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Woei Chet Lim's homepage
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Office: G.3.05
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


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.

Current active projects:

Previous positions:


Education:


Award:


Link to ResearcherID page

Link to Google scholar page


Journal articles:

  1. "Stiff fluid spike solutions from Bianchi type V seed solutions"
    D. Gregoris, W.C. Lim, A.A. Coley arXiv:1705.02747.

  2. "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.

  3. "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).

  4. "Non-orthogonally transitive G_2 spike solution"
    W.C. Lim Classical and Quantum Gravity, 32, 162001 (8pp) (2015); arXiv:1507.02754.
    Errata: In (16), the n_30 term should read n_30 exp(-(w+1)tau). Ignore equations (53)--(54). The last sentence in the paragraph before (49) should refer to n_10 and n_30.

  5. "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.

  6. "General relativistic density perturbations"
    W.C. Lim, A.A. Coley, Classical and Quantum Gravity, 31, 015020 (13pp) (2014); arXiv:1311.1857.

  7. "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.

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

  9. "Spike oscillations"
    J.M. Heinzle, C. Uggla, W.C. Lim, Physical Review D, 86, 104049 (26pp) (2012); arXiv:1206.0932.

  10. "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.

  11. "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.

  12. "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.

  13. "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.

  14. "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.

  15. "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.

  16. "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.

  17. "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.

  18. "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.

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

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

  21. "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.

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

  23. "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.

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

  25. "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.

  26. "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.

  27. "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).

  28. "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.

  29. "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.

  30. "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.

  31. "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:


Personal

I grew up in Kuantan, Malaysia. After finishing Form 5 in Kuantan, I began my journey oversea. I studied Grade 13 in Hamilton, Ontario, Canada. After that, I went to the University of Waterloo for BMath, MMath and PhD. I did 3 postdocs in Canada, USA and Germany before joining the department here.

In my spare time, I volunteer at the Hamilton branch of Buddhist Compassion Relief Tzu Chi Foundation. I also like reading non-fictions.

Maintained by Woei Chet Lim. Last modified August 21, 2017.