ORCID Profile
0000-0001-6618-8470
Current Organisation
Flinders University
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Mathematical Physics | Theoretical Physics | Mathematics Not Elsewhere Classified | Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter | Mathematical Sciences Not Elsewhere Classified | Numerical and Computational Mathematics not elsewhere classified | Quantum Chemistry
ANZSRC Socio-Economic Objective (SEO)
Mathematical sciences | Expanding Knowledge in the Mathematical Sciences | Physical sciences | Chemical sciences |
Related Links
Publications
Series analysis of the generalized contact process
Publisher: Elsevier BV
Date: 02-1994
Critical behavior of the pair contact process
Publisher: American Physical Society (APS)
Date: 08-03-1993
Time-dependent perturbation theory for nonequilibrium lattice models
Publisher: American Physical Society (APS)
Date: 10-1991
A transfer matrix approach to the enumeration of plane meanders
Publisher: IOP Publishing
Date: 16-08-2000
Self-avoiding polygons on the square lattice
Publisher: IOP Publishing
Date: 1999
Universal amplitude ratioΓ − ∕
Publisher:
American Physical Society (APS)
Date:
08-2006
Publisher: American Physical Society (APS)
Date: 08-2006
Time-dependent perturbation theory for nonequilibrium lattice models
Publisher: Springer Science and Business Media LLC
Date: 04-1993
DOI: 10.1007/BF01048090
Series expansions for the percolation probability of a generalized Domany - Kinzel cellular automaton
Publisher: IOP Publishing
Date: 21-12-1997
Critical behavior of branching annihilating random walks with an odd number of offsprings
Publisher: American Physical Society (APS)
Date: 1993
Low-density series expansions for directed percolation: IV. Temporal disorder
Publisher: IOP Publishing
Date: 03-02-2005
Scaling analysis of time-dependent simulations of the three-dimensional contact process
Publisher: American Physical Society (APS)
Date: 12-1992
Nonequilibrium phase transitions in systems with infinitely many absorbing states
Publisher: American Physical Society (APS)
Date: 09-1993
Series analysis
Publisher: Springer Netherlands
Date: 2009
On the existence of critical exponents for self-avoiding walks
Publisher: IOP Publishing
Date: 07-10-2022
Abstract: We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctness.
Time-dependent perturbation theory for diffusive non-equilibrium lattice models
Publisher: IOP Publishing
Date: 21-02-1993
Exact enumerations
Publisher: Springer Netherlands
Date: 2009
Non-equilibrium critical behaviour on fractal lattices
Publisher: IOP Publishing
Date: 21-09-1991
On the number of benzenoid hydrocarbons
Publisher: American Chemical Society (ACS)
Date: 22-03-2002
DOI: 10.1021/CI010098G
Abstract: We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b(h) with h hexagons. We obtain b(h) up to h = 35. We prove that b(h) approximately const.kappa(h), prove the rigorous bounds 4.789 < or = kappa < or = 5.905, and estimate that kappa = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function summation operator b(h)z(h) approximately A(z) log(1 - kappa z), estimate A(1/kappa) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration (h) of benzenoids of size h grows as h(2 nu), with nu = 0.64115(5).
The hard hexagon partition function for complex fugacity
Publisher: IOP Publishing
Date: 18-10-2013
Size and area of square lattice polygons
Publisher: IOP Publishing
Date: 05-05-2000
Correction-to-scaling exponents for two-dimensional self-avoiding walks
Publisher: Springer Science and Business Media LLC
Date: 09-2005
Self-avoiding walks and polygons on the triangular lattice
Publisher: IOP Publishing
Date: 26-10-2004
Polygonal polyominoes on the square lattice
Publisher: IOP Publishing
Date: 27-04-2001
Self-avoiding walks contained within a square
Publisher: IOP Publishing
Date: 12-10-2022
Abstract: We have studied self-avoiding walks contained within an L × L square whose end-points can lie anywhere within, or on, the boundaries of the square. We prove that such walks behave, asymptotically, as walks crossing a square (WCAS), being those walks whose end-points lie at the south-east and north-west corners of the square. We provide numerical data, enumerating all such walks, and analyse the sequence of coefficients in order to estimate the asymptotic behaviour. We also studied a subset of these walks, those that must contain at least one edge on all four boundaries of the square. We provide compelling evidence that these two classes of walks grow identically. From our analysis we conjecture that the number of such walks C L , for both problems, behaves as C L ∼ λ L 2 + b L + c ⋅ L g , where (Guttmann and Jensen 2022 J. Phys. A: Math. Theor. ) λ = 1.744 5498 ± 0.000 0012, b = −0.043 54 ± 0.0005, c = −1.35 ± 0.45, and g = 3.9 ± 0.1. Finally, we also studied the equivalent problem for self-avoiding polygons, also known as cycles in a square grid. The asymptotic behaviour of cycles has the same form as walks, but with different values of the parameters c , and g . Our numerical analysis shows that λ and b have the same values as for WCAS and that c = 1.776 ± 0.002 while g = −0.500 ± 0.005 and hence probably equals − 1 2 .
