Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory

In this paper we study the Yang-Baxter integrable structure of Conformal Field Theories with extended conformal symmetry generated by the W_3 algebra. We explicitly construct various T- and Q-operators which act in the irreducible highest weight modules of the W_3 algebra. These operators can be viewed as continuous field theory analogues of the commuting transfer matrices and Q-matrices of the integrable lattice systems associated with the quantum algebra U_q(\hat{sl}(3)). We formulate several conjectures detailing certain analytic characteristics of the Q-operators and propose exact asymptotic expansions of the T- and Q-operators at large values of the spectral parameter. We show, in particular, that the asymptotic expansion of the T-operators generates an infinite set of local integrals of motion of the W_3 CFT which in the classical limit reproduces an infinite set of conserved Hamiltonians associated with the classical Boussinesq equation. We further study the vacuum eigenvalues of the Q-operators (corresponding to the highest weight vector of the W_3 module) and show that they are simply related to the expectation values of the boundary exponential fields in the non-equilibrium boundary affine Toda field theory with zero bulk mass.Comment: LaTeX, 87 pages, 1 figure. Misprints correcte

An optimized protocol for isolation of high-quality RNA through laser capture microdissection of leaf material.

Laser Capture Microdissection is a powerful tool that allows thin slices of specific cell types to be separated from one another. However, the most commonly used protocol, which involves embedding tissue in paraffin wax, results in severely degraded RNA. Yields from low abundance cell types of leaves are particularly compromised. We reasoned that the relatively high temperature used for sample embedding, and aqueous conditions associated with sample preparation prior to microdissection contribute to RNA degradation. Here, we describe an optimized procedure to limit RNA degradation that is based on the use of low-melting-point wax as well as modifications to sample preparation prior to dissection, and isolation of paradermal, rather than transverse sections. Using this approach, high-quality RNA suitable for down-stream applications such as quantitative reverse transcriptase-polymerase chain reactions or RNA-sequencing is recovered from microdissected bundle sheath strands and mesophyll cells of leaf tissue.The work was supported by a C4 Rice project grant from The Bill and Melinda Gates Foundation to the University of Oxford (2015-­2019)

Rice bundle sheath cell shape is regulated by the timing of light exposure during leaf development

Plant leaves contain multiple cell types which achieve distinct characteristics whilst still coordinating development within the leaf. The bundle sheath possesses larger individual cells and lower chloroplast content than the adjacent mesophyll, but how this morphology is achieved remains unknown. To identify regulatory mechanisms determining bundle sheath cell morphology we tested the effects of perturbing environmental (light) and endogenous signals (hormones) during leaf development of Oryza sativa (rice). Total chloroplast area in bundle sheath cells was found to increase with cell size as in the mesophyll but did not maintain a ‘set‐point’ relationship, with the longest bundle sheath cells demonstrating the lowest chloroplast content. Application of exogenous cytokinin and gibberellin significantly altered the relationship between cell size and chloroplast biosynthesis in the bundle sheath, increasing chloroplast content of the longest cells. Delayed exposure to light reduced the mean length of bundle sheath cells but increased corresponding leaf length, whereas premature light reduced final leaf length but did not affect bundle sheath cells. This suggests that the plant hormones cytokinin and gibberellin are regulators of the bundle sheath cell‐chloroplast relationship and that final bundle sheath length may potentially be affected by light‐mediated control of exit from the cell cycle

Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetry

The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given.Comment: 7 pages (revtex), minor modifications. To appear in Mod. Phys. Lett.

Insights into C4 metabolism from comparative deep sequencing.

C4 photosynthesis suppresses the oxygenation activity of Ribulose Bisphosphate Carboxylase Oxygenase and so limits photorespiration. Although highly complex, it is estimated to have evolved in 66 plant lineages, with the vast majority lacking sequenced genomes. Transcriptomics has recently initiated assessments of the degree to which transcript abundance differs between C3 and C4 leaves, identified novel components of C4 metabolism, and also led to mathematical models explaining the repeated evolution of this complex phenotype. Evidence is accumulating that this complex and convergent phenotype is partly underpinned by parallel evolution of structural genes, but also regulatory elements in both cis and trans. Furthermore, it appears that initial events associated with acquisition of C4 traits likely represent evolutionary exaptations related to non-photosynthetic processes.We thank the BBSRC for grant BB/1002243/1 and the EU 3to4 program for financial support.This is the accepted manuscript. The final version is available at http://www.sciencedirect.com/science/article/pii/S1369526615000680

Effect of random forcing on fluid lubricated bearing

A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation for incompressible flow and is coupled to the axial displacement of the bearing faces as modelled by spring-mass-damper systems. Representative dynamics of a highly rotating bearing subject to external potentially destabilising random forcing is developed. An external force characterised by a noise term is imposed on the rotor, where both white noise and coloured noise are considered. For industrial applications it is important to evaluate potential bearing failure that can arise when the face clearance becomes sufficiently small. Therefore, a quantity of interest is the average time for the face clearance to reach a prescribed tolerance. A computational technique to evaluate the bearing characteristics is implemented based on a simple random walk for a Dirichlet problem for a linear parabolic partial differential equation combined with a Monte Carlo technique. Results of numerical experiments are presented, to give indicative predictions of possible face contact, which has the potential to result in bearing failure