403,063 research outputs found
A New Approach to Axial Vector Model Calculations II
We further develop the new approach, proposed in part I (hep-th/9807072), to
computing the heat kernel associated with a Fermion coupled to vector and axial
vector fields. We first use the path integral representation obtained for the
heat kernel trace in a vector-axialvector background to derive a Bern-Kosower
type master formula for the one-loop amplitude with vectors and
axialvectors, valid in any even spacetime dimension. For the massless case we
then generalize this approach to the full off-diagonal heat kernel. In the D=4
case the SO(4) structure of the theory can be broken down to by use of the 't Hooft symbols. Various techniques for explicitly
evaluating the spin part of the path integral are developed and compared. We
also extend the method to external fermions, and to the inclusion of isospin.
On the field theory side, we obtain an extension of the second order formalism
for fermion QED to an abelian vector-axialvector theory.Comment: Sequel to hep-th/9807072, references added, some clarifications and
corrections, 29 pages, RevTex, 8 diagrams using epsfig.st
Mathematical Tools for Calculation of the Effective Action in Quantum Gravity
We review the status of covariant methods in quantum field theory and quantum
gravity, in particular, some recent progress in the calculation of the
effective action via the heat kernel method. We study the heat kernel
associated with an elliptic second-order partial differential operator of
Laplace type acting on smooth sections of a vector bundle over a Riemannian
manifold without boundary. We develop a manifestly covariant method for
computation of the heat kernel asymptotic expansion as well as new algebraic
methods for calculation of the heat kernel for covariantly constant background,
in particular, on homogeneous bundles over symmetric spaces, which enables one
to compute the low-energy non-perturbative effective action.Comment: 71 pages, 2 figures, submitted for publication in the Springer book
(in preparation) "Quantum Gravity", edited by B. Booss-Bavnbek, G. Esposito
and M. Lesc
Weak convergence results for inhomogeneous rotating fluid equations
We consider the equations governing incompressible, viscous fluids in three
space dimensions, rotating around an inhomogeneous vector B(x): this is a
generalization of the usual rotating fluid model (where B is constant). We
prove the weak convergence of Leray--type solutions towards a vector field
which satisfies the usual 2D Navier--Stokes equation in the regions of space
where B is constant, with Dirichlet boundary conditions, and a heat--type
equation elsewhere. The method of proof uses weak compactness arguments
Effect of Distributed Superficial-Velocity in Deep-Bed Grain Drying
This paper deals with influence of velocity field distribution to heat and mass transfer process in deep bed grain dryers. Two-dimensional (2D) models of deep-bed grain dryers were built by considering simultaneously momentum, heat, and mass transfer in the drying air phase. The Navier-Stokes momentum equations are applied to simulate pressure drop and velocity field of the drying airflow. Effect of velocity distribution to the heat and mass transfer coefficient distribution were simulated along the height of grains bed. The dynamic equations are solved numerically by using finite difference method by utilization of alternating direction implicit method, while the momentum equations are solved numerically by utilization of SIMPLE algorithm. The simulation results showed that velocity distribution along the grains bed - 5 cm of bed height - did not so influenced to the heat and mass transfer coefficient. Further, the vector plot of drying air superficial velocity field and contour of pressure distribution along deep bed of grain was simulated
Exact heat kernel on a hypersphere and its applications in kernel SVM
Many contemporary statistical learning methods assume a Euclidean feature
space. This paper presents a method for defining similarity based on
hyperspherical geometry and shows that it often improves the performance of
support vector machine compared to other competing similarity measures.
Specifically, the idea of using heat diffusion on a hypersphere to measure
similarity has been previously proposed, demonstrating promising results based
on a heuristic heat kernel obtained from the zeroth order parametrix expansion;
however, how well this heuristic kernel agrees with the exact hyperspherical
heat kernel remains unknown. This paper presents a higher order parametrix
expansion of the heat kernel on a unit hypersphere and discusses several
problems associated with this expansion method. We then compare the heuristic
kernel with an exact form of the heat kernel expressed in terms of a uniformly
and absolutely convergent series in high-dimensional angular momentum
eigenmodes. Being a natural measure of similarity between sample points
dwelling on a hypersphere, the exact kernel often shows superior performance in
kernel SVM classifications applied to text mining, tumor somatic mutation
imputation, and stock market analysis
Solving magnetostatic field problems with NASTRAN
Determining the three-dimensional magnetostatic field in current-induced situations has usually involved vector potentials, which can lead to excessive computational times. How such magnetic fields may be determined using scalar potentials is reviewed. It is shown how the heat transfer capability of NASTRAN level 17 was modified to take advantage of the new method
Covariant techniques for computation of the heat kernel
The heat kernel associated with an elliptic second-order partial differential
operator of Laplace type acting on smooth sections of a vector bundle over a
Riemannian manifold, is studied. A general manifestly covariant method for
computation of the coefficients of the heat kernel asymptotic expansion is
developed. The technique enables one to compute explicitly the diagonal values
of the heat kernel coefficients, so called Hadamard-Minackshisundaram-De
Witt-Seeley coefficients, as well as their derivatives. The elaborated
technique is applicable for a manifold of arbitrary dimension and for a generic
Riemannian metric of arbitrary signature. It is very algorithmic, and well
suited to automated computation. The fourth heat kernel coefficient is computed
explicitly for the first time. The general structure of the heat kernel
coefficients is investigated in detail. On the one hand, the leading derivative
terms in all heat kernel coefficients are computed. On the other hand, the
generating functions in closed covariant form for the covariantly constant
terms and some low-derivative terms in the heat kernel coefficients are
constructed by means of purely algebraic methods. This gives, in particular,
the whole sequence of heat kernel coefficients for an arbitrary locally
symmetric space.Comment: 31 pages, LaTeX, no figures, Invited Lecture at the University of
Iowa, Iowa City, April, 199
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