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Dažu brīvās magnētohidrodinamiskās siltumkonvekcijas problēmu skaitliskie un asimptotiskie atrisinājumi stipros magnētiskos laukos
Get PDFThe Change in Impedance of a Single-Turn Coil due to a Cylindrical Flaw in a Conducting Half-Space
No full textSemi-analytical solution of an eddy current testing problem is obtained in the present paper for the case of a cylindrical flaw in a conducting half-space. The axis of the flaw coincides with the axis of an excitation coil. It is assumed that the vector potential is zero at a sufficiently large distance from the axis of the coil. Method of truncated eigenfunction expansions is used in the paper in order to construct the solution of the Maxwell’s equations. The change in impedance of the coil is calculated for different frequencies of the excitation current. The model described in the paper can be used in practice for quality testing of spot welds by eddy current method
Teaching Linear Algebra, Analytic Geometry and Basic Vector Calculus with Mathematica at Riga Technical University
No full textRakstā stāstīts par jaunu matemātikas mācīšanas moduli, pielietotu Rīgas Tehniskajā Universitātē, pirmā kursa studentiem mācot lineāro algebru, vektoru algebru un analītisko ģeometriju. Modulis satur trīs komponentes: lekcijas, praktiskās nodarbības un laboratorijas darbus. Laboratorijas darbi notiek katru otro nedēļu un satur to pašu vielu, kas tiek aplūkota lekcijās un praktiskajās nodarbībās. Rakstā apkopoti arī studentu aptaujas rezultāti par paketes Mathematica lietošanu matemātikas kursā
The Change in Impedance of a Single-Turn Coil Located above a Moving Medium
No full textThe effect of a moving medium on the change in impedance of a single-turn coil located above the medium is investigated in the present paper. Two cases are considered in detail: (a) a moving half-space and (b) a moving plate. The change in impedance in both cases is expressed in terms of double integrals and is evaluated numerically. Three different norms are used to measure the difference between the change in impedance for fixed and moving medium. Results of numerical calculations are presented
Double Conductor Line Above a Multilayer Medium with Varying Electrical and Magnetic Properties
No full textAnalytical solution of eddy current testing problem is constructed in the present paper. The source of alternating current is a double conductor line consisting of two infinitely long parallel wires. The double conductor line is located above a conducting multilayer medium. It is assumed that the electrical conductivity and magnetic permeability of each conducting layer are exponential functions of the vertical coordinate. The solution is obtained by means of the Fourier sine and cosine integral transforms. The system of ordinary differential equations in the transformed space is solved analytically using modified Bessel functions of complex argument
Temporal Instability of Particle-Laden Curved Shallow Mixing Layers with Non-Constant Friction Coefficient
No full textIn the present paper we analyze the combined effect of small curvature, non-uniform friction and presence of small heavy particles in a carrier fluid on linear stability of shallow mixing layers. The linear stability problem is solved numerically. Marginal stability curves and marginal stability surfaces are constructed for different values of the parameters of the problem. It is shown that for the case of stably curved mixing layers all three parameters (particle loading parameter, small curvature and non-uniform friction) stabilize the flow
The Use of the Package "Mathematica" in Teaching of Mathematics in Riga Technical University
No full textIn Riga Technical University at the Faculty of Computer Science and Information Technology the teaching model was changed over the last three years. Five Latvian universities, including Riga Technical University, have completed the European ESF project “Introduction of the computer mathematical systems into teaching process in universities”. Within the framework of this project and under the support of ESF the licensed software “MATHEMATICA” was obtained and used in teaching of mathematics. In addition, user manuals were developed.
The first year students of the Faculty of Computer Science and Information Technology take the two-semester course “High mathematics” (6 and 5 academic hours per week in each of two semesters, respectively). All mathematical subjects considered at lectures and tutorials are also considered at lab sessions using the package MATHEMATICA. Students learn basic commands of MATHEMATICA so that they are able to solve equations and systems of equations, to perform operations with matrices and vectors, to calculate limits and derivatives, to solve differential equations and so on.
The lab sessions bring innovation into teaching of mathematics and make it more attractive. The results of the students’ survey show that students appreciate this introduction of labs into teaching of mathematics. Moreover, they readily use the package MATHEMATICA not only in the course of “Higher Mathematics”, but also in other subjects related to mathematics
On the Electromagnetic Field of a Coil Located above a Moving Half-Space with Varying Properties
No full textIn the present paper we consider a coil with alternating current located above a conducting half-space. The electrical conductivity and magnetic permeability of the half-space are exponential functions of the vertical coordinate. The half-space is moving with constant velocity in a horizontal direction.The problem is solved analytically by the method of Fourier integral transforms
Linear Stability Analysis of Mixing Layers in Two-Phase Shallow Flows
No full textLinear stability analysis of mixing layers in two-phase shallow flows is performed in the present paper. Hyperbolic tangent base flow velocity profile is used to model shallow mixing layer of two merging streams. the nonlinear system of shallow water equations under the rigid-lid assumption is linearized in the neighborhood of the base flow and is reduced to one linear partial differential equation. The use of the method of normal modes transforms the obtained partial differencial equation to eigenvalue