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Kim Christensen

Publications and source records attributed to Kim Christensen.

11 recordsLinked to original sources
PubMed2005

Universality class of one-dimensional directed sandpile models.

A general n-state directed "sandpile" model is introduced. The stationary properties of the n-state model are derived for n<infinity, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.

Journal Article↗
PubMed2005

Spectral analysis of protein-protein interactions in Drosophila melanogaster.

Within a case study on the protein-protein interaction network (PIN) of Drosophila melanogaster we investigate the relation between the network's spectral properties and its structural features. The frequencies of loops of any size within the network can be derived from the spectrum; also the prevalence of specific subgraphs as a result of the network's evolutionary history affects its spectrum. The discrete part of the spectral density shows fingerprints of the PIN's topological features including a preference for loop structures. Duplicate nodes are also characteristic for PINs and we discuss their representation in the PIN's spectrum as well as their biological implications.

Animals↗
PubMed2004

Avalanche behavior in an absorbing state Oslo model.

Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this paper, we transform the self-organized critical Oslo model into an absorbing state Oslo model and analyze the avalanche behavior. We find that the resulting gap exponent D is consistent with its value in the self-organized critical model. For the avalanche size exponent tau an analysis of the effect of the external drive and the boundary conditions is required.

Journal Article↗
PubMed2002

Rain: relaxations in the sky.

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power of 1.4. This is the rain equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterized by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal H=0.76>0.5. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organized criticality, which refers to the tendency of slowly driven nonequilibrium systems towards a state of scale-free behavior.

Journal Article↗
PubMed2002

Time-dependent extinction rate and species abundance in a tangled-nature model of biological evolution.

We present a model of evolutionary ecology consisting of a web of interacting individuals, a tangle-nature model. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and the macroevolutionary mode of the dynamics are emergent properties. The macrodynamics exhibit intermittent two-mode switching with a gradually decreasing extinction rate. The generated ecologies become gradually better adapted as well as more complex in a collective sense. The form of the species abundance curve compares well with observed functional forms. The model's error threshold can be understood in terms of the characteristics of the two dynamical modes of the system.

Biological Evolution↗
PubMed2002

Tangled nature: a model of evolutionary ecology.

We discuss a simple model of co-evolution. In order to emphasize the effect of interaction between individuals, the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination and diversity are entirely a consequence of co-evolutionary interaction between individuals. For comparison, we consider both asexual and sexually reproducing populations. In either case, the system evolves through periods of hectic reorganization separated by periods of coherent stable coexistence.

Animals↗
PubMed2002

Unified scaling law for earthquakes.

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d(f) of earthquakes appear as critical indices.

Journal Article↗
PubMed2002

Unified scaling law for earthquakes.

We propose and verify a unified scaling law that provides a framework for viewing the probability of the occurrence of earthquakes in a given region and for a given cutoff magnitude. The law shows that earthquakes occur in hierarchical correlated clusters, which overlap with other spatially separated correlated clusters for large enough time periods and areas. For a small enough region and time-scale, only a single correlated group can be sampled. The law links together the Gutenberg--Richter Law, the Omori Law of aftershocks, and the fractal dimensions of the faults. The Omori Law is shown to be the short time limit of general hierarchical phenomenon containing the statistics of both "main shocks" and "aftershocks," indicating that they are created by the same mechanism.

Journal Article↗
PubMed2001

A complexity view of rainfall.

We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.

Climate↗