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references.bib
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@article{Nelson1979,
author = {Nelson, David R and Halperin, B I},
doi = {10.1103/PhysRevB.19.2457},
journal = {Phys. Rev. B},
month = {mar},
pages = {2457--2484},
publisher = {American Physical Society},
title = {{Dislocation-Mediated Melting in Two Dimensions}},
volume = {19},
year = {1979}
}
@article{Theran2015,
abstract = {Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface, the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing trian-gles, which is the focus of this paper. Another way of rendering such networks isostatic, is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This ap-proach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level needs such boundary conditions, if the observed structure is to be computer-refined so that the interior atoms have the perception of being in an infinite isostatic environment. FIG. 1. Showing a piece of bilayer of vitreous silica imaged in SPM (Scanning Probe Microscope) 5 to show the Si atoms as red discs and the O atoms as black discs. The local covalent bonding leads to the yellow almost-equilateral triangles that are freely jointed, which we will refer to as pinned. The triangles at the surface have either one or two vertices unpinned.},
author = {Theran, Louis and Nixon, Anthony and Ross, Elissa and Sadjadi, Mahdi and Servatius, Brigitte and Thorpe, M. F.},
file = {:Users/David/Documents/Work/DPhil/Papers/282.pdf:pdf},
issn = {15502376},
journal = {Phys. Rev. E},
pages = {053306},
title = {{Anchored Boundary Conditions for Locally Isostatic Networks}},
volume = {92},
year = {2015}
}
@article{Wales2006,
author = {Wales, David J and Bogdan, Tetyana V},
doi = {10.1021/jp0680544},
file = {:Users/David/Documents/Work/DPhil/Papers/jp0680544.pdf:pdf},
journal = {J Phys Chem B},
pages = {20765--20776},
title = {{Potential Energy and Free Energy Landscapes}},
volume = {110},
year = {2006}
}
@article{Baise2018,
author = {Baise, Mia and Maffettone, Phillip M and Trousselet, Fabien and Funnell, Nicholas P and Coudert, Fran{\c{c}}ois-Xavier and Goodwin, Andrew L},
doi = {10.1103/PhysRevLett.120.265501},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.120.265501.pdf:pdf},
issn = {1079-7114},
journal = {Phys. Rev. Lett.},
keywords = {doi:10.1103/PhysRevLett.120.265501 url:https://doi},
pages = {265501},
publisher = {American Physical Society},
title = {{Negative Hydration Expansion in ZrW2O8: Microscopic Mechanism, Spaghetti Dynamics, and Negative Thermal Expansion}},
volume = {120},
year = {2018}
}
@article{Shokef2011,
abstract = {Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher-order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order by disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level and, contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.},
author = {Shokef, Yair and Souslov, Anton and Lubensky, T. C.},
doi = {10.1073/pnas.1014915108},
file = {:Users/David/Documents/Work/DPhil/Papers/11804.full.pdf:pdf},
issn = {00278424},
journal = {PNAS},
keywords = {Colloidal monolayer,Geometric frustration,Magnetoelasticity},
pages = {11804--11809},
pmid = {21730164},
title = {{Order by Disorder in the Antiferromagnetic Ising Model on an Elastic Triangular Lattice}},
volume = {108},
year = {2011}
}
@article{Gibson2006,
abstract = {The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.},
author = {Gibson, Matthew C. and Patel, Ankit B. and Nagpal, Radhika and Perrimon, Norbert},
doi = {10.1038/nature05014},
file = {:Users/David/Documents/Work/DPhil/Papers/nature05014.pdf:pdf},
isbn = {1476-4687 (Electronic)},
issn = {14764687},
journal = {Nature},
pages = {1038--1041},
pmid = {16900102},
title = {{The Emergence of Geometric Order in Proliferating Metazoan Epithelia}},
volume = {442},
year = {2006}
}
@article{Edwards1994,
abstract = {In this paper we present an alternative derivation of the Aboav-Weaire law. By first making the assumption that the mean of the number of sides surrounding a cell is a function of the time, leads to Mn, the mean number of sides surrounding a cell of sides n, as a linear function of the second moment $\mu$, and is independent of n. This indicates that the local mean increases with time. When written in the form of the general Aboav-Weaire relation we find in their notation that a = 1 and b = 6 7. The analysis also leads to the relation that the deviation from the ensemble average, 6, is proportional to $\mu$, and b is the coefficient of proportionality. The initial assumption is removed and the assumption that Mn is now a function of time and the number of sides is made. This assumption leads to Mn as a linear function of the ratio $\mu$/(n+1). This applies in the limit of small $\mu$ and the assumption that Mn can be expanded as a Maclaurin series. When written in the form of the general Aboav-Weaire law a = 1 and b = 0. This implies that the deviation from the mean 6 is then proportional to $\mu$/(n+1). A similar analysis is applied to three dimensions and when the faces of the cells are considered we find that the average number of faces of the cells surrounding a cell of face {\{}cauchy integral{\}} is a linear function of $\mu$/({\{}cauchy integral{\}}+;1), where $\mu$ is the second moment of the faces with mean 14. This analysis of the mean number of sides surrounding a cell is extended to finding the mean area surrounding a cell of sides n and area A, MAn. It is found that the mean area of the cells MAn is given by MAn = Aa + (Aa - A)/n, where Aa is the local cell area average which in the first approximation can be treated as the ensemble average area. Similarly the mean volume of cells surrounding a cell of faces {\{}cauchy integral{\}} and volume v is given by Mv{\{}cauchy integral{\}} = va + (va - v)/{\{}cauchy integral{\}}, where va is the average local volume. In this case cells of small areas (volumes) are surrounded by cells of areas (volumes) greater than the average area (volume). We can reverse the argument to show that the large area (volume) cells are surrounded by small area (volume) cells. The results of this analysis indicates that the cells are not randomly distributed. {\textcopyright} 1994.},
author = {Edwards, S. F. and Pithia, K. D.},
doi = {10.1016/0378-4371(94)90222-4},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0378437194902224-main.pdf:pdf},
