Analytical Solution Of Problem Research Articles

Analytic solutions of magnetic field problems in slotless permanent magnet machines

The Grinberg method is used to derive general 2D and 3D analytical solutions of the magnetic field problem in the slotless permanent magnet machines. The machines with the internal and external rotors are presented. The radial and unidirectional magnetisation of the poles is considered. The effect of magnetisation and shapes of the magnet poles on the field distribution is analyzed. The 2D and 3D analytic solutions of the problem are compared. As a result of comparison the effect of the finite axial length of the machine on the flux density in the air gap is evaluated.

Analytical solution of stability problem for two composite half-planes compressed along interfacial cracks

Abstract The plane stability problem for two composite half-planes compressed along the interface, which contains an arbitrary number of cracks, is considered. An exact analytical solution of the problem is found for elastic and elastic–plastic, isotropic and orthotropic, compressible and incompressible half-planes in the common form for finite and small deformations. This solution was developed using complex potentials within the exact approach based on equations of the three-dimensional linearised theory of deformable bodies’ stability. Critical loads are rigorously proved to be independent of the number and disposition of interfacial cracks.

A hybrid boundary element method for shallow water acoustic propagation over an irregular bottom

A hybrid numerical model combining a boundary element method (BEM) and eigenfunction expansions is developed to solve acoustic wave propagation in shallow water. Waves are assumed harmonic and, therefore, the governing equation reduces to a Helmholtz equation. Accurate numerical integration techniques are implemented in the BEM, for calculating singular and quasi-singular integrals. For the latter, an adaptive integration technique is developed and tested for computational domains with very small aspect ratios, representative of shallow water environments. The model is validated by comparing the numerical solution to analytic solutions for problems with simple boundary geometries (e.g. rectangular, step, and sloped domains). Results indicate good agreement between the two solutions. Effects of node resolution, adaptive integrations, and number of modes in radiated fields, on the accuracy of the solution, are assessed. Finally, the model is used to study acoustic transmission over a rectangular bump in the bottom, as a function of frequency and bump geometry. Expected results are obtained below the first cut-off frequency over the bump, i.e. the transmission of energy beyond the bump through evanescent modes. A similar effect is commonly noted in layered media and is known as ‘tunneling’.

未知化合核の構造を微量でいかに速く決定するか マススペクトロメトリーによる薬物代謝物の分子量と構造決定

Mass spectrometry (MS) has been used extensively because of the development of ionization methods followed by their improvement and the solution of analytical problems in inorganic and organic chemistry, biochemistry and medicine. MS has become a powerful and standard method for the identification, structural determination and elucidation of wide variety of compounds, when it is employed in complementary with other physical methods such as nuclear magnetic resonance (NMR), X-ray diffraction and infrared spectroscopy (IR). However, there are still many problems to be solved in MS. In this paper, I proposed the improved methods which may be helpful for solving the problems.

An on-line expert system-based fault-tolerant control system

Fault-tolerant control systems have been studied very actively during recent years. Software and hardware redundancy techniques are the most common methods used to solve the problems. In recent years, expert systems or artificial intelligence have been used successfully in fault diagnosis of the dynamic systems and their suitability for fault-tolerant control problems has also been demonstrated. In this paper an on-tine expert system-based fault-tolerant control system (ESFTC) is considered which allows reconfiguration of the controller in feedback process systems during sensor or actuator failures or misoperudon. It forms an on-line expert system, which consists of an analytical problem solution, a process knowledge base, a knowledge acquisition part and an inference mechanism. The analytical problem solution is based on process coefficient changes, which are symptoms of process faults. A controller is reconfigured based on the symptoms. The process knowledge base comprises analytical knowledge in the form of process performances and heuristic knowledge in the form of fault trees and fault statistics. In the phase of knowledge acquisition the process specific knowledge, like theoretical process models, the abnormal behavior, failures and misoperation, is compiled The inference mechanism performs the fault-tolerant controller, based on the observable symptoms, controller trees, fault probabilities and process history. Case study experiments with the Yeast Fermentation Process Control System show the performance of the fault-tolerant controller.

Interaction of cylindrical explosion waves in a viscoplastic medium with a stationary barrier

Analytical solution of problems involving the interaction of shock waves with barriers have been obtained in several papers [1-7]. Simplified model representations if soil media have been used, permitting certain wave parameters to be obtained in analytical form. Numerical solutions have been published [8-11] for problems of the interaction of shock waves with a stationary barrier situated in an elastic, viscoelatic medium, in a liquid containing gas bubbles, and in air. The source of the explosion has been ignored in all these papers. In the present article we investigate a confined underground detonation of a cylindrical explosive charge in damp, but not saturated, soil bounded by a stationary barrier, whose symmetry axis coincides with that of the charge.

