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Fluid Mechanics of Mosaic Ciliated Tissues
www.damtp.cam.ac.uk/user/gold/pdfs/mosaic.pdf2 Nov 2021: 1) aresurrounded by nonciliated cells: “goblet cells” that covermost of the tissue secreting mucus-like material [24],mosaically scattered small cells [25,26] secreting serotoninvesicles that modulate the ciliary beat frequency ... 24] S. Nagata, -
Swirling Instability of the Microtubule Cytoskeleton
www.damtp.cam.ac.uk/user/lauga/papers/185.pdf17 Jan 2021: actin. Here, through a combination of direct computationson the coupled filament-flow problem [24] and studies of acontinuum theory for dense filament suspensions [28], weconfirm this hypothesis by showing the existence ... ffiffiffiffiffiffiffiffiffiffif -
1 The Expanding Universe‣ Cosmology by David Tong
www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S1.html18 Oct 2021: a. (. t. ′. ). (1.24). This is the size of the observable universe. ... Indeed, mathematically it could be that the integral on the left-hand side of (1.24) does not converge at. -
Purely viscous acoustic propulsion of bimetallic rods
www.damtp.cam.ac.uk/user/lauga/papers/202.pdf12 Sep 2021: 99, 178103 (2007). [24] A. Somasundar, S. Ghosh, F. Mohajerani, L. -
The bank of swimming organisms at the micron scale (BOSO-Micro)
www.damtp.cam.ac.uk/user/lauga/papers/195.pdf8 Jul 2021: cells swim [24–28]. Absolute pressure [29], pH [30] and even magnetic field [31] have also. ... Bi = 0.11 0.06 (n = 2),hB/Li = 0.63 0.24 (n = 9)). -
Stabilizing viscous extensional flows using reinforcement learning
www.damtp.cam.ac.uk/user/lauga/papers/205.pdf1 Dec 2021: Biological and bioinspired appli-cations at high Reynolds numbers include control and energyoptimization in fish swimming [24–26], gliding and perching[27], and locomotion in potential flows [28]. ... Dt 1 = Dt βt δt Qt. (24)To ensure convergence, it -
2 Free Fields‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S2.html18 Oct 2021: 24. d. 𝒪. (. a. 2. ). where, in the last line, we’ve used the fact that. ... π. 24. (. 1. d. 1. L. -. d. ). 𝒪. (. a. 2. ). (2.113). This is still infinite in the limit. -
1 Geodesics in Spacetime‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S1.html16 Oct 2021: q. of the test particle. The equality (1.24) is sometimes called the weak equivalence principle. ... principle (1.24) is that it’s not possible to tell the difference between constant acceleration and a constant gravitational field. -
1 Classical Field Theory‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S1.html18 Oct 2021: ϕ. (. y. ). (1.24). A priori, there’s no reason for this. -
Fluid Mechanics of Mosaic Ciliated Tissues
www.damtp.cam.ac.uk/user/lauga/papers/204.pdf29 Nov 2021: 1) aresurrounded by nonciliated cells: “goblet cells” that covermost of the tissue secreting mucus-like material [24],mosaically scattered small cells [25,26] secreting serotoninvesicles that modulate the ciliary beat frequency ... 24] S. Nagata, -
5 Phase Transitions‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S5.html18 Oct 2021: 5 Phase Transitions. 5 Phase Transitions. A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein condensation. In that case, we -
1 From Spins to Fields‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S1.html16 Oct 2021: 1.24). Here, the notation. {. s. i. }. |. m. (. 𝐱. ). means that we sum over all configurations of spins such that the coarse graining yields. ... We will invoke one last notational flourish. We’re left in (1.24) with a sum over all possible -
Swirling Instability of the Microtubule Cytoskeleton
www.damtp.cam.ac.uk/user/gold/pdfs/swirling.pdf13 Jan 2021: actin. Here, through a combination of direct computationson the coupled filament-flow problem [24] and studies of acontinuum theory for dense filament suspensions [28], weconfirm this hypothesis by showing the existence ... ffiffiffiffiffiffiffiffiffiffif -
Principles of Quantum Mechanics University of Cambridge Part II ...
