5,561 research outputs found
Poincar\'e profiles of groups and spaces
We introduce a spectrum of monotone coarse invariants for metric measure
spaces called Poincar\'{e} profiles. The two extremes of this spectrum
determine the growth of the space, and the separation profile as defined by
Benjamini--Schramm--Tim\'{a}r. In this paper we focus on properties of the
Poincar\'{e} profiles of groups with polynomial growth, and of hyperbolic
spaces, where we deduce a connection between these profiles and conformal
dimension. As applications, we use these invariants to show the non-existence
of coarse embeddings in a variety of examples.Comment: 55 pages. To appear in Revista Matem\'atica Iberoamerican
Active Inter-cellular Forces in Collective Cell Motility
The collective behaviour of confluent cell sheets is strongly influenced both
by polar forces, arising through cytoskeletal propulsion and by active
inter-cellular forces, which are mediated by interactions across cell-cell
junctions. We use a phase-field model to explore the interplay between these
two contributions and compare the dynamics of a cell sheet when the polarity of
the cells aligns to (i) their main axis of elongation, (ii) their velocity, and
(iii) when the polarity direction executes a persistent random walk.In all
three cases, we observe a sharp transition from a jammed state (where cell
rearrangements are strongly suppressed) to a liquid state (where the cells can
move freely relative to each other) when either the polar or the inter-cellular
forces are increased. In addition, for case (ii) only, we observe an additional
dynamical state, flocking (solid or liquid), where the majority of the cells
move in the same direction. The flocking state is seen for strong polar forces,
but is destroyed as the strength of the inter-cellular activity is increased.Comment: 15 pages,22 figure
A constitutive model for simple shear of dense frictional suspensions
Discrete particle simulations are used to study the shear rheology of dense,
stabilized, frictional particulate suspensions in a viscous liquid, toward
development of a constitutive model for steady shear flows at arbitrary stress.
These suspensions undergo increasingly strong continuous shear thickening (CST)
as solid volume fraction increases above a critical volume fraction, and
discontinuous shear thickening (DST) is observed for a range of . When
studied at controlled stress, the DST behavior is associated with non-monotonic
flow curves of the steady-state stress as a function of shear rate. Recent
studies have related shear thickening to a transition between mostly lubricated
to predominantly frictional contacts with the increase in stress. In this
study, the behavior is simulated over a wide range of the dimensionless
parameters , and , with the dimensionless shear stress and the coefficient of
interparticle friction: the dimensional stress is , and , where is the magnitude of repulsive force at contact
and is the particle radius. The data have been used to populate the model
of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev.
Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity
divergences or \textquotedblleft jamming\textquotedblright\ points at volume
fraction (random close packing) for the
low-stress lubricated state, and at for
any nonzero in the frictional state; a generalization provides the normal
stress response as well as the shear stress. A flow state map of this material
is developed based on the simulation results.Comment: 12 pages, 10 figure
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