Publications
The easiest way to access details of most my publications is via my arXiv, Google Scholar, and ORCID pages.
Articles, book chapters, and other publications
Nathan Clisby, Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps, arXiv:1703.10557 (2017). |
Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling, and Nathan Clisby, Exact enumeration of self-avoiding walks on BCC and FCC lattices, arXiv:1703.09340 (2017). See here for the SAWdoubler release page, which implements the length-doubling enumeration algorithm. |
Nathan Clisby, Scale-free Monte Carlo method for calculating the critical exponent γ of self-avoiding walks, arXiv:1701.08415, submitted to J. Phys. A: Math. Theor. (2017). |
Nathan Clisby and Burkhard Dünweg, High precision estimate of the hydrodynamic radius for self-avoiding walks, Phys. Rev. E. 94: 052102 (2016). Chosen as an Editor's suggestion. |
Eric Horwath, Nathan Clisby, and Peter Virnau, Knots in finite memory walks. J. Phys.: Conf. Ser. 750: 012010 (2016). |
Nathan Clisby, Andrew R. Conway, and Anthony J. Guttmann, Three-dimensional terminally attached self-avoiding walks and bridges, arXiv:1504.02085, J. Phys. A.: Math. Theor. 49: 015004 (2016). |
Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796, J. Phys. A.: Math. Theor. 46: 235001 (2013). |
Nathan Clisby, Calculation of the connective constant for self-avoiding walks via the pivot algorithm, arXiv:1302.2106, J. Phys. A.: Math. Theor. 46: 245001 (2013). Chosen for IOP Select, and highlighted in Europhysics News, Vol. 44, No. 5 (2013). |
Alan Lauder, Ian G. Enting, John O. Carter, Nathan Clisby, Annette L. Cowie, Beverley K. Henry, and Michael R. Raupach, Offsetting methane emissions — an alternative to emission equivalence metrics, International Journal of Greenhouse Gas Control 12: 419–429 (2013). |
Nathan Clisby and Iwan Jensen, A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice, J. Phys. A.: Math. Theor. 45: 115202 (2012). |
Ian G. Enting and Nathan Clisby, Series Analysis of a Kosterlitz-Thouless Transition: The 6-State Planar Potts Model, J. Stat. Phys. 145: 696–712 (2011). |
Nathan Clisby, Efficient implementation of the pivot algorithm for self–avoiding walks, arXiv:1005.1444, J. Stat. Phys. 140: 349–392 (2010). |
Nathan Clisby, Accurate estimate of the critical exponent ν for self–avoiding walks via a fast implementation of the pivot algorithm, arXiv:1002.0494, Phys. Rev. Lett. 104: 055702 (2010). |
Ian G. Enting and Nathan Clisby, Submission to the Senate Select Committee on Climate Policy, no. 360 at http://bit.ly/149cCLQ, and cached version (2009). |
Nathan Clisby and Gordon Slade, Polygons and the lace expansion, in Polygons, Polyominoes and Polycubes, Lecture notes in Physics Vol. 775, Ed. A. J. Guttmann (Springer, 2009) pp. 117–142. |
Ian G. Enting, David Karoly, Jim Falk, Nathan Clisby, Roger Bodman, and Domenica Settle (CASPI), The Science of Stabilising Greenhouse Gas Concentrations, a commissioned report for the Garnaut Climate Change Review, available at http://bit.ly/bTizEv, cached version (2008). |
Marvin Bishop, Nathan Clisby, and Paula Whitlock, The equation of state of hard hyperspheres in nine dimensions for low to moderate densities, J. Chem. Phys. 128: 034506 (2008). |
Nathan Clisby, Richard Liang, and Gordon Slade, Self–avoiding walk enumeration via the lace expansion, J. Phys. A: Math. Theor. 40: 10973–11017 (2007). |
Nathan Clisby and Barry M. McCoy, Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions, cond–mat/0503525, J. Stat. Phys. 122: 15–57 (2006). |
Nathan Clisby and Barry M. McCoy, New results for virial coefficients of hard spheres in D dimensions, cond–mat/0410511, in proceedings of STATPHYS 22, Pramana — J. Phys. 64: 775–783 (2005). |
Nathan Clisby, Negative Virial Coefficients for Hard Spheres, Ph.D. thesis, Stony Brook University (2004). |
Nathan Clisby and Barry M. McCoy, Analytic calculation of B₄ for hard spheres in even dimensions, cond–mat/0303098, J. Stat. Phys. 114: 1343–1360 (2004). |
Nathan Clisby and Barry M. McCoy, Negative virial coefficients and the dominance of loose packed diagrams for D–dimensional hard spheres, cond–mat/0303100, J. Stat. Phys. 114: 1361–1392 (2004). |
Shane A. Canney, Maarten Vos, Anatoli S. Kheifets, Nathan Clisby, Ian E. McCarthy, and Eric Weigold, Measured energy–momentum densities of the valence band of aluminium, J. Phys.: Condens. Matter, 9: 1931–1950 (1997). |
Other documents
Nathan Clisby, Richard Liang, and Gordon Slade, Self–avoiding walk enumeration via the lace expansion, enumeration tables at http://www.math.ubc.ca/~slade. |
Nathan Clisby and Barry M. McCoy, New results for the virial coefficients of D–dimensional hard spheres, cond–mat/0303101 (2003). |
Nathan Clisby and Barry M. McCoy, Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions — Collection of Tables (2004). |
Seminars and Posters
Increasingly I'm using custom-designed simulations in my presentations, which may make it difficult to follow some material in my recent talks.Fast algorithms for Monte Carlo simulation of self-avoiding walks, “Special Functions and Concrete Mathematics” session of the The 4th International Congress on Mathematical Software, Seoul, Korea (August 2014). |
Assorted Topics in the Monte Carlo Simulation of Polymers, “Polymer Models and Combinatorics” session of the SIAM Conference on Discrete Mathematics, Minneapolis (June 2014). |
Monte Carlo calculation of the hydrodynamic radius for self-avoiding walks (with Burkhard Duenweg), Statistical Mechanics of Soft Matter, RMIT, Melbourne (November 2013). |
