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kintheory
www.damtp.cam.ac.uk/user/tong/kintheory/four.pdf16 Sep 2023: Im(!) =! (!20! 2)2 2!2. (4.24). This is an odd function. ... oscillator, we can now use the explicit form (4.24) to derive. -
susyqm
www.damtp.cam.ac.uk/user/tong/susy/susyqm3.pdf4 Oct 2023: We can compute the Witten index by simply. summing over the critical points X, just as we did in (1.24). -
10th_Popov_Prize
www.damtp.cam.ac.uk/user/mjc249/talks/Popov_talk_FoCM_mjc.pdf15 Jul 2023: 24/37. š“ šš modality,š < š , š = š¦š š=1š samples. ... 24] Colbrook, Matthew J. "Computing semigroups with error control." SIAM Journal on Numerical Analysis 60.1 (2022): 396-422. -
Preprint typeset in JHEP style - HYPER VERSION 2018 ...
www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf26 Jun 2024: in (1.24) because E = (0,0,E) lies parallel to the side of the torus, not perpendicular. ... Instead, both (1.23) and (1.24) are best thought of as integrating the 2-form FĀµĪ½ over. -
2. Yang-Mills Theory Pure electromagnetism is a free theory ...
www.damtp.cam.ac.uk/user/tong/gaugetheory/2ym.pdf26 Jun 2024: where. KĀµ = Āµtr. A@A. 2i. 3AAA. (2.24). This means that, as in the Maxwell case, the theta term does not change the. ... derivative (2.24), the temporal component was K0 = 42W. For now, the key property of W(A) that we will need is. -
Supersymmetric Quantum Mechanics David Tong Department of Appliedā¦
www.damtp.cam.ac.uk/user/tong/susy/susyqm.pdf18 Mar 2024: Then, using our previous result (1.24), we have. Tr (1)FeĪ²H =X. ... 24 ā. Note that weāre not assuming that all critical points of h correspond to true E = 0. -
Preprint typeset in JHEP style - HYPER VERSION January ...
www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf1 Apr 2024: Ļ(x,y) = Ļn,k(x mE/eB2,y) (1.24). and the energies are now given by. ... holomorphic and anti-holomorphic derivatives. =1. 2. (. x+ i. y. )and Ģ =. 1. 2. (. x i. y. ). ā 24 ā. which obey z = ĢzĢ = 1 and zĢ = Ģz = 0. -
Under consideration for publication in J. Fluid Mech. 1 ...
www.damtp.cam.ac.uk/user/hinch/publications/BHS.pdf27 Dec 2023: š0. š»(Ģ)dĢ. (3.25)403. We note that solutions (3.24) satisfy the matching conditions between the inner404and outer regions. -
J. Fluid Mech. (2024), vol. 988, A10, doi:10.1017/jfm.2024.223 Flowā¦
www.damtp.cam.ac.uk/user/hinch/publications/JFM988_A10.pdf10 Jun 2024: Received 10 October 2023; revised 27 December 2023; accepted 24 February 2024). ... F(Z, Ī¶ ) = 13Ī¶. Z0. H(ZĢ) dZĢ. (3.25). We note that solutions (3.24) satisfy the matching conditions between theinner and outer regions. -
Quantum Mechanics David Tong Department of Applied Mathematics and ...
www.damtp.cam.ac.uk/user/tong/qm/qm.pdf26 Jun 2024: 2.1.2 The Infinite Potential Well 24. 2.1.3 The Gaussian Wavepacket 27. ... 24 ā. easy to deal with. The SchroĢdinger equation equation is. -
Dow nloa ded from http s://r oyal soci etyp ...
www.damtp.cam.ac.uk/user/lauga/papers/219.pdf2 Jan 2024: Open Sci. 10:230223. https://doi.org/10.1098/rsos.230223. Received: 24 February 2023. Accepted: 30 May 2023. ... Existing theoretical literature onsquirmers echoes the significant influence of boundaries and confinement on their dynamics [24]. -
J. Fluid Mech. (2018), vol. 837, pp. 520ā545. cĀ© ...
www.damtp.cam.ac.uk/user/drh39/2018_JPfinger.pdf1 Dec 2023: J. Fluid Mech. (2018), vol. 837, pp. 520ā545. c Cambridge University Press 2018doi:10.1017/jfm.2017.829. 520. The dynamics of miscible viscous fingering fromonset to shutdown. Japinder S. Nijjer1,ā , Duncan R. Hewitt1 and Jerome A. Neufeld1,2,3. -
J. Fluid Mech. (2022), vol. 936, A17, doi:10.1017/jfm.2022.48ā¦
www.damtp.cam.ac.uk/user/drh39/2022_swim.pdf1 Dec 2023: 1/4Īµ. 0. dĪ¶|X ā²1|. log Īµ1]Īµ0. 1. (3.12). For the sinusoidal waveform, J 1.24, and the predictions from (3.11) are included infigure 3(d). -
Lent Term, 2015 ElectromagnetismUniversity of Cambridge Mathematicalā¦
www.damtp.cam.ac.uk/user/tong/em/electro.pdf27 Apr 2024: 2.2.3 General Charge Distributions 20. 2.2.4 Field Lines 23. 2.2.5 Electrostatic Equilibrium 24. -
This isa spec ific indiv idualās copy of the ...
