This paper deals with the design of perfectly matched layers (PMLs) for transient acoustic wave propagation in generally-shaped convex truncated domains. After reviewing key elements to derive PML equations for such domains, we present two time-dependent formulations for the pressure-velocity system. These formulations are obtained by using a complex coordinate stretching of the time-harmonic v...

A new finite plane wave series expansion for spherical wave functions of the first kind is presented in this paper. The formulation converts the spherical wave function described in the spherical coordinate system into a series of plane wave functions represented in the Cartesian coordinate system. The series expansion will be very useful in modal analysis of three dimensional guided wave struc...

By embedding images as surfaces in a high dimensional coordinate space defined by each pixel’s Cartesian coordinates and color values, we directly define and employ cotangent-based, discrete differentialgeometry operators. These operators define discrete energies useful for image segmentation and colorization.

It is convenient to think of an object's location as a point within a Cartesian framework; the x axis corresponds to right and left, the y axis to up and down, and the z axis to forward or backward. When an observer is looking straight ahead, binocular disparities provide information about distance along the z axis from the fixation plane. In this coordinate system, changes in disparity are tre...

A distinction is made between data description and representational space in the context of circumplex models. The representational space provides the language in which data are described, and different languages have their advantages and disadvantages. For instance, points in a two-dimensional Cartesian grid can form a circle. Such a circular pattern corresponds to a description of the data pa...

The coordinate system in which humans learn novel motor skills is controversial. The representation of sensorimotor skills has been extensively studied by examining generalization after learning perturbations specifically designed to be ambiguous as to their coordinate system. Recent studies have found that learning is not represented in any simple coordinate system and can potentially be accou...

The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domai...

The article reveals important territorial aspects of sustainable development infrastructure enterprises from information and administrative component on the example local territories (communities) Donetsk region in Ukraine. A point-rating evaluation dimension for communities carry out parameters, which focus a set statistical data context economic, social environmental components. authors built...

This paper demonstrates that sonar images correlate badly because target geometry and image fringes correlate in different coordinate systems. It is shown that if the receiver is a line array, all point objects have the same image in a coordinate system with axes of range and the sine of target bearing (the (r, s) coordinate system). Results from an ocean experiment are presented. The ocean exp...