issn = {03784371},
journal = {Physica A},
pages = {577--584},
title = {{A Note on the Aboav-Weaire Law}},
volume = {205},
year = {1994}
}
@article{Isobe2015,
author = {Isobe, Masaharu and Krauth, Werner},
doi = {10.1063/1.4929529},
file = {:Users/David/Documents/Work/DPhil/Papers/Hard-sphere{\_}melting{\_}and{\_}crystallization{\_}with{\_}event.pdf:pdf},
journal = {J. Chem. Phys.},
keywords = {bond-orientational order parameter,coarsening,event-chain monte carlo,event-driven molecular dynamics,hard spheres,nucleation},
pages = {084509},
title = {{Hard-Sphere Melting and Crystallization with Event-Chain Monte Carlo}},
volume = {143},
year = {2015}
}
@article{Roy2019,
author = {Roy, Projesh Kumar and Heuer, Andreas},
doi = {10.1103/PhysRevLett.122.016104},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.122.016104.pdf:pdf},
issn = {1079-7114},
journal = {Phys. Rev. Lett.},
keywords = {doi:10.1103/PhysRevLett.122.016104 url:https://doi},
pages = {016104},
publisher = {American Physical Society},
title = {{Ring Statistics in 2D Silica: Effective Temperatures in Equilibrium}},
volume = {122},
year = {2019}
}
@article{Rivier1990,
author = {Rivier, N},
file = {:Users/David/Documents/Work/DPhil/Papers/ajp-jphyscol199051C731.pdf:pdf},
journal = {J. Phys. Colloq.},
pages = {309--317},
title = {{Geometry and Fluctuations of Surfaces}},
volume = {51},
year = {1990}
}
@phdthesis{Whitaker2019,
author = {Whitaker, Oliver},
file = {:Users/David/Documents/Work/DPhil/Papers/Thesis{\_}Final.pdf:pdf},
school = {University of Oxford},
title = {{Modelling of Complex Ring Networks in Two- and Three-Dimensions}},
year = {2019}
}
@article{Boots1983,
author = {Boots, B N},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0098300483900067-main.pdf:pdf},
journal = {Comput. Geosci.},
keywords = {algorithm,fortran,simulation,stochastic geometry,subroutine,voronoi polygon},
number = {3},
pages = {351--365},
title = {{The Spatial Arrangement of Random Voronoi Polygons}},
volume = {9},
year = {1983}
}
@article{Aboav1984,
author = {Aboav, D. A.},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0026080084900752-main.pdf:pdf},
journal = {Metallography},
pages = {383--396},
title = {{The Arrangement of Cells in a Net. III}},
volume = {17},
year = {1984}
}
@article{Aboav1970,
author = {Aboav, D A},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0026080070900388-main.pdf:pdf},
journal = {Metallography},
pages = {383--390},
title = {{Arrangement of Grains in a Polycrystal}},
volume = {3},
year = {1970}
}
@article{Postulka2016,
author = {Postulka, Lars and Winter, Stephen M and Mihailov, Adam G and Mailman, Aaron and Assoud, Abdeljalil and Robertson, Craig M and Wolf, Bernd and Lang, Michael and Oakley, Richard T},
doi = {10.1021/jacs.6b05079},
file = {:Users/David/Documents/Work/DPhil/Papers/jacs.6b05079.pdf:pdf},
journal = {J. Am. Chem. Soc.},
pages = {10738--10741},
title = {{Spin Frustration in an Organic Radical Ion Salt Based on a Kagome-Coupled Chain Structure}},
volume = {138},
year = {2016}
}
@article{Jhang2017,
author = {Jhang, Jin-Hao and Zhou, Chao and Dagdeviren, Omur E and Hutchings, Gregory S and Schwarz, D and Altman, Eric I},
doi = {10.1039/c7cp02382k},
file = {:Users/David/Documents/Work/DPhil/Papers/c7cp02382k.pdf:pdf},
journal = {Phys Chem Chem Phys},
pages = {14001--14011},
publisher = {Royal Society of Chemistry},
title = {{Growth of Two Dimensional Silica and Aluminosilicate Bilayers on Pd(111 ): From Incommensurate to Commensurate Crystalline}},
volume = {19},
year = {2017}
}
@article{GELLATLY1982,
author = {Gellatly, B. J. and Finney, J. L.},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-002230938290093X-main.pdf:pdf},
journal = {J. Non. Cryst. Solids},
pages = {313--329},
title = {{Characterisation of Models of Multicomponent Amorphous Metals: The Radical Alternative to the Voronoi Polyhedron}},
volume = {50},
year = {1982}
}
@article{Mousseau2001,
abstract = {Continuous random network (CRN) models are often used as models for elemental and binary tetrahedral semiconductors such as a-Si and a-GaAs. Here, we review algorithms to generate CRN models. We discuss their structural properties and compare with those models obtained via different computational approaches, as well as with experiment. Additionally, we discuss current results towards the generation of para-crystalline models. ?? 2002 Elsevier Science Ltd. All rights reserved.},
author = {Mousseau, Normand and Barkema, G. T.},
doi = {10.1016/S1359-0286(02)00005-0},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-S1359028602000050-main.pdf:pdf},
isbn = {1359-0286},
issn = {13590286},
journal = {Curr. Opin. Solid State Mater. Sci.},
pages = {497--502},
title = {{Fast Bond-Transposition Algorithms for Generating Covalent Amorphous Structures}},
volume = {5},
year = {2001}
}
@book{barabasi2016n,
abstract = {La 4{\`{e}}me de couverture indique : "Networks are everywhere, from the Internet, to social networks, and the genetic networks that determine our biological existence. Illustrated throughout in full colour, this pioneering textbook, spanning a wide range of topics from physics to computer science, engineering, economics and the social sciences, introduces network science to an interdisciplinary audience. From the origins of the six degrees of separation to explaining why networks are robust to random failures, the author explores how viruses like Ebola and H1N1 spread, and why it is that our friends have more friends than we do. Using numerous real-world examples, this innovatively designed text includes clear delineation between undergraduate and graduate level material"},
address = {Cambridge},
author = {Barab{\'{a}}si, Albert-L{\'{a}}szl{\'{o}} and P{\'{o}}sfai, M{\'{a}}rton},
isbn = {9781107076266 1107076269},
keywords = {required sna snaseminar},
publisher = {Cambridge University Press},
title = {{Network Science}},
year = {2016}
}
@article{Steinberg2019,
author = {Steinberg, Lee and Russo, John and Frey, Jeremy},
doi = {10.1186/s13321-019-0369-0},
file = {:Users/David/Documents/Work/DPhil/Papers/s13321-019-0369-0-2.pdf:pdf},
isbn = {1332101903690},
issn = {1758-2946},
journal = {J. Cheminform.},
keywords = {Persistent homology,Topological data analysis,Water networks,persistent homology,topological data analysis,water networks},
number = {48},
