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Woei Chet Lim's homepage
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Office: G.3.09
Phone: (+64) 7 858 5148
Email: wclim@waikato.ac.nz


Teaching

MATH311-12A Advanced Calculus
MATH259-12B Mathematical Modelling
MATH542-12B Partial Differential Equations 2

MATH311-13A Advanced Calculus
MATH255-13B / ENGG284-13B Differential Equations
MATH333-13Y / MATH565-13B General Relativity

MATH311-14A Advanced Calculus
MATH255-14B / ENGG284-14B Differential Equations
MATH543-14B Nonlinear Dynamics and Chaos

(On study leave during the 15A semester)
MATH255-15B / ENGG284-15B Differential Equations
MATH333-15Y / MATH565-15B General Relativity
MATH541-15B Classical Partial Differential Equations

MATH311-16A Advanced Calculus
MATH541-16A Classical Partial Differential Equations
MATH255-16B / ENGG284-16B Differential Equations

MATH251-17A / ENGG285-17A Multivariable Calculus
MATH255-17B / ENGG284-17B Differential Equations
MATH333-17Y / MATH565-17B General Relativity

ENGG285-17T Multivariable Calculus

(On study leave during the 18A semester)
ENGEN201-18B Engineering Mathematics 2
MATHS201-18B Continuing Calculus (first 8 weeks)
MATHS203-18B Differential Equations and Modelling (last 4 weeks)
MATH541-18B Classical Partial Differential Equations

ENGEN201-19S Engineering Mathematics 2 (first half)

MATHS101-19A Introduction to Calculus
MATHS565-19A General Relativity
ENGEN201-19B Engineering Mathematics 2
MATHS201-19B Continuing Calculus (first 8 weeks)
MATHS203-19B Differential Equations and Modelling (last 4 weeks)

MATHS101-20A Introduction to Calculus
MATHS543-20A Nonlinear Dynamics and Chaos
ENGEN201-20B Engineering Mathematics 2
MATHS201-20B Continuing Calculus (first 8 weeks)

ENGEN201-20C (NET) Engineering Mathematics 2

ENGEN201-21A Engineering Mathematics and Modelling 2
MATHS201-21A Continuing Calculus (first 8 weeks)
MATHS565-21A General Relativity
(On study leave during the 21B trimester)

ENGEN201-22H (NET) Engineering Mathematics and Modelling 2

ENGEN201-22A Engineering Mathematics and Modelling 2
MATHS201-22A Continuing Calculus (first 8 weeks)
MATHS203-22B Differential Equations and Modelling
MATHS543-22B Nonlinear Dynamics and Chaos

ENGEN201-23H (NET) Engineering Mathematics and Modelling 2

ENGEN101-23A (HAM) Engineering Mathematics and Modelling 1A
ENGEN201-23A Engineering Mathematics and Modelling 2
MATHS201-23A Continuing Calculus (first 8 weeks)
MATHS565-23B General Relativity
ENGEN101-23B (HAM) Engineering Mathematics and Modelling 1A

(Tentative teaching allocation for 2024)
ENGEN201-24H (NET) Engineering Mathematics and Modelling 2

ENGEN101-24A (HAM) Engineering Mathematics and Modelling 1A / MATHS103-24A (HAM) Mathematics 1A
ENGEN201-24A Engineering Mathematics and Modelling 2 / MATHS201-24A Continuing Calculus
MATHS301-24A Real and Complex Analysis (complex half)
ENGEN101-24B (HAM) Engineering Mathematics and Modelling 1A / MATHS103-24B (HAM) Mathematics 1A
MATHS303-24B Applied Mathematics / MATHS503-24B Advanced Applied Mathematics

Research

My field of research is mathematical and computational cosmology. My research involves modelling the universe as a whole, using a system of partial differential equations (PDEs). As PDEs seldom admit exact solutions, I use dynamical systems and asymptotic analyses in simpler regimes of the model, and perform numerical simulations in general regimes.

