Feynman Rules for QCD in Space-Cone Gauge

We present the Lagrangian and Feynman rules for QCD written in space-cone gauge and after eliminating unphysical degrees of freedom from the gluonic sector. The main goal is to clarify and allow for straightforward application of these Feynman rules. We comment on the connection between BCFW recursion relations and space-cone gauge.Comment: 7 pages, typos corrected, diagrams and clarifying text adde

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes

We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level.Comment: 28 pages, 8 figures, JHEP

Unusual identities for QCD at tree-level

We discuss a set of recently discovered quadratic relations between gauge theory amplitudes. Such relations give additional structural simplifications for amplitudes in QCD. Remarkably, their origin lie in an analogous set of relations that involve also gravitons. When certain gluon helicities are flipped we obtain relations that do not involve gravitons, but which refer only to QCD.Comment: Talk given at XIV Mexican School on Particles and Fields, Morelia, Nov. 201

Data Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. Part I. Theory and Scheme

This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace, that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker-Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian mixture models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’ Law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.United States. Office of Naval Research (Grant N00014-08-1-1097)United States. Office of Naval Research (Grant 00014-09-1-0676)United States. Office of Naval Research (Grant N00014-08-1-0586

Numerical Analysis of the Effects of Solid Metal Fuel Particle Characteristics on the Combustion Process

ABSTRACT Combustion using aluminum particles as fuel is an attractive energy source where high energy densities are desired. Very little experimental literature or computational results are available for metal combustion in high-pressure chambers, as most experimental and computational work has been done on chamber operating at near atmospheric pressures. This paper attempts to improve our understanding of metal-fueled combustion chambers at pressures above atmospheric. A numerical model of solid Aluminum fuel particle combustion is developed to investigate the effects of radiation and fuel particle size on the combustion process. Of specific interest are particle specific burn rate, residence time, combustion efficiency, coupled radiation effects, and flame characteristics. This computational model is applied to a linear-type dump combustor. The effects of a range of particle sizes are investigated using mono-dispersed and polydispersed particle distributions. Combustion efficiency and characterization of the combustion process are addressed by studying particle ignition delay, surface combustion time, and particle flame radiation intensity as a function of particle diameter and mass fraction. The computational results of this detailed theoretical combustor reveal fundamental physics relating particle sizes and distributions to the variables commonly used to define the effectiveness and performance of the combustion process. The computational models include nonisotropic turbulence models, empirically derived ignition criteria and reaction rates, as well as convective and radiant heat transfer. The numerical results were compared with test data with reasonable agreement

Data assimilation with Gaussian mixture models using the dynamically orthogonal field equations

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 177-180).Data assimilation, as presented in this thesis, is the statistical merging of sparse observational data with computational models so as to optimally improve the probabilistic description of the field of interest, thereby reducing uncertainties. The centerpiece of this thesis is the introduction of a novel such scheme that overcomes prior shortcomings observed within the community. Adopting techniques prevalent in Machine Learning and Pattern Recognition, and building on the foundations of classical assimilation schemes, we introduce the GMM-DO filter: Data Assimilation with Gaussian mixture models using the Dynamically Orthogonal field equations. We combine the use of Gaussian mixture models, the EM algorithm and the Bayesian Information Criterion to accurately approximate distributions based on Monte Carlo data in a framework that allows for efficient Bayesian inference. We give detailed descriptions of each of these techniques, supporting their application by recent literature. One novelty of the GMM-DO filter lies in coupling these concepts with an efficient representation of the evolving probabilistic description of the uncertain dynamical field: the Dynamically Orthogonal field equations. By limiting our attention to a dominant evolving stochastic subspace of the total state space, we bridge an important gap previously identified in the literature caused by the dimensionality of the state space. We successfully apply the GMM-DO filter to two test cases: (1) the Double Well Diffusion Experiment and (2) the Sudden Expansion fluid flow. With the former, we prove the validity of utilizing Gaussian mixture models, the EM algorithm and the Bayesian Information Criterion in a dynamical systems setting. With the application of the GMM-DO filter to the two-dimensional Sudden Expansion fluid flow, we further show its applicability to realistic test cases of non-trivial dimensionality. The GMMDO filter is shown to consistently capture and retain the far-from-Gaussian statistics that arise, both prior and posterior to the assimilation of data, resulting in its superior performance over contemporary filters. We present the GMM-DO filter as an efficient, data-driven assimilation scheme, focused on a dominant evolving stochastic subspace of the total state space, that respects nonlinear dynamics and captures non-Gaussian statistics, obviating the use of heuristic arguments.by Thomas Sondergaard.S.M

Data Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. Part II. Applications

The properties and capabilities of the GMM-DO filter are assessed and exemplified by applications to two dynamical systems: (1) the Double Well Diffusion and (2) Sudden Expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the EM algorithm and Bayesian Information Criterion with Gaussian Mixture Models in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of non-trivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including: the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes and stochastic coefficients; the fitting of Gaussian Mixture Models; and, the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution

Outcome after heart-lung or lung transplantation in patients with Eisenmenger syndrome

Objective The optimal timing for transplantation is unclear in patients with Eisenmenger syndrome (ES). We investigated post-transplantation survival and transplantation-specific morbidity after heart-lung transplantation (HLTx) or lung transplantation (LTx) in a cohort of Nordic patients with ES to aid decision-making for scheduling transplantation. Methods We performed a retrospective, descriptive, population-based study of patients with ES who underwent transplantation from 1985 to 2012. Results Among 714 patients with ES in the Nordic region, 63 (9%) underwent transplantation. The median age at transplantation was 31.9 (IQR 21.1-42.3) years. Within 30 days after transplantation, seven patients (11%) died. The median survival was 12.0 (95% CI 7.6 to 16.4) years and the overall 1-year, 5-year, 10-year and 15-year survival rates were 84.1%, 69.7%, 55.8% and 40.6%, respectively. For patients alive 1 year post-transplantation, the median conditional survival was 14.8 years (95% CI 8.0 to 21.8), with 5-year, 10-year and 15-year survival rates of 83.3%, 67.2% and 50.0%, respectively. There was no difference in median survival after HLTx (n=57) and LTx (n=6) (14.9 vs 10.6 years, p=0.718). Median cardiac allograft vasculopathy, bronchiolitis obliterans syndrome and dialysis/kidney transplantation-free survival rates were 11.2 (95% CI 7.8 to 14.6), 6.9 (95% CI 2.6 to 11.1) and 11.2 (95% CI 8.8 to 13.7) years, respectively. The leading causes of death after the perioperative period were infection (36.7%), bronchiolitis obliterans syndrome (23.3%) and heart failure (13.3%). Conclusions This study shows that satisfactory post-transplantation survival, comparable with contemporary HTx and LTx data, without severe comorbidities such as cardiac allograft vasculopathy, bronchiolitis obliterans syndrome and dialysis, is achievable in patients with ES, with a conditional survival of nearly 15 years.Peer reviewe

New Identities among Gauge Theory Amplitudes

Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.Comment: 7 page