pages = {1--11},
publisher = {Springer International Publishing},
title = {{A New Topological Descriptor for Water Network Structure}},
volume = {11},
year = {2019}
}
@article{Torrie1977,
author = {Torrie, G M and Valleau, J P},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0021999177901218-main.pdf:pdf},
journal = {J. Comput. Phys.},
pages = {187--199},
title = {{Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling}},
volume = {23},
year = {1977}
}
@article{Metropolis1953,
author = {Metropolis, N and Rosenbluth, A W and Rosenbluth, M N and Teller, A H and Teller, E},
doi = {10.1063/1.1699114},
file = {:Users/David/Documents/Work/DPhil/Papers/1.1699114.pdf:pdf},
journal = {J. Chem. Phys.},
number = {6},
pages = {1087--1092},
title = {{Equation of State Calculations by Fast Computing Machines}},
volume = {21},
year = {1953}
}
@article{Onodera2019,
author = {Onodera, Yohei and Kohara, Shinji and Tahara, Shuta and Masuno, Atsunobu and Inoue, Hiroyuki and Shiga, Motoki and Hirata, Akihiko and Tsuchiya, Koichi and Hiraoka, Yasuaki and Obayashi, Ippei and Ohara, Koji and Mizuno, Akitoshi and Sakata, Osami},
file = {:Users/David/Documents/Work/DPhil/Papers/127{\_}19143.pdf:pdf},
journal = {J. Ceram. Soc. Japan},
number = {12},
pages = {853--863},
title = {{Understanding Diffraction Patterns of Glassy, Liquid and Amorphous Materials via Persistent Homology Analyses}},
volume = {127},
year = {2019}
}
@article{Delannay1994,
abstract = {Stationary topological properties of 2D cellular structures generated by$\backslash$nrandom fragmentation have been calculated by computer simulations. The$\backslash$nprobability distributions of the number n of cell sides agree with a$\backslash$nrecent mean-field model. Two-cell correlations are almost linear in n.$\backslash$nThe most disordered structure approaches a `'topological gas'' with weak$\backslash$ncorrelations in the arrangement of cells. Variation with disorder of the$\backslash$nAboav-Weaire parameter is discussed for 2D cellular structures.},
author = {Delannay, Renaud and {Le Ca{\"{e}}r}, G{\'{e}}rard},
doi = {10.1103/PhysRevLett.73.1553},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.73.1553.pdf:pdf},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {11},
pages = {1553--1556},
title = {{Topological Characteristics of 2D Cellular Structures Generated by Fragmentation}},
volume = {73},
year = {1994}
}
@article{Vogel2014,
author = {Vogel, N and Ally, J and Bley, K and Kappl, M and Landfester, K and Weiss, C K},
doi = {10.1039/c4nr00401a},
file = {:Users/David/Documents/Work/DPhil/Papers/c4nr00401a.pdf:pdf},
journal = {Nanoscale},
pages = {6879--6885},
title = {{Direct visualization of the Interfacial Position of Colloidal Particles and Their Assemblies}},
volume = {6},
year = {2014}
}
@article{Ressouche2009,
author = {Ressouche, E and Simonet, V and Canals, B and Gospodinov, M and Skumryev, V},
doi = {10.1103/PhysRevLett.103.267204},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.103.267204-2.pdf:pdf},
journal = {Phys. Rev. Lett.},
pages = {267204},
title = {{Magnetic Frustration in an Iron-Based Cairo Pentagonal Lattice}},
volume = {103},
year = {2009}
}
@article{Kosterlitz1973,
abstract = {A new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists. The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. The critical behaviour found in this model displays very weak singularities. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet. for reasons that are given. {\textcopyright} 1973 IOP Publishing Ltd.},
author = {Kosterlitz, J. M. and Thouless, D. J.},
doi = {10.1088/0022-3719/6/7/010},
file = {:Users/David/Documents/Work/DPhil/Papers/J{\_}M{\_}Kosterlitz{\_}1973{\_}J.{\_}Phys.{\_}C{\%}3A{\_}Solid{\_}State{\_}Phys.{\_}6{\_}1181.pdf:pdf},
issn = {00223719},
journal = {J. Phys. C},
pages = {1181--1203},
title = {{Ordering, Metastability and Phase Transitions in Two-Dimensional Systems}},
volume = {6},
year = {1973}
}
@article{Stone1986,
author = {Stone, A J and Wales, D J},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0009261486806613-main.pdf:pdf},
journal = {Chem. Phys. Lett.},
number = {5,6},
pages = {501--503},
title = {{Theoretical Studies of Icosahedra C60 and some Related Species}},
volume = {128},
year = {1986}
}
@book{Nocedal2006,
author = {Nocedal, Jorge and Wright, Stephen J},
edition = {2},
file = {:Users/David/Documents/Work/DPhil/Papers/Numerical{\_}Optimization2006.pdf:pdf},
isbn = {9780387303031},
publisher = {Springer},
title = {{Numerical Optimization}},
year = {2006}
}
@article{Pusey1986,
author = {Pusey, P N and Megen, W Van},
file = {:Users/David/Documents/Work/DPhil/Papers/320340a0.pdf:pdf},
journal = {Nature},
pages = {340},
title = {{Phase Behaviour of Concentrated Suspensions of Nearly Hard Colloidal Spheres}},
volume = {320},
year = {1986}
}
@article{Huang2012,
author = {Huang, Pinshane Y and Kurasch, Simon and Srivastava, Anchal and Skakalova, Viera and Kotakoski, Jani and Krasheninnikov, Arkady V and Hovden, Robert and Mao, Qingyun and Meyer, Jannik C and Smet, Jurgen H and Muller, David and Kaiser, Ute},
doi = {10.1017/S1431927612009336},
file = {:Users/David/Documents/Work/DPhil/Papers/nl204423x.pdf:pdf},
issn = {14358115},
journal = {Nano Lett.},
keywords = {1 2d,2d,2d silica,boron nitride,crystals such as,graphene and monolayer hexagonal,graphene imaging substrates,n stark contrast with,s model,sio 2,transmission electron microscopy,two-dimensional,two-dimensional glass,zachariasen},
pages = {1081--1086},
title = {{Direct Imaging of a Two-Dimensional Silica Glass on Graphene}},
volume = {12},
year = {2012}
}
@article{Tong2017,
author = {Tong, Mingming and Cole, Katie and Brito-Parada, Pablo R and Neethling, Stephen and Cilliers, Jan J},
doi = {10.1021/acs.langmuir.6b03663},
file = {:Users/David/Documents/Work/DPhil/Papers/acs.langmuir.6b03663.pdf:pdf},
journal = {Langmuir},
pages = {3839--3846},
title = {{Geometry and Topology of Two-Dimensional Dry Foams: Computer Simulation and Experimental Characterization}},
volume = {33},
year = {2017}
}
@article{Rossky1978,
abstract = {A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties. {\textcopyright} 1978 American Institute of Physics.},
author = {Rossky, P. J. and Doll, J. D. and Friedman, H. L.},
doi = {10.1063/1.436415},
file = {:Users/David/Documents/Work/DPhil/Papers/1.436415.pdf:pdf},
issn = {00219606},