Analytical Solutions for Problems with Elliptical Hole Enforced by Elastic Ring and Their Numerical Examples. 1st Report. Cases of Isotropic Elasticity under Out-of-Plane Loadings.

The analysis of a two-dimensional elastic medium containing an elliptical elastic ring with free or fixed inner boundary under uniform antiplane stress at infinity is performed. This analysis is based on the complex variable method using a conformal mapping technique, and assumes the sliding boundary condition between the elastic ring and the matrix. Using this solution, we show the effects of thickness and elastic properties of the elastic ring on distributions of stress and displacement.

Analytical Solutions for Harmonic Wave Propagation in Poroelastic Media

This paper presents several analytical solutions for problems of harmonic wave propagation in a poroelastic medium. The pressure‐solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. Then these equations are solved for several particular situations. Closed‐form analytical solutions are obtained for several basic problems: independent plane harmonic waves; radiation from a harmonically oscillating plane wall; radiation from a pulsating sphere; and the interior eigenvalue problem for a sphere, for the cases of both a rigid surface and a traction‐free surface. Finally, a series solution is obtained for the case of a plane wave impinging on a spherical inhomogeneity. This inhomogeneity is composed of poroelastic material having different properties from those of the infinite poroelastic medium in which it is embedded, and the incident wave may be composed of any linear combination of Biot “fast” and “slow”...

Improvement of the method of canonical elements for modeling transfer processes in systems with curvilinear boundaries

The author discusses some methodological aspects of generalization and improvement of the accuracy of the method of canonical elements. Data of numerical experiments are compared to well-known exact analytical solutions of problems of heat transfer in regions with curvilinear boundaries.

Analytical solutions for axisymmetric radiation and scattering from a spherical shell with internal circular plates

Analytical solutions for problems of radiation and scattering from a spherical thin shell containing one or more circular thin plates are presented. The geometry of both the structure and the loading is axisymmetric. These solutions can be used to evaluate computational methods for radiation and scattering from finite three-dimensional structures having internal complexity. In this case the internal complexity is associated with the internal plates, which are represented in terms of their axisymmetric modes of vibration. The motion of the spherical shell is represented in terms of spherical harmonics. The analytical solutions are verified with numerical results obtained using an adaptive multi-level substructuring approach, which obtains an optimally reduced finite element model of the structure, which is coupled with a boundary element model of the acoustic fluid. [Work supported by ONR.]

Solution of the shallow water equations by least squares collocation

A method of solution of the shallow water equations in their primitive form that yield solutions free of numerical oscillations, is presented. The method is based on the least squares collocation concept. The focus is on the accuracy of the solution procedure. Comparison of the numerical solution with analytic solutions for problems of irregular geometry are presented. Key features are the ability of the method to solve the equations in an irregular domain with a completely orthogonal computational mesh and the inherent nondissipative noise control of the temporal and spatial approximations.

Analytical solution of convective diffusion problem with variable boundary condition

We consider the problem of convective diffusion of water-soluble substances for industrial and household wastewater seepage. The solution of this problem reduces to solving a boundary-value problem of mathematical physics described by a parabolic partial differential equation of second order with variable boundary conditions. An analytical solution of the problem is obtained in the form of a functional series.

Process Fault Diagnosis Based on Process Model Knowledge: Part II—Case Study Experiments

A computer assisted fault diagnosis system (CAFD) is considered which allows the early detection and localization of process faults during normal operation or on request. It is based on an on-line engineering expert system and consists of an analytical problem solution, a process knowledge base, a knowledge acquisition component and an inference mechanism. The analytic problem solution uses a process parameter estimation, and the detection of process coefficient changes, which are symptoms of process faults. The process knowledge base is comprised of analytical knowledge in the form of process models and heuristic knowledge in the form of fault trees and fault statistics. In the phase of knowledge acquisition the process specific knowledge like theoretical process models, the normal behavior and fault trees is compiled. The inference mechanism performs the fault diagnosis, based on the observed symptoms, the fault trees, fault probabilities and the process history. This is described in Part I. In Part II, case study experiments with a d.c. motor, centrifugal pump, a heat exchanger and an industrial robot show practical results of the model based fault diagnosis.

