Improved Perturbation Theory for Improved Lattice Actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.Comment: 17 pages, 3 tables, 6 figure

The Nusselt numbers of horizontal convection

We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $\kappa$ is the molecular diffusivity of buoyancy $b$. This connection between $\mathbf{J}$ and $\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $\kappa\langle|\boldsymbol{\nabla} b|^2\rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent "surface Nusselt number", defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{\rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|\mathbf{\nabla}b|^2$ demanded by $\kappa\langle|\mathbf{\nabla}b|^2\rangle$.Comment: 16 pages, 7 figure

Changes in cardiorespiratory fitness and cardiovascular health in the workplace: a case study

Background: Cardiorespiratory fitness (CRF) is an independent predictor of cardiovascular (CV) and all-cause mortality, contributing a higher proportion of CV risk compared to other traditionally recognised risk factors. However, CRF is not included in usual workplace wellness protocols and, as such, employers are not aware of the importance of this factor.Aim: The aim of this case study was to explore the effect of a 12-week exercise intervention programme on CRF, CV health and medical health claims in a male participant who was employed by a corporate company with existing chronic diseases.Findings: Health outcome measures improved after the 12-week exercise intervention programme. CRF showed the greatest improvement and medical health claims were lowered during the three-month post-intervention period.Implications: CRF should be included as a health outcome measure in worksite wellness programmes and monitored. Keywords: cardiopulmonary fitness, exercise interventions, medical health claims, corporate wellnes

Model of host-pathogen Interaction dynamics links In vivo optical imaging and immune responses

Tracking disease progression in vivo is essential for the development of treatments against bacterial infection. Optical imaging has become a central tool for in vivo tracking of bacterial population development and therapeutic response. For a precise understanding of in vivo imaging results in terms of disease mechanisms derived from detailed postmortem observations, however, a link between the two is needed. Here, we develop a model that provides that link for the investigation of Citrobacter rodentium infection, a mouse model for enteropathogenic Escherichia coli (EPEC). We connect in vivo disease progression of C57BL/6 mice infected with bioluminescent bacteria, imaged using optical tomography and X-ray computed tomography, to postmortem measurements of colonic immune cell infiltration. We use the model to explore changes to both the host immune response and the bacteria and to evaluate the response to antibiotic treatment. The developed model serves as a novel tool for the identification and development of new therapeutic interventions

Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with $d \leq 5$ will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with $d<5$) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Green's functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the $K-\pi$ matrix element are being performed in simulations with 4 dynamical ($N_f = 2+1+1$) twisted mass fermions and the Iwasaki improved gluon action.Comment: 7 pages, 1 figure, 3 tables, LATTICE2014 proceeding

A path-independent approach to integrated variance under the CEV model

In this paper, a closed form path-independent approximation of the fair variance strike for a variance swap under the constant elasticity of variance (CEV) model is obtained by applying the small disturbance asymptotic expansion. The realized variance is sampled continuously in a risk-neutral market environment. With the application of a Brownian bridge, we derive a theorem for the conditionally expected product of a Brownian motion at two different times for arbitrary powers. This theorem enables us to provide a conditional Monte-Carlo scheme for simulating the fair variance strike. Compared with results in the recent literature, the method outlined in our paper leads to a simplified approach for pricing variance swaps. The method may also be applied to other more sophisticated volatility derivatives. An empirical comparison of this model with the Heston model and a conditional Monte Carlo scheme is also presented using option data on the S&P 500

Fuel Production Using Membrane Reactors

The constant increase in population has led to greater fossil fuel consumption, and subsequently a significant increase in greenhouse gases emission to the atmosphere. This presents a serious threat to the environment and impacts climate change to a great extent. Fossil fuel supplies are depleting fast, and the price of these fuels is also increasing due to their heightened demand. The environmental concerns regarding this are the increased emissions of harmful pollutants such as carbon dioxide, sulphur dioxide and hydrocarbons. Here we review the alternative fuel technologies which are currently employed to aid the eradication of the current environmental problems. Most notably, this review will demonstrate how membrane reactors are implemented to improve and intensify the existing renewable fuel production processes. Furthermore, the advantages of membrane reactors when compared to the conventional ones, will be discussed; and the environmental benefits these particular reactors pose will also be highlighted. We will showcase how these membrane reactors have been applied successfully to improve biodiesel, hydrogen and Fischer-Tropsch synthesis processes. The application of membranes aids the increase in the conversion of desired products, whilst shifting the equilibrium of the reaction and reducing undesired by-products. Membrane reactors also overcome immiscibility issues that hinder conventional reactor processes. Moreover, they have also demonstrated a significant reduction in the separation and purification of impurities, as they couple them both in one step. This shows drastic economic and energy requirement reductions in the amount of wastewater treatment associated with conventional fuel production reactor

The chromomagnetic operator on the lattice

We study matrix elements of the "chromomagnetic" operator on the lattice. This operator is contained in the strangeness-changing effective Hamiltonian which describes electroweak effects in the Standard Model and beyond. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with other operators of equal and lower dimensionality, including also non gauge invariant quantities; it is thus quite a challenge to extract from lattice simulations a clear signal for the hadronic matrix elements of this operator. We compute all relevant mixing coefficients to one loop in lattice perturbation theory; this necessitates calculating both 2-point (quark-antiquark) and 3-point (gluon-quark-antiquark) Green's functions at nonzero quark masses. We use the twisted mass lattice formulation, with Symanzik improved gluon action. For a comprehensive presentation of our results, along with detailed explanations and a more complete list of references, we refer to our forthcoming publication [1].Comment: 7 pages, 1 figure. Talk presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German