Coordinate Domain Research Articles

The Gaussian beam expansion applied to Fresnel field integrals

A general result of the Gaussian angular-spectrum expansion is presented for computing the Fresnel field integral. The reciprocity relation of the Gaussian expansion parameters in both coordinate and angular-spectrum domains is obtained. Some examples are provided that demonstrate the usefulness of this relation.

INCREASING OF ACCURACY FOR ENGINEERING CALCULATION OF HEAT TRANSFER PROBLEMS IN TWO LAYER MEDIA

In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differential equations is taken. Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equations in two layered domain of Cartesian, cylindrical (with axial symmetry) and spherical coordinates (with radial symmetry). In a stationary case the exact finite difference scheme is obtained. Šiame straipsnyje yra nagrinejami paprasti dvisluoksnes srities šilumos laidumo problemos modeliavimo algoritmai, keičiant diferencialines lygtis dalinemis išvestinemis i paprastas diferencialines lygtis. Parodoma, kad didesnio tikslumo pasiekimui, vietoje pirmos eiles paprastu diferencialiniu lygčiu pradinio uždavinio nagrinejamos antros eiles diferencialines lygtys. Ši proced ura leidžia gauti paprasta inžinerini dvisluoksies srities šilumos laidumo lygties sprendini stačiakampeje, cilindrineje (su ašiu simetrija) ir sferineje (su spinduline simetrija) koordinačiu sistemoje. Tiksli baigtiniu skirtumu schema buvo sudaryta stacionariam atvejui.

DSC‐Ritz method for high‐mode frequency analysis of thick shallow shells

AbstractThis paper addresses a challenging problem in computational mechanics—the analysis of thick shallow shells vibrating at high modes. Existing methods encounter significant difficulties for such a problem due to numerical instability. A new numerical approach, DSC‐Ritz method, is developed by taking the advantages of both the discrete singular convolution (DSC) wavelet kernels of the Dirichlet type and the Ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions. As wavelets are localized in both frequency and co‐ordinate domains, they give rise to numerical schemes with optimal accurate, stability and flexibility. Numerical examples are considered for Mindlin plates and shells with various edge supports. Benchmark solutions are obtained and analyzed in detail. Experimental results validate the convergence, stability, accuracy and reliability of the proposed approach. In particular, with a reasonable number of grid points, the new DSC‐Ritz method is capable of producing highly accurate numerical results for high‐mode vibration frequencies, which are hitherto unavailable to engineers. Moreover, the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher‐order vibration modes of a Mindlin plate and those calculated via an analytical relationship linking Kirchhoff and Mindlin plates. Copyright © 2004 John Wiley & Sons, Ltd.

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes

Convex underestimators of nonconvex functions, frequently used in deterministic global optimization algorithms, strongly influence their rate of convergence and computational efficiency. A good convex underestimator is as tight as possible and introduces a minimal number of new variables and constraints. Multilinear monomials over a coordinate aligned hyper-rectangular domain are known to have polyhedral convex envelopes which may be represented by a finite number of facet inducing inequalities. This paper describes explicit expressions defining the facets of the convex and concave envelopes of trilinear monomials over a box domain with bounds of opposite signs for at least one variable. It is shown that the previously used approximations based on the recursive use of the bilinear construction rarely yield the convex envelope itself.

The method of modifications for linear network analysis in the basis of the Walsh functions

The paper shows advantages of realization of algorithms for linear network analysis in the domain of natural coordinates and of the Walsh transforms with the use of the method of modifications.

Two types of coordination in clause combining

This paper argues for a constructional approach to the analysis of coordination in English, with comparative evidence from a number of other Germanic languages. The analysis of coordination proposed here is functionally based on the notion of illocutionary force and formally reflected in the behavior of the basic clause types (declarative–imperative–interrogative) in the clauses that make up the coordinate construction. On the one hand, it is argued that this approach can help to explain why traditional syntactic criteria like clause order and word order can be used to distinguish coordinate constructions from subordinate ones, and that it can easily handle cases where one conjunction allows both coordinate and subordinate construal. On the other hand, it is argued that this approach also allows one to make a subdivision within the coordinate category depending on the presence or absence of restrictions in illocution type for the second member of the coordinate construction, and that this subdivision allows for a principled account of other features which subdivide the coordinate domain, like subject ellipsis and use in conjoining non-clausal categories.

Material property estimation in thin plates using focused, synthetic-aperture acoustic beams.

