Hopf Algebras of Heap Ordered Trees and Permutations

It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations and show that there is a direct bialgebra isomorphism between the Hopf algebra of heap-ordered trees and the bialgebra of permutations.Comment: 10 pages LaTeX, minor revisio

Asymmetric exclusion processes with constrained dynamics

Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of non-conservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior, negative differential resistance, two-step structural relaxation, dynamical heterogeneity and, possibly, a jamming transition driven by the external field.Comment: 4 pages, 4 figures; revised version: minor changes, added references; to be publishe

SPAR VI Technical Report for Experiment 76-22: Directional Solidification of Magnetic Composites

Samples of eutectic Bi/MnBi were directionally solidified during a low-g interval aboard the SPAR 6 flight and in a l-g environment under identical furnace velocity and thermal conditions. The Bi/MnBi eutectic is characterized by a regular rod eutectic whose morphology may be sensitive to thermo-solutal convection and by its components, MnBi, which is ferromagnetic. Morphological analyses on samples show statistically smaller interrod spacings and rod diameters with respect to samples grown under identical solidification furnace conditions in l-g. An adjustment between the interrod spacing, growth velocity, and total undercooling at the solidification interface is proposed. Morphological analyses on samples grown in l-g indicate little difference between results for different growth orientations with respect to the gravity vector. The magnetic properties are significantly affected, however, by the presence of a nonequilibrium magnetic phase and the nonequilibrium phase transforms to the equilibrium ferromagnetic phase during isothermal heat treatment

Non-axisymmetric instability of shear-banded Taylor-Couette flow

Recent experiments show that shear-banded flows of semi-dilute worm-like micelles in Taylor-Couette geometry exhibit a flow instability in the form of Taylor-like vortices. Here we perform the non-axisymmetric linear stability analysis of the diffusive Johnson-Segalman model of shear banding and show that the nature of this instability depends on the applied shear rate. For the experimentally relevant parameters, we find that at the beginning of the stress plateau the instability is driven by the interface between the bands, while most of the stress plateau is occupied by the bulk instability of the high-shear-rate band. Our work significantly alters the recently proposed stability diagram of shear-banded flows based on axisymmetric analysis.Comment: 6 pages, 5 figures, main text and supplementary material; accepted to Phys. Rev. Let

A simple example of modeling hybrid systems using bialgebras: Preliminary version

The authors describe how to construct a hybrid control system using a specific set of data and conditions specified within the paper. Furthermore, they give examples of how to create continuous systems, discrete systems, and simple hybrid systems. Finally, they touch upon Heisenberg and state space representation

Orientation selection in lamellar phases by oscillatory shears

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shear. The resulting secondary flows break the degeneracy between parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.Comment: 4 pages, 3 figure

Four dimensional topological quantum field theory, Hopf categories, and the canonical bases

We propose a new mwthod of constructing 4D-TQFTs. The method uses a new type of algebraic structure called a Hopf Category. We also outline the construction of a family of Hopf categories related to the quantum groups, using the canonical bases.Comment: 38 page

Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid

We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation

Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicularly oriented lamellae in a uniform, oscillatory, shear flow, and show that the configuration can be hydrodynamically unstable for the constitutive law chosen. It is argued that this instability and the secondary flows it creates can be used to infer a possible mechanism for orientation selection in shear experiments.Comment: 26 pages, 10 figure