Woei Chet Lim's
homepage
Office: G.3.05
Phone: (+64) 7 858 5148
Email: wclim@waikato.ac.nz
Teaching
MATH31112A Advanced Calculus
MATH25912B Mathematical Modelling
MATH54212B Partial Differential Equations 2
MATH31113A Advanced Calculus
MATH25513B / ENGG28413B Differential Equations
MATH33313Y / MATH56513B General Relativity
MATH31114A Advanced Calculus
MATH25514B / ENGG28414B Differential Equations
MATH54314B Nonlinear Dynamics and Chaos
(On study leave during the 15A semester)
MATH25515B / ENGG28415B Differential Equations
MATH33315Y / MATH56515B General Relativity
MATH54115B Classical Partial Differential Equations
MATH31116A Advanced Calculus
MATH54116A Classical Partial Differential Equations
MATH25516B / ENGG28416B Differential Equations
MATH25117A / ENGG28517A Multivariable Calculus
MATH25517B / ENGG28417B Differential Equations
MATH33317Y / MATH56517B General Relativity
ENGG28517T Multivariable Calculus
(On study leave during the 18A semester)
ENGEN20118B Engineering Mathematics 2
MATHS20118B Continuing Calculus (first 8 weeks)
MATHS20318B Differential Equations and Modelling (last 4 weeks)
MATH54118B Classical Partial Differential Equations
ENGEN20119S Engineering Mathematics 2 (first half)
MATHS10119A Introduction to Calculus
MATHS56519A General Relativity
ENGEN20119B Engineering Mathematics 2
MATHS20119B Continuing Calculus (first 8 weeks)
MATHS20319B Differential Equations and Modelling (last 4 weeks)
MATHS10120A Introduction to Calculus
MATHS54320A Nonlinear Dynamics and Chaos
ENGEN20120B Engineering Mathematics 2
MATHS20120B Continuing Calculus (first 8 weeks)
ENGEN20120C (NET) Engineering Mathematics 2
ENGEN20121A Engineering Mathematics and Modelling 2
MATHS20121A Continuing Calculus (first 8 weeks)
MATHS56521A General Relativity
(On study leave during the 21B trimester)
ENGEN20122H (NET) Engineering Mathematics and Modelling 2
ENGEN20122A Engineering Mathematics and Modelling 2
MATHS20122A Continuing Calculus (first 8 weeks)
MATHS20322B Differential Equations and Modelling
MATHS54322B Nonlinear Dynamics and Chaos
ENGEN20123H (NET) Engineering Mathematics and Modelling 2
(Very tentative 23AB teaching allocation:)
ENGEN10123A (HAM) Engineering Mathematics and Modelling 1A
ENGEN20123A Engineering Mathematics and Modelling 2
MATHS20123A Continuing Calculus (first 8 weeks)
MATH341/54123B Classical Partial Differential Equations (shared with Sean Oughton)
MATHS56523B 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 todate has focussed on
the socalled inhomogeneous Mixmaster behaviour near a gravitational
singularity. A large part of my doctoral thesis is devoted to this topic.
The shockcapturing 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 nonOT G_2 spike solution, which generalizes the OT G_2 spike solution.
My other projects todate include:
 Dynamics of spatially homogeneous (Bianchi) models
 Derivation and application of the boost formula
 Derivation of asymptotic expansions for cosmological models
 Analyzing singularities in exact solutions
My longterm goal is to investigate what the full nonlinear field
equations of general relativity predict about the evolution of
inhomogeneity.
Current active projects:
 Various aspects of spikes.
I also work on an engineering project with Prof. Jonathan Scott.
Previous positions:
 Postdoctoral fellow (Geometric Analysis and Gravitation division)
Max Planck Institute for Gravitational Physics (Albert Einstein Institute). September 2008  December 2011.
 Postdoctoral fellow (with Frans Pretorius)
Department of Physics,
University of Alberta, Canada. September 2006  January 2007.
Department of Physics,
Princeton University, USA. February 2007  August 2008.
 Postdoctoral fellow (with Alan Coley)
Department of Mathematics and Statistics,
Dalhousie University, Canada. September 2004  August 2006.
Education:
 PhD Applied Math, University of Waterloo, Canada (2004)
Thesis:
"The dynamics of inhomogeneous cosmologies".
Supervisor: John Wainwright
 MMath Applied Math, University of Waterloo, Canada (2000)
Thesis: "Anisotropy of the cosmic microwave background
temperature in Bianchi universes".
Supervisor: John Wainwright
 BMath Honours Joint Applied Math & Computer Science,
University of Waterloo, Canada (1998)
Award:

S. Chandrasekhar Award
for the best postdoctoral presentation in all Mathematical General Relativity sessions
(A1 Exact Solutions and their Interpretation,
A2 Mathematical Relativity and Other Progress in Classical Gravity,
A3 Modified Gravity Theories) at the 19th International Conference on General Relativity
and Gravitation in Mexico City, July 59, 2010.
Link to ResearcherID page
Link to Google scholar page
Journal articles:

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

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

"Transition analysis of the nonOT 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.

