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Sep 20, 2013
09/13

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T. S. Evans

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Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree...

Source: http://arxiv.org/abs/cond-mat/0607196v3

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Sep 18, 2013
09/13

by
T. S. Evans

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I study how to apply relativistic quantum field theory to condensed matter systems. The motivation for this is examined and then two separate elements are considered. First we identify the precise relationship between relativistic and non-relativistic fields. Second we consider the need for a chemical potential and how one includes this in static and dynamical calculations.

Source: http://arxiv.org/abs/hep-ph/9510298v1

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Sep 20, 2013
09/13

by
T. S. Evans

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An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to the relevant literature and useful resources is also given.

Source: http://arxiv.org/abs/cond-mat/0405123v1

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Sep 19, 2013
09/13

by
T. S. Evans

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The zero four-momentum and equal mass limits are taken for the bubble diagram of scalar fields. It is seen that RTF and ITF are in complete agreement. However contributions from this diagram to both retarded and time-ordered functions do depend on the order of the limits and can be infinite in some cases. This shows explicitly that the relation between the free energy and a derivative expansion of a thermal effective action is generally much more complicated that is the case at zero temperature.

Source: http://arxiv.org/abs/hep-ph/9307335v1

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Sep 21, 2013
09/13

by
T. S. Evans

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Thermal field theory is reviewed briefly. It is noted that, until recently, it was not known what type of real-time Green function is being calculated in the Euclidean approach. The formal answer to this question is then given and the unexpectedly complicated answer is discussed. The physical implications of the results are then considered. (Talk given at the Lake Louise Winter Institute on Particle Physics and Cosmology, 20th - 26th February, 1994, Lake Louise, Canada)

Source: http://arxiv.org/abs/hep-ph/9404262v3

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Sep 23, 2013
09/13

by
T. S. Evans

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A new time contour is used to derive real-time thermal field theory. Unlike previous path integral approaches, no contributions to the generating functional are dropped.

Source: http://arxiv.org/abs/hep-ph/9310339v1

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Sep 18, 2013
09/13

by
T. S. Evans

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The thermal expectation values of all possible bosonic generalised retarded functions evaluated at zero energy are studied. The relationship of such functions to calculational schemes, technical problems and physical applications is outlined. It is then shown that all generalised retarded functions constructed from any one set of bosonic fields are equal at zero energy. This is done completely generally and is not limited to any approximation scheme such as perturbation theory.

Source: http://arxiv.org/abs/hep-ph/9504266v1

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Sep 19, 2013
09/13

by
T. S. Evans

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I study derivative expansions of effective actions at finite temperature, illustrating how the standard methods are badly defined at finite temperature. I then show that by setting up the initial conditions at a finite time, these problems are solved.

Source: http://arxiv.org/abs/hep-ph/0010138v1

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Sep 17, 2013
09/13

by
T. S. Evans

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I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key idea is that in many cases the process involves copying of properties of near neighbours in the network and this is a type of short random walk which in turn produce a natural preferential attachment mechanism. Applying this to networks of fixed size I show...

Source: http://arxiv.org/abs/0711.0603v1

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Sep 18, 2013
09/13

by
T. S. Evans

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Elizalde, Vanzo, and Zerbini have shown that the effective action of two free Euclidean scalar fields in flat space contains a `multiplicative anomaly' when zeta-function regularization is used. This is related to the Wodzicki residue. I show that there is no anomaly when using a wide range of other regularization schemes and further that this anomaly can be removed by an unusual choice of renormalisation scales. I define new types of anomalies and show that they have similar properties. Thus...

Source: http://arxiv.org/abs/hep-th/9803184v3

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Sep 22, 2013
09/13

by
T. S. Evans

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A new time contour is used to derive real-time thermal field theory. Unlike previous path integral approaches, no contributions to the generating functional are dropped.

Source: http://arxiv.org/abs/hep-ph/9209252v2

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Sep 21, 2013
09/13

by
T. S. Evans

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The vacuum energy density or free energy of a free charged Bose gas at non-zero densities is studied in the context of the debate about Multiplicative Anomalies. Some zeta-function regularised calculations of the free energy in the literature are reexamined, clarified and extended. A range of apparently distinct answers can obtained. Equivalent dimensional regularisation results are also presented for comparison. I conclude that operator ordering and normal ordering are not responsible for...

Source: http://arxiv.org/abs/hep-th/0104128v1

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Sep 19, 2013
09/13

by
T. S. Evans

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It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.

Source: http://arxiv.org/abs/1009.0638v1

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Sep 22, 2013
09/13

by
T. S. Evans

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The properties of the various types of bosonic Green functions at finite temperature in the zero energy limit are considered in the light of recent work.