journal = {J. Chem. Phys.},
pages = {4628--4633},
title = {{Brownian Dynamics as Smart Monte Carlo Simulation}},
volume = {69},
year = {1978}
}
@article{Fugacci2016,
author = {Fugacci, Ulderico and Scaramuccia, Sara and Iuricich, Federico and Floriani, Leila De},
file = {:Users/David/Documents/Work/DPhil/Papers/stag2016-2.pdf:pdf},
journal = {Smart Tools Apps Comput. Graph.},
keywords = {2,3,according to acm ccs,categories and subject descriptors,computer and education,computer and information,computer science education,k,persistent homology,science education,shape analysis,topological data analysis},
title = {{Persistent Homology: A Step-by-Step Introduction for Newcomers}},
year = {2016}
}
@misc{eumap,
author = {Eurostat},
publisher = {Eurostat},
title = {{NUTS Geodata {\textcopyright} EuroGeographics for the administrative boundaries}},
url = {https://ec.europa.eu/eurostat/web/gisco/geodata/reference-data/administrative-units-statistical-units/nuts},
year = {2016}
}
@article{Blunt2008,
author = {Blunt, Matthew O and Russell, James C and Gim{\'{e}}nez-L{\'{o}}pez, Mar{\'{i}}a Carmen and Garrahan, J P and Lin, Xiang and Schr{\"{o}}der, Martin and Champness, Neil R and Beton, Peter H},
file = {:Users/David/Documents/Work/DPhil/Papers/20145272.pdf:pdf},
journal = {Science},
pages = {1077--1081},
title = {{Random Tiling and Topological Defects in a Two-Dimensional Molecular Network}},
volume = {322},
year = {2008}
}
@article{Tan2017,
author = {Tan, Chaoliang and Cao, Xiehong and Wu, Xue-jun and He, Qiyuan and Yang, Jian and Zhang, Xiao and Chen, Junze and Zhao, Wei and Han, Shikui and Nam, Gwang-hyeon and Sindoro, Melinda and Zhang, Hua},
doi = {10.1021/acs.chemrev.6b00558},
file = {:Users/David/Documents/Work/DPhil/Papers/acs.chemrev.6b00558.pdf:pdf},
journal = {Chem. Rev.},
pages = {6225--6331},
title = {{Recent Advances in Ultrathin Two-Dimensional Nanomaterials}},
volume = {117},
year = {2017}
}
@article{Djordjevic1995,
author = {Djordjevic, B R and Thorpe, M F and Wooten, F},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevB.52.5685.pdf:pdf},
journal = {Phys. Rev. B},
number = {8},
pages = {5685--5690},
title = {{Computer Model of Tetrahedral Amorphous Diamond}},
volume = {52},
year = {1995}
}
@article{Boccaletti2006,
author = {Boccaletti, S and Latora, V and Moreno, Y and Chavez, M and Hwang, D-U},
doi = {10.1016/j.physrep.2005.10.009},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-S037015730500462X-main.pdf:pdf},
journal = {Phys. Rep.},
pages = {175--308},
title = {{Complex Networks: Structure and Dynamics}},
volume = {424},
year = {2006}
}
@article{Aboav1980,
abstract = {A tessellation of Dirichlet polygons is generated from a pattern of points distributed at random over a rectangular grid, and a simple method is devised to disturb the clumps that are a characteristic feature of such a pattern, by subjecting the pattern to a clustering process. The process consists in applying a regular, periodic variation to the line-spacing of the grid. If the period of the variation is sufficiently small, or sufficiently large, the clumping is found to be scarcely affected by the clustering; but there is a narrow range of scale within which the two aggregative processes appear to interfere with each other. This interference is accompanied by a sudden and marked change in the topological properties of neighboring polygons of the tessellation, and an attempt is made to describe this change quantitatively in terms of previously established parameters. The importance of finding a physical counterpart of this geometrical effect is stressed. {\textcopyright} 1985.},
author = {Aboav, D. A.},
doi = {10.1016/0026-0800(85)90058-8},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-002608008090021X-main-2.pdf:pdf},
isbn = {1749717506},
issn = {00260800},
journal = {Metallography},
pages = {43--58},
title = {{The Arrangement of Cells in a Net. I}},
volume = {13},
year = {1980}
}
@article{Simonov2020,
author = {Simonov, Arkadiy and Baerdemaeker, Trees De and Bostr{\"{o}}m, Hanna L B and G{\'{o}}mez, Mar{\'{i}}a Laura R{\'{i}}os and Gray, Harry J and Chernyshov, Dmitry and Bosak, Alexey and B{\"{u}}rgi, Hans-Beat and Goodwin, Andrew L},
doi = {10.1038/s41586-020-1980-y},
file = {:Users/David/Documents/Work/DPhil/Papers/s41586-020-1980-y.pdf:pdf},
issn = {1476-4687},
journal = {Nature},
pages = {256},
publisher = {Springer US},
title = {{Hidden Diversity of Vacancy Networks in Prussian Blue Analogues}},
volume = {578},
year = {2020}
}
@article{Roy2019a,
author = {Roy, Projesh Kumar and Heuer, Andreas},
file = {:Users/David/Documents/Work/DPhil/Papers/Roy{\_}2019{\_}J.{\_}Phys.{\%}3A{\_}Condens.{\_}Matter{\_}31{\_}225703-3.pdf:pdf},
journal = {J. Phys. Condens. Matter},
keywords = {2d materials,maximum entropy method,md simulations,ring statistics},
pages = {225703},
publisher = {IOP Publishing},
title = {{Relating Local Structures, Energies, and Occurrence Probabilities in a Two-Dimensional Silica Network}},
volume = {31},
year = {2019}
}
@article{Wooten1985,
author = {Wooten, F and Winer, K and Weaire, D},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.54.1392.pdf:pdf},
journal = {Phys. Rev. Lett.},
number = {13},
pages = {1392--1395},
title = {{Computer Generation of Structural Models of Amorphous Si and Ge}},
volume = {54},
year = {1985}
}
@article{Carter2018,
author = {Carter, Benjamin M G D and Turci, Francesco and Ronceray, Pierre and Royall, C Patrick},
doi = {10.1063/1.5024462},
file = {:Users/David/Documents/Work/DPhil/Papers/1.5024462.pdf:pdf},
journal = {J. Chem. Phys.},
pages = {204511},
title = {{Structural Covariance in the Hard Sphere Fluid}},
volume = {148},
year = {2018}
}
@article{Zomorodian2005,
author = {Zomorodian, Afra and Carlsson, Gunnar},
file = {:Users/David/Documents/Work/DPhil/Papers/Zomorodian-Carlsson2005{\_}Article{\_}ComputingPersistentHomology.pdf:pdf},
journal = {Discret. Comput Geom},
pages = {249--274},
title = {{Computing Persistent Homology}},
volume = {33},
year = {2005}
}
@article{Chremos2007,
