Statistical physics on paper
We use statistical physics ideas for applied research in the experimental studies of complex materials … or the other way around: We perform experiments on complex materials in order to explore ideas of modern statistical physics. Our particular interests are fracture experiments on paper, a (quasi)-two dimensional disordered material, which produces evidence of criticality and fluctuations.
X-ray tomography picture from a sheet of paper. Colors indicate the density of paper. The experimental data is used for studying the 3D displacement field after creep loading of the sample.
Inordinary sheet of paper with colored fibers. Specially manufactured sample has been made for studying a non-affine deformation of fibers during the creep loading of the sheet.
Our main experimental methods have been the acoustic emission (AE) and the digital image correlation (DIC) during mode I tensile and creep testing of ordinary paper sheets. The statistics of the AE, “crackling noise”, can be described by power-laws; the probability distribution of released energy and AE durations and intervals. Such work can be used to test the theories of fracture in random systems, and it also helps to understand the failure of paper depending on its material composition (Phys. Rev. Lett. 89, 2002, 185503, and Phys. Rev. Lett. 99, 2007, 145504).
The schematic presentation of the digital image correlation method. The reference image and the test image are taken from a sample under load. Using DIC one obtains information about the local deformation field and its fluctuations.
The study of the deformation fields by using DIC during the creep of paper has an intriguing connection to modern statistical physics. Andrade’s creep during the initial stage of the creep experiment on paper can be interpreted as an absorbing state phase transition, theory which we can test by studying the scaling and fluctuations of the deformation field. The novel method of studying disordered material has also lead us to explore unexplained and unexpected phenomena of order parameter fluctuations during a non-equilibrium phase transition. (Phys. Rev. Lett. 105, 2010, 100601)
The strain field from a sheet of paper during creep experiment. A sample with a large initial edge notch is put under stress. The reference image is taken before loading the sample and the test image is the sample under stress.
Networks in market segmentation
We study applications of community detection algorithms on complex networks to market segmentation using Smartphone usage data. We are able to produce interesting divisions of the user base into segments with similar usage patterns, giving a coarse-grained representation of the customers, useful for extracting low-dimensional data for marketing purposes. This research in done in collaboration with the Department of Communications and Networking, TKK.
A network of the Smartphone users divided into three communities (colored yellow, red, and blue) according to the usage patterns. The red links connect users in different communities.
We study host-parasitoid systems in explicit two-dimensional space. These show a variety of interesting behavior, the most notable example of which are noise-sustained oscillations coupled to spontaneously forming erratic spirals in spatial dimensions (see figure below). Our research so far has been published in Phys. Rev. E 78 050903 (2008) (arXiv) and in J. Stat. Mech. P04042 (2009) (arXiv).
A snapshot from a simulation of the host–parasitoid system with the spontaneous formation of erratic spirals. Black stands for empty space, red for the hosts, and blue for the parasitoids. Click on the figure for an animation.
A snapshot and a corresponding time series from a simulation of the host–parasitoid system on an empirically measured metapopulation landscape on Åland (landscape data courtesy of Metapopulation Research Group, University of Helsinki). The habitat is formed of distinct patches with variables sizes (not shown) drawn as the dots. Green dots are empty patches, red ones inhabited by the host, and blue ones inhabited by the parasitoids.