My research to-date has focussed on the so-called inhomogeneous Mixmaster behaviour near a gravitational singularity. A large part of my doctoral thesis is devoted to this topic. The shock-capturing numerical code CLAWPACK, as well as two finite difference codes developed by myself, were used to simulate inhomogeneous Mixmaster behaviours, and results indicate that in a typical model, the effect of inhomogeneity is negligible along most worldlines, except for special worldlines where the effect becomes important from time to time, and leads to recurring formation of spikes. In 2007, I discovered the explicit OT G_2 spike solution. Better numerical codes were then developed. Numerical simulations of G_2 models confirm the recurrence of spikes over different Gowdy eras, and that the explicit spike solution describes the spikes. In 2015, I discovered the explicit non-OT G_2 spike solution, which generalizes the OT G_2 spike solution.

My other projects to-date include: My long-term goal is to investigate what the full nonlinear field equations of general relativity predict about the evolution of inhomogeneity.

Previous positions:


Education:


Award:


Link to ResearcherID page

Link to Google scholar page


Journal articles:

  1. "Periodic boundary conditions and G_2 cosmology"
    A.A. Coley, W.C. Lim Classical and Quantum Gravity, 41, 015009 (12pp) (2024) ; arXiv:2312.03285.

  2. "Cosmological global dynamical systems analysis"
    A. Alho, W.C. Lim, C. Uggla Classical and Quantum Gravity, 39, 145010 (14pp) (2022) ; arXiv:2201.07596.

  3. "Numerical confirmations of joint spike transitions in G_2 cosmologies"
    W.C. Lim Classical and Quantum Gravity, 39, 065010 (16pp) (2022) ; arXiv:2202.02480.

  4. "Transition analysis of the non-OT G_2 stiff fluid spike solution"
    W.C. Lim, M.Z.A. Moughal Classical and Quantum Gravity, 39, 025010 (16pp) (2022) ; arXiv:2111.15122.
    Errata: n_3 in Eq (2) should be n_2. n_3^3 in Eq (4) should be n_3^2.

  5. "Cylindrical spikes"
    M.Z.A. Moughal, W.C. Lim Classical and Quantum Gravity, 38, 075029 (22pp) (2021); arXiv:2102.12028.
    Note: This is an abridged version of Moughal's thesis, arXiv:2102.09776.

  6. "Stiff fluid spike solutions from Bianchi type V seed solutions"
    D. Gregoris, W.C. Lim, A.A. Coley Classical and Quantum Gravity, 34, 235013 (21pp) (2017); arXiv:1705.02747.
    Errata: Reference [4] should be Lim et al 2009, PRD 79, 123526, not 103526.

  7. "On the first G_1 stiff fluid spike solution in General Relativity"
    A.A. Coley, D. Gregoris, W.C. Lim Classical and Quantum Gravity, 33, 215010 (11pp) (2016); arXiv:1606.07177.
    Errata: Reference [17] should be Lim et al 2009, PRD 79, 123526, not 103526.

  8. "Spikes and matter inhomogeneities in massless scalar field models"
    A.A. Coley, W.C. Lim Classical and Quantum Gravity, 33, 015009 (20pp) (2016); arXiv:1511.07095.
    Errata: In (39), the n_30 term should read n_30 exp(-(w+1)tau). Reference [6] should be Lim et al 2009, PRD 79, 123526, not 103526.

  9. "Non-orthogonally transitive G_2 spike solution"
    W.C. Lim Classical and Quantum Gravity, 32, 162001 (8pp) (2015); arXiv:1507.02754.
    Errata: In (10) and the line below it, n_10 and n_20 should be swapped. In (16), the n_30 term should read n_30 exp(-(w+1)tau). In (44), A^2 should be ln A^2. Ignore equations (53)--(54). The last sentence in the paragraph before (49) should refer to n_10 and n_30. Reference [15] should be Lim et al 2009, PRD 79, 123526, not 103526.

