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

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

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

Determination of the zeta potential for highly charged colloidal suspensions

We compute the electrostatic potential at the surface, or zeta potential $\zeta$, of a charged particle embedded in a colloidal suspension using a hybrid mesoscopic model. We show that for weakly perturbing electric fields, the value of $\zeta$ obtained at steady state during electrophoresis is statistically indistinguishable from $\zeta$ in thermodynamic equilibrium. We quantify the effect of counterions concentration on $\zeta$. We also evaluate the relevance of the lattice resolution for the calculation of $\zeta$ and discuss how to identify the effective electrostatic radius.Comment: 8 pages, 3 figures with 2 panel

The growth of metastable peritectic compounds

The influence of gravitationally driven thermosolutal convection on the directional solidification of peritectic alloys is considered as well as the relationships between the solidification processing conditions, and the microstructure, chemistry, and magnetic properties of such alloys. Analysis of directionally solidified Pb-Bi peritectic samples indicates that appreciable macrosegregation occurs due to thermosolutal convection and/or Soret diffusion. A peritectic solidification model which accounts for partial mixing in the liquid ahead of the planar solidification interface and describes macrosegregation has been developed. Two-phase dendritic and banded microstructures were grown in the Pb-Bi peritectic system, refined two-phase microstructures have were observed, and candidate formation mechanisms proposed. Material handling, containment, casting, microstructural and magnetic characterization techniques were developed for the Sm-Co system. Alloys produced with these procedures are homogeneous

Modeling a high mass turn down in the stellar initial mass function

Statistical sampling from the stellar initial mass function (IMF) for all star-forming regions in the Galaxy would lead to the prediction of ~1000 Msun stars unless there is a rapid turn-down in the IMF beyond several hundred solar masses. Such a turndown is not necessary for dense clusters because the number of stars sampled is always too small. Here we explore several mechanisms for an upper mass cutoff, including an exponential decline of the star formation probability after a turbulent crossing time. The results are in good agreement with the observed IMF over the entire stellar mass range, and they give a gradual turn down compared to the Salpeter function above ~100 Msun for normal thermal Jeans mass, M_J. The upper mass turn down should scale with M_J in different environments. A problem with the models is that they cannot give both the observed power-law IMF out to the high-mass sampling limit in dense clusters, as well as the observed lack of supermassive stars in whole galaxy disks. Either there is a sharper upper-mass cutoff in the IMF, perhaps from self-limitation, or the IMF is different for dense clusters than for the majority of star formation that occurs at lower density. Dense clusters seem to have an overabundance of massive stars relative to the average IMF in a galaxy.Comment: 19 pages, 2 figures, Astrophysical Journal, Vol 539, August 10, 200

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