abstract = {The neighbor network in a two-dimensional polydisperse hard-disk fluid with diameter distribution p(sigma) approximately sigma(-4) is examined using constant-pressure Monte Carlo simulations. Graphs are constructed from vertices (disks) with edges (links) connecting each vertex to k neighboring vertices defined by a radical tessellation. At packing fractions in the range 0.24{\textless} or =eta{\textless} or =0.36, the decay of the network degree distribution is observed to be consistent with the power law k(-gamma) where the exponent lies in the range 5.6{\textless} or =gamma{\textless} or =6.0 . Comparisons with the predictions of a maximum-entropy theory suggest that this apparent power-law behavior is not the asymptotic one and that p(k) approximately k(-4) in the limit k--{\textgreater}infinity. This is consistent with the simple idea that for large disks, the number of neighbors is proportional to the disk diameter. A power-law decay of the network degree distribution is one of the characteristics of a scale-free network. The assortativity of the network is measured and is found to be positive, meaning that vertices of equal degree are connected more often than in a random network. Finally, the equation of state is determined and compared with the prediction from a scaled-particle theory. Very good agreement between simulation and theory is demonstrated.},
author = {Chremos, Alexandros and Camp, Philip J.},
doi = {10.1103/PhysRevE.76.056108},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevE.76.056108.pdf:pdf},
isbn = {1539-3755},
issn = {15393755},
journal = {Phys. Rev. E},
pages = {056108},
pmid = {18233719},
title = {{Neighbor Network in a Polydisperse Hard-Disk Fluid: Degree Distribution and Assortativity}},
volume = {76},
year = {2007}
}
@article{Algara-Siller2015,
author = {Algara-Siller, G and Lehtinen, O and Wang, F C and Nair, R R and Kaiser, U and Wu, H A and K, Geim A and Grigorieva, I V},
doi = {10.1038/nature14295},
file = {:Users/David/Documents/Work/DPhil/Papers/nature14295-2.pdf:pdf},
journal = {Nature},
pages = {443},
title = {{Square Ice in Graphene Nanocapillaries}},
volume = {519},
year = {2015}
}
@article{Sykes1964,
author = {Sykes, M F and Essam, J W},
file = {:Users/David/Documents/Work/DPhil/Papers/1.1704215.pdf:pdf},
journal = {J. Math. Phys.},
number = {8},
pages = {1117},
title = {{Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions}},
volume = {5},
year = {1964}
}
@article{Xia2015,
author = {Xia, Kelin and Feng, Xin and Tong, Yiying and Wei, Guo},
doi = {10.1002/jcc.23816},
file = {:Users/David/Documents/Work/DPhil/Papers/Xia{\_}et{\_}al-2015-Journal{\_}of{\_}Computational{\_}Chemistry.pdf:pdf},
journal = {J. Comput. Chem.},
pages = {408--422},
title = {{Persistent Homology for the Quantitative Prediction of Fullerene Stability}},
volume = {36},
year = {2015}
}
@misc{chmap,
author = {{Federal Office of Topography}},
publisher = {swisstopo},
title = {{swissBOUNDARIES3D}},
url = {https://shop.swisstopo.admin.ch/en/products/landscape/boundaries3D},
year = {2019}
}
@article{Tu1998,
author = {Tu, Yuhai and Tersoff, J and Grinstein, G and Vanderbilt, David},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.81.4899.pdf:pdf},
journal = {Phys. Rev. Lett.},
number = {22},
pages = {4899--4902},
title = {{Properties of a Continuous-Random-Network Model for Amorphous Systems}},
volume = {81},
year = {1998}
}
@article{Kumar2014,
abstract = {The recent synthesis and characterisation of bilayers of vitreous silica has produced valuable new information on ring sizes and distributions. In this paper, we compare the ring statistics of experimental samples with computer generated samples. The average ring size is fixed at six by topology, but the width, skewness and other moments of the distribution of ring edges are characteristics of particular samples. We examine the Aboav-Weaire law that quantifies the propensity of smaller rings to be adjacent to larger rings, and find similar results for available experimental samples which however differ somewhat from computer-generated bilayers. We introduce a new law for the areas of rings of various sizes.},
author = {Kumar, Avishek and Sherrington, David and Wilson, Mark and Thorpe, M F},
doi = {10.1088/0953-8984/26/39/395401},
file = {:Users/David/Documents/Work/DPhil/Papers/278.pdf:pdf},
issn = {0953-8984},
journal = {J. Phys. Condens. Matter},
keywords = {bilayers,in colour only in,modelling,ring statistics,silica,some figures may appear,the online journal},
pages = {395401},
pmid = {25191795},
title = {{Ring Statistics of Silica Bilayers}},
volume = {26},
year = {2014}
}
@article{Dunn1957,
author = {Dunn, C G and Koch, E F},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0001616057901220-main.pdf:pdf},
journal = {Acta Metall.},
pages = {548},
title = {{Comparison of Dislocation Densities of Primary and Secondary Recrystallization Grains of Si-Fe}},
volume = {5},
year = {1957}
}
@article{Camp2003,
author = {Camp, Philip J},
doi = {10.1103/PhysRevE.68.061506},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevE.68.061506.pdf:pdf},
journal = {Phys. Rev. E},
pages = {061506},
title = {{Structure and Phase Behavior of a Two-Dimensional System with Core-Softened and Long-Range Repulsive Interactions}},
volume = {68},
year = {2003}
}
@article{Kapko2010,
author = {Kapko, V and Drabold, D A and Thorpe, M F},
doi = {10.1002/pssb.200945581},
file = {:Users/David/Documents/Work/DPhil/Papers/pssb.200945581.pdf:pdf},
isbn = {1480965308},
journal = {Phys. Status Solidi},
keywords = {amorphous graphene,continuous random network,density of states},
number = {5},
pages = {1197--1200},
title = {{Electronic Structure of a Realistic Model of Amorphous Graphene}},
volume = {247},
year = {2010}
}
@article{Strogatz2001,
author = {Strogatz, Steven H},
file = {:Users/David/Documents/Work/DPhil/Papers/35065725-2.pdf:pdf},
journal = {Nature},
pages = {268},
title = {{Exploring Complex Networks}},
volume = {410},
year = {2001}
}
@article{Miklius2012,
abstract = {Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a unimodal distribution of both areas and ... $\backslash$n},
author = {Miklius, Matthew P. and Hilgenfeldt, Sascha},
doi = {10.1103/PhysRevLett.108.015502},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.108.015502.pdf:pdf},
issn = {00319007},
journal = {Phys. Rev. Lett.},
pages = {015502},
title = {{Analytical Results for Size-Topology Correlations in 2D Disk and Cellular Packings}},
volume = {108},
year = {2012}
}
@article{Anderson2013,
author = {Anderson, Joshua A and Jankowski, Eric and Grubb, Thomas L and Engel, Michael and Glotzer, Sharon C},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-S0021999113004968-main-2.pdf:pdf},