Three friendly walkers
Publisher: IOP Publishing
Date: 09-12-2016
Polygons pulled from an adsorbing surface
Publisher: IOP Publishing
Date: 18-01-2018
Low-density series expansions for directed percolation: III. Some two-dimensional lattices
Publisher: IOP Publishing
Date: 22-06-2004
Directed percolation near a wall
Publisher: IOP Publishing
Date: 21-04-1996
Low-density series expansions for directed percolation: I. A new efficient algorithm with applications to the square lattice
Publisher: IOP Publishing
Date: 1999
Role of conformational entropy in force-induced biopolymer unfolding
Publisher: American Physical Society (APS)
Date: 19-03-2007
Conservation laws and universality in branching annihilating random walks
Publisher: IOP Publishing
Date: 21-08-1993
ROLE OF PULLING DIRECTION IN UNDERSTANDING THE ANISOTROPY OF THE RESISTANCE OF PROTEINS TO FORCE-INDUCED MECHANICAL UNFOLDING
Publisher: World Scientific Pub Co Pte Lt
Date: 20-02-2010
DOI: 10.1142/S0217984910022469
Abstract: Recent advances in single molecule experiments have made it possible to investigate the mechanical anisotropy of protein stability in greater detail. It has been found that proteins can exhibit a erse range of responses when pulled in different directions. We review some of the experimental and numerical work related to the study of the resistance of proteins to force-induced mechanical unfolding. Based on model studies in the framework of statistical mechanics, we discuss the possible molecular origin of the anisotropy of protein resistance to unfolding.
Improved lower bounds on the connective constants for two-dimensional self-avoiding walks
Publisher: IOP Publishing
Date: 18-11-2004
Punctured polygons and polyominoes on the square lattice
Publisher: IOP Publishing
Date: 28-02-2000
The Potts model on Kagomé and honeycomb lattices
Publisher: IOP Publishing
Date: 07-12-1997
Honeycomb lattice polygons and walks as a test of series analysis techniques
Publisher: IOP Publishing
Date: 06-2006
Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
Publisher: IOP Publishing
Date: 14-10-2008
Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices
Publisher: IOP Publishing
Date: 02-12-2022
Abstract: We have analysed the recently extended series for the number of self-avoiding walks (SAWs) C L ( 1 ) that cross an L × L square between diagonally opposed corners. The number of such walks is known to grow as λ S L 2 . We have made more precise the estimate of λ S , based on additional series coefficients provided by several authors, and refined analysis techniques. We estimate that λ S = 1.744 5498 ± 0.000 0012. We have also studied the subdominant behaviour, and conjecture that C L ( 1 ) ∼ λ S L 2 + b L + c ⋅ L g , where b = − 0.043 54 ± 0.0001 , c = 0.5624 ± 0.0005 , and g = 0.000 ± 0.005. We implemented a very efficient algorithm for enumerating paths on the square and hexagonal lattices making use of a minimal perfect hash function and in-place memory updating of the arrays for the counts of the number of paths. Using this algorithm we extended and then analysed series for SAWs spanning the square lattice and self-avoiding polygons (SAPs) crossing the square lattice. These are known to also grow as λ S L 2 . The sub-dominant term λ b is found to be the same as for SAWs crossing the square, while the exponent g = 1.75 ± 0.01 for spanning SAWs and g = − 0.500 ± 0.005 for SAPs. We have also studied the analogous problems on the hexagonal lattice, and generated series for a number of geometries. In particular, we study SAWs and SAPs crossing rhomboidal, triangular and square domains on the hexagonal lattice, as well as SAWs spanning a rhombus. We estimate that the analogous growth constant λ H = 1.387 249 51 ± 0.000 000 05 , so an even more precise estimate than found for the square lattice. We also give estimates of the sub-dominant terms.
