# ProfessorKimChristensen

Faculty of Natural SciencesDepartment of Physics

Professor of Theoretical Physics

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### Contact

+44 (0)20 7594 7574k.christensen

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### Assistant

Mrs Carolyn Dale +44 (0)20 7594 7579

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### Location

1226, Center for Complexity ScienceElectrical EngineeringSouth Kensington Campus

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## Publications

Publication Type
Year
to

74 results found

Yao Q, Evans TS, Christensen K, 2019, How the network properties of shareholders vary with investor type and country, PLoS One, Vol: 14, Pages: 1-19, ISSN: 1932-6203

We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types of shareholder. We create a suitable randomised version of these networks to enable us to find significant features in our networks. For that we find the roles played by different types of shareholder in these networks, and also show how these roles differ in the two countries we study.

Journal article

Franks N, Worley A, Falkenberg McGillivray M, Sendova-Franks A, Christensen Ket al., 2019, Digging the optimum pit: antlions, spirals and spontaneous stratification, Proceedings of the Royal Society B: Biological Sciences, Vol: 286, ISSN: 1471-2954

Most animal traps are constructed from self-secreted silk, so antlions are rare among trap builders because they use only materials found in the environment. We show how antlions exploit the properties of the substrate to produce very effective structures in the minimum amount of time. Our modelling demonstrates how antlions (1) exploit self-stratification in granular media differentially to expose deleterious large grains at the bottom of the construction trench where they can be ejected preferentially and (2) minimize completion time by spiral rather than central digging. Both phenomena are confirmed by our experiments. Spiral digging saves time because it enables the antlion to eject material initially from the periphery of the pit where it is less likely to topple back into the centre. As a result, antlions can produce their pits — lined almost exclusively with small slippery grains to maximize powerful avalanches and hence prey capture — much more quickly than if they simply dig at the pit’s centre. Our demonstration, for the first time, of an animal utilizing self-stratification in granular media exemplifies the sophistication of extended phenotypes even if they are only formed from material found in the animal’s environment.

Journal article

Fernandez-Anez N, Christensen K, Frette V, Rein Get al., 2019, Simulation of fingering behavior in smoldering combustion using a cellular automaton, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 99, ISSN: 1539-3755

Smoldering is the slow, low-temperature, flameless burning of porous fuels and the most persistent type of combustion phenomena. It is a complex physical process that is not yet completely understood, but it is known that it is driven by heat transfer, mass transfer, and fuel chemistry. A specific case of high interest and complexity is fingering behavior. Fingering is an instability that occurs when a thin fuel layer burns against an oxygen current. These instabilities appear when conduction rather than convection is the dominant mode of heat transfer to the fuel ahead and the availability of oxygen is limited during the combustion of a thin fuel, such as paper. The pattern of the fingers can be characterized through the distance between them and their width, and can be classified into three different regimes: isolated fingers, tip-splitting fingers, or no fingers forming and a smooth continuous front. In this paper, a multilayer cellular automaton based on three governing principles (heat, oxygen, and fuel) is shown to reproduce all the regimes and the details of finger structures observed in previous experiments. It is shown how when oxygen is not limited, a smooth smoldering front is formed. If the oxygen speed decreases beyond a critical value, fingers appear first as tip-splitting fingers and later as isolated fingers, increasing the distance between them and decreasing their thickness. The oxygen consumed during oxidation influences these critical values with a positive correlation. This cellular automaton provides an alternative approach to simulate smoldering combustion in large systems over long times. That the model is able to reproduce the complex pattern formation seen in a fingering experiment validates the model. In the future, we could apply the model in various other geometries to make predictions on the outcome of smoldering combustion processes.

Journal article

Garcia Millan R, Pruessner G, Pickering L, Christensen Ket al., 2018, Correlations and hyperuniformity in the avalanche size of the Oslo Model, Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 122, ISSN: 1286-4854

Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$ . We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo model. We support our findings with numerical results.