www.damtp.cam.ac.uk/user/dbs26/PQM/chap1.pdf8 Oct 2021: and absolutely impossible for me to do so in a course of 24 lectures). -
3 The Strong Force In the middle of the ...
www.damtp.cam.ac.uk/user/tong/pp/pp3.pdf23 Apr 2021: 3 The Strong Force. In the middle of the 20th century, the number of seemingly “fundamental” particles. exploded. The electron, proton and neutron had long been known. These were joined,. in 1947, by a new particle called the pion, whose role -
A nonlinear journey - from chaos to random media
www.damtp.cam.ac.uk/user/or100/2020_ENS_Varsity.pdf19 Apr 2021: Rath Spivack University of Cambridge)A nonlinear journey - from chaos to random media March 1, 2020 24 / 25. -
Capillary-Induced Motion of Particles Bridging Interfaces of a…
www.damtp.cam.ac.uk/user/hinch/publications/PhysRevLett.122.098001.pdf25 Oct 2021: a temperature of about 24 C (1 C), and a relativehumidity of 35% (2%). ... N. Manoharan, Nat. Mater. 11, 138 (2012).[24] M. Zanini, C. Marschelke, S. -
Turing’s Diffusive Threshold in Random Reaction-Diffusion Systems
www.damtp.cam.ac.uk/user/gold/pdfs/turing.pdf9 Jun 2021: activator” [24,25], the com-plicated instability conditions for N > 2 [26] do not lendthemselves to analytical progress.Here, we analyze the diffusive threshold for Turing. ... Natl. Acad. Sci. U.S.A.115, 6572 (2018). [24] A. J. Koch and H. -
Oldroyd B, and not A?
www.damtp.cam.ac.uk/user/hinch/talks/OldroydTalk4.pdf9 Sep 2021: 24. Popularity of Oldroyd-B. Enduring use of Oldroyd-B:. I Only 3 parameters to fit data,. -
Direct measurement of unsteady microscale Stokes flow using optically …
www.damtp.cam.ac.uk/user/lauga/papers/194.pdf8 Jul 2021: B. Microsphere motion. The dynamics of a microsphere forced by an optical trap whose position is laterally oscillated isa well-studied problem [24]. ... Phys. 1, 28 (2018).[24] K. C. Neuman and S. M. Block, Optical trapping, Rev. -
Computing semigroups and solutions of time-fractional PDEs with error …
www.damtp.cam.ac.uk/user/mjc249/talks/GSSI_mjc_final1 Dec 2021: 24/34. Laplace transform. Method: Apply the above stable and exponentially convergent quadrature rule. ... 24/34. Fractional beam equations. x. u = y = displacement F (x,t) = forcing. -
Hydrodynamic synchronization in strong confinement
www.damtp.cam.ac.uk/user/lauga/papers/187.pdf8 Jul 2021: Since all the prefactors in Eq. (24), including r2and 〈y1, y2〉, are positive numbers, the phase difference (2)0 isthe linearly stable solution to Eq. ... 24) is not entirelyequivalent to the Adler’s equation. It is important to note thatboth r2 and. -
Oldroyd B, and not A? John Hincha, Oliver Harlenb,∗ ...