Source: http://arxiv.org/abs/hep-ph/9209253v2

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Jul 20, 2013
07/13

by
T. S. Evans; M. Ivin

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We test an optimised hopping parameter expansion on various Z_2 lattice scalar field models: the Ising model, a spin-one model and lambda (phi)^4. We do this by studying the critical indices for a variety of optimisation criteria, in a range of dimensions and with various trial actions. We work up to seventh order, thus going well beyond previous studies. We demonstrate how to use numerical methods to generate the high order diagrams and their corresponding expressions. These are then used to...

Source: http://arxiv.org/abs/hep-ph/0406202v1

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Sep 23, 2013
09/13

by
T. S. Evans; R. Lambiotte

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In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node partition of the line graph of the original network. In this way we show that any algorithm which produces a partition of nodes can be used to produce a partition of links. We discuss the role of the degree heterogeneity and propose a weighted version of the...

Source: http://arxiv.org/abs/0903.2181v2

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Sep 23, 2013
09/13

by
T. S. Evans; A. Giometto

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It has been shown recently that in many different cultural phenomena the turnover rate on the most popular artefacts in a population exhibit some regularities. A very simple expression for this turnover rate has been proposed by Bentley et al. and its validity in two simple models for copying and innovation is investigated in this paper. It is found that Bentley's formula is an approximation of the real behaviour of the turnover rate in the Wright-Fisher model, while it is not valid in the...

Source: http://arxiv.org/abs/1105.4044v1

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Sep 17, 2013
09/13

by
T. S. Evans; R. Lambiotte

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In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications...

Source: http://arxiv.org/abs/0912.4389v2

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Sep 21, 2013
09/13

by
T. Clemson; T. S. Evans

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We study a networked version of the minority game in which agents can choose to follow the choices made by a neighbouring agent in a social network. We show that for a wide variety of networks a leadership structure always emerges, with most agents following the choice made by a few agents. We find a suitable parameterisation which highlights the universal aspects of the behaviour and which also indicates where results depend on the type of social network.

Source: http://arxiv.org/abs/1106.0296v2

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Sep 23, 2013
09/13

by
T. S. Evans; J. P. Saramaki

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We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organisation. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size...

Source: http://arxiv.org/abs/cond-mat/0411390v2

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Sep 18, 2013
09/13

by
T. S. Evans; D. A. Steer

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We consider Wick's Theorem for finite temperature and finite volume systems. Working at an operator level with a path ordered approach, we show that contrary to claims in the literature, expectation values of normal ordered products can be chosen to be zero and that results obtained are independent of volume. Thus the path integral and operator approaches to finite temperature and finite volume quantum field theories are indeed seen to be identical. The conditions under which normal ordered...

Source: http://arxiv.org/abs/hep-ph/9601268v1

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Sep 18, 2013
09/13

by
T. S. Evans; A. D. K. Plato

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Recently we showed that a simple model of network rewiring could be solved exactly for any time and any parameter value. We also showed that this model can be recast in terms of several well known models of statistical physics such as Urn model and the Voter model. We also noted that it has been applied to a wide range of problems. Here we consider various generalisations of this model and include some new exact results.

Source: http://arxiv.org/abs/0707.3783v1

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Sep 22, 2013
09/13

by
D. J. Bedingham; T. S. Evans

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We calculate the ultra-relativistic Bose-Einstein condensation temperature of a complex scalar field with weak lambda Phi^4 interaction. We show that at high temperature and finite density we can use dimensional reduction to produce an effective three-dimensional theory which then requires non-perturbative analysis. For simplicity and ease of implementation we illustrate this process with the linear delta expansion.

Source: http://arxiv.org/abs/hep-ph/0011286v2

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Sep 20, 2013
09/13

by
T. S. Evans; A. D. K. Plato

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We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and innovation, or models of homogeneity in genes in the presence of mutation. We show that the mean field equations in the literature are incomplete and provide the full equations. We then give an exact solution for both their long time solution and for their...

Source: http://arxiv.org/abs/physics/0608052v1

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Sep 19, 2013
09/13

by
T. S. Evans; A. C. Pearson

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We derive Feynman rules for gauge theories exhibiting spontaneous symmetry breaking using the real-time formalism of finite temperature field theory. We also derive the thermal propagators where only the physical degrees of freedom are given thermal boundary conditions. We analyse the abelian Higgs model and find that these new propagators simplify the calculation of the thermal contribution to the self energy.