Journal article

McGillivray MF, Cheng W, Peters NS, Christensen Ket al., 2018, Machine learning methods for locating re-entrant drivers from electrograms in a model of atrial fibrillation, ROYAL SOCIETY OPEN SCIENCE, Vol: 5, ISSN: 2054-5703

Mapping resolution has recently been identified as a key limitation in successfully locating the drivers of atrial fibrillation (AF). Using a simple cellular automata model of AF, we demonstrate a method by which re-entrant drivers can be located quickly and accurately using a collection of indirect electrogram measurements. The method proposed employs simple, out-of-the-box machine learning algorithms to correlate characteristic electrogram gradients with the displacement of an electrogram recording from a re-entrant driver. Such a method is less sensitive to local fluctuations in electrical activity. As a result, the method successfully locates 95.4% of drivers in tissues containing a single driver, and 95.1% (92.6%) for the first (second) driver in tissues containing two drivers of AF. Additionally, we demonstrate how the technique can be applied to tissues with an arbitrary number of drivers. In its current form, the techniques presented are not refined enough for a clinical setting. However, the methods proposed offer a promising path for future investigations aimed at improving targeted ablation for AF.

Journal article

Fernandez-Anez N, Christensen K, Rein G, 2017, Two-dimensional model of smouldering combustion using multi-layer cellular automaton: The role of ignition location and direction of airflow, Fire Safety Journal, Vol: 91, Pages: 243-251, ISSN: 0379-7112

Smouldering combustion is one of the most common and persistent fire hazards of reactive porous media, such as biomass. In this work, a two-dimensional multi-layer cellular automaton has been developed to study the process of smouldering and the roles of both the ignition location and the direction of airflow for generic biomass. Three different configurations are studied: line front, with forward and opposed airflow respectively, and radial front. The first two configurations simulate ignition of one edge of the sample, while the radial front simulates ignition of a spot at the centre of the sample. The resulting spread patterns of line vs. radial front are significantly different. Furthermore, when smouldering occurs with similar characteristics, where both line front and radial front are self-sustained, the smouldering radial front has a higher growth rate than the line front. However, in the studied cases where enough oxygen is always available for oxidation, the direction of the airflow does not influence the spread of the smouldering front, and the line front with forward and opposed airflow present similar behaviour. Finally, two non-zero minimum values have been detected for self-sustained spread according to the moisture of the fuel (probability of drying) and its tendency for thermal degradation (probability of pyrolysis). This model provides a powerful but simple way of reproducing the complex dynamics of smouldering processes which can be used to investigate different scenarios.

Journal article

Manani K, Christensen K, Peters NICHOLAS, 2016, Myocardial architecture and patient variability in clinical patterns of atrial fibrillation, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 94, ISSN: 1063-651X

Atrial fibrillation (AF) increases the risk of stroke by a factor of 4–5 and is the most common abnormal heart rhythm. The progression of AF with age, from short self-terminating episodes to persistence, varies between individuals and is poorly understood. An inability to understand and predict variation in AF progression has resulted in less patient-specific therapy. Likewise, it has been a challenge to relate the microstructural features of heart muscle tissue (myocardial architecture) with the emergent temporal clinical patterns of AF. We use a simple model of activation wave-front propagation on an anisotropic structure, mimicking heart muscle tissue, to show how variation in AF behavior arises naturally from microstructural differences between individuals. We show that the stochastic nature of progressive transversal uncoupling of muscle strands (e.g., due to fibrosis or gap junctional remodeling), as occurs with age, results in variability in AF episode onset time, frequency, duration, burden, and progression between individuals. This is consistent with clinical observations. The uncoupling of muscle strands can cause critical architectural patterns in the myocardium. These critical patterns anchor microreentrant wave fronts and thereby trigger AF. It is the number of local critical patterns of uncoupling as opposed to global uncoupling that determines AF progression. This insight may eventually lead to patient-specific therapy when it becomes possible to observe the cellular structure of a patient's heart.

Journal article

Dhar D, Pruessner G, Expert P, Christensen K, Zachariou Net al., 2016, Directed Abelian sandpile with multiple downward neighbors, Physical Review E, Vol: 042107, ISSN: 1539-3755

We study the directed Abelian sandpile model on a square lattice, with K downward neighborsper site, K > 2. The K = 3 case is solved exactly, which extends the earlier known solution forthe K = 2 case. For K > 2, the avalanche clusters can have holes and side-branches and are thusqualitatively different from the K = 2 case where avalanche clusters are compact. However, we findthat the critical exponents for K > 2 are identical with those for the K = 2 case, and the largescale structure of the avalanches for K > 2 tends to the K = 2 case.

