1,477 research outputs found
Topics in complex systems
No full textThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Fundamental laws of physics, although successful in explaining many phenomena observed in nature and society, cannot account for the behaviour of complex, non-Hamiltonian systems. Much effort has been devoted to better understanding the topological properties of these systems. Neither ordered nor disordered, these systems of high variability are found in many areas of science. Studies on sandpiles, earthquakes and lattice gases have all yielded evidence of complexity in the form of power law distributions. This scalefree characteristic is believed to be the hall-mark of complexity known as self-organised criticality. Systems in the self-organised critical state regulate themselves and are resistant to error and attacks. The aim of this thesis is to further current knowledge of complex systems by proposing and analysing
three models of real systems. Statistical mechanics and numerical simulations are used to analyse these models. The first model mimics herd behaviour in social groups and encompasses growth and addition. It has been found that when the growth rate is fast enough, the group size distribution conforms to a power law. When the growth rate is slow, the system runs out of free agents in finite time. The second model aims to capture the basic empirical measurements from hospital waiting lists. This model illustrates how the power law distributions found in empirical studies might arise, but also indicates that these distributions are unlikely to be caused by the preferential behaviour of patients or physicians. The third model is a salary comparison model; the salary distributions of most of its variants are power laws. Both mean field and 1-d versions of the model are analysed, and differences between the two versions are identified by looking at the mean absolute difference between the salaries in each version
The Anisotropic Bak-Sneppen model
No full textThe Bak-Sneppen model is shown to fall into a different universality class with the introduction of a preferred direction, mirroring the situation in spin systems. This is first demonstrated by numerical simulations and subsequently confirmed by analysis of the multitrait version of the model, which admits exact solutions in the extremes of zero and maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law `tail' which passes through the system for any non-zero anisotropy but remains fixed for the isotropic case, thus explaining the crossover in behaviour. Finally, we identify the maximally anisotropic model which is more tractable and yet more generally applicable than the isotropic system
Crossover to self-organized criticality in an inertial sandpile model
No full textWe introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the system no longer evolves to a self-organized critical state. A range of mean-field theories based on a kinetic equation approach is presented which confirm the numerical findings. We conclude by considering the physical applications of this model, particularly with reference to recent experimental results
The energetic particle environment of a GJ 436 b-like planet
No full text<p>This data set corresponds to the simulation data presented in the article "The energetic particle environment of a GJ 436b-like planet" (Rodgers-Lee, et al., MNRAS, 2023). Details of the stellar wind and cosmic ray models used for the simulations are available in the article.</p>
<p>Each data file consists of the temperature, pressure and heights in the exoplanet atmosphere at a given orbital distance from the star (shown in Fig.3 of Rodgers-Lee et al. 2023). The number density, n(z), of the exoplanet atmosphere can be calculated from the temperature and pressure. Further details relating to the temperature pressure profiles are given in Section 2.3 of Rodgers-Lee et al. (2023). The last two but one columns in the data files are the ionisation rates for molecular hydrogen from Galactic cosmic rays and stellar energetic particles (shown in Fig.4 of Rodgers-Lee et al. 2023). The last column is the assumed planetary effective temperature.</p>
<p>The data is given for a number of different orbital distances between 0.01 - 0.2au. File names are formatted as "zenodo_GJ436_manysp_solar_aX_tp.dat" where "X" corresponds to 100 x orbital distance in au (e.g. "a1" corresponds to a=0.01au) considered. The first line describes the data in the file. The second line gives the column headings and units.</p>
Complex scale-free networks with tunable power-law exponent and clustering
No full textThis article is made available through the Brunel Open Access Publishing Fund. It is distributed under a Creative Commons License (http://creativecommons.org/licenses/by/3.0/). Copyright @ 2013 Elsevier B.V.We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes mm “ambassador” nodes and ll of each ambassador’s descendants where mm and ll are random variables selected from any choice of distributions plpl and qmqm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant mm and the number of selected descendants from each ambassador is the constant ll, the power-law exponent is (2l+1)/l(2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of ll and mm. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.EPSR
Stable distribution in fragmentation processes
No full textWe introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant (scaling) solutions which depend on p and the precise details of the fragmentation process. Various features of these models are compared with those of conventional fragmentation models.
To get Figures e-mail to G.J. [email protected]
Kinetics of node splitting in evolving complex networks
No full textCopyright @ 2012 Elsevier B.V. All rights reserved. This is a preprint version of the published article which can be accessed at the link below.We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree k into k nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p, or splitting with probability 1-p. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.Engineering and Physical Sciences Research Counci
The energetic particle environment of a GJ 436 b-like planet
No full textA key first step to constrain the impact of energetic particles in exoplanet atmospheres is to detect the chemical signature of ionisation due to stellar energetic particles and Galactic cosmic rays. We focus on GJ436, a well-studied M dwarf with a warm Neptune-like exoplanet. We demonstrate how the maximum stellar energetic particle momentum can be estimated from the stellar X-ray luminosity. We model energetic particle transport through the atmosphere of a hypothetical exoplanet at orbital distances between au from GJ436, including GJ436b's orbital distance (0.028au). For these distances we find that, at top-of-atmosphere, stellar energetic particles ionise molecular hydrogen at a rate of . In comparison, Galactic cosmic rays alone lead to . At 10au we find that ionisation due to Galactic cosmic rays equals that of stellar energetic particles: for the top-of-atmosphere ionisation rate. At GJ436b's orbital distance, the maximum ion-pair production rate due to stellar energetic particles occurs at pressure bar while Galactic cosmic rays dominate for bar. These high pressures are similar to what is expected for a post-impact early Earth atmosphere. The results presented here will be used to quantify the chemical signatures of energetic particles in warm Neptune-like atmospheres
Some applications of graph theory
No full textThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.For the abstract of this thesis, please see the attached PDF.This work was funded by a Marie Curie Early Stage Training Fellowship
(NET-ACE-programme) under grant number MEST-CT-2004-6724
The energetic particle environment of a GJ 436 b-like planet
No full textA key first step to constrain the impact of energetic particles in exoplanet atmospheres is to detect the chemical signature of ionization due to stellar energetic particles and Galactic cosmic rays. We focus on GJ 436, a well-studied M dwarf with a warm Neptune-like exoplanet. We demonstrate how the maximum stellar energetic particle momentum can be estimated from the stellar X-ray luminosity. We model energetic particle transport through the atmosphere of a hypothetical exoplanet at orbital distances between a = 0.01 and 0.2 au from GJ 436, including GJ 436 b’s orbital distance (0.028 au). For these distances, we find that, at the top of atmosphere, stellar energetic particles ionize molecular hydrogen at a rate of ζStEP,H2 ∼ 4 × 10−10 to 2 × 10−13 s−1. In comparison, Galactic cosmic rays alone lead to ζGCR,H2 ∼ 2 × 10−20–10−18 s−1. At 10 au, we find that ionization due to Galactic cosmic rays equals that of stellar energetic particles: ζGCR,H2 = ζStEP,H2 ∼ 7 × 10−18 s−1 for the top-of-atmosphere ionization rate. At GJ 436 b’s orbital distance, the maximum ion-pair production rate due to stellar energetic particles occurs at pressure P ∼ 10−3 bar, while Galactic cosmic rays dominate for P > 102 bar. These high pressures are similar to what is expected for a post-impact early Earth atmosphere. The results presented here will be used to quantify the chemical signatures of energetic particles in warm Neptune-like atmospheres
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