1,721 research outputs found
Is there a Relationship between the Elongational Viscosity and the First Normal Stress Difference in Polymer Solutions?
We investigate a variety of different polymer solutions in shear and
elongational flow. The shear flow is created in the cone-plate-geometry of a
commercial rheometer. We use capillary thinning of a filament that is formed by
a polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) as an
elongational flow. We compare the relaxation time and the elongational
viscosity measured in the CaBER with the first normal stress difference and the
relaxation time that we measured in our rheometer. All of these four quantities
depend on different fluid parameters - the viscosity of the polymer solution,
the polymer concentration within the solution, and the molecular weight of the
polymers - and on the shear rate (in the shear flow measurements).
Nevertheless, we find that the first normal stress coefficient depends
quadratically on the CaBER relaxation time. A simple model is presented that
explains this relation
A refined Razumov-Stroganov conjecture II
We extend a previous conjecture [cond-mat/0407477] relating the
Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to
refined numbers of alternating sign matrices. By considering the O(1) loop
model on a semi-infinite cylinder with dislocations, we obtain the generating
function for alternating sign matrices with prescribed positions of 1's on
their top and bottom rows. This seems to indicate a deep correspondence between
observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf
macro
Finite-size left-passage probability in percolation
We obtain an exact finite-size expression for the probability that a
percolation hull will touch the boundary, on a strip of finite width. Our
calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and
the results are expressed in terms of symplectic characters. In the large size
limit, we recover the scaling behaviour predicted by Schramm's left-passage
formula. We also derive a general relation between the left-passage probability
in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the
open XXZ chain with diagonal, complex boundary terms.Comment: 21 pages, 8 figure
Supersymmetry on Jacobstahl lattices
It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A:
Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the
open XXZ chain with anisotropy but to systems having
dimensions given by Jacobstahl sequences.For each system the ground state is
unique. The continuum limit of the spectra of the Jacobstahl systems coincide,
up to degeneracies, with that of the invariant XXZ chain for
. The relation between the Jacobstahl systems and the open XXZ
chain is explained.Comment: 6 pages, 0 figure
Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
The raise and peel model of a one-dimensional fluctuating interface (model A)
is extended by considering one source (model B) or two sources (model C) at the
boundaries. The Hamiltonians describing the three processes have, in the
thermodynamic limit, spectra given by conformal field theory. The probability
of the different configurations in the stationary states of the three models
are not only related but have interesting combinatorial properties. We show
that by extending Pascal's triangle (which gives solutions to linear relations
in terms of integer numbers), to an hexagon, one obtains integer solutions of
bilinear relations. These solutions give not only the weights of the various
configurations in the three models but also give an insight to the connections
between the probability distributions in the stationary states of the three
models. Interestingly enough, Pascal's hexagon also gives solutions to a
Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few
references are adde
Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras
We extend the results of spin ladder models associated with the Lie algebras
to the case of the orthogonal and symplectic algebras $o(2^n),\
sp(2^n)$ where n is the number of legs for the system. Two classes of models
are found whose symmetry, either orthogonal or symplectic, has an explicit n
dependence. Integrability of these models is shown for an arbitrary coupling of
XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late
Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. For totally asymmetric diffusion we calculate
the spectral gap, which characterizes the approach to stationarity at large
times. We observe boundary induced crossovers in and between massive, diffusive
and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio
Limit shapes for the asymmetric five vertex model
We compute the free energy and surface tension function for the five-vertex
model, a model of non-intersecting monotone lattice paths on the grid in which
each corner gets a positive weight. We give a variational principle for limit
shapes in this setting, and show that the resulting Euler-Lagrange equation can
be integrated, giving explicit limit shapes parameterized by analytic
functions.Comment: 37 pages, 21 figure
A refined Razumov-Stroganov conjecture
We extend the Razumov-Stroganov conjecture relating the groundstate of the
O(1) spin chain to alternating sign matrices, by relating the groundstate of
the monodromy matrix of the O(1) model to the so-called refined alternating
sign matrices, i.e. with prescribed configuration of their first row, as well
as to refined fully-packed loop configurations on a square grid, keeping track
both of the loop connectivity and of the configuration of their top row. We
also conjecture a direct relation between this groundstate and refined totally
symmetric self-complementary plane partitions, namely, in their formulation as
sets of non-intersecting lattice paths, with prescribed last steps of all
paths.Comment: 20 pages, 4 figures, uses epsf and harvmac macros a few typos
correcte
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