www.damtp.cam.ac.uk/user/hinch/publications/Oldroyd12b.pdf25 Oct 2021: 24. I (Significance of limited free rotation for the viscosity and flow birefringence. ... J. Chem. Phys. 24, 269–. 278. [34] J.G. Kirkwood and J Riseman (1948) The Intrinsic Viscosities and Diffu-. -
Direct measurement of unsteady microscale Stokes flow using optically …
www.damtp.cam.ac.uk/user/gold/pdfs/unsteady.pdf27 May 2021: B. Microsphere motion. The dynamics of a microsphere forced by an optical trap whose position is laterally oscillated isa well-studied problem [24]. ... Phys. 1, 28 (2018).[24] K. C. Neuman and S. M. Block, Optical trapping, Rev. -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justsix.pdf7 Apr 2021: qg = 2n with n 2 Z (6.24). This is the famous Dirac quantisation condition. ... In this. case, it’s sucient to impose the Dirac quantisation condition (6.24) where q is the. -
Field Theory in Cosmology: Example Sheet 1 1. For ...
www.damtp.cam.ac.uk/user/ep551/example_sheet_1_FT_in_Cosmo.pdf15 Apr 2021: Notice that by the Friedmann equation. 3M2PlH2 = Λ (24). A metric with this property is called conformally flat. -
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: of Bristol, 24 Tyndall Avenue, Bristol BS8 1TQ, UK. ... uθ = cΩ I1(κr)K1(κ) K1(κr)I1(κ)I1(κc)K1(κ) K1(κc)I1(κ), (4.24)where. α0 = cκΩ. I1(κ)I1(κc)K1(κ) -
Geometry of catenoidal soap film collapse induced by boundary…
www.damtp.cam.ac.uk/user/gold/pdfs/CatenoidCollapse.pdf8 Sep 2021: 3Institut Universitaire de France (IUF), 75005 Paris, France. (Received 9 May 2021; accepted 24 August 2021; published 8 September 2021). ... 24). It follows that the rescaled area S = A/a2 monotonically de-creases in time,. -
solidstate
www.damtp.cam.ac.uk/user/tong/aqm/solid2.pdf7 Apr 2021: ai bj = 2 ij (2.24)? is sometimes referred to as the dual lattice. ... 52 –. The condition (2.24) can also be stated as the requirement that. -
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: of Bristol, 24 Tyndall Avenue, Bristol BS8 1TQ, UK. ... uθ = cΩ I1(κr)K1(κ) K1(κr)I1(κ)I1(κc)K1(κ) K1(κc)I1(κ), (4.24)where. α0 = cκΩ. I1(κ)I1(κc)K1(κ) -
5. Discrete Symmetries In this section, we discuss the ...
www.damtp.cam.ac.uk/user/tong/aqm/aqmfive.pdf25 Aug 2021: L1 = L (5.24). – 137 –. We can also see how it acts on states. ... 5.24). S1 = S (5.26). For a spin- 12 particle, we have S =2 with the vector of Pauli matrices. -
solidstate
www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf7 Apr 2021: magnetic field,. An =2eB. (n ) (3.24). This quantisation of area is actually a variant of the Landau level quantisation that we. ... N =. 0. which should clearly be an integer. The quantisation (3.24) due to a background magnetic field. -
Energetics of synchronization for model flagella and cilia
www.damtp.cam.ac.uk/user/lauga/papers/189.pdf8 Jul 2021: For larger ciliatedcells [24], or for multicellular aquatic organisms equippedwith many short flagella [25], the synchronization dynamicstakes the form of metachronal waves, akin to spectator wavesin sport stadiums. ... p = p1 O(2 ), (24). σ = σ1 O(2 ). -
Hydrodynamics and direction change of tumbling bacteria
www.damtp.cam.ac.uk/user/lauga/papers/199.pdf20 Jul 2021: RESEARCH ARTICLE. Hydrodynamics and direction change of. tumbling bacteria. Mariia DvoriashynaID, Eric LaugaID. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United. Kingdom. e.lauga@damtp.cam.ac.uk. -
Asymptotic theory of hydrodynamic interactions between slender…
www.damtp.cam.ac.uk/user/lauga/papers/196.pdf10 Sep 2021: D. Leading-order dynamics. The induced flow, Eq. (24), makes no contributions to Eq. ... 24). Wefind that the first-order correction to the force distribution is given by. -
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. -
Dynamics of a helical swimmer crossing viscosity gradients
www.damtp.cam.ac.uk/user/lauga/papers/201.pdf10 Sep 2021: coli bacteria showingchemo-attraction to self-produced autoinducers [24]. A mechanical example of taxis, viscotaxis, emerges when a cell adapts its motion in responseto viscosity gradients. ... U2 (h) = A2 D2hB2 C2h , (23). where. A2 = ξ λ′ (1 βT )R -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justfour.pdf7 Apr 2021: magnetic field,. An =2eB. (n ) (4.24). This quantisation of area is actually a variant of the Landau level quantisation that we. ... N =. 0. which should clearly be an integer. The quantisation (4.24) due to a background magnetic field. -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/SIAM_2021_mjc23 Jul 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM. -
Preprint typeset in JHEP style - HYPER VERSION Lent ...
