On the coupling between an ideal fluid and immersed particles

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom

Characters of graded parafermion conformal field theory

The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z_k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously known) and one of spinon type (which is new). The main result of this paper is a proof of the equivalence of these three forms using q-series methods combined with the combinatorics of lattice paths. The pivotal step in our approach is the observation that the graded parafermion theory -- which is equivalent to the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x (su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal model M(k+2,2k+3) and the Z_k parafermion model, respectively. This factorisation allows for a new combinatorial description of the graded parafermion characters in terms of the one-dimensional configuration sums of the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page

A surrogate function for one-dimensional phylogenetic likelihoods

Phylogenetics has seen an steady increase in substitution model complexity, which requires increasing amounts of computational power to compute likelihoods. This model complexity motivates strategies to approximate the likelihood functions for branch length optimization and Bayesian sampling. In this paper, we develop an approximation to the one-dimensional likelihood function as parametrized by a single branch length. This new method uses a four-parameter surrogate function abstracted from the simplest phylogenetic likelihood function, the binary symmetric model. We show that it offers a surrogate that can be fit over a variety of branch lengths, that it is applicable to a wide variety of models and trees, and that it can be used effectively as a proposal mechanism for Bayesian sampling. The method is implemented as a stand-alone open-source C library for calling from phylogenetics algorithms; it has proven essential for good performance of our online phylogenetic algorithm sts

Microclimate modification and insect pest exclusion using agronet improve pod yield and quality of french bean

French bean [Phaseolus vulgaris (L.)] is among the leading export vegetable in Africa, mostly produced by small-scale farmers. Unfavorable environmental conditions and heavy infestations by insect pests are among the major constraints limiting production of the crop. Most French bean producers grow their crop in open fields outdoors subject to harsh environmental conditions and repeatedly spray insecticides in a bid to realize high yield. This has led to rejection of some of the produce at the export market as a result of stringent limits on maximum residue levels. Two trials were conducted at the Horticulture Research and Teaching Field, Egerton University, Kenya, to evaluate the potential of using agricultural nets (herein referred to as agronets) to improve the microclimate, reduce pest infestation, and increase the yield and quality of French bean. A randomized complete block design with five replications was used. French bean seeds were direct-seeded, sprayed with an alpha-cypermethrin-based insecticide (control), covered with a treated agronet (0.9 mm 3 0.7 mm average pore size made of 100 denier yarn knitted into a mesh impregnated with alpha-cypermethrin), or covered with an untreated-agronet (0.9 mm 3 0.7 mm average pore size made of 100 denier yarn knitted into a mesh not impregnated with insecticide). Alpha-cypermethrin and agronets were manufactured by Tagros Chemicals (India) and A to Z Textile Mills (Tanzania), respectively. Covering French bean with the agronets modified the microclimate of the growing crop with air temperature increased by '10%, relative humidity by 4%, and soil moisture by 20%, whereas photosynthetic active radiation (PAR) and daily light integral (DLI) were decreased by '1% and 11.5%, respectively. Populations of silverleaf whitefly [Bemisia tabaci (Gennadius)] and black bean aphids [Aphis fabae (Scopoli)] were reduced under agronet covers as contrasted with control plots. Furthermore, populations of both pests were reduced on French bean grown under impregnated agronets compared with untreated agronets, but only on three of the five sampling dates [30, 44, and 72 days after planting (DAP)] for silver leaf whitefly or at only one of the five sampling dates (30 DAP) for black bean aphid. Covering French bean with agronets advanced seedling emergence by 2 days and increased seedling emergence over 90% compared with control plots. French bean plants covered with both agronet treatments had faster development, better pod yield, and quality compared with the uncovered plants. These findings demonstrate the potential of agronets in improving French bean performance while minimizing the number of insecticide sprays within the crop cycle, which could lead to less rejection of produce in the export market and improved environmental quality. (Résumé d'auteur

Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions

We present a new path description for the states of the non-unitary M(k+1,2k+3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid model. The proposed path representation is actually very similar to the one underlying the unitary minimal models M(k+1,k+2), with an analogous Fermi-gas interpretation. This interpretation leads to fermionic expressions for the finitized M(k+1,2k+3) characters, whose infinite-length limit represent new fermionic characters for the irreducible modules. The M(k+1,2k+3) models are also shown to be related to the Z_k graded parafermions via a (q to 1/q) duality transformation.Comment: 43 pages (minor typo corrected and minor rewording in the introduction

Poisson homology of r-matrix type orbits I: example of computation

In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the $r$-matrix Poisson family