Mechanical Stress Inference for Two Dimensional Cell Arrays

Many morphogenetic processes involve mechanical rearrangement of epithelial tissues that is driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress {\it in vivo} on sub-cellular scale, little is understood about the role of mechanics of development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the {\it Drosophila} embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics

Soft grain compression: beyond the jamming point

We present the experimental studies of highly strained soft bidisperse granular systems made of hyperelastic and plastic particles. We explore the behavior of granular matter deep in the jammed state from local field measurement from the grain scale to the global scale. By mean of digital image correlation and accurate image recording we measure for each compression step the evolution of the particle geometries and their right Cauchy-Green strain tensor fields. We analyze the evolution of the usual macroscopic observables (stress, packing fraction, coordination, fraction of non-rattlers, \textit{etc}.) along the compression process through the jamming point and far beyond. We also analyze the evolution of the local strain statistics and evidence a crossover in the material behavior deep in the jammed state. We show that this crossover depends on the particle material. We argue that the strain field is a reliable observable to describe the evolution of a granular system through the jamming transition and deep in the dense packing state whatever is the material behavior.Comment: 10 figure

A study of fragmentation processes using a discrete element method

We present a model of solids made from polygonal cells connected via beams. We calculate the macroscopic elastic moduli from the beam and cell parameters. This modellisation is particularly suited for the simulation of fragmentation processes. We study the effects of an explosion inside a circular disk and the impact of a projectile and obtain the fragment size distribution. We find that if breaking only happens under tensile forces a layer on the free wall opposed to impact is first ejected. In that case the distribution follows a power-law with an exponent that in most cases is around two.Comment: 16 pages in LaTex format, 17 PostScript figures. Figures are available upon request from the authors. Submitted to Int. J. of Mod. Phys.

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Geo-modelling of paleokarst reservoirs - from cave-survey to geocellular paleokarst model

Hydrocarbon reservoirs exhibiting features inherited from former karst processes acting on the reservoir rocks are relatively common worldwide. However, on the Norwegian continental shelf, paleokarst plays have only recently been identified in the Barents Sea. The substantial resource potential of the new plays is balanced by the known inherent complexity of paleokarst, and highlights the need for improved understanding of these reservoirs. Paleokarst reservoir characteristics are the sum of complex depositional, erosional and diagenetic processes, which tend to produce reservoirs with extreme and highly localized contrasts in permeability. In order to study how different paleokarst reservoirs respond to production and injection it is necessary to employ reservoir models. These models can provide guidelines for production strategies and ensure safe and optimal recovery. As individual paleokarst features are generally below seismic resolution, the obvious way to construct models of likely paleokarst reservoirs is to employ maps of present day karst features as a starting point and forward model their likely collapse, diagenesis and infill. Such models provide analogues for subsurface reservoirs. At present, industrial reservoir modelling software packages do not include dedicated tools or workflows for handling common paleokarst features such as cave networks. For this reason, work- arounds and a lot of out-of-the box" thinking must be applied to create a realistic and natural looking paleokarst reservoir. Some work has previously been done with respect to modelling cave systems in a stochastic manner, but there has been limited work concentrating on deterministically modelling of cave systems based on existing caves. The present thesis is a contribution to this on- going effort. The workflow employs the RMS^TM 2013.1.2 reservoir modelling suite, and is based on a survey of the Setergrotta cave, located in the northern parts of Norway. It allows deterministic incorporation of the original cave geometry into a geo-cellular model. A forward modelling" of the expected collapse and infill was carried out, and the model populated stochastically with likely petrophysical properties. Fracture modelling was performed for the host rock outside the collapsed cave passages and included as part of the petrophysical model. Due to time constraints, only very limited dynamic testing of the final model was carried out. Different upscaled versions of the reservoir model were tested to investigate the effect of upscaling on the fluid flow through the reservoir. Streamline simulations used for this exercise suggests that upscaling up to a certain level does not affect fluid patterns, and that preferential flow along collapsed passages will only occur if there is a strong contrast between permeability of the passages and the surrounding host rock. The streamline simulation results should be subjected to more detailed investigations using more advanced flow simulation tools.Master i GeovitenskapMAMN-GEOVGEOV39

The State of the Art in Cartograms

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible to gain insight into patterns and trends in the world around us and have been very popular visualizations for geo-referenced data for over a century. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms. A particular focus is the study of the major cartogram dimensions: statistical accuracy, geographical accuracy, and topological accuracy. We review the history of cartograms, describe the algorithms for generating them, and consider task taxonomies. We also review quantitative and qualitative evaluations, and we use these to arrive at design guidelines and research challenges