www.damtp.cam.ac.uk/user/sjc1/teaching/PM/notes.pdf23 Aug 2023: 24. 3.6 Stokes Phenomena in the Complex Plane. 27. 3.6.1 Terminology. ... 0 Perturbation Methods (16 Lectures). 0.1 Introduction. ā¢ 24 lectures prised into 16. ā¢ -
Vector Calculus University of Cambridge Part IA Mathematical Triposā¦
www.damtp.cam.ac.uk/user/tong/vc/vc.pdf12 Jun 2024: 1.3.3 An Application: Work and Potential Energy 24. 1.3.4 A Subtlety 25. ... 24 ā. We learn that a conservative force, one that can be written as (1.18), has a conserved. -
COMPUTING SPECTRA ā ON THE SOLVABILITY COMPLEXITY INDEX HIERARCHYANDā¦
www.damtp.cam.ac.uk/research/afha/anders/SCI_FINAL.pdf20 Nov 2023: Brown [27ā29]) and Toeplitztheory (see A. BoĢttcher & B. Silberman [24ā26]). -
J. Fluid Mech. (2017), vol. 828, pp. 33ā56. cĀ© ...
www.damtp.cam.ac.uk/user/drh39/2017_taylor.pdf1 Dec 2023: Received 24 February 2017; revised 22 May 2017; accepted 10 July 2017;first published online 30 August 2017). -
Vigorous convection in porous media
www.damtp.cam.ac.uk/user/drh39/2020_hewittreview.pdf1 Dec 2023: u = 0. (2.1). In place of the NavierāStokes equations for an unconfined fluid, in a porous medium the Darcyvelocity u is governed by Darcyās Law [23,24], which -
Preprint typeset in JHEP style - HYPER VERSION Statistical ...
www.damtp.cam.ac.uk/user/tong/statphys/statphys.pdf29 Dec 2023: Z(1.24). If we make a measurement described by an operator OĢ, then the probability that wefind ourselves in the eigenstate |Ļā© is given by. -
G-Adaptive mesh refinement - leveraging graphneural networks andā¦
www.damtp.cam.ac.uk/user/gam37/preprints/preprint_g-adaptive_mesh_refinement.pdf11 Jun 2024: There has been a proliferation of architectures inspiredby spectral graph theory [11], convolutional (GCN) [24], message passing (MPNN) [15] and atten-tional (GAT) [40] approaches. ... 24] T. N. Kipf and M. Welling. Semi-Supervised Classification with -
Supersymmetric Field Theory University of Cambridge Part IIIā¦
www.damtp.cam.ac.uk/user/tong/susy/susy.pdf27 Dec 2023: Supersymmetric Field Theory. University of Cambridge Part III Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,. Wilberforce Road,. Cambridge, CB3 OBA, UK. -
Part IIC Michaelmas term 2021 QUANTUM INFORMATION AND COMPUTATION ...
www.damtp.cam.ac.uk/user/examples/D27L.pdf19 Nov 2023: Part IIC Michaelmas term 2021. QUANTUM INFORMATION. AND COMPUTATION. Lecture notes. Richard Jozsa, DAMTP Cambridgerj310@cam.ac.uk. āJoy in looking and comprehending is natureās most beautiful gift.āA. Einstein, aphorism 1953. 1. CONTENTS. 1 -
J. Fluid Mech. (2020), vol. 882, A11. cĀ© Cambridge ...
www.damtp.cam.ac.uk/user/drh39/2020_squirm.pdf1 Dec 2023: J. Fluid Mech. (2020), vol. 882, A11. c Cambridge University Press 2019doi:10.1017/jfm.2019.812. 882 A11-1. Translating and squirming cylinders in aviscoplastic fluid. R. Supekar1,ā , D. R. Hewitt2 and N. J. Balmforth3. 1Department of Mechanical -
doi:
www.damtp.cam.ac.uk/user/drh39/2013_shutdown.pdf1 Dec 2023: J. Fluid Mech. (2013), vol. 719, pp. 551ā586. c Cambridge University Press 2013 551doi:10.1017/jfm.2013.23. Convective shutdown in a porous medium athigh Rayleigh number. Duncan R. Hewitt1,ā , Jerome A. Neufeld1,2,3 and John R. Lister1. -
J. Fluid Mech. (2022), vol. 941, A56, doi:10.1017/jfm.2022.335ā¦
www.damtp.cam.ac.uk/user/drh39/2022_layeredconvection.pdf1 Dec 2023: J. Fluid Mech. (2022), vol. 941, A56, doi:10.1017/jfm.2022.335. Evolution of convection in a layered porousmedium. Duncan R. Hewittā . Department of Mathematics, University College London, 25 Gordon Street, London WC1H 0AY, UK. (Received 30 -
WHEN CAN YOU TRUST FEATURE SELECTION? ā I: A ...
www.damtp.cam.ac.uk/research/afha/anders/InitialSubmitFeatureSelectionDeterministic.pdf18 Dec 2023: 1. INTRODUCTION. In the wake of the many AI-based algorithms throughout the society and the sciences, potentially yielding hal-lucinations and instabilities [4, 23, 23, 24, 31, 34, 38, 40, -
David Tong -- Publications in Theoretical Physics -- University ofā¦
www.damtp.cam.ac.uk/user/tong/pub.html5 Jan 2024: JHEP 0304 (2003) 031, hep-th/0303151. [24] Comments on Condensates in Non-Supersymmetric Orbifold Field Theories. -
SpecSolve:SpectralMethodsforSpectralMeasures
www.damtp.cam.ac.uk/user/mjc249/pdfs/spectral_methods_for_spectral_measures.pdf26 Jul 2023: are associated with banded differentiation and multiplication matrices, and expansion coefficients can be computed from function samples in quasi-linear time with the FFT [24]. ... J. Integral Equ. Appl. 19, 163ā 207 (2007). 24. Iserles, A., Webb, M.: -
Dr H. Fawzi Mathematical Tripos Part II: Michaelmas Term ...
www.damtp.cam.ac.uk/user/hf323/M23-II-NA/Lect12.pdf30 Oct 2023: If. u(x,y) =k,lZ. uĢk,leiĻ(kxly). 24. is the Fourier expansion of u, the bivariate versions of the algebra of Fourier expansions gives(denoting ux = u/x and -
1975-1980 1981-1990 1991-2000 2001-2010 2011-2020 2021-2030ā¦
www.damtp.cam.ac.uk/user/mrep/webpubs.pdf11 Mar 2024: The kinematics of hexagonal magnetoconvection. Geo.Astro. Fluid Dyn., 24:109ā136, 1983. 24. ... Phys. Fluids, 24,107103, 2012. 1975-1980 1981-1990 1991-2000 2001-2010 2011-2020 2021-2030. 184. -
J. Fluid Mech. (2021), vol. 920, A35, doi:10.1017/jfm.2021.449ā¦
www.damtp.cam.ac.uk/user/drh39/2021_lereun_mixedconv.pdf1 Dec 2023: J. Fluid Mech. (2021), vol. 920, A35, doi:10.1017/jfm.2021.449. High-Rayleigh-number convection inporousāfluid layers. Thomas Le Reun1,ā and Duncan R. Hewitt2. 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical -
WHEN CAN YOU TRUST FEATURE SELECTION? ā II: ON ...
www.damtp.cam.ac.uk/research/afha/anders/InitialSubmitFeatureSelectionProbabilistic.pdf18 Dec 2023: Condition in optimisation: The concept of condition numbers has proven a crucial to computational math-ematics and numerical analysis for securing trustworthy algorithms that are accurate and stable [24, 35].J. -
topicsinqm
www.damtp.cam.ac.uk/user/tong/aqm/topics3.pdf2 Jul 2024: atom. It is another thing to solve it! No exact solutions of (3.24) are known for. ... in (3.24). In this case, the Hamiltonian reduces to N copies of. -
PowerPoint Presentation
www.damtp.cam.ac.uk/user/pvl/u3ac_heidelberg_2023.pdf17 Aug 2023: Slide 19. Slide 20. Slide 21. Slide 22. Slide 23. Slide 24. -
Nick_retirement_conference
www.damtp.cam.ac.uk/user/mjc249/talks/Nick_NEP_mjc.pdf17 Aug 2023: Eval #Eval #. 24. Example: Ghost essential spectra. š„. š(š„). truncated domain. ... Slide 24: Example: Instability. Slide 25: Example: Ghost essential spectra. Slide 26: Example: Ghost essential spectra. -