Journal article

Zachariou N, Expert P, Takayasu M, Christensen Ket al., 2015, Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks, PLOS One, Vol: 10, ISSN: 1932-6203

The main finding of this paper is a novel avalanche-size exponent τ 1.87 when the generalisedsandpile dynamics evolves on the real-world Japanese inter-firm network. The topologyof this network is non-layered and directed, displaying the typical bow tie structurefound in real-world directed networks, with cycles and triangles. We show that one canmove from a strictly layered regular lattice to a more fluid structure of the inter-firm networkin a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distributionfor the interactions, forces the scaling exponent of the avalanche-size probabilitydensity function τ out of the two-dimensional directed sandpile universality class τ = 4/3,into the mean field universality class τ = 3/2. Numerical investigation shows that these twoclasses are the only that exist on the directed sandpile, regardless of the underlying topology,as long as it is strictly layered. Randomly adding a small proportion of links connectingnon adjacent layers in an otherwise layered network takes the system out of the mean fieldregime to produce non-trivial avalanche-size probability density function. Although these donot display proper scaling, they closely reproduce the behaviour observed on the Japaneseinter-firm network.

Journal article

Christensen K, Manani KA, Peters NS, 2015, Simple model for identifying critical regions in atrial fibrillation, Physical Review Letters, Vol: 114, ISSN: 0031-9007

Journal article

Christensen K, Papavassiliou D, de Figueiredo A, Franks NR, Sendova-Franks ABet al., 2015, Universality in ant behaviour, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 12, ISSN: 1742-5689

Journal article

Christensen K, Kleppe G, Vold M, Frette Vet al., 2014, Quantitative projections of a quality measure: Performance of a complex task, PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, Vol: 415, Pages: 503-513, ISSN: 0378-4371

Journal article

Sarker MOF, Dahl TS, Arcaute E, Christensen Ket al., 2014, Local interactions over global broadcasts for improved task allocation in self-organized multi-robot systems, ROBOTICS AND AUTONOMOUS SYSTEMS, Vol: 62, Pages: 1453-1462, ISSN: 0921-8890

Journal article

Richardson TO, Christensen K, Franks NR, Jensen HJ, Sendova-Franks ABet al., 2011, Ants in a labyrinth: A statistical mechanics approach to the division of labour, PLOS One, Vol: 6, ISSN: 1932-6203

Division of labour (DoL) is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic) interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.

Journal article

Richardson TO, Christensen K, Franks NR, Jensen HJ, Sendova-Franks ABet al., 2011, Group dynamics and record signals in the ant Temnothorax albipennis, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 8, Pages: 518-528, ISSN: 1742-5689

Journal article

Expert P, Lambiotte R, Chialvo DR, Christensen K, Jensen HJ, Sharp DJ, Turkheimer Fet al., 2011, Self-similar correlation function in brain resting-state functional magnetic resonance imaging, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 8, Pages: 472-479, ISSN: 1742-5689

Journal article

Richardson TO, Robinson EJH, Christensen K, Jensen JH, Christensen K, Jensen HJ, Franks NR, Sendova-Franks ABet al., 2011, Comment on P. Nouvellet, JP Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model", JOURNAL OF THEORETICAL BIOLOGY, Vol: 269, Pages: 356-358, ISSN: 0022-5193

Journal article

Espinosa A, Cardoso PP, Arcaute E, Christensen Ket al., 2011, Complexity approaches to self-organisation: a case study from an Irish eco-village, KYBERNETES, Vol: 40, Pages: 536-558, ISSN: 0368-492X

Journal article

Frette V, Kleppe G, Christensen K, 2011, Analysis of ship maneuvering data from simulators, 11th Granada Seminar on Computational and Statistical Physics, Publisher: AMER INST PHYSICS, Pages: 276-276, ISSN: 0094-243X