The method developed here exploits the wide angular range of focused acoustic probes and the large synthetic aperture of scanned transducers to permit a rapid and reliable estimation of material properties in thin plates. It is found in several tests with various materials that estimates of elastic behavior using this method agree with contact measurements to within less than 5%. The method utilizes transmission (or reflection) coefficient reconstruction for an infinite thin plate, across a wide range of frequency and wave number, from which elastic property estimates are made. Data collected over a large synthetic acoustic aperture are processed with temporal and spatial Fourier transforms applied to change the acquired data from the coordinate and time domains to the wave number and frequency domains. Extrinsic real-beam effects on the data are accounted for with a complex transducer point analysis. Transmission measurements yield reconstructed data extending to the mode cutoffs, permitting easy and nearly unambiguous estimation of a subset of the elastic stiffnesses. For anisotropic plates, elastic stiffnesses are estimated with an inversion procedure that uses only limited data carefully selected from different portions of the measured scattering coefficient. Estimates are made by reconstructing in a stepwise fashion, based on sensitivity studies, where only one stiffness is estimated from the data at any one time, restricting the optimization to a robust one-dimensional search.

Inductive Limits of Area-Preserving Diffeomorphism Groups

A compact oriented surface with a given area form is considered. For each coordinate domain, we take the group of diffeomorphisms supported in this domain and preserving the area form. Finally, consider codimension 1 normal subgroups in these groups. For each pair of coordinate domains one of which contains the closure of the other, there is an obvious inclusion of the corresponding groups. We describe the inductive limits (amalgams) of these two families of groups.

A General Criterion of Integer Ambiguity Search

A general criterion for integer ambiguity searching is derived in this paper. The criterion takes into account not only the residuals caused by ambiguity parameter changing, but also the residuals caused by coordinates changing through ambiguity fixing. The search can be carried out in a coordinate domain, in an ambiguity domain or in both domains. The three searching scenarios are theoretically equivalent. The optimality and uniqueness properties of the proposed criterion are also discussed. A numerical explanation of the general criterion is outlined. The theoretical relationship between the general criterion and the commonly used least squares ambiguity search (LSAS) criterion is derived in an equivalent case in detail. It shows that the LSAS criterion is just one of the terms of the equivalent criterion. Numerical examples are given to illustrate the behaviour of the two components of the equivalent criterion.

3-D traveltime computation using the fast marching method

We present a fast algorithm for solving the eikonal equation in three dimensions, based on the fast marching method. The algorithm is of the order O(N log N), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain. The method is unconditionally stable and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity. In addition, the method resolves any overturning propagation wavefronts. We begin with the mathematical foundation for solving the eikonal equation using the fast marching method and follow with the numerical details. We then show examples of traveltime propagation through the SEG/EAGE salt model using point‐source and plane‐wave initial conditions and analyze the error in constant velocity media. The algorithm allows for any shape of the initial wavefront. While a point source is the most commonly used initial condition, initial plane waves can be used for controlled illumination or for downward continuation of the traveltime field from one depth to another or from a topographic depth surface to another. The algorithm presented here is designed for computing first‐arrival traveltimes. Nonetheless, since it exploits the fast marching method for solving the eikonal equation, we believe it is the fastest of all possible consistent schemes to compute first arrivals.

Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning

An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase observations is suggested in this paper. The algorithm combines the search procedures in the coordinate domain, the observation domain and the estimated ambiguity domain (and therefore benefits from the integration of their most positive elements). A three-step procedure is then proposed to enhance the reliability of the ambiguity resolution by: (1) improving the stochastic model for the double-differenced functional model in real time; (2) refining the criteria which distinguish the integer ambiguity set that generates the minimum quadratic form of residuals from that corresponding to the second minimum one; and (3) developing a fault detection and adaptation procedure. Three test scenarios were considered, one static baseline (11.3 km) and two kinematic experiments (baseline lengths from 5.2 to 13.7 km). These showed that the mean computation time for one epoch is less than 0.1 s, and that the success rate reaches 98.4% (compared to just 68.4% using standard ratio tests).

A class of exact and higher-order surface boundary conditions for layered structures

A class of exact and higher-order surface impedance boundary conditions (HOIBCs) is derived. Initially, exact impedance boundary conditions (IBCs) are derived first in the spectral and then in the coordinate domain. It is shown that in the coordinate domain they are expressed by a dyadic operator acting on the convolution product between the scalar Green's function, corresponding to the considered structure, and the tangential magnetic field. Next, it is demonstrated that the higher-order impedance boundary conditions in the spatial domain correspond to an appropriate expansion of the mentioned convolution product in the space domain. Finally, the accuracy of the HOIBCs is estimated by comparing the exact solution with that obtained through the HOIBCs for some typical canonical problems. The corresponding error curves presented refer to the worst error situation for each one of the chosen cases.