Monte Carlo simulation of self-avoiding walks,“Self-avoiding walk” session of the 36th Conference on Stochastic Processes and Their Applications, Boulder, Colorado (July/August 2013). |
The importance of fast algorithms for simulating complex systems (video version), Mathematics of Planet Earth Conference, Melbourne (July 2013). Provides a comparison between the gains from computer hardware and better algorithms over the past 30 years. For a general audience. |
Offsetting Ongoing Methane Emissions — An Alternative to Emission Equivalence Metrics (with Ian G. Enting, Alan Lauder, John O. Carter, Annette L. Cowie, Beverley K. Henry, and Michael R. Raupach), Poster at AGU Fall Meeting, San Francisco (December 2012). |
Endless self-avoiding walks, Inaugural meeting of the Australian and New Zealand Association of Mathematical Physics, Lorne, Victoria (December 2012). |
There are 7 × 10^{26 018 276} self-avoiding walks of 38 797 311 steps on Z^{3}, Max Planck Institute for Polymer Research in Mainz, and the University of Leipzig (November 2012). This is a longer version of talk below with the same title. |
Connections between graph theory and the virial expansion, Monash University (Discrete Mathematics), October 2012. |
There are 7 × 10^{26 018 276} self-avoiding walks of 38 797 311 steps on Z^{3}, Keynote seminar in the “Combinatorics” session of the 56th Annual Meeting of the Australian Mathematical Society, Ballarat, Victoria (September 2012). |
How to calculate the connective constant for self-avoiding walks really, really accurately, Annual Statistical Mechanics Meeting, Melbourne (December 2011). |
Fast Monte Carlo simulation of self-avoiding walks and related models of polymers, Statphys 24 in Cairns (July 22, 2010). Abstract: We have developed a new data structure which enables efficient Monte Carlo simulation of polymers with hundreds of millions of monomers. Thus far, we have implemented this data structure for self-avoiding walks, and then used the pivot algorithm to simulate walks on the simple cubic lattice with up to 270 million steps. Consequently we have determined the critical exponents ν and γ to unprecedented precision. |
Subtleties in the Monte Carlo simulation of lattice polymers, Statistical Physics of Lattice Polymers in Melbourne (July 9, 2010). Abstract: In the context of our recent calculation of the critical exponent γ for SAWs via Monte Carlo simulation, we discuss the occurrence of non-obvious length scales in lattice polymer systems. If these length scales are not identified it can lead to surprisingly long integrated autocorrelation times for the simulation. We describe our resolution of this problem, which is quite generic, and discuss the relevance of our work to other systems such as confined polymers and polymer knotting. |
CUDA and GPU programming: an opportunity for scientists, High Performance GPU Computing with NVIDIA CUDA in Melbourne (May 27, 2009). I was the local organiser of this workshop on CUDA programming, for which Mark Harris from NVIDIA was the principal speaker. I gave a talk about my perspective on CUDA and GPU programming, which included discussion about a CUDA project of mine on the enumeration of self–avoiding walks. |
Critical exponents for self–avoiding walks from a fast implementation of the pivot algorithm, Statistical Mechanics Meeting in Melbourne (December 1–2, 2008). Overview of the pivot algorithm (including images of a sequence of pivots applied to a long SAW on the square lattice), with heuristic description of the algorithmic improvements I have made to the implementation. N.B.: the exponent estimates have since been refined. |
An empirical estimate of 20th Century climate-to-carbon feedback (with Ian G. Enting), Poster at the 2008 Western Pacific Geophysics Meeting (July 29 – August 1, 2008). |
Fast algorithms for self–avoiding walks, Concepts of Entropy and Their Applications (November 26 – December 11, 2007). Appropriate for a general audience. Discusses enumeration of self–avoiding walks and introduces the “geometric splitting” algorithm, the first known sub–exponential method of enumerating SAWs. This work will not be published in any other form for the immediate future, as although the algorithm is interesting (to me!), unfortunately as it stands it is not practically useful, as efficiency for achievable lengths is quite poor due to large constant factors. There are some prospects for improving this situation, but it will not be easy. |
Laplace transform analysis of the coupled climate–carbon system (with Ian G. Enting), 51st Meeting of the Australian Mathematical Society, (September 25–28, 2007). |
Self–avoiding walk enumeration via the lace expansion (with Richard Liang and Gordon Slade), Poster at Statphys 23 (July 9–13, 2007). Summary of key results and ideas. |
Self–avoiding walk enumeration via the lace expansion (with Richard Liang and Gordon Slade), Complex '07 (July 2–5, 2007). Appropriate for a general audience. |
Self–avoiding walk enumeration via the lace expansion (with Richard Liang and Gordon Slade), Statistical Mechanics Conference, Rutgers University (December 17–19, 2006). For a statistical mechanics audience, only includes preliminary analysis. |
The finite lattice method, Summer School in Probability, University of British Columbia (June 6–30, 2005). |
Virial Coefficients for D-Dimensional Hard Spheres, The Australian National University (August 3, 2004). |