Conference paper

Peters O, Christensen K, Neelin JD, 2011, Rainfall and Dragon Kings, European Physical Journal. Special Topics

Journal article

Richardson TO, Robinson EJH, Christensen K, Jensen HJ, Franks NR, Sendova-Franks ABet al., 2010, Record dynamics in ants, PLOS One, Vol: 5, ISSN: 1932-6203

The success of social animals (including ourselves) can be attributed to efficiencies that arise from a division of labour. Many animal societies have a communal nest which certain individuals must leave to perform external tasks, for example foraging or patrolling. Staying at home to care for young or leaving to find food is one of the most fundamental divisions of labour. It is also often a choice between safety and danger. Here we explore the regulation of departures from ant nests. We consider the extreme situation in which no one returns and show experimentally that exiting decisions seem to be governed by fluctuating record signals and ant-ant interactions. A record signal is a new ‘high water mark’ in the history of a system. An ant exiting the nest only when the record signal reaches a level it has never perceived before could be a very effective mechanism to postpone, until the last possible moment, a potentially fatal decision. We also show that record dynamics may be involved in first exits by individually tagged ants even when their nest mates are allowed to re-enter the nest. So record dynamics may play a role in allocating individuals to tasks, both in emergencies and in everyday life. The dynamics of several complex but purely physical systems are also based on record signals but this is the first time they have been experimentally shown in a biological system.

Journal article

Pancaldi V, King PR, Christensen K, 2009, Hierarchical coarse-graining transform, Phys Rev E, Vol: 79

Journal article

Arcaute E, Christensen K, Sendova-Franks AB, Dahl T, Espinosa A, Jensen HJet al., 2009, Division of labour in ant colonies in terms of attractive fields, Ecological Complexity, Vol: 6, Pages: 396-402

Journal article

Pancaldi V, King PR, Christenen K, 2008, Wavelet-based upscaling of advection equations, Physica A: Statistical Mechanics and its Applications, Vol: 387, Pages: 4760-4770

Journal article

Christensen K, Farid N, Pruessner G, Stapleton Met al., 2008, On the scaling of probability density functions with apparent power-law exponent less than unity, Eur. Phys. J. B, Vol: 62, Pages: 331-336

Journal article

Pancaldi V, Christensen K, King P, 2007, Two-phase flow up-scaling using Haar wavelets, Vth IMA conference on modelling permeable rocks

Conference paper

Pancaldi V, Christensen K, King PR, 2007, Upscaling of the saturation equation, 69th European Association of Geoscientists and Engineers Conference and Exhibition 2007: Securing The Future. Incorporating SPE EUROPEC 2007, Vol: 1, Pages: 224-228

Given the high level of detail present in numerical models, fluid dynamic simulations of subsurface flow in porous media are very intensive in computational time. Moreover, to account for the inherent uncertainty in the information available, many realizations of the same model should be constructed to extract statistical data. For this purpose, less detailed coarse scale models are often constructed, starting from the fine scale ones but with a reduced number of grid cells. Each grid cell is now bigger in physical terms and must contain information relative to the entire portion of rock contained in it. The challenge in this process is to find equivalent properties for the important variables in the system, ensuring that the original knowledge about the geological reservoir is preserved as much as possible. Upscaling is the procedure with which these coarse scale effective properties are obtained. We present an upscaling method for the saturation equation governing advcction of a passive tracer in a porous medium. The upscaling rule is such that the saturation on the coarse scale closely matches the averaged fine scale saturation. Results are presented in one-dimensional systems and compared to analytical solutions.

Journal article

Welinder P, Pruessner G, Christensen K, 2007, Multiscaling in the sequence of areas enclosed by coalescing random walkers, New J. Phys., Vol: 9, Pages: 149-166

Journal article

Pancaldi V, Christensen K, King P, 2007, Permeability up-scaling using Haar wavelets, Transport in Porous Media, Vol: 67, Pages: 395-412

Journal article

Peters O, Christensen K, 2006, Rain viewed as relaxational events, JOURNAL OF HYDROLOGY, Vol: 328, Pages: 46-55, ISSN: 0022-1694

Journal article

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