10,721 research outputs found
Emergence of active nematic behaviour in monolayers of isotropic cells
There is now growing evidence of the emergence and biological functionality
of liquid crystal features, including nematic order and topological defects, in
cellular tissues. However, how such features that intrinsically rely on
particle elongation, emerge in monolayers of cells with isotropic shapes is an
outstanding question. In this article we present a minimal model of cellular
monolayers based on cell deformation and force transmission at the cell-cell
interface that explains the formation of topological defects and captures the
flow-field and stress patterns around them. By including mechanical properties
at the individual cell level, we further show that the instability that drives
the formation of topological defects and leads to active turbulence, emerges
from a feedback between shape deformation and active driving. The model allows
us to suggest new explanations for experimental observations in tissue
mechanics, and to propose designs for future experiments
Modelling of vorticity, sound and their interaction in two-dimensional superfluids
Vorticity in two-dimensional superfluids is subject to intense research
efforts due to its role in quantum turbulence, dissipation and the BKT phase
transition. Interaction of sound and vortices is of broad importance in
Bose-Einstein condensates and superfluid helium [1-4]. However, both the
modelling of the vortex flow field and of its interaction with sound are
complicated hydrodynamic problems, with analytic solutions only available in
special cases. In this work, we develop methods to compute both the vortex and
sound flow fields in an arbitrary two-dimensional domain. Further, we analyse
the dispersive interaction of vortices with sound modes in a two-dimensional
superfluid and develop a model that quantifies this interaction for any vortex
distribution on any two-dimensional bounded domain, possibly non-simply
connected, exploiting analogies with fluid dynamics of an ideal gas and
electrostatics. As an example application we use this technique to propose an
experiment that should be able to unambiguously detect single circulation
quanta in a helium thin film.Comment: 23 pages, 8 figure
Simple mechanisms that impede the Berry phase identification from magneto-oscillations
The phase of quantum magneto-oscillations is often associated with the Berry
phase and is widely used to argue in favor of topological nontriviality of the
system (Berry phase ). Nevertheless, the experimentally determined
value may deviate from arbitrarily, therefore more care should be
made analyzing the phase of magneto-oscillations to distinguish trivial systems
from nontrivial. In this paper we suggest two simple mechanisms dramatically
affecting the experimentally observed value of the phase in three-dimensional
topological insulators: (i) magnetic field dependence of the chemical
potential, and (ii) possible nonuniformity of the system. These mechanisms are
not limited to topological insulators and can be extended to other
topologically trivial and non-trivial systems.Comment: 9 pages, 4 figures, in published version the title was change
Local, Smooth, and Consistent Jacobi Set Simplification
The relation between two Morse functions defined on a common domain can be
studied in terms of their Jacobi set. The Jacobi set contains points in the
domain where the gradients of the functions are aligned. Both the Jacobi set
itself as well as the segmentation of the domain it induces have shown to be
useful in various applications. Unfortunately, in practice functions often
contain noise and discretization artifacts causing their Jacobi set to become
unmanageably large and complex. While there exist techniques to simplify Jacobi
sets, these are unsuitable for most applications as they lack fine-grained
control over the process and heavily restrict the type of simplifications
possible.
In this paper, we introduce a new framework that generalizes critical point
cancellations in scalar functions to Jacobi sets in two dimensions. We focus on
simplifications that can be realized by smooth approximations of the
corresponding functions and show how this implies simultaneously simplifying
contiguous subsets of the Jacobi set. These extended cancellations form the
atomic operations in our framework, and we introduce an algorithm to
successively cancel subsets of the Jacobi set with minimal modifications
according to some user-defined metric. We prove that the algorithm is correct
and terminates only once no more local, smooth and consistent simplifications
are possible. We disprove a previous claim on the minimal Jacobi set for
manifolds with arbitrary genus and show that for simply connected domains, our
algorithm reduces a given Jacobi set to its simplest configuration.Comment: 24 pages, 19 figure
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