2,062 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
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
Optimizing evacuation flow in a two-channel exclusion process
We use a basic setup of two coupled exclusion processes to model a stylised
situation in evacuation dynamics, in which evacuees have to choose between two
escape routes. The coupling between the two processes occurs through one common
point at which particles are injected, the process can be controlled by
directing incoming individuals into either of the two escape routes. Based on a
mean-field approach we determine the phase behaviour of the model, and
analytically compute optimal control strategies, maximising the total current
through the system. Results are confirmed by numerical simulations. We also
show that dynamic intervention, exploiting fluctuations about the mean-field
stationary state, can lead to a further increase in total current.Comment: 16 pages, 6 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
Relaxation rate of the reverse biased asymmetric exclusion process
We compute the exact relaxation rate of the partially asymmetric exclusion
process with open boundaries, with boundary rates opposing the preferred
direction of flow in the bulk. This reverse bias introduces a length scale in
the system, at which we find a crossover between exponential and algebraic
relaxation on the coexistence line. Our results follow from a careful analysis
of the Bethe ansatz root structure.Comment: 22 pages, 12 figure
Bethe Ansatz solution of a decagonal rectangle triangle random tiling
A random tiling of rectangles and triangles displaying a decagonal phase is
solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square
triangle and the octagonal rectangle triangle tiling an exact expression for
the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte
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
Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model
We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg
model on a finite system of length L with open boundary conditions and parallel
updates. We find numerically that in both the high and low density regimes the
autocorrelation function of the system density behaves like 1-|t|/tau with a
finite support [-tau,tau]. This is in contrast to the usual exponential decay
typical of equilibrium systems. Furthermore, our results suggest that in fact
tau=L/c, and in the special case of maximum velocity 1 (corresponding to the
totally asymmetric simple exclusion process) we can identify the exact
dependence of c on the input, output and hopping rates. We also emphasize that
the parameter tau corresponds to the integrated autocorrelation time, which
plays a fundamental role in quantifying the statistical errors in Monte Carlo
simulations of these models.Comment: 7 pages, 6 figure
Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
We study a model of strongly correlated fermions in one dimension with
extended N=2 supersymmetry. The model is related to the spin XXZ
Heisenberg chain at anisotropy with a real magnetic field on the
boundary. We exploit the combinatorial properties of the ground state to
determine its exact wave function on finite lattices with up to 30 sites. We
compute several correlation functions of the fermionic and spin fields. We
discuss the continuum limit by constructing lattice observables with well
defined finite size scaling behavior. For the fermionic model with periodic
boundary conditions we give the emptiness formation probability in closed form.Comment: 4 pages, 4 eps figure
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