0. (This too is left. as a problem on the exercise sheet.) We find. ... Scattered flux. Incident flux. – 20 –. We can also define the total cross-section.
  17. CAN STABLE AND ACCURATE NEURAL NETWORKS BE COMPUTED? – ...

    www.damtp.cam.ac.uk/research/afha/anders/Stable_Accurate_NN_Final.pdf
    16 Feb 2021: Our proof techniquesstem from the Solvability Complexity Index (SCI) hierarchy that has recently been used to settle longstandingquestions in scientific computing [15, 18–20, 40, 41, 65], and that generalises the ... In all cases N = 20, m = N 1 and
  18. Cop yrig ht © 201 6 U nive rsity ...

    www.damtp.cam.ac.uk/user/tong/vc/benjonathan.pdf
    19 May 2021: Example: f(x,y) = x2y. x. y1. 20. D. D. f(x,y) dA =. 1. 0. ( 22y. 0. x2y dx. ). dy =. 1. ... which means(x,y,z). (ρ,ϕ,z)= ρ dV = ρdρ dϕ dz. – 20 –. Cop. yrig. ht. 201. 6 U. nive. rsity. of C. ambr.
  19. justaqm

    www.damtp.cam.ac.uk/user/tong/aqm/justfour.pdf
    7 Apr 2021: r? = r (B̂ r) B̂. Integrating (4.20), we find. r?(t) = r?(0) eB. ... dk. |k̇|. We can use (4.20) to relate |k̇| to the perpendicular velocity,.
  20. 2 The Hot Universe‣ Cosmology by David Tong

    www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S2.html
    18 Oct 2021: ζ. (. 3. ). 1.20. It is sometimes referred to as Apéry’s constant.
  21. 23 Apr 2021: A.1 Ray Physics 20. A.2 The Electron 23. A.3 The Proton 25. ... 20 –. With hindsight, these early discharge tubes can be viewed as the world’s first particle.
  22. Dynamics of a helical swimmer crossing viscosity gradients

    www.damtp.cam.ac.uk/user/lauga/papers/201.pdf
    10 Sep 2021: Received 9 December 2020; accepted 20 July 2021; published 23 August 2021). ... U1 (h) = A1B1 C1h , (19). where. A1 = ξ λ(1 βT )R sin ψ cos ψ, (20).
  23. Can stable and accurate neural networks always be computed?

    www.damtp.cam.ac.uk/user/mjc249/talks/Munich_mjc1
    26 May 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.
  24. Field Theory in Cosmology: Example Sheet 1 1. For ...

    www.damtp.cam.ac.uk/user/ep551/example_sheet_1_FT_in_Cosmo.pdf
    15 Apr 2021: ds2 = dt2 a2 (δij γij) dxidxj (20). =1. H2τ2[dτ2 (δij γij) dxidxj. ],
  25. Swirling Instability of the Microtubule Cytoskeleton

    www.damtp.cam.ac.uk/user/lauga/papers/185.pdf
    17 Jan 2021: For afilament of length L and bending modulus A [20], thebuckling force is π2A=4L2 50 pN=L2, where L ismeasured in microns. ... 028103-5. oocyte posterior determination, J. Cell Biol. 217, 3497(2018). [20] F.
  26. Part III MathematicsFluid Dynamics of Climate (PHH part) Michaelmas…

    www.damtp.cam.ac.uk/user/phh/atmosocean/notes2020-21_lectures11-15_19-24.pdf
    16 Sep 2021: P.H.Haynes Part III Fluid Dynamics of Climate Michaelmas 2020 20. act as a rigid lid for the tropospheric circulation.) It follows that NH/f0 ' 1000km,f0Λ/N ' 5 105s1
  27. Inverse ProblemsLecture notes, Michaelmas term 2020 University of…

    www.damtp.cam.ac.uk/research/cia/files/teaching/Inverse_Problems_2020/LectureNotes2020.pdf
    18 May 2021: 20 CHAPTER 2. GENERALISED SOLUTIONS. 1. A†A = PN(A),. 2. AA† = PR(A).
  28. Morphoelasticity of large bending deformations of cell sheets during…

    www.damtp.cam.ac.uk/user/gold/pdfs/morpho_bending.pdf
    22 Feb 2021: Ex-tensions of the classical Föppl–von Kármán equations [20,21]have been derived and residual stresses in Kirchhoff platetheories [22] have been studied in this case. ... 8].Inset: Cartoon of constricted triangular cells in the bend region. Scalebars
  29. solidstate

    www.damtp.cam.ac.uk/user/tong/aqm/solid2.pdf
    7 Apr 2021: Tl1Tl2 = Tl1l2 (2.20). with [Tl1, Tl2] = 0. The translation operator is a close cousin of the familiar momentum operator. ... Figure 20: The reduced zone scheme. Crystal Momentum. The quantity p = k is the quantity that replaces momentum in the presence
  30. Field Theory in Cosmology (Part III) Enrico Pajer Contents ...

    www.damtp.cam.ac.uk/user/ep551/field_theory_in_Cosmology.pdf
    15 Apr 2021: k < kH.c. = aH =1. |τ|(Hubble crossing) , (2.20). where “H.c.” stands for Hubble crossing, sometime also called horizon crossing. ... 20. Box 2.1 Free theories and Gaussianity All free theories can be understood by analogywith the most famous free
  31. Preprint typeset in JHEP style - HYPER VERSION Lent ...

    www.damtp.cam.ac.uk/user/tong/aqm/solidstate.pdf
    7 Apr 2021: These. are satisfied by the monomials,. ψ0 = wMe|w|. 2/4l2B Lzψ0 = Mψ0 (1.20). ... 20 –. To set the scene, let’s go back to the Lorentz force law.
  32. Preprint typeset in JHEP style - HYPER VERSION Statistical ...

    www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf
    17 Apr 2021: β 1kBT. (1.20). And the normalization factor that sits in the denominator of the probability is written,. ... result known as the fluctuation-dissipation theorem. – 20 –. The other point to take away from (1.27) is the size of the fluctuations as
  33. Can stable and accurate neural networks always be computed?

    www.damtp.cam.ac.uk/user/mjc249/talks/popup_final_mjc
    22 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.
  34. 8 Jul 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,.
  35. justaqm

    www.damtp.cam.ac.uk/user/tong/aqm/justsix.pdf
    7 Apr 2021: These. are satisfied by the monomials,. 0 = wMe|w|. 2/4l2B ) Lz 0 = M 0 (6.20). ... for some positive integer M. Degeneracy Revisited. In symmetric gauge, the profiles of the wavefunctions (6.20) form concentric rings.
  36. Rebound and scattering of motile Chlamydomonas algae in confined…

    www.damtp.cam.ac.uk/user/lauga/papers/192.pdf
    8 Jul 2021: has been quantified experimentally and modelled inthe far field using three point forces for the body and twoflagella.16–20. ... 2a. The chambers consists in a triangular shapewith concave curved sides with identical radius of curvature R.The thickness
  37. The bank of swimming organisms at the micron scale (BOSO-Micro)

    www.damtp.cam.ac.uk/user/lauga/papers/195.pdf
    8 Jul 2021: motors embedded in the cell wall [20]. For the latter, the flagella undergo three-dimensional. ... grown into a mature field of research [10, 20, 43–48]. Despite many theoretical advances, the.
  38. Energetics of synchronization for model flagella and cilia

    www.damtp.cam.ac.uk/user/lauga/papers/189.pdf
    8 Jul 2021: ψ. x. (x(2)s ,y(2)s ). = b cos(x t ), (20). ... 0 5 10 15 20-3.5. -3. -2.5. -2. -1.5. -1. -0.5.
  39. 2 Hilbert Space The realm of Quantum Mechanics is ...

    www.damtp.cam.ac.uk/user/dbs26/PQM/chap2.pdf
    8 Oct 2021: ha0|ai = (a0 a) (2.20). using the Dirac -function. Then we write. | ... The Copenhagen interpretation. – 20 –. is the most widely accepted version of quantum mechanics, but it’s not uncontroversial.
  40. J. DIFFERENTIAL GEOMETRY17 (1982) 6 6 1 - 6 ...

    www.damtp.cam.ac.uk/user/tong/susy/morse.pdf
    19 Apr 2021: They arethe solutions, in other words, of the equation. (20)dλ. Moreover, the instanton calculation shows that the only relevant solutions of(20) are the ones which correct two critical points
  41. Lecture Notes on Cosmological Soft Theorems Enrico Pajera aDepartment …

    www.damtp.cam.ac.uk/user/ep551/notes_cosmo_soft_theorems.pdf
    16 Apr 2021: 5.1 Gauge transformations 18. 5.2 Perfect fluids 20. 5.2.1 The long story 20. ... energy-momentum tensor Tµν, we define. gµν(x,t) = ḡµν(t) hµν(x,t) , (2.20).
  42. Asymptotic theory of hydrodynamic interactions between slender…

    www.damtp.cam.ac.uk/user/lauga/papers/196.pdf
    10 Sep 2021: 20)In order to solve Eq. (11) as an asymptotic series, we need to expand the flow induced by the. ... 20), (28), (33), (35), (40), and (44),but these coefficients have been evaluated either analytically with RFT or computationally withSBT.
  43. Stabilizing viscous extensional flows using reinforcement learning

    www.damtp.cam.ac.uk/user/lauga/papers/205.pdf
    1 Dec 2021: 20)Finally, since vπ̂ (xt ) = Rt γ vπ̂ (xt 1 ), we can use the. ... 4) with the speedparameters during each step. For numerical integration, weemployed the fourth-order Runge-Kutta scheme RK4 withstep size dt /20.
  44. justaqm

    www.damtp.cam.ac.uk/user/tong/aqm/justone.pdf
    23 Apr 2021: We can expand (1.20) in 1/U0. (This too is left. as a problem on the exercise sheet.) We find. ... Scattered flux. Incident flux. – 20 –. We can also define the total cross-section.
  45. J. Fluid Mech. (2021), vol. 916, A17, doi:10.1017/jfm.2021.181…

    www.damtp.cam.ac.uk/user/lauga/papers/190.pdf
    8 Jul 2021: F = 3. 3f ds, (2.19). L = 3. 3r f ds ẑ′, (2.20).
  46. justaqm

    www.damtp.cam.ac.uk/user/tong/aqm/justthree.pdf
    7 Apr 2021: Tl1Tl2 = Tl1l2 (3.20). with [Tl1, Tl2] = 0. The translation operator is a close cousin of the familiar momentum operator. ... Moreover, we want the eigenvalues. to respect the group structure (3.20).
  47. Part III - Classical and Quantum Solitons

    www.damtp.cam.ac.uk/user/examples/3P11e.pdf
    20 Apr 2021: 20. 2 Vortices III Classical and Quantum Solitons. To better understand this, we can think of θ as an angular variable, i.e.

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