684 research outputs found
Da Vinci Fluids, catch-up dynamics and dense granular flow
We introduce and study a da Vinci Fluid, a fluid whose dissipation is
dominated by solid friction. We analyse the flow rheology of a discrete model
and then coarse-grain it to the continuum. We find that the model gives rise to
behaviour that is characteristic of dense granular fluids. In particular, it
leads to plug flow. We analyse the nucleation mechanism of plugs and their
development. We find that plug boundaries generically expand and we calculate
the growth rate of plug regions. In systems whose internal effective friction
coefficient is relatively uniform we find that the linear size of plug regions
grows as (time). The suitability of the model to granular materials is
discussed.Comment: 5 pages, 3 figures, edited for clarifications and added reference
Fractional electric charge and quark confinement
Owing to their fractional electric charges, quarks are blind to
transformations that combine a color center phase with an appropriate
electromagnetic one. Such transformations are part of a global -like
center symmetry of the Standard Model that is lost when quantum chromodynamics
(QCD) is treated as an isolated theory. This symmetry and the corresponding
topological defects may be relevant to non-perturbative phenomena such as quark
confinement, much like center symmetry and ordinary center vortices are in pure
SU() gauge theories. Here we report on our investigations of an analogous
symmetry in a 2-color model with dynamical Wilson quarks carrying half-integer
electric charge.Comment: Conference proceedings for the XXIX International Symposium on
Lattice Field Theory, 201
Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems
We discuss the statistical mechanics of granular matter and derive several
significant results. First, we show that, contrary to common belief, the volume
and stress ensembles are inter-dependent, necessitating the use of both. We use
the combined ensemble to calculate explicitly expectation values of structural
and stress-related quantities for two-dimensional systems. We thence
demonstrate that structural properties may depend on the angoricity tensor and
that stress-based quantities may depend on the compactivity. This calls into
question previous statistical mechanical analyses of static granular systems
and related derivations of expectation values. Second, we establish the
existence of an intriguing equipartition principle - the total volume is shared
equally amongst both structural and stress-related degrees of freedom. Third,
we derive an expression for the compactivity that makes it possible to quantify
it from macroscopic measurements.Comment: 5 pages, including 2 figures, To appear in Phys. Rev. Let
Torus counting and self-joinings of Kleinian groups
For any , we obtain counting and equidistribution results for tori
with small volume for a class of -dimensional torus packings, invariant
under a self-joining of a
Kleinian group formed by a -tuple of convex cocompact
representations . More precisely, if is a -admissible -dimensional torus packing, then for any
bounded subset with contained in a proper
real algebraic subvariety, we have Here
is the critical exponent of
with respect to the -metric on the product ,
is the limit set of
, and is a locally finite Borel measure on
which can be explicitly described. The class of
admissible torus packings we consider arises naturally from the Teichm\"{u}ller
theory of Kleinian groups. Our work extends previous results of Oh-Shah on
circle packings (i.e. one-dimensional torus packings) to -torus packings.Comment: 36 pages, 2 figures, To appear in Crelle's journa
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