3,652 research outputs found

### On the coupling between an ideal fluid and immersed particles

In this paper we use Lagrange-Poincare reduction to understand the coupling
between a fluid and a set of Lagrangian particles that are supposed to simulate
it. In particular, we reinterpret the work of Cendra et al. by substituting
velocity interpolation from particle velocities for their principal connection.
The consequence of writing evolution equations in terms of interpolation is
two-fold. First, it gives estimates on the error incurred when interpolation is
used to derive the evolution of the system. Second, this form of the equations
of motion can inspire a family of particle and hybrid particle-spectral methods
where the error analysis is "built-in". We also discuss the influence of other
parameters attached to the particles, such as shape, orientation, or
higher-order deformations, and how they can help with conservation of momenta
in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom

### Characters of graded parafermion conformal field theory

The graded parafermion conformal field theory at level k is a close cousin of
the much-studied Z_k parafermion model. Three character formulas for the graded
parafermion theory are presented, one bosonic, one fermionic (both previously
known) and one of spinon type (which is new). The main result of this paper is
a proof of the equivalence of these three forms using q-series methods combined
with the combinatorics of lattice paths. The pivotal step in our approach is
the observation that the graded parafermion theory -- which is equivalent to
the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x
(su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal
model M(k+2,2k+3) and the Z_k parafermion model, respectively. This
factorisation allows for a new combinatorial description of the graded
parafermion characters in terms of the one-dimensional configuration sums of
the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page

### Large-eddy simulation of the flow in a lid-driven cubical cavity

Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity
have been carried out at a Reynolds number of 12000 using spectral element
methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model
and a dynamic mixed model, have been both implemented and used to perform
long-lasting simulations required by the relevant time scales of the flow. All
filtering levels make use of explicit filters applied in the physical space (on
an element-by-element approach) and spectral (modal) spaces. The two
subgrid-scales models are validated and compared to available experimental and
numerical reference results, showing very good agreement. Specific features of
lid-driven cavity flow in the turbulent regime, such as inhomogeneity of
turbulence, turbulence production near the downstream corner eddy, small-scales
localization and helical properties are investigated and discussed in the
large-eddy simulation framework. Time histories of quantities such as the total
energy, total turbulent kinetic energy or helicity exhibit different evolutions
but only after a relatively long transient period. However, the average values
remain extremely close

### Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances
which are i.i.d., positive, bounded uniformly from above but whose support
extends all the way to zero. Our focus is on the detailed properties of the
paths of the random walk conditioned to return back to the starting point at
time $2n$. We show that in the situations when the heat kernel exhibits
subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the
walk gets trapped for a time of order $n$ in a small spatial region. This shows
that the strategy used earlier to infer subdiffusive lower bounds on the heat
kernel in specific examples is in fact dominant. In addition, we settle a
conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

### New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions

We present a new path description for the states of the non-unitary
M(k+1,2k+3) models. This description differs from the one induced by the
Forrester-Baxter solution, in terms of configuration sums, of their
restricted-solid-on-solid model. The proposed path representation is actually
very similar to the one underlying the unitary minimal models M(k+1,k+2), with
an analogous Fermi-gas interpretation. This interpretation leads to fermionic
expressions for the finitized M(k+1,2k+3) characters, whose infinite-length
limit represent new fermionic characters for the irreducible modules. The
M(k+1,2k+3) models are also shown to be related to the Z_k graded parafermions
via a (q to 1/q) duality transformation.Comment: 43 pages (minor typo corrected and minor rewording in the
introduction

### Particles in RSOS paths

We introduce a new representation of the paths of the Forrester-Baxter RSOS
models which represents the states of the irreducible modules of the minimal
models M(p',p). This representation is obtained by transforming the RSOS paths,
for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at
certain heights. These new paths are much simpler in that their weight is
nothing but the sum of the position of the peaks. This description paves the
way for the interpretation of the RSOS paths in terms of fermi-type charged
particles out of which the fermionic characters could be obtained
constructively. The derivation of the fermionic character for p'=2 and p=kp'+/-
1 is outlined. Finally, the particles of the RSOS paths are put in relation
with the kinks and the breathers of the restricted sine-Gordon model.Comment: 15 pages, few typos corrected, version publishe

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