journal = {J. Comput. Phys.},
pages = {27--38},
publisher = {Elsevier Inc.},
title = {{Massively Parallel Monte Carlo for Many-Particle Simulations on GPUs}},
volume = {254},
year = {2013}
}
@article{Hilhorst2006,
abstract = {In planar cellular systems mn denotes the average sidedness of a cell neighbouring an n-sided cell. Aboav's empirical law states that nm(n) is linear in n. A downward curvature is nevertheless observed in the numerical nmn data of the random Voronoi froth. The exact large-n expansion of mn obtained in the present work, namely, m(n) = 4 + 3(pi/n)1/2 + (.) (.) (.) , explains this curvature. Its inverse square root dependence on n sets a new theoretical paradigm. Similar curved behaviour may be expected, and must indeed be looked for, in experimental data of sufficiently high resolution. We argue that it occurs, in particular, in diffusion-limited colloidal aggregation on the basis of recent simulation data due to Fernandez-Toledano et al (2005 Phys. Rev. E 71 041401) and earlier experimental results by Earnshaw and Robinson (1994 Phys. Rev. Lett. 72 3682).},
author = {Hilhorst, H. J.},
doi = {10.1088/0305-4470/39/23/004},
file = {:Users/David/Documents/Work/DPhil/Papers/Hilhorst{\_}2006{\_}J.{\_}Phys.{\_}A{\%}3A{\_}Math.{\_}Gen.{\_}39{\_}004.pdf:pdf},
journal = {J. Phys. A},
pages = {7227--7243},
title = {{Planar Voronoi Cells: The violation of Aboav's Law Explained}},
volume = {39},
year = {2006}
}
@article{Kim2016,
author = {Kim, Sangwoo and Cassidy, Justin J and Yang, Boyuan and Carthew, Richard W and Hilgenfeldt, Sascha},
doi = {10.1016/j.bpj.2016.11.004},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-S0006349516310311-main.pdf:pdf},
issn = {0006-3495},
journal = {Biophys. J.},
pages = {2735--2746},
publisher = {Biophysical Society},
title = {{Hexagonal Patterning of the Insect Compound Eye: Facet Area Variatio, Defects, and Disorder}},
volume = {111},
year = {2016}
}
@book{StaufferDietrich2014,
author = {Stauffer, Dietrich and Aharony, Amnon},
booktitle = {Introd. to percolation theory},
edition = {2nd ed.},
isbn = {9781482272376 (PDF)},
keywords = {Clusters,Fractals,Percolation (Statistical physics)},
title = {{Introduction to Percolation Theory}},
year = {2014}
}
@article{Wilson2012a,
author = {Wilson, Mark},
doi = {10.1039/c2cp41644a},
file = {:Users/David/Documents/Work/DPhil/Papers/c2cp41644a.pdf:pdf},
journal = {Phys Chem Chem Phys},
pages = {12701--12714},
title = {{Model Investigations of Network-Forming Materials}},
volume = {14},
year = {2012}
}
@article{Thorneywork2018,
author = {Thorneywork, Alice L and Schnyder, Simon K and Aarts, Dirk G A L and Horbach, J{\"{u}}rgen and Roth, Roland and Dullens, Roel P A and Thorneywork, Alice L and Schnyder, Simon K and Aarts, Dirk G A L},
doi = {10.1080/00268976.2018.1492745},
file = {:Users/David/Documents/Work/DPhil/Papers/ThorneyworkMolPhys2018.pdf:pdf},
journal = {Mol. Phys.},
keywords = {Hard disks,colloids,fluctuations,hard disks,structure factors,two-dimensional systems},
pages = {3245--3257},
title = {{Structure Factors in a Two-Dimensional Binary Colloidal Hard Sphere System}},
volume = {116},
year = {2018}
}
@article{Suwa2010,
author = {Suwa, Hidemaro and Todo, Synge},
doi = {10.1103/PhysRevLett.105.120603},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.105.120603.pdf:pdf},
journal = {Phys. Rev. Lett.},
pages = {120603},
title = {{Markov Chain Monte Carlo Method without Detailed Balance}},
volume = {105},
year = {2010}
}
@book{Frenkel2002,
author = {Frenkel, Daan and Smit, Berend},
edition = {2},
publisher = {Academic Press},
title = {{Understanding Molecular Simulation: From Algorithms to Applications}},
year = {2002}
}
@article{Jaster1999,
author = {Jaster, A},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevE.59.2594.pdf:pdf},
journal = {Phys. Rev. E},
number = {3},
pages = {2594--2602},
title = {{Computer Simulations of the Two-Dimensional Melting Transition Using Hard Disks}},
volume = {59},
year = {1999}
}
@article{Beck1954,
author = {Beck, Paul A},
doi = {10.1080/00018735400101203},
file = {:Users/David/Documents/Work/DPhil/Papers/Annealing of cold worked metals-2.pdf:pdf},
journal = {Adv. Phys.},
number = {11},
pages = {245--324},
title = {{Annealing of Cold Worked Metals}},
volume = {3},
year = {1954}
}
@article{Phillips1985,
author = {Phillips, J C and Thorpe, M F},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0038109885903813-main.pdf:pdf},
journal = {Solid State Commun.},
number = {8},
pages = {699--702},
title = {{Constraint Theory, Vector Percolation and Glass Formation}},
volume = {53},
year = {1985}
}
@article{Lewis1928,
author = {Lewis, F. T.},
doi = {10.1023/A:1012518317520},
file = {:Users/David/Documents/Work/DPhil/Papers/Lewis-1928-The{\_}Anatomical{\_}Record.pdf:pdf},
issn = {1573837X},
journal = {Anat. Rec.},
number = {3},
pages = {341--376},
title = {{The Correlation Between Cell Division and the Shapes and Sizes of Prismatic Cell in the Epidermis of Cucumis}},
volume = {38},
year = {1928}
}
@book{Landau2014,
author = {Landau, David P and Binder, Kurt},
doi = {10.1017/CBO9781139696463},
edition = {4},
publisher = {Cambridge University Press},
title = {{A Guide to Monte Carlo Simulations in Statistical Physics}},
year = {2014}
}
@article{Falco2017,
author = {Falco, Simone and Jiang, Jiawei and {De Cola}, Francesco and Petrinic, Nik},
doi = {10.1016/j.commatsci.2017.04.018},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-S0927025617302094-main.pdf:pdf},
issn = {0927-0256},
journal = {Comput. Mater. Sci.},
keywords = {grain structure reconstruction,laguerre-voronoi tessellation,polycrystalline materials},
pages = {20--28},
publisher = {Elsevier B.V.},
title = {{Generation of 3D Polycrystalline Microstructures with a Conditioned Laguerre-Voronoi Tessellation Technique}},
volume = {136},
year = {2017}
}
@article{Buchner2016a,
abstract = {The random network theory has been the long-accepted structural model for silica glasses. Now, a large bilayer silica sheet that was recently imaged with STM in atomic resolution provides the opportunity for real space structure analysis. General patterns in the formation of amorphous structures may be identified by looking at larger building blocks beyond single rings. Assessments of ring arrangements around each Si atom and ring neighborhoods are compared against uncorrelated structure predictions. A theoretical model of a two-dimensional silica network is investigated in parallel. Significant deviations of the observed structures from the uncorrelated prediction correspond qualitatively with a simple geometric approximation for bond angle frustration.},
