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

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

The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance

The raise and peel model describes the stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes, and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects (D). The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster changing its shape. If a tile hits two adjacent defects, the defect annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction D + D -->0, in which the particles (defects) D hop at long distances changing the medium and annihilate. Between the hops the medium also changes (tiles hit clusters changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformal invariant quantum chain.Comment: 8 pages, 12figure

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 $\Delta =-{1/2}$ 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 $U_q(sl(2))$ invariant XXZ chain for $q=\exp(i\pi/3)$. The relation between the Jacobstahl systems and the open XXZ chain is explained.Comment: 6 pages, 0 figure

Chronic GLP-1 receptor activation by exendin-4 induces expansion of pancreatic duct glands in rats and accelerates formation of dysplastic lesions and chronic pancreatitis in the Kras(G12D) mouse model.

Pancreatic duct glands (PDGs) have been hypothesized to give rise to pancreatic intraepithelial neoplasia (PanIN). Treatment with the glucagon-like peptide (GLP)-1 analog, exendin-4, for 12 weeks induced the expansion of PDGs with mucinous metaplasia and columnar cell atypia resembling low-grade PanIN in rats. In the pancreata of Pdx1-Cre; LSL-Kras(G12D) mice, exendin-4 led to acceleration of the disruption of exocrine architecture and chronic pancreatitis with mucinous metaplasia and increased formation of murine PanIN lesions. PDGs and PanIN lesions in rodent and human pancreata express the GLP-1 receptor. Exendin-4 induced proproliferative signaling pathways in human pancreatic duct cells, cAMP-protein kinase A and mitogen-activated protein kinase phosphorylation of cAMP-responsive element-binding protein, and increased cyclin D1 expression. These GLP-1 effects were more pronounced in the presence of an activating mutation of Kras and were inhibited by metformin. These data reveal that GLP-1 mimetic therapy may induce focal proliferation in the exocrine pancreas and, in the context of exocrine dysplasia, may accelerate formation of neoplastic PanIN lesions and exacerbate chronic pancreatitis

Conformal invariance and its breaking in a stochastic model of a fluctuating interface

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter $u$ (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for $0<u<1$ the system is massive, for $u=1$ it is massless and conformal invariant. For $u>1$ the conformal invariance is broken. The system is in a scale invariant but not conformal invariant phase. As far as we know it is the first example of a system which shows such a behavior. Moreover in the broken phase, the critical exponents vary continuously with the parameter $u$. This stays true also for the critical exponent $\tau$ which characterizes the probability distribution function of avalanches (the critical exponent $D$ staying unchanged).Comment: 22 pages and 20 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

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

The Wave Functions for the Free-Fermion Part of the Spectrum of the SUq(N)SU_q(N) Quantum Spin Models

We conjecture that the free-fermion part of the eigenspectrum observed recently for the $SU_q(N)$ Perk-Schultz spin chain Hamiltonian in a finite lattice with $q=\exp (i\pi (N-1)/N)$ is a consequence of the existence of a special simple eigenvalue for the transfer matrix of the auxiliary inhomogeneous $SU_q(N-1)$ vertex model which appears in the nested Bethe ansatz approach. We prove that this conjecture is valid for the case of the SU(3) spin chain with periodic boundary condition. In this case we obtain a formula for the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model ($q=\exp (2 i \pi/3)$), which permit us to find one by one all components of this eigenvector and consequently to find the eigenvectors of the free-fermion part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known case of the $SU_q(2)$ case at $q=\exp(i2\pi/3)$ our numerical and analytical studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure