Chang‐Yeol Jung

It has been suggested that a Compton camera should be used in single photon emission computed tomography because a conventional gamma camera has low efficiency. It brings about a cone transform, which maps a function onto the set of its surface integrals over cones determined by the detector position, the central axis, and the opening angle of the Compton camera. We provide inversion formulas using complete Compton data for three- and two-dimensional cases. Numerical simulations are presented to

Abstract Our aim in this article is to show how one can improve the numerical solution of singularity perturbed problems involving boundary layers. Incorporating the structures of boundary layers into finite element spaces can improve the accuracy of approximate solutions and result in significant simplifications. In this article we discuss convection‐diffusion equations in the two‐dimensional space with a homogeneous Dirichlet boundary condition and a mixed boundary condition. © 2004 Wiley Peri

A Compton camera has been suggested for use in single photon emission computed tomography because a conventional gamma camera has low efficiency. Here we consider a cone transform brought about by a Compton camera with line detectors. A cone transform takes a given function on the 3-dimensional space and assigns to it the surface integral of the function over cones determined by the 1-dimensional vertex space, the 1-dimensional central axis, and the 1-dimensional opening angle. We generalize thi

Turning points occur in many circumstances in fluid mechanics. When the viscosity is small, very complex phenomena can occur near turning points, which are not yet well understood. A model problem, corresponding to a linear convection-diffusion equation (e.g., suitable linearization of the Navier-Stokes or Bénard convection equations) is considered. Our analysis shows the diversity and complexity of behaviors and boundary or interior layers which already appear for our equations simpler than the

The purpose of this paper is to mathematically investigate the formation of a plasma sheath near the surface of a ball-shaped material immersed in a bulk plasma, and to obtain qualitative information of such a plasma sheath layer. Specifically, we study existence and the quasi-neutral limit behavior of the stationary spherical symmetric solutions for the Euler–Poisson equations in a three-dimensional annular domain. We first propose a suitable condition on the velocity at the sheath edge, referr

In this article, we consider the barotropic quasigeostrophic equation of the ocean in the context of the β-plane approximation and small viscosity (see, e.g., [21, 22]). The aim is to study the behavior of the solutions when the viscosity goes to zero. To avoid the substantial complications due to the corners (see, e.g., [25]) which will be addressed elsewhere, we assume periodicity in one direction (0y). The behavior of the solution in the boundary layers at x = 0, 1 necessitate the introductio

We study the boundary layers and singularities generated by a convection-diffusion equation in a circle with noncompatible data. More precisely, the boundary of the circle has two characteristic points where the boundary conditions and the external data $f$ are not compatible. Very complex singular behaviors are observed, and we analyze them systematically for highly noncompatible data. The problem studied here is a simplified model for problems of major importance in fluid mechanics and thermoh

In this article, we discuss reaction-diffusion problems which produce ordinary boundary layers and elliptic corner layers. Using the classical polynomial Q 1 -finite elements spaces enriched with the so-called boundary layer elements which absorb the singularities due to the boundary and corner layers we are able to attain high numerical accuracies. We essentially obtain ε-uniform approximation errors in a weighted energy norm with significant simplifications in the numerical implementations; he