Modeling force-induced bio-polymer unfolding
Publisher: Springer Science and Business Media LLC
Date: 17-05-2009
Critical exponents for an irreversible surface reaction model
Publisher: American Physical Society (APS)
Date: 03-1990
Enumeration of compact self-avoiding walks
Publisher: Elsevier BV
Date: 12-2001
High order Fuchsian equations for the square lattice Ising model: 5
Publisher: IOP Publishing
Date: 17-06-2009
Enumeration of self-avoiding walks on the square lattice
Publisher: IOP Publishing
Date: 11-05-2004
A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice
Publisher: IOP Publishing
Date: 28-02-2012
Series expansions for two-dimensional directed percolation
Publisher: Elsevier BV
Date: 03-1996
A parallel algorithm for the enumeration of benzenoid hydrocarbons
Publisher: IOP Publishing
Date: 27-02-2009
The exact perimeter generating function for a model of punctured staircase polygons
Publisher: IOP Publishing
Date: 06-05-2008
Integrability versus non-integrability: hard hexagons and hard squares compared
Publisher: IOP Publishing
Date: 20-10-2014
Critical exponents for branching annihilating random walks with an even number of offspring
Publisher: American Physical Society (APS)
Date: 11-1994
Self-avoiding walks crossing a square
Publisher: IOP Publishing
Date: 05-10-2005
Low-density series expansions for directed percolation: II. The square lattice with a wall
Publisher: IOP Publishing
Date: 11-08-1999
Series expansions of the percolation probability on the directed triangular lattice
Publisher: IOP Publishing
Date: 07-02-1996
Exact generating function for 2-convex polygons
Publisher: IOP Publishing
Date: 23-01-2008
Kinetic phase transitions in a surface-reaction model with diffusion: Computer simulations and mean-field theory
Publisher: American Physical Society (APS)
Date: 08-1990
Compressed self-avoiding walks, bridges and polygons
Publisher: IOP Publishing
Date: 20-10-2015
Osculating and neighbour-avoiding polygons on the square lattice
Publisher: IOP Publishing
Date: 21-09-2001
A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
Publisher: IOP Publishing
Date: 12-05-2003
A numerical adaptation of self-avoiding walk identities from the honeycomb to other 2D lattices
Publisher: IOP Publishing
Date: 15-12-2012
The perimeter generating function of punctured staircase polygons
Publisher: IOP Publishing
Date: 29-03-2006
Critical behaviour of a surface reaction model with infinitely many absorbing states
Publisher: IOP Publishing
Date: 07-02-1994
Low-temperature series expansions for the spin-1 Ising model
Publisher: IOP Publishing
Date: 07-11-1994
Universal features of cluster numbers in percolation
Publisher: American Physical Society (APS)
Date: 13-11-2017
The gerrymander sequence, or A348456
Publisher: Elsevier BV
Date: 07-2023
Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
Publisher: IOP Publishing
Date: 06-04-2020
Role of pulling direction in understanding the energy landscape of proteins
Publisher: American Physical Society (APS)
Date: 13-08-2008
Percolation and epidemics in a two-dimensional small world
Publisher: American Physical Society (APS)
Date: 16-01-2002
Pressure exerted by a grafted polymer on the limiting line of a semi-infinite square lattice
Publisher: IOP Publishing
Date: 27-02-2013
Two-dimensional self-avoiding walks and polymer adsorption: Critical fugacity estimates
Publisher: IOP Publishing
Date: 16-01-2012
Prudent walks and polygons
Publisher: IOP Publishing
Date: 04-02-2009
Low-temperature series expansions for the square lattice Ising model with spin S > 1
Publisher: IOP Publishing
Date: 21-07-1996
Study of the Potts model on the honeycomb and triangular lattices: Low-temperature series and partition function zeros
Publisher: IOP Publishing
Date: 13-03-1998
Self-avoiding walks, neighbour-avoiding walks and trails on semiregular lattices
Publisher: IOP Publishing
Date: 09-10-1998
Low-density series expansions for directed percolation on square and triangular lattices
Publisher: IOP Publishing