"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.

"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.

"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.

"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.

"Nonorthogonally 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.

"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.

"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.

"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).

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

"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].

"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.

"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.

"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.

"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: (tautau_0). In the last line of (B2), w should have absolute value sign.

"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.

"New explicit spike solution  nonlocal 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.

"Latetime behaviour of the tilted Bianchi type VI1/9
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.

"Latetime 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, 38593895 (2007);
grqc/0703038.

"Cosmic microwave background limits on spatially homogeneous
cosmological models with a cosmological constant",
A.A. Coley, W.C. Lim,
Classical and Quantum Gravity, 24, 889895 (2007);
astroph/0610498.

"Kinematic and Weyl singularities",
W.C. Lim, S. Hervik, A.A. Coley,
Classical and Quantum Gravity, 24, 595604 (2007);
grqc/0608134.

"Fluid observers and tilting cosmology",
A.A. Coley, S. Hervik, W.C. Lim,
Classical and Quantum Gravity, 23, 35733591 (2006),
grqc/0605128.

"Tilted Bianchi VII_0 cosmologies  the radiation bifurcation",
W.C. Lim, R.J. Deeley, J. Wainwright,
Classical and Quantum Gravity, 23, 32153234 (2006);
grqc/0601040.

"Tilt and phantom cosmology",
A.A. Coley, S. Hervik, W.C. Lim,
Physics Letters B, 638, 310313 (2006);
grqc/0512085.

"The latetime behaviour of vortic Bianchi type VIII Universes",
S. Hervik, W.C. Lim,
Classical and Quantum Gravity, 23, 30173035 (2006);
grqc/0512070.
CQG 2005/2006 highlight paper.

"Asymptotic silencebreaking singularities",
W.C. Lim, C. Uggla, J. Wainwright,
Classical and Quantum Gravity, 23, 26072630 (2006);
grqc/0511139.

"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, 845866 (2006);
grqc/0509032.

"Asymptotic analysis of spatially inhomogeneous stiff and ultrastiff
cosmologies",
A.A. Coley, W.C. Lim,
Classical and Quantum Gravity, 22, 30733082 (2005);
grqc/0506097.

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

"Isotropic singularity in inhomogeneous brane cosmological models",
A.A. Coley, Y. He, W.C. Lim,
Classical and Quantum Gravity, 21, 13111342 (2004);
grqc/0312075.

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

"Anisotropic universes with isotropic cosmic microwave background
radiation",
W.C. Lim, U.S. Nilsson, J. Wainwright,
Classical and Quantum Gravity, 18, 55835590 (2001);
grqc/9912001.

"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, L1L3 (1999);
astroph/9904252.
Conference proceedings:

"General Relativistic Tilt and Dark Energy",
A.A. Coley, S. Hervik, W.C. Lim,
AIP Conf. Proc., 1083,
6573 (2008).

"Cosmological models from a dynamical systems perspective",
J. Wainwright, W.C. Lim,
Journal of Hyperbolic Differential Equations, 2,
437470 (2005);
grqc/0409082.
Essay competition:

"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, 21872190
(2006),
grqc/0605089.
Conference and workshop presentations:

"Monotonic functions in Bianchi models with a scalar field",
presented at
 Joerg Frauendiener's 60th birthday conference, University of Otago, August 29, 2018.
 the NZMS Colloquium at University of Otago, December 46, 2018.
 the 10th Australasian Conference on General Relativity and Gravitation at Victoria University, Wellington, December 1012, 2019.

"Spike dynamics near spacelike singularities",
presented at KTH, Stockholm, April 26, 2018, and at the 2nd workshop on "Singularities of general relativity and their quantum fate", Banach Mathematical Center, Warsaw, May 2125, 2018.

"Exact G_1 spike solutions in general relativity",
presented at
 the 9th Australasian Conference on General Relativity and Gravitation at Gravity Discovery Centre, Gingin, November 2730, 2017.
 the NZMS Colloquium at University of Auckland, December 57, 2017.
 the 6th ANZAMP meeting, Takapuna, January 30  February 1, 2018.

"Spiky relativistic dynamics near spacelike singularities",
presented at the NZMS Colloquium at Victoria University, Wellington, December 57, 2016.

"NonOT G_2 spike solution",
presented at
 the 8th Australasian Conference on General Relativity and Gravitation at Monash University, Melbourne, December 24, 2015.
 the 16th Canadian Conference on General Relativity and Relativistic Astrophysics in Vancouver, July 68, 2016.
 the 21st International Conference on General Relativity and Gravitation at Columbia University in New York City, July 1015, 2016.