Wave propagation and vibration of elastic rods with interfacial frictional slip

Wave propagation and vibration of elastic rods interacting with their environment according to the Coulomb dry friction law, are studied. Exact solutions of the nonlinear problems of impact of semi-infinite or finite rods, with constant stress and velocity or by a rigid body are obtained. Problems of smooth loading and unloading of a semi-infinite rod are solved as well. A method of exact analytical solution of problems of vibration for steplike loading is developed. The cases of suddenly applied stress which is maintained constant afterwards or changes sign steplike with the period of free vibration, are studied. Continuously distributed and localized friction are considered. It is shown that extension of a zone of disturbances and dissipation in a system with friction, stricly depends on the history of loading.

Analytical Solution of Magnetic Declination Problem

The magnetic declination problem involves the determination of present magnetic bearings (or azimuths) of township surveys for the purpose of retracement, based on original survey data. This paper presents an analytical solution of a problem which has been solved only graphically. The analytical solution, which takes the form of simple formulas, gives the present magnetic azimuth of a line in terms of the original magnetic bearing, original and present declinations, and integer variables designating the directions of bearing and declinations. The formulas can be applied without the need for drawing sketches and are amenable to computation by calculators or computers. A calculator program for performing the computations is included. The analytical solution should save considerable time in preparing the retracement surveys, especially when they involve a large number of traverse lines.

An approximate analytic solution of the spectral inverse problem

An important problem of nonrelativistic quantum theory is: Given a bound-state energy spectrum, determine the space dependence of a potential function that will produce that spectrum. This is sometimes called the ‘‘spectral inverse’’ problem. Here, by use of the first-order WKB energy quantization condition, an approximate analytic solution of this problem is given for the case of one-dimensional symmetric oscillators and for a class of radial oscillators. This is done by reformulating the WKB quantization condition as an Abel integral equation that relates the quantum number to the potential’s space dependence. The resultant integral equation can be solved exactly. The harmonic oscillator and the hydrogen atom problems are used to demonstrate the method. The solution for the case of one-dimensional asymmetric oscillators is also briefly discussed and the Morse oscillator is used as an example. Finally, the history of the spectral inverse problem is reviewed and the conditions necessary for its exact solution are discussed. In particular, the conditions required for the inversion process to be unique are considered.

A finite difference scheme with arbitrary mesh systems for solving high-order partial differential equations

A finite difference technique for arbitrary irregular mesh systems is developed for numerical solutions of high-order boundary value problems. A successive differencing scheme is used to formulate the higher-order differencing equations. The details of the computational procedure for plate bending problems which are governed by a biharmonic equation are presented. In order to demonstrate the validity of the formulation procedure, numerical results obtained from the present technique were first compared with the analytical solutions for problems having regular and curved boundaries. For the regular boundary problem, the present results were also compared with that from the conventional finite difference method which is only suitable for treating regular meshes. Computations were then conducted to evaluate the accuracy of the solutions with different mesh arrangements. These studies have shown that, if well implemented, this method not only maintains the inherent simplicity of the finite difference method, but also puts it into a more programmable and flexible formulation so that the geometric generality, such as that in the finite element method, can be achieved.

Numerical analysis of a generalized plane ‘elastica’ with non‐linear material behaviour

AbstractThis article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non‐linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton‐type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non‐linearities.

Approximate analytical solution of problem of formation of a relativistic electron beam in a coaxial diode for different isolating magnetic fields

Approximate analytical solution of problem of formation of a relativistic electron beam in a coaxial diode for different isolating magnetic fields

The Quest for Sensitivity, Specificity, and Speed in Chemical Analysis

Abstract One of the fascinating features of analytical chemistry is the continuous challenge it provides the practitioners of this profession. As we are confronted with our current analytical problems and anticipate even more thought provoking and complex problems in the future it is reassuring to pause and examine the progress that has been made and is being made in the development of sensitive, specific and rapid methods of chemical analysis. Relevant to solving complex analytical problems and in handling samples of unusual complexity I would like to quote a sentence from one of Professor Laitinen's recent editorials in ANALYTICAL CHEMISTRY: “It boils down to the fact that complex mixtures will become increasingly important in the future, but no matter how sophisticated the instrumentation may become, the analytical chemist will continue to be the most important component in the solution of analytical problems”1. A review of the historical developments in analytical chemistry does indicate the importance of individuals and their unique resourcefulness, creativity and rational thinking in responding to practical problems and their own scientific curiosity.