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Fractals, critical phenomena


The Front Structure of Growing Fungus Colonies truecm

Fungus grown on agar plates show interesting and complex patterns where the colony gets trapped at some places finally showing up as a cellular structure described by a specific characteristic length scale in the front. We believe that this cellular structure is determined by the production of waste products in an optimal growth zone at the interface. In this zone the cells double on a specific time scale and the produced waste slowly diffuses in the growth zone. We model this using an analogy to solidification fronts where diffusing impurities determines the wavelength of the cellular behavior. We plan to simulate the corresponding diffusion equation and hope to be able to predict the wave length of the growing colony. truecm

M. H. Jensen, T. Sams, K. Sneppen, (B. E. Christensen) truecm

1/f Noise in Sea-level Elevations truecm

We have analyzed a 101 year record of sea-level elevations. The data consist of hourly recordings of sea-level elevations from 1889 to 1990 for the port of Esbjerg in Denmark. The power spectrum shows three distinct regimes. In the frequency range from 1/2 hour to 1/3 day the spectrum shows 1/f behavior (plus the tidal components). This is followed at lower frequencies by a two-decade region of 1/f noise, finally crossing over to white noise at a frequency of 1/3 year. This is one of the rare examples where a lower cutoff to 1/f noise is found. We believe the 1/f noise is simply the result a diffusive process observed in a particular way, possibly crossing over to a wave-equation at shorter time-scales. In addition, intermittent behavior is suggested by stretched exponential probability density distributions. By using methods based on the correlation integral both the 1/f noise and the high frequency part of the spectrum have been checked for low-dimensionality. truecm

(H. Svensmark), (J.D. Pietrzak) and P. Dimon truecm

From Macro- to Microeconomy: A Cascade Picture truecm

We study the flow of values from the macro-scale of the economy to the micro-scale. Using a cascade picture we formulate a dynamical model from the flow of values through the steps of the economy. The model has the structure of a shell model where the scales are separated exponentially. Using the sum of values at all scales as a conserved quantity we study the fluctuations of the values at the different scales and hope to be able to reproduce the observed distribution functions for various indexes in the economy. truecm

M.H. Jensen and K. Sneppen truecm

Self-Adaptive Neural Networks truecm

We have undertaken neural network studies with particular emphasis on reinforcement learning and behavior (conditioning problems etc.). Models are developed that are feature focusing, dynamical, and able to function in an changeable environment. The research takes place on different levels. On the macroscopic level, we study the scientific descriptions of behavioral processes, and their `translations' into neural network problems. On the microscopic level, we investigate numerically and mathematically the dynamical rules underlying the models.

Our basic research has invoked a surprisingly large interest from various industries. The interest concerns customer information, resource allocation, process control, and data acquisition. truecm

P. AlstrÝm, P. Andresťn, K. N. Berntsen, M. Krogh, J. Nordfalk, N. K. Petersen and A. Vallespin Gomez truecm

Biological Evolution: Fitness Optimization and the Decay in Extinction Rate truecm

Fossil records indicate that the background extinction rate has decreased since Cambrian time. As pointed out by Raup and Sepkoski, this observation may be a natural consequence of fitness optimization leading to prolonged survival of species through evolutionary time. Based on this view, we have investigated simple mechanisms that lead to fitness optimization and a related decay in extinction rate. In our model, species evolve through punctuated equilibria. We consider two different rules for extinction. The first assumes that a fixed fraction of evolutionary jumps leads to extinctions. The second specifically introduces a competition rule acting among neighbors in a suitably defined ecology. We have numerically determined some of the evolutionary measures defined in biological evolution theory, and compared them with data from fossil records. Our simple model displays a behavior strikingly similar to the vastly more complex biological world. truecm

(M. R. Schmidt), (P. Sibani) and P. AlstrÝm truecm

Self-Organized Criticality, Stochastic Cellular Automata and the Game of Life truecm

The question of self-organized criticality in Conway's game of life is studied in the broader context of stochastic cellular automata. A main question is to what extent the probing underlying the claimed criticality can be seen as a limit case of a system with probabilities approaching 0 (or 1), i.e. the deterministic limit. We have carried out extensive numerical studies of a selected stochastic cellular automaton with a phase transitions line ending near the deterministic limit describing Conway's game of life. Static as well as dynamical exponents are determined and compared to those obtained in directed percolation and other related models. truecm

P. AlstrÝm, J. Nordfalk and N. K. Petersen

next up previous contents
Next: Biology and physiology Up: RESEARCH PROJECTS Previous: Turbulence

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