  10. "Demonstration of the spike phenomenon using the LTB models"
    A.A. Coley, W.C. Lim Classical and Quantum Gravity, 31, 115012 (15pp) (2014); arXiv:1405.5252.
    Errata: Reference [4] should be Lim et al 2009, PRD 79, 123526, not 103526.

  11. "General relativistic density perturbations"
    W.C. Lim, A.A. Coley, Classical and Quantum Gravity, 31, 015020 (13pp) (2014); arXiv:1311.1857.
    Errata: Reference [4] should be Lim et al 2009, PRD 79, 123526, not 103526.

  12. "Spherically symmetric cosmological spacetimes with dust and radiation - numerical implementation"
    W.C. Lim, M. Regis, C. Clarkson, Journal of Cosmology and Astroparticle Physics, 10, 010 (17pp) (2013); arXiv:1308.0902.
    Errata: In (3.4) and (3.18), the 8/9 mu/G_+ v^2 term should have the opposite sign. Reference [15] should be Lim et al, PRD 79, 123526 (2009).

  13. "The electromagnetic spike solutions"
    E. Nungesser, W.C. Lim, Classical and Quantum Gravity, 30, 235020 (11pp) (2013); arXiv:1304.2964.

  14. "Spike oscillations"
    J.M. Heinzle, C. Uggla, W.C. Lim, Physical Review D, 86, 104049 (26pp) (2012); arXiv:1206.0932.
    Errata: (2b) is incorrect. See Ref [51].

  15. "Generating matter inhomogeneities in general relativity"
    A.A. Coley, W.C. Lim, Physical Review Letters, 108, 191101 (5pp) (2012); longer version at arXiv:1205.2142.

  16. "Future asymptotics of tilted Bianchi type II cosmologies"
    S. Hervik, W.C. Lim, P. Sandin, C. Uggla, Classical and Quantum Gravity, 27, 185006 (18pp) (2010); arXiv:1004.3661.

  17. "Properties of kinematic singularities"
    A.A. Coley, S. Hervik, W.C. Lim, M.A.H. MacCallum, Classical and Quantum Gravity, 26, 215008 (8pp) (2009); arXiv:0907.1620.

  18. "Spikes in the Mixmaster regime of G_2 cosmologies"
    W.C. Lim, L. Andersson, D. Garfinkle, F. Pretorius, Physical Review D, 79, 123526 (15pp) (2009); arXiv:0904.1546.
    Errata: In (A2), the exponent should have the opposite sign: -(tau-tau_0). In the last line of (B2), w should have absolute value sign.

  19. "Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1"
    D. Garfinkle, W.C. Lim, F. Pretorius, P.J. Steinhardt, Physical Review D, 78, 083537 (8pp) (2008); arXiv:0808.0542.

  20. "New explicit spike solution -- non-local component of the generalized Mixmaster attractor"
    W.C. Lim, Classical and Quantum Gravity, 25, 045014 (17pp) (2008); arXiv:0710.0628.
    Errata: The third minus sign in (28) should be a plus. The factor 4 in (34) should not be there.
    CQG 2007/2008 highlight paper.

  21. "Late-time behaviour of the tilted Bianchi type VI-1/9 models"
    S. Hervik, R.J. van den Hoogen, W.C. Lim, A.A. Coley, Classical and Quantum Gravity, 25, 015002 (15pp) (2008); arXiv:0706.3184.

  22. "Late-time behaviour of the tilted Bianchi type VIh models"
    S. Hervik, R.J. van den Hoogen, W.C. Lim, A.A. Coley, Classical and Quantum Gravity, 24, 3859-3895 (2007); gr-qc/0703038.

  23. "Cosmic microwave background limits on spatially homogeneous cosmological models with a cosmological constant",
    A.A. Coley, W.C. Lim, Classical and Quantum Gravity, 24, 889-895 (2007); astro-ph/0610498.

