63 research outputs found

    On the ground state energy scaling in quasi-rung-dimerized spin ladders

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    On the basis of periodic boundary conditions we study perturbatively a large N asymptotics (N is the number of rungs) for the ground state energy density and gas parameter of a spin ladder with slightly destroyed rung-dimerization. Exactly rung-dimerized spin ladder is treated as the reference model. Explicit perturbative formulas are obtained for three special classes of spin ladders.Comment: 4 page

    Convection in colloidal suspensions with particle-concentration-dependent viscosity

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    The onset of thermal convection in a horizontal layer of a colloidal suspension is investigated in terms of a continuum model for binary-fluid mixtures where the viscosity depends on the local concentration of colloidal particles. With an increasing difference between the viscosity at the warmer and the colder boundary the threshold of convection is reduced in the range of positive values of the separation ratio psi with the onset of stationary convection as well as in the range of negative values of psi with an oscillatory Hopf bifurcation. Additionally the convection rolls are shifted downwards with respect to the center of the horizontal layer for stationary convection (psi>0) and upwards for the Hopf bifurcation (psi<0).Comment: 8 pages, 6 figures, submitted to European Physical Journal

    Comparative study of non-invasive force and stress inference methods in tissue

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    In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate force- inference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed.Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on morphogenesis and evolution
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