Method of temporary coordinate domains for moving boundary value problems (semiconductor processing simulation)

An approach to the numerical solution of moving boundary value problems that is based on the idea of temporary coordinate domains is presented. The method generalizes the concept of coordinate transformations in two respects. First, the physical structure itself at some moment is chosen as the coordinate domain. Thus, the coordinate domain is no longer determined a priori and without regard to the actual physical structure. Second, the coordinate domain is adapted to the geometrical evolution of the structure by redefining it at appropriate time points. In this way the geometrical restrictions of conventional coordinate transformation methods are eliminated. The method is used to simulate thermal processing. It is assumed that the geometry and the material flow are handled by a separate module for simulations of oxide growth. The redistribution of dopants, including segregation at material interfaces, is modeled by diffusion equations and interface conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi-analytical finite strip method

A semi-analytical finite strip method mapping arbitrarily shaped plates into a natural co-ordinate plane using Serendipity functions is presented. The product of normalized beam characteristic orthogonal polynomials and Hermitian polynomials form the displacement function for the strip in the natural co-ordinate domain. Flexural free vibration analysis of various shaped plates is performed. Results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested, the flexural frequencies obtained are in excellent agreement with those found in the literature.

A numerical method for the solution of three-dimensional incompressible viscous flow using the boundary-fitted curvilinear coordinate transformation and domain decomposition technique.

A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdmains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90°elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor.

Protein kinase C in the regulation of smooth muscle contraction

The cellular and molecular mechanisms underlying smooth muscle contraction are reviewed in the light of recent studies of smooth muscle ultrastructure and of the role of polyphosphoinositide turnover and protein kinase C function in smooth muscle contraction. A new model of smooth muscle contraction is proposed that differs radically from accepted views, particularly the latch bridge hypothesis, in terms of both Ca2+ messenger function and the molecular events underlying this process. A coordinate fibrillar domain model of contraction is proposed in which the initial and sustained phases of contraction are mediated by different cellular and molecular events. The initial phase of response is mediated by a rise in [Ca2+]c and the resulting calmodulin-dependent activation of both myosin light chain kinase and the dissociation of caldesmon from the actin-caldesmon-tropomyosin-myosin fibrillar domain. These events lead to an interaction between actin and the phosphorylated light chains of myosin just as in previous models. However, this initial phase is followed by a sustained phase in which a rise in [Ca2+]sm stimulates the plasma membrane-associated, Ca2+-sensitive form of protein kinase C that results in the phosphorylation of both structural and regulatory components of the filamin-actin-desmin fibrillar domain. These events underlie the tonic phase of contraction.

Analytic extension of the Schwarzschild-de Sitter metric

In this paper, we derive co-ordinates that are regular, respectively, in the neighbourhood of the two horizons which exist in the so-called Schwarzschild-de Sitter solution known in general relativity, and construct a manifold that is the analytic extension of the manifold being the domain of classical Schwarzschild-de Sitter coordinates.

Mathematical analysis of fluid flow in porous media with general anisotropy

The fundamental solution to the unsteady state fluid flow problem in anisotropic (r, θ, Z) coordinate domain was developed. The governing equation was solved using the expedience of an appropriate coordinate transformation with the Webber integral transform. The general boundary condition was principally considered, but the solution could be extended to cover the Neuman boundary condition case without difficulty. Also, solution to the isotropic problem could be deduced as a limiting case of the derived solution.

On control of time for reaching a domain by random motion

The problem is examined of maximizing the time for reaching the boundaries of the domain of a dynamic system moving under constant random perturbations of Gaussian white noise type and under pulsed action simulated by a Poisson process. Certain properties of the maximum time and of the optimal control are studied. The controlled motion of a rigid body acted on by random perturbing moments relative to the center of mass is examined as an example. The presence of random perturbations causes the kinetic moment of the rigid body to take arbitrarily large values. The purpose of controlling the rigid body's motion is to maximize the time for the kinetic moment to achieve some limit admissible value. The problem of retaining the system within a specified domain of phase coordinates has been taken up in a number of papers. In /1/ it was shown that certain questions on the motion control of an artificial satellite on synchronous orbits reduce to the maximization of the probability of retaining the system within a specified domain during a prescribed time interval. Another example of similar kind is connected with the working of water storage basins mentioned in /2/.

Reactive domains of energy hypersurfaces and the stability of minimum energy reaction paths

Special properties of the Riemannian metric for energy hypersurfaces, defined within the framework of the Born-Oppenheimer approximation, are utilized in devising a partitioning scheme for domains of nuclear coordinates. The chemically important coordinate domains are distinguished from domains of lesser importance by their curvature properties. Conditions are derived for the stability of minimum energy reaction paths, and the effects of instability regions are investigated. Instability domains along minimum energy paths may allow small vibrational perturbations to alter the outcome of the chemical reaction.