"Demonstration of the spike phenomenon using the LTB models",
presented at
 the Centennial GRG conference at Penn State University in State College, PA, June 812, 2015.
 the NZMS Colloquium at Massey University, Palmerston North, December 35, 2019.

"Spiky inhomogeneous exact solutions in general relativity",
presented at the Australian Institute of Physics Congress at ANU, Canberra, December 8, 2014.

"Tilt, spikes and generation of matter overdensities",
presented at the 7th Australasian Conference on General Relativity and Gravitation on Hamilton Island, December 10, 2013.

"BKL singularity, spikes and inhomogeneous cosmology",
presented at the MSRI programme "Mathematical General Relativity", November 26, 2013.

"Generating matter inhomogeneities in general relativity",
presented at the 13th Marcel Grossmann meeting in Stockholm, July 16, 2012.
Newer version presented at the 20th International Conference on General Relativity
and Gravitation in Warsaw, July 713, 2013.

"Dynamics near spacelike singularities is more inhomogeneous than conjectured by BKL",
presented at
 SFB seminar at AEI, October 25, 2010.
 Swedish GR meeting in Karlstad, December 34, 2010.
 University of Cape Town cosmology seminar, February 22, 2011.
 Workshop on "Dynamics of General Relativity: Analytical and Numerical Approaches",
at the Erwin Schroedinger Institute for Mathematical Physics, Vienna, July 20, 2011.
 The 6th Australasian Conference on General Relativity and Gravitation in Queenstown, February 11, 2012.

"Spike crossings in spacetimes with one Killing vector field",
presented at the 19th International Conference on General Relativity
and Gravitation in Mexico City, July 59, 2010.
Received the S. Chandrasekhar Award for the best postdoctoral presentation in all Mathematical General Relativity sessions
(A1 Exact Solutions and their Interpretation,
A2 Mathematical Relativity and Other Progress in Classical Gravity,
A3 Modified Gravity Theories).

"Spiky Mixmaster dynamics", presented at the 13th Canadian
Conference on General
Relativity and Relativistic Astrophysics in Calgary, May 1618, 2009.
Also presented at the Atlantic Relativity MiniConference in
Fredericton, April 25, 2009;
at the 12th Marcel Grossmann meeting in Paris, July 1318, 2009;
and at the "New Developments in Lorentzian Geometry" conference at TU Berlin, November 1820, 2009.

"Spikes  nonlocal component of the generalized Mixmaster attractor",
presented at the Geometric Analysis and Gravitation seminar at AEI, September 29, 2008.
Also presented at the workshop for Geometry, Analysis, and General Relativity,
at the MittagLeffler Institute, Stockholm, November, 2008.
Also presented at the Free University nonlinear analysis seminar, Berlin, July 15, 2010.

"Spikes in the Mixmaster regime of G_2 cosmologies",
presented at the 11th Eastern Gravity Meeting in State College, PA, May 1213, 2008.

"Inhomogeneous Mixmaster and spikes", presented at the IGC inaugural
conference at Penn State University in State College, PA, August 911,
2007.

"Kinematic and Weyl singularities", presented at the 12th Canadian
Conference on General Relativity and Relativistic Astrophysics in
Fredericton, May 1719, 2007.
Also presented at the 18th International Conference on General Relativity
and Gravitation in Sydney, Australia, July 813, 2007.

"Fluid observers and tilting cosmology", presented at the
Atlantic Relativity MiniConference in Fredericton, May 6, 2006.
Also presented at the 2nd International Meeting on Gravitation and
Cosmology in Santa Clara, Cuba, May 29June 1, 2006, and at
the APCTPTPI Meeting at the University of Alberta, December 1823, 2006.

"Dynamical systems approach to inhomogeneous cosmology", presented at
the dynamical systems workshop for Global Problems in Mathematical
Relativity, September 1225, 2005, at the Isaac Newton Institute for
Mathematical Sciences, University of Cambridge.

"Spiky spatial inhomogeneities", presented at the 11th Canadian
Conference on General
Relativity and Relativistic Astrophysics in Vancouver, May 1921, 2005.
Also presented at the Atlantic Relativity MiniConference in Fredericton,
April 30, 2005.

"Asymptotic isotropization in inhomogeneous cosmology", presented at
the 10th Canadian Conference on General
Relativity and Relativistic Astrophysics in Guelph, May 2831, 2003.

"Perturbations of the FriedmannLemaitre models: limitations and
pitfalls", presented at the 9th Canadian Conference on General
Relativity and Relativistic Astrophysics in Edmonton, May 2426, 2001.
Maintained by Woei Chet Lim. Last updated 30 June, 2022.