  24. "Kinematic and Weyl singularities",
    W.C. Lim, A.A. Coley, S. Hervik, Classical and Quantum Gravity, 24, 595-604 (2007); gr-qc/0608134.

  25. "Fluid observers and tilting cosmology",
    A.A. Coley, S. Hervik, W.C. Lim, Classical and Quantum Gravity, 23, 3573-3591 (2006), gr-qc/0605128.

  26. "Tilted Bianchi VII_0 cosmologies -- the radiation bifurcation",
    W.C. Lim, R.J. Deeley, J. Wainwright, Classical and Quantum Gravity, 23, 3215-3234 (2006); gr-qc/0601040.

  27. "Tilt and phantom cosmology",
    A.A. Coley, S. Hervik, W.C. Lim, Physics Letters B, 638, 310-313 (2006); gr-qc/0512085.

  28. "The late-time behaviour of vortic Bianchi type VIII Universes",
    S. Hervik, W.C. Lim, Classical and Quantum Gravity, 23, 3017-3035 (2006); gr-qc/0512070.
    CQG 2005/2006 highlight paper.

  29. "Asymptotic silence-breaking singularities",
    W.C. Lim, C. Uggla, J. Wainwright, Classical and Quantum Gravity, 23, 2607-2630 (2006); gr-qc/0511139.

  30. "The futures of Bianchi type VII0 cosmologies with vorticity",
    S. Hervik, R.J. van den Hoogen, W.C. Lim, A.A. Coley, Classical and Quantum Gravity, 23, 845--866 (2006); gr-qc/0509032.

  31. "Asymptotic analysis of spatially inhomogeneous stiff and ultra-stiff cosmologies",
    A.A. Coley, W.C. Lim, Classical and Quantum Gravity, 22, 3073--3082 (2005); gr-qc/0506097.

  32. "Asymptotic silence of generic cosmological singularities",
    L. Andersson, H. van Elst, W.C. Lim, C. Uggla, Physical Review Letters, 94, 051101 (4pp) (2005); gr-qc/0402051;
    Popular article "Quiet at the end" by Davide Castelvecchi in Physical Review Focus, 15 , story 8 (2005).

  33. "Isotropic singularity in inhomogeneous brane cosmological models",
    A.A. Coley, Y. He, W.C. Lim, Classical and Quantum Gravity, 21, 1311--1342 (2004); gr-qc/0312075.

  34. "Asymptotic isotropization in inhomogeneous cosmology",
    W.C. Lim, H. van Elst, C. Uggla, J. Wainwright, Physical Review D, 69, 103507 (22pp) (2004); gr-qc/0306118.

  35. "Anisotropic universes with isotropic cosmic microwave background radiation",
    W.C. Lim, U.S. Nilsson, J. Wainwright, Classical and Quantum Gravity, 18, 5583--5590 (2001); gr-qc/9912001.

  36. "An almost isotropic cosmic microwave temperature does not imply an almost isotropic universe",
    U.S. Nilsson, C. Uggla, J. Wainwright, W.C. Lim, The Astrophysical Journal, 522, L1--L3 (1999); astro-ph/9904252.

Conference proceedings:

  1. "General Relativistic Tilt and Dark Energy",
    A.A. Coley, S. Hervik, W.C. Lim, AIP Conf. Proc., 1083, 65--73 (2008).

  2. "Cosmological models from a dynamical systems perspective",
    J. Wainwright, W.C. Lim, Journal of Hyperbolic Differential Equations, 2, 437--470 (2005); gr-qc/0409082.

Essay competition:

  1. "Cosmology: a bird's eye view", honorable mention in the Gravity Research Foundation Essay Competition, 2006
    A.A. Coley, S. Hervik, W.C. Lim, International Journal of Modern Physics D, 15, 2187-2190 (2006), gr-qc/0605089.


Conference and workshop presentations:


Maintained by Woei Chet Lim. Last updated 12 January, 2024.