author = {B{\"{u}}chner, Christin and Liu, Liwei and Stuckenholz, Stefanie and Burson, Kristen M. and Lichtenstein, Leonid and Heyde, Markus and Gao, Hong Jun and Freund, Hans Joachim},
doi = {10.1016/j.jnoncrysol.2015.12.020},
file = {:Users/David/Documents/Work/DPhil/Papers/747e.pdf:pdf},
issn = {00223093},
journal = {J. Non. Cryst. Solids},
keywords = {2D network,Amorphous,Glass,Oxide thin film,Silica,Structure},
pages = {40--47},
publisher = {Elsevier B.V.},
title = {{Building Block Analysis of 2D Amorphous Networks Reveals Medium Range Correlation}},
volume = {435},
year = {2016}
}
@article{Sun2015a,
author = {Sun, Yongfu and Gao, Shan and Lei, Fengcai and Xiao, Chong and Xie, Yi},
doi = {10.1021/ar500164g},
file = {:Users/David/Documents/Work/DPhil/Papers/ar500164g.pdf:pdf},
journal = {Acc. Chem. Res.},
pages = {3--12},
title = {{Ultrathin Two-Dimensional Inorganic Materials: New Opportunities for Solid State Nanochemistry}},
volume = {48},
year = {2015}
}
@article{Kumar1994,
abstract = {Abstract It is well known that the two-dimensional Poisson-Voronoi tesselation does not conform to the Aboav-Weaire law for the average number of sides for the neighbours of an n-sided cell. We offer a variant of Weaire's original derivation which takes into account certain features of this type of pattern, and results in a different form of the law, which is similar to that found from computer simulation.},
author = {Kumar, Susmit and Kurtz, Stewart K. and Weaire, Denis},
doi = {10.1080/01418639408240119},
file = {:Users/David/Documents/Work/DPhil/Papers/Average number of sides for the neighbours in a Poisson Voronoi tesselation.pdf:pdf},
issn = {13642812},
journal = {Philos. Mag. B},
number = {3},
pages = {431--435},
title = {{Average Number of Sides for the Neighbours in a Poisson-Voronoi Tesselation}},
volume = {69},
year = {1994}
}
@article{Flores2017,
author = {Flores, J C},
doi = {10.1039/c6sm02849g},
file = {:Users/David/Documents/Work/DPhil/Papers/c6sm02849g-2.pdf:pdf},
journal = {Soft Matter},
pages = {1352--1356},
publisher = {Royal Society of Chemistry},
title = {{Mean-field Crack Networks on Desiccated Films and their Applications: Girl with a Pearl Earring}},
volume = {13},
year = {2017}
}
@article{Widom1966,
author = {Widom, B},
journal = {J Chem Phys},
pages = {3888},
title = {{Random Sequential Addition of Hard Spheres to a Volume}},
volume = {44},
year = {1966}
}
@article{Wilson2012b,
author = {Wilson, Mark},
doi = {10.1088/0953-8984/24/28/284114},
file = {:Users/David/Documents/Work/DPhil/Papers/Wilson{\_}2012{\_}J.{\_}Phys.{\%}3A{\_}Condens.{\_}Matter{\_}24{\_}284114.pdf:pdf},
journal = {J. Phys. Condens. Matter},
pages = {284114},
title = {{The Effects of Topology on the Structural, Dynamic and Mechanical Properties of Network-Forming Materials}},
volume = {24},
year = {2012}
}
@article{Kapfer2015,
author = {Kapfer, Sebastian C and Krauth, Werner},
doi = {10.1103/PhysRevLett.114.035702},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.114.035702.pdf:pdf},
journal = {Phys. Rev. Lett.},
pages = {035702},
title = {{Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions}},
volume = {114},
year = {2015}
}
@article{Chiu1994,
author = {Chiu, S N},
file = {:Users/David/Downloads/1427808.pdf:pdf},
journal = {Adv. Appl. Probab.},
pages = {565--576},
title = {{Mean-Value Formulae for the Neighbourhood of the Typical Cell of a Random Tessellation}},
volume = {26},
year = {1994}
}
@article{Gervois1992,
author = {Gervois, A. and Troadec, J. P. and Lemaitre, J.},
doi = {10.1088/0305-4470/25/23/014},
file = {:Users/David/Documents/Work/DPhil/Papers/A{\_}Gervois{\_}1992{\_}J.{\_}Phys.{\_}A{\%}3A{\_}Math.{\_}Gen.{\_}25{\_}014.pdf:pdf},
issn = {03054470},
journal = {J. Phys. A},
pages = {6169--6177},
title = {{Universal Properties of Voronoi Tessellations of Hard Discs}},
volume = {25},
year = {1992}
}
@article{Niesse1996,
author = {Niesse, J A and Mayne, Howard R},
file = {:Users/David/Documents/Work/DPhil/Papers/1.472311.pdf:pdf},
journal = {J. Chem. Phys.},
pages = {4700},
title = {{Global Geometry Optimization of Atomic Clusters Using a Modified Genetic Algorithm in Space-Fixed Coordinates}},
volume = {105},
year = {1996}
}
@article{Allain1995,
author = {Allain, C and Limat, L},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.74.2981.pdf:pdf},
journal = {Phys. Rev. Lett.},
number = {15},
pages = {2981},
title = {{Regular Patterns of Cracks Formed by Directional Drying of a Collodial Suspension}},
volume = {74},
year = {1995}
}
@article{Chiu1995,
abstract = {A brief review of Aboav's law (the relationship between the average number of edges of a randomly chosen neighboring cell of a typical n-cell and n) and Lewis' law (the relationship between the mean area of a typical n-cell and n) is presented. These two laws now play central roles in Rivier's maximum entropy theory of statistical crystallography. A discussion of the mathematical forms of these laws is our emphasis in this article. {\textcopyright} 1995.},
author = {Chiu, S. N.},
doi = {10.1016/1044-5803(94)00081-U},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-104458039400081U-main.pdf:pdf},
issn = {10445803},
journal = {Mater. Charact.},
pages = {149--165},
title = {{Aboav-Weaire's and Lewis' Laws - A Review}},
volume = {34},
year = {1995}
}
@article{Barkema2000,
abstract = {The continuous random network (CRN) model is an idealized model for perfectly coordinated amorphous semiconductors. The quality of a CRN can be assessed in terms of topological and configurational properties, including coordination, bond-angle distributions, and deformation energy. Using a variation on the sillium approach proposed 14 years ago by Wooten, Winer, and Weaire, we present 1000-atom and 4096-atom configurations with a degree of strain significantly less than the best CRN available at the moment and comparable to experimental results. The low strain is also reflected in the electronic properties. The electronic density of state obtained from ab initio calculation shows a perfect band gap, without any defect, in agreement with experimental data.},
