The Hamiltonian Analysis for Yang-Mills Theory on R×S2R\times S^2

Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified to a plane

The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page

Modeling on-grate MSW incineration with experimental validation in a batch incinerator

This Article presents a 2-D steady-state model developed for simulating on-grate municipal solid waste incineration, termed GARBED-ss. Gas-solid reactions, gas flow through the porous waste particle bed, conductive, convective, and radiative heat transfer, drying and pyrolysis of the feed, the emission of volatile species, combustion of the pyrolysis gases, the formation and oxidation of char and its gasification by water vapor and carbon dioxide, and the consequent reduction of the bed volume are described in the bed model. The kinetics of the pyrolysis of cellulosic and noncellulosic materials were experimentally derived from experimental measurements. The simulation results provide a deep insight into the various phenomena involved in incineration, for example, the complete consumption of oxygen in a large zone of the bed and a consequent char-gasification zone. The model was successfully validated against experimental measurements in a laboratory batch reactor, using an adapted sister version in a transient regime. © 2010 American Chemical Society

Effect of phonon-phonon interactions on localization

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J~1/N dependence, implying diffusive transport of energy.Comment: 4 pages, 2 figures, Published versio