Convergence analysis of oversampled collocation boundary elementā¦
www.damtp.cam.ac.uk/user/gam37/preprints/preprint_oversampled_collocation_maierhoferhuybrechs.pdf1 May 2024: 18] and Huybrechs & Olteanu [24]). In the current manuscript,we aim to provide an introductory but rigorous analysis of the least-squares oversampled col-location method. ... uĻā²Nā2Ī± chl2Ī±āuāl, (22)āuĻā²Nār2Ī± chl2Ī±rāuāl, (23). and -
This isasp ecificindividualāscopyofthenotes. Itis nottoā¦
www.damtp.cam.ac.uk/user/sjc1/teaching/NSTIB/Mich/notes.pdf16 Aug 2023: 23. 1.8.4 The Jacobian. 24. 1.8.5 Properties of Jacobians. 25. 1.8.6 Orthogonality. ... 1.24)As proof we observe that the value of both the LHS and the RHS:. -
Natural Sciences Tripos Part IA Mathematical Methods I ā ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/nstIAm_Anders_2023.pdf24 Nov 2023: Using (25) and then (24) yields the useful result. (a b)2 = a2 b2 2a b. ... b. a. cb c. h. Figure 24: Parallelepiped formed from the vectors a,b,c. -
standardmodel
www.damtp.cam.ac.uk/user/tong/sm/standardmodel6.pdf26 Jun 2024: 6.24). Of these, U(1)3 acts on V22, leaving the overall sum 1 2 3 4 unchanged. -
Publications: Refereed Journals Jing Gao & Arieh Iserles, "A ā¦
www.damtp.cam.ac.uk/user/na/people/Arieh/Arieh_Iserles/Papers.html22 Feb 2024: Num. Anal. 24 (2004), 365ā391. A. Iserles, "On the global error of discretization methods for highly-oscillatory ordinary differential equations'', BIT 42 (2002), 561ā599. ... Comp. Maths 14 (2001), 1ā24. A. Iserles, "On Cayley-transform methods -
brum_mjc
www.damtp.cam.ac.uk/user/mjc249/talks/birmingham_mjc.pdf20 Sep 2023: Too little ortoo much arousal results inpoorer performance. 24. ā¢ Inf.-dim. ... Slide 23: Quadrature with trajectory data. Slide 24: Example: Verified modes. -
3. Introducing Riemannian Geometry We have yet to meet ...
www.damtp.cam.ac.uk/user/tong/gr/three.pdf31 May 2024: Claim:. d? F =? J , rĀµF Āµ = J (3.24). -
cosmo
www.damtp.cam.ac.uk/user/tong/cosmo/three.pdf26 Jun 2024: 1. ar vĢ = HĢ. 1. arvĢ. Take the gradient of (3.24) to get. ... 1.24). In such a situation, it would make little sense to talk about perturbations with. -
Multiflagellarity leads to the size-independent swimming speed ofā¦
www.damtp.cam.ac.uk/user/lauga/papers/220.pdf2 Jan 2024: 1B), owing to the cell-to-cell variations inmetabolism and the number and morphology of flagella (24).Thanks to the large sample size of our experiments, we are able tomeasure the -
6. Black Holes Black holes are among the most ...
www.damtp.cam.ac.uk/user/tong/gr/six.pdf31 May 2024: 6. Black Holes. Black holes are among the most enigmatic objects in the universe. They are described. by deceptively simple solutions to the Einstein equations, yet hold a host of insights. and surprises, from the meaning of causal structure, to -
doi:
www.damtp.cam.ac.uk/user/drh39/2013_thixo.pdf1 Dec 2023: in figures 11 and 12. Figure 11 shows profiles of samples with different ageing timesTage on inclines of 20; figure 12 shows profiles on slightly steeper inclines of 24.As a -
Natural Sciences Tripos Part IA Mathematical Methods I ā ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/nstIAm_Anders_Notes_2023.pdf3 Oct 2023: Scalar product properties:. 1. The scalar product is commutative,. a b = b a , (24). ... Using (25) and then (24) yields the useful result. (a b)2 = a2 b2 2a b. -
Preprint typeset in JHEP style - HYPER VERSION Michaelmas ...
www.damtp.cam.ac.uk/user/tong/gr/gr.pdf31 May 2024: should identify. g00(x) (1. 2Ī¦(x). c2. )(1.24). where Ī¦(x) is the Newtonian gravitational field. ... 1.24) but with a linear gravitational potential Ī¦ of the kind that we would invoke for. -
S-D NLEVPs
www.damtp.cam.ac.uk/user/mjc249/talks/strathclyde_2023_NEP_mjc.pdf15 Jul 2023: 24] Colbrook, Matthew J. "Computing semigroups with error control." SIAM Journal on Numerical Analysis 60.1 (2022): 396-422. ... Slide 23: Example: Loaded string. Slide 24: Example: One-dimensional acoustic wave.
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