Date: 21-11-1996
Universality class of a one-dimensional cellular automaton
Publisher: American Physical Society (APS)
Date: 03-1991
Perimeter generating functions for the mean-squared radius of gyration of convex polygons
Publisher: IOP Publishing
Date: 02-11-2005
Effect of confinement: Polygons in strips, slabs and rectangles
Publisher: Springer Netherlands
Date: 2009
Scaling function and universal amplitude combinations for self-avoiding polygons
Publisher: IOP Publishing
Date: 03-09-2001
Pulling self-interacting polymers in two dimensions
Publisher: American Physical Society (APS)
Date: 23-03-2009
Critical behavior of the three-dimensional contact process
Publisher: American Physical Society (APS)
Date: 1992
Square lattice Ising model χ(5) ODE in exact arithmetic
Publisher: IOP Publishing
Date: 21-04-2010
Series expansions of the percolation probability for directed square and honeycomb lattices
Publisher: IOP Publishing
Date: 07-09-1995
Comment on ‘Series expansions from the corner transfer matrix renormalization group method: the hard-squares model’
Publisher: IOP Publishing
Date: 28-11-2012
High-order Fuchsian equations for the square lattice Ising model: χ(6)
Publisher: IOP Publishing
Date: 26-02-2010
Statistics of lattice animals (polyominoes) and polygons
Publisher: IOP Publishing
Date: 17-07-2000
Square lattice self-avoiding walks and biased differential approximants
Publisher: IOP Publishing
Date: 30-09-2016
Analysis of mean cluster size in directed compact percolation near a damp wall
Publisher: IOP Publishing
Date: 11-03-2014
Critical exponents of plane meanders
Publisher: IOP Publishing
Date: 18-05-2000
Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
Publisher: IOP Publishing
Date: 21-11-2016
Enumerations of lattice animals and trees
Publisher: Springer Science and Business Media LLC
Date: 2001
Scaling prediction for self-avoiding polygons revisited
Publisher: IOP Publishing
Date: 25-08-2004
Extrapolation procedure for low-temperature series for the square lattice spin-1 Ising model
Publisher: IOP Publishing
Date: 21-07-1996
Analyticity of the Ising susceptibility: an interpretation
Publisher: IOP Publishing
Date: 09-08-2017
Pulling adsorbed self-avoiding walks from a surface
Publisher: IOP Publishing
Date: 11-12-2014
Related Organisations
Related Funding Activities
Quantum Many-Body Systems Network: Breakthrough Science And Frontier Technologies
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End Date: 2003
Funder: Australian Research Council
View Funded ActivityAdvanced Computational And Analytic Studies In Lattice Statistical Mechanics And Applications
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View Funded ActivityProject DP140101110
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View Funded ActivitySearching For Solvability In Statistical Mechanics And Beyond Using Advanced Enumerative Combinatorics
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Funder: Australian Research Council
View Funded ActivityAdvanced Numerical And Analytical Techniques For Exact Studies In Combinatorics And Statistical Mechanics
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View Funded ActivityDiscovery Projects - Grant ID: DP140101110
Start Date: 2014
End Date: 12-2018
Amount: $370,000.00
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View Funded ActivityDiscovery Projects - Grant ID: DP0208244
Start Date: 2002
End Date: 12-2006
Amount: $620,000.00
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View Funded ActivityDiscovery Projects - Grant ID: DP120101593
Start Date: 04-2012
End Date: 03-2015
Amount: $300,000.00
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View Funded ActivityDiscovery Projects - Grant ID: DP0770705
Start Date: 2008
End Date: 12-2012
Amount: $891,000.00
Funder: Australian Research Council
View Funded ActivitySpecial Research Initiatives - Grant ID: SR0354741
Start Date: 2004
End Date: 12-2004
Amount: $10,000.00
Funder: Australian Research Council
View Funded Activity