www.damtp.cam.ac.uk/user/tong/aqm/justaqm.pdf25 Aug 2021: 1.2.2 The Scattering Amplitude 22. 1.2.3 Partial Waves 24. 1.2.4 The Optical Theorem 27. ... r(1.24). The 1/r fall-off follows from solving the free Schrödinger equation; we’ll see this ex-. -
2 Hilbert Space The realm of Quantum Mechanics is ...
www.damtp.cam.ac.uk/user/dbs26/PQM/chap2.pdf8 Oct 2021: hx| i =Z. R (x0) hx|x0i dx0 = (x). (2.24). In other words, the position space wavefunctions we’re familiar with are nothing but the. -
1 The Fundamentals of Statistical Mechanics‣ Statistical Physics by…
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S1.html18 Oct 2021: ρ. =. e. -. β. H. Z. (1.24). If we make a measurement described by an operator. ... In the quantum context, it is sometimes written in terms of the density matrix (1.24) as. -
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: and. -. 𝑑. x. x. e. -. a. x. 2. =. 0. (2.24). where the second equality follows because the integrand is odd (and suitably well behaved at infinity). ... σ. ). exp. (. -. x. 2. σ. |. α. |. 2. ). =. k. 0. where, to get the final equality, we did the -
5 Quantizing the Dirac Field‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S5.html18 Oct 2021: v. r. (. p. ). Figure 23: An incoming anti-fermion. Figure 24: An outgoing anti-fermion. •. -
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 -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justthree.pdf7 Apr 2021: ai bj = 2 ij (3.24)? is sometimes referred to as the dual lattice. ... 91 –. The condition (3.24) can also be stated as the requirement that. -
Rechargeable self-assembled droplet microswimmers driven by surface…
www.damtp.cam.ac.uk/user/lauga/papers/198.pdf10 Sep 2021: Active Brownian motion tunable by light. J. Phys. Condens. Matter 24, 284129 (2012). ... Soft Matter 16, 4961–4968 (2020). 24. Shao, J. et al. Erythrocyte membrane modified Janus polymeric motors for thrombus therapy. -
Artificial polariton molecules
www.damtp.cam.ac.uk/user/ngb23/publications/PhysRevB.103.L060507.pdf27 Feb 2021: 1 Moscow, 121205, Russia. (Received 11 June 2020; revised 5 November 2020; accepted 8 February 2021; published 24 February 2021). ... The coupling of two polaritonic/photonic (nonequilib-rium) CCs was studied in the framework of the weak lasingregime -
Field Theory in Cosmology (Part III) Enrico Pajer Contents ...
www.damtp.cam.ac.uk/user/ep551/field_theory_in_Cosmology.pdf15 Apr 2021: M2Plä. a= 1. 6(ρ 3p). (1.24). Second, by taking the time derivative of the Friedmann equation and using the continuityequation to get rid of ρ̇, we can find the ... ̇K = ä2K. ȧ3ä (ρ 3p) (1 3w) , (1.27). where in the second step I used the -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/popup_final_mjc22 Jul 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM.
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