Source: http://arxiv.org/abs/hep-ph/9307229v3

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Sep 19, 2013
09/13

by
T. S. Evans; M. Ivin; M. Mobius

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We use an optimised perturbation expansion called the linear delta-expansion to study the phase transition in a Higgs sector with a continuous symmetry and large couplings. Our results show how to use this non-perturbative method successfully for such problems. We also show how to simplify the method without losing any flexibility.

Source: http://arxiv.org/abs/hep-ph/9911492v1

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Sep 23, 2013
09/13

by
T. S. Evans; D. A. Steer

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We perform a well defined derivative expansion to obtain the time dependent effective theory for a BCS superconductor at finite temperature, using an arbitrary curve in the complex time plane. Our expansion is unique, being free of any problems related to the order in which analytical continuation and the derivative expansion are made, or equivalently to the order in which the zero momentum and zero energy limits are taken. In other words Landau damping terms are present but do not lead to the...

Source: http://arxiv.org/abs/cond-mat/9909103v1

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Sep 18, 2013
09/13

by
T. S. Evans; A. C. Pearson

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We argue that the asymptotic condition should not be applied in the derivation of the real time formalism of thermal field theory. It is shown that, contrary to popular belief, the generating functional of time ordered Green functions does not factorise. When no asymptotic condition is applied to the real time formalism, we find that the normal two component Feynman rules arises naturally. In addition, the extra Feynman rule that is applied when calculating vacuum diagrams is simply derived. We...

Source: http://arxiv.org/abs/hep-ph/9412217v1

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Sep 20, 2013
09/13

by
T. S. Evans; A. D. K. Plato

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We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the...

Source: http://arxiv.org/abs/cond-mat/0612214v2

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Sep 23, 2013
09/13

by
T. S. Evans; R. Lambiotte; P. Panzarasa

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This paper investigates the role of homophily and focus constraint in shaping collaborative scientific research. First, homophily structures collaboration when scientists adhere to a norm of exclusivity in selecting similar partners at a higher rate than dissimilar ones. Two dimensions on which similarity between scientists can be assessed are their research specialties and status positions. Second, focus constraint shapes collaboration when connections among scientists depend on opportunities...

Source: http://arxiv.org/abs/1006.1788v2

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Sep 18, 2013
09/13

by
R. J. Rivers; T. S. Evans

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We shall show that the density of defects produced at a second-order phase transition is determined by the correlation length of the fields. This is true both for defects appearing in the Ginzburg regime and for defects produced at a quench, when the Ginzburg regime is irrelevant. (Invited lectures given by R.J.R. to the Nato Advanced Study Institute and Euroconference on Formation and Interaction of Topological Defects, Isaac Newton Institute, Cambridge (UK), September, 1994.)

Source: http://arxiv.org/abs/astro-ph/9412059v1

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Jun 30, 2018
06/18

by
D. S. Reiss; J. J. Price; T. S. Evans

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We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part of this task, bypassing the use of CAD software and the need for manual design. As a proof of concept, a physical object representing a modified forest fire model was successfully printed. Automated conversion methods similar to the ones developed here can be...

Topics: Physics, Physics Education, Mathematics, History and Overview, Computing Research Repository,...

Source: http://arxiv.org/abs/1412.7977

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Jun 30, 2018
06/18

by
S. R. Goldberg; H. Anthony; T. S. Evans

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The distribution of the number of academic publications as a function of citation count for a given year is remarkably similar from year to year. We measure this similarity as a width of the distribution and find it to be approximately constant from year to year. We show that simple citation models fail to capture this behaviour. We then provide a simple three parameter citation network model using a mixture of local and global search processes which can reproduce the correct distribution over...

Topics: Physics, Digital Libraries, Physics and Society, Computing Research Repository, Social and...

Source: http://arxiv.org/abs/1408.2970

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Sep 22, 2013
09/13

by
T. S. Evans; H. F. Jones; A. Ritz

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We describe an application of the linear $\de$-expansion to the calculation of correlation functions in SU(2)-Higgs lattice gauge theory. A significant advantage of the technique is that an infinite volume lattice may be used, allowing the non-analyticity in certain observables at a phase transition to be observed directly. We illustrate the approach with a preliminary application to the 3D SU(2)-Higgs model, as the dimensionally reduced effective theory for the electroweak standard model at...

Source: http://arxiv.org/abs/hep-ph/9707539v1

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Sep 18, 2013
09/13

by
T. S. Evans; A. D. K. Plato; T. You

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Exact analytic solutions and various numerical results for the rewiring of bipartite networks are discussed. An interpretation in terms of copying and innovation processes make this relevant in a wide variety of physical contexts. These include Urn models and Voter models, and our results are also relevant to some studies of Cultural Transmission, the Minority Game and some models of ecology.