author = {Barkema, G. and Mousseau, Normand},
doi = {10.1103/PhysRevB.62.4985},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevB.62.4985.pdf:pdf},
isbn = {0163-1829},
issn = {0163-1829},
journal = {Phys. Rev. B},
number = {8},
pages = {4985--4990},
pmid = {11138044},
title = {{High-Quality Continuous Random Networks}},
volume = {62},
year = {2000}
}
@article{Ratsch2003,
author = {Ratsch, C and Venables, J A},
file = {:Users/David/Documents/Work/DPhil/Papers/e32727f95674c4d203b228e7d0a1fe801870-2.pdf:pdf},
journal = {J. Vac. Sci. Technol. A},
pages = {S96},
title = {{Nucleation Theory and the Early Stages of Thin Film Growth}},
volume = {21},
year = {2003}
}
@article{Blanc1979,
abstract = {The description of isotropic polycrystalline structures such as those encountered in normal grain growth, is approached from a probabilistic point of view. The discussion is restricted to the distribution of grain shapes in two dimensional sections, as characterized by the topological parameter n, i.e. the number of sides or nearest neighbours, which is also known to be somehow related to grain dimensions. Assuming that only two elementary transformations (interchange of grain neighbours and creation or annihilation of 3-sided grains) can take place in the array, it is predicted that the mean coordination number mn of the nearest neighbours of all n-sided grains is related to n through Weaire's relation: mn = 5 + (6 + $\mu$2)/n in which $\mu$2 is the second central moment of the overall distribution of grain coordination numbers. The latter is generated by Monte-Carlo simulation and it is suggested that a 'normal polycrystalline structure' may be viewed as that grain array most likely to develop when both elementary transformations repeatedly occur at random. Since their relative proportions remain a priori unknown, at least one degree of freedom is available in the model and evolutionary processes, e.g. grain growth can be accounted for within its framework. It is shown with a particular example, that actual microstructures may be found, which can be adequately described by the present model. {\textcopyright} 1979.},
author = {Blanc, M. and Mocellin, A.},
doi = {10.1016/0001-6160(79)90139-1},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0001616079901391-main.pdf:pdf},
issn = {00016160},
journal = {Acta Metall.},
pages = {1231--1237},
title = {{Grain Coordination in Plane Sections of Polycrystals}},
volume = {27},
year = {1979}
}
@article{Hahn1994,
author = {Hahn, U and Lorz, U},
file = {:Users/David/Documents/Work/DPhil/Papers/HAHN{\_}et{\_}al-1994-Journal{\_}of{\_}Microscopy.pdf:pdf},
journal = {J. Microsc.},
keywords = {model test,parameter estimation,random plane section,spatial poisson-voronoi tessellation,stereology,stochastic geometry},
number = {3},
pages = {176--185},
title = {{Stereological Analysis of the Spatial Poisson-Voronoi Tessellation}},
volume = {175},
year = {1994}
}
@article{Anderson1973,
author = {Anderson, P W},
file = {:Users/David/Documents/Work/DPhil/Papers/1-s2.0-0025540873901670-main.pdf:pdf},
journal = {Mat. Res. Bull.},
pages = {153--160},
title = {{Resonating Valence Bonds: A New Kind of Insulator?}},
volume = {8},
year = {1973}
}
@article{Greneche1990,
author = {Greneche, J M and Coey, J M D},
file = {:Users/David/Documents/Work/DPhil/Papers/ajp-jphys{\_}1990{\_}51{\_}3{\_}231{\_}0.pdf:pdf},
isbn = {0199000510302},
journal = {J. Phys. Fr.},
pages = {231--242},
title = {{The Topologically-Disordered Square Lattice}},
volume = {51},
year = {1990}
}
@article{Fowler1996,
author = {Fowler, P W and Heine, T and Manolopoulos, D E and Mitchell, D and Orlandi, G and Schmidt, R and Seifert, G and Zerbetto, F},
doi = {10.1021/jp9532226},
file = {:Users/David/Documents/Work/DPhil/Papers/jp9532226.pdf:pdf},
journal = {J Phys Chem},
pages = {6984--6991},
title = {{Energetics of Fullerenes with Four-Membered Rings}},
volume = {100},
year = {1996}
}
@article{Zheng2014,
author = {Zheng, Qing-Na and Wang, Lei and Zhong, Yu-Wu and Liu, Xuan-He and Chen, Ting and Yan, Hui-Juan and Wang, Dong and Yao, Jian-Nian and Wan, Li-Jun},
doi = {10.1021/la5002418},
file = {:Users/David/Documents/Work/DPhil/Papers/la5002418.pdf:pdf},
journal = {Langmuir},
pages = {3034--3040},
title = {{Adaptive Reorganization of 2D Molecular Nanoporous Network Induced by Coadsorbed Guest Molecule}},
volume = {30},
year = {2014}
}
@article{Buzano2004,
author = {Buzano, C and Stefanis, E De and Pelizzola, A and Pretti, M},
doi = {10.1103/PhysRevE.69.061502},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevE.69.061502.pdf:pdf},
journal = {Phys. Rev. E},
pages = {061502},
title = {{Two-Dimensional Lattice-Fluid Model with Waterlike Anomalies}},
volume = {69},
year = {2004}
}
@article{Otter2017,
author = {Otter, Nina and Porter, Mason A and Tillmann, Ulrike and Grindrod, Peter and Harrington, Heather A},
doi = {10.1140/epjds/s13688-017-0109-5},
file = {:Users/David/Documents/Work/DPhil/Papers/s13688-017-0109-5.pdf:pdf},
journal = {EPJ Data Sci.},
keywords = {persistent homology,point-cloud data,topological data analysis},
pages = {1},
publisher = {The Author(s)},
title = {{A Roadmap for the Computation of Persistent Homology}},
volume = {6},
year = {2017}
}
@article{Kotakoski2011,
abstract = {While crystalline two-dimensional materials have become an experimental reality during the past few years, an amorphous 2-D material has not been reported before. Here, using electron irradiation we create an sp2-hybridized one-atom-thick flat carbon membrane with a random arrangement of polygons, including four-membered carbon rings. We show how the transformation occurs step-by-step by nucleation and growth of low-energy multi-vacancy structures constructed of rotated hexagons and other polygons. Our observations, along with first-principles calculations, provide new insights to the bonding behavior of carbon and dynamics of defects in graphene. The created domains possess a band gap, which may open new possibilities for engineering graphene-based electronic devices.},
author = {Kotakoski, J. and Krasheninnikov, A. V. and Kaiser, U. and Meyer, J. C.},
doi = {10.1103/PhysRevLett.106.105505},
file = {:Users/David/Documents/Work/DPhil/Papers/PhysRevLett.106.105505.pdf:pdf},
isbn = {0031-9007$\backslash$n1079-7114},
issn = {00319007},
journal = {Phys. Rev. Lett.},
pages = {105505},
pmid = {21469806},