28,757 research outputs found
Canonical description of ideal magnetohydrodynamic flows and integrals of motion
In the framework of the variational principle the canonical variables
describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with
spatially varying entropy and nonzero values of all topological invariants) are
introduced. The corresponding complete velocity representation enables us not
only to describe the general type flows in terms of single-valued functions,
but also to solve the intriguing problem of the ``missing'' MHD integrals of
motion. The set of hitherto known MHD local invariants and integrals of motion
appears to be incomplete: for the vanishing magnetic field it does not reduce
to the set of the conventional hydrodynamic invariants. And if the MHD analogs
of the vorticity and helicity were discussed earlier for the particular cases,
the analog of Ertel invariant has been so far unknown. It is found that on the
basis of the new invariants introduced a wide set of high-order invariants can
be constructed. The new invariants are relevant both for the deeper insight
into the problem of the topological structure of the MHD flows as a whole and
for the examination of the stability problems. The additional advantage of the
proposed approach is that it enables one to deal with discontinuous flows,
including all types of possible breaks.Comment: 16 page
Quantification of Nematic Cell Polarity in Three-dimensional Tissues
How epithelial cells coordinate their polarity to form functional tissues is
an open question in cell biology. Here, we characterize a unique type of
polarity found in liver tissue, nematic cell polarity, which is different from
vectorial cell polarity in simple, sheet-like epithelia. We propose a
conceptual and algorithmic framework to characterize complex patterns of
polarity proteins on the surface of a cell in terms of a multipole expansion.
To rigorously quantify previously observed tissue-level patterns of nematic
cell polarity (Morales-Navarette et al., eLife 8:e44860, 2019), we introduce
the concept of co-orientational order parameters, which generalize the known
biaxial order parameters of the theory of liquid crystals. Applying these
concepts to three-dimensional reconstructions of single cells from
high-resolution imaging data of mouse liver tissue, we show that the axes of
nematic cell polarity of hepatocytes exhibit local coordination and are aligned
with the biaxially anisotropic sinusoidal network for blood transport. Our
study characterizes liver tissue as a biological example of a biaxial liquid
crystal. The general methodology developed here could be applied to other
tissues or in-vitro organoids.Comment: 27 pages, 9 color figure
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