Source: http://arxiv.org/abs/0809.2568v1

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Sep 23, 2013
09/13

by
T. S. Evans; N. Hopkins; B. S. Kaube

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We find evidence for the universality of two relative bibliometric indicators of the quality of individual scientific publications taken from different data sets. One of these is a new index that considers both citation and reference counts. We demonstrate this universality for relatively well cited publications from a single institute, grouped by year of publication and by faculty or by department. We show similar behaviour in publications submitted to the arXiv e-print archive, grouped by...

Source: http://arxiv.org/abs/1110.3271v2

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Sep 19, 2013
09/13

by
T. S. Evans; T. W. B. Kibble; D. A. Steer

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We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations...

Source: http://arxiv.org/abs/hep-ph/9801404v1

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Sep 18, 2013
09/13

by
T. S. Evans; R. J. Rivers; C. Knappett

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In this article we examine a variety of quantitative models for describing archaeological networks, with particular emphasis on the maritime networks of the Aegean Middle Bronze Age. In particular, we discriminate between those gravitational networks that are most likely (maximum entropy) and most efficient (best cost/benefit outcomes).

Source: http://arxiv.org/abs/1102.0251v2

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Sep 18, 2013
09/13

by
T. S. Evans; H. F. Jones; A. Ritz

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The phase structure of the 3D SU(2)--Higgs model, the dimensionally reduced effective theory for the electroweak model at finite temperature, is analysed on the lattice using a variant of the linear $\de$--expansion. We develop a systematic variational cumulant expansion for general application to the study of gauge invariant operators in 3D gauge-Higgs models, with emphasis on the symmetric phase. In particular, the technique is not restricted to finite lattice volumes, and application to the...

Source: http://arxiv.org/abs/hep-ph/9710271v1

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Sep 18, 2013
09/13

by
T. S. Evans; H. F. Jones; D. Winder

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We use an optimised hopping parameter expansion for the free energy (linear delta expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first order as the chemical potential increases.

Source: http://arxiv.org/abs/hep-ph/0008307v1

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Sep 20, 2013
09/13

by
T. S. Evans; A. J. Gill; R. J. Rivers

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We examine string (vortex) formation at a quench for a weakly-coupled global U(1) theory when the excitation spectrum is non-relativistic. It is so similar to vortex production in the corresponding relativistic plasma as to reinforce arguments for the similarity of vortex production in the early universe and in low-temperature many-body physics.

Source: http://arxiv.org/abs/hep-ph/9507423v2

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Sep 19, 2013
09/13

by
L. M. A. Bettencourt; T. S. Evans; R. J. Rivers

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We develop winding number correlation functions that allow us to assess the role of field fluctuations on vortex formation in an Abelian gauge theory. We compute the behavior of these correlation functions in simple circumstances and show how fluctuations are important in the vicinity of the phase transition. We further show that, in our approximation, the emerging population of long/infinite string is produced by the classical dynamics of the fields alone, being essentially unaffected by field...

Source: http://arxiv.org/abs/hep-ph/9506215v1

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Sep 19, 2013
09/13

by
D. A. Steer; A. Gomez Nicola; R. J. Rivers; T. S. Evans

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We focus on the massive Thirring model in 1+1 dimensions at finite temperature and non-zero chemical potential, and comment on some parallels between this model and QCD. In QCD, calculations of physical quantities such as transport coefficients are extremely difficult. In the massive Thirring model, similar calculations are greatly simplified by exploiting the duality which exists with the sine-Gordon model and its relation, at high temperature, to the exactly solvable classical Coulomb gas on...

Source: http://arxiv.org/abs/hep-th/0010178v1

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Sep 23, 2013
09/13

by
R. Lambiotte; R. Sinatra; J. -C. Delvenne; T. S. Evans; M. Barahona; V. Latora

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The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency...

Source: http://arxiv.org/abs/1012.1211v1

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Sep 20, 2013
09/13

by
T. S. Evans; A. Gomez Nicola; R. J. Rivers; D. A. Steer

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The conductivity of a finite temperature 1+1 dimensional fermion gas described by the massive Thirring model is shown to be related to the retarded propagator of the dual boson sine-Gordon model. Duality provides a natural resummation which resolves infra-red problems, and the boson propagator can be related to the fermion gas at non-zero temperature and chemical potential or density. In addition, at high temperatures, we can apply a dimensional reduction technique to find resummed closed...

Source: http://arxiv.org/abs/hep-th/0204166v1