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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 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. -
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. -
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. -
IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Stratified Sampling Based ...
www.damtp.cam.ac.uk/research/afha/anders/CSPaper_Loss_Colbrook_Hansen.pdf8 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. -
Geometry of catenoidal soap film collapse induced by boundary…
www.damtp.cam.ac.uk/user/gold/pdfs/CatenoidCollapse.pdf8 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]. -
Artificial polariton molecules
www.damtp.cam.ac.uk/user/ngb23/publications/PhysRevB.103.L060507.pdf27 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. -
solidstate
www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf7 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,. -
5. Discrete Symmetries In this section, we discuss the ...
www.damtp.cam.ac.uk/user/tong/aqm/aqmfive.pdf25 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. -
3 The Strong Force In the middle of the ...
www.damtp.cam.ac.uk/user/tong/pp/pp3.pdf23 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 -
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 -
Preprint typeset in JHEP style - HYPER VERSION Lent ...
www.damtp.cam.ac.uk/user/tong/aqm/justaqm.pdf25 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. -
CAN STABLE AND ACCURATE NEURAL NETWORKS BE COMPUTED? – ...
www.damtp.cam.ac.uk/research/afha/anders/Stable_Accurate_NN_Final.pdf16 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 -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justfour.pdf7 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,. -
Cop yrig ht © 201 6 U nive rsity ...
www.damtp.cam.ac.uk/user/tong/vc/benjonathan.pdf19 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. -
Particle PhysicsCERN Lectures David Tong Department of Applied…
www.damtp.cam.ac.uk/user/tong/pp/pp1.pdf23 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. -
Dynamics of a helical swimmer crossing viscosity gradients
www.damtp.cam.ac.uk/user/lauga/papers/201.pdf10 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). -
Rebound and scattering of motile Chlamydomonas algae in confined…
www.damtp.cam.ac.uk/user/lauga/papers/192.pdf8 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 -
Part III MathematicsFluid Dynamics of Climate (PHH part) Michaelmas…
www.damtp.cam.ac.uk/user/phh/atmosocean/notes2020-21_lectures11-15_19-24.pdf16 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 -
Inverse ProblemsLecture notes, Michaelmas term 2020 University of…
www.damtp.cam.ac.uk/research/cia/files/teaching/Inverse_Problems_2020/LectureNotes2020.pdf18 May 2021: 20 CHAPTER 2. GENERALISED SOLUTIONS. 1. A†A = PN(A),. 2. AA† = PR(A). -
solidstate
www.damtp.cam.ac.uk/user/tong/aqm/solid2.pdf7 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 -
Field Theory in Cosmology (Part III) Enrico Pajer Contents ...
www.damtp.cam.ac.uk/user/ep551/field_theory_in_Cosmology.pdf15 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 -
Preprint typeset in JHEP style - HYPER VERSION Lent ...
www.damtp.cam.ac.uk/user/tong/aqm/solidstate.pdf7 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. -
Preprint typeset in JHEP style - HYPER VERSION Statistical ...
www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf17 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 -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justsix.pdf7 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. -
2 The Hot Universe‣ Cosmology by David Tong
www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S2.html18 Oct 2021: ζ. (. 3. ). 1.20. It is sometimes referred to as Apéry’s constant. -
The bank of swimming organisms at the micron scale (BOSO-Micro)
www.damtp.cam.ac.uk/user/lauga/papers/195.pdf8 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. -
Energetics of synchronization for model flagella and cilia
www.damtp.cam.ac.uk/user/lauga/papers/189.pdf8 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. -
2 Hilbert Space The realm of Quantum Mechanics is ...
www.damtp.cam.ac.uk/user/dbs26/PQM/chap2.pdf8 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. -
Lecture Notes on Cosmological Soft Theorems Enrico Pajera aDepartment …
www.damtp.cam.ac.uk/user/ep551/notes_cosmo_soft_theorems.pdf16 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). -
Asymptotic theory of hydrodynamic interactions between slender…
www.damtp.cam.ac.uk/user/lauga/papers/196.pdf10 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. -
J. DIFFERENTIAL GEOMETRY17 (1982) 6 6 1 - 6 ...
www.damtp.cam.ac.uk/user/tong/susy/morse.pdf19 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 -
Stabilizing viscous extensional flows using reinforcement learning
www.damtp.cam.ac.uk/user/lauga/papers/205.pdf1 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. -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justone.pdf23 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. -
J. Fluid Mech. (2021), vol. 916, A17, doi:10.1017/jfm.2021.181…
www.damtp.cam.ac.uk/user/lauga/papers/190.pdf8 Jul 2021: F = 3. 3f ds, (2.19). L = 3. 3r f ds ẑ′, (2.20). -
Morphoelasticity of large bending deformations of cell sheets during…
www.damtp.cam.ac.uk/user/gold/pdfs/morpho_bending.pdf22 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 -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justthree.pdf7 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). -
Part III - Classical and Quantum Solitons
www.damtp.cam.ac.uk/user/examples/3P11e.pdf20 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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