Clustering transition in a system of particles self-consistently driven by a shear flow

We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists in that the effective velocity of every particle is given by the average of the external flow velocities felt by the particles located at a distance less than a typical radius, $R$. Numerical analysis reveals the existence of a transition to clustering depending on the parameters of the external flow and on $R$. A continuum description in terms of the number density of particles is derived, and a linear stability analysis of the density equation is performed in order to characterize the transitions observed in the model of interacting particles.Comment: 11 pages, 2 figures. To appear in PR

Source identification and quantification of particulate matter emitted from livestock houses

There is need to identify and quantify the contribution of different sources to airborne particulate matter (PM) emissions from animal houses. To this end, we compared the chemical and morphological characteristics of fine and coarse PM from known sources collected from animal houses with the characteristics of on-farm fine and coarse airborne PM using two methods: classification rules based on decision trees and multiple linear regression. Fourteen different farms corresponding to seven different housing systems for poultry and pigs were sampled during winter. A total of 28 fine and 28 coarse on-farm airborne PM samples were collected, together with a representative sample of each known source per farm (56 known source samples in total). Source contributions were calculated as relative percentage contributions in particle numbers and then estimated in particle mass. Based on particle numbers, results showed that in poultry houses, most on-farm airborne PM originated from feathers (ranging from 4% to 43% in fine PM and from 6% to 35% in coarse PM) and manure (ranging from 9% to 85% in fine PM and from 30% to 94% in coarse PM). For pigs, most on-farm airborne PM originated from manure (ranging from 70% to 98% in fine PM and from 41% to 94% in coarse PM). Based on particle mass, for poultry most on-farm airborne PM still originated from feathers and manure; for pigs, however, most PM originated from skin and manure. Feed had a negligible contribution to on-farm airborne PM compared with other sources. Results presented in this study improve the understanding of sources of PM in different animal housing systems, which may be valuable when choosing optimal PM reduction technique

PT-Symmetric Quantum Theory Defined in a Krein Space

We provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry is unbroken, and so on. The linear space in which PT-symmetric quantum theory is naturally defined is a Krein space constructed by introducing an indefinite metric into a Hilbert space composed of square integrable complex functions in a complex contour. We show that in this Krein space every PT-symmetric operator is P-Hermitian if and only if it has transposition symmetry as well, from which the characteristic properties of the PT-symmetric Hamiltonians found in the literature follow. Some possible ways to construct physical theories are discussed within the restriction to the class K(H).Comment: 8 pages, no figures; Refs. added, minor revisio

A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry

We develop a systematic algorithm for constructing an N-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multi-parameter family of N-fold supersymmetric models, which shall be referred to as "type C". We investigate various aspects of these type C models in detail. It turns out that in certain cases these systems exhibit a novel phenomenon, namely, partial breaking of N-fold supersymmetry.Comment: RevTeX 4, 28 pages, no figure

Monomial integrals on the classical groups

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas turn out to be of similar form. They are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows to obtain analytical expressions very efficiently. Those expressions contain the matrix dimension as a free parameter.Comment: 16 page

On the Space Time of a Galaxy

We present an exact solution of the averaged Einstein's field equations in the presence of two real scalar fields and a component of dust with spherical symmetry. We suggest that the space-time found provides the characteristics required by a galactic model that could explain the supermassive central object and the dark matter halo at once, since one of the fields constitutes a central oscillaton surrounded by the dust and the other scalar field distributes far from the coordinate center and can be interpreted as a halo. We show the behavior of the rotation curves all along the background. Thus, the solution could be a first approximation of a ``long exposition photograph'' of a galaxy.Comment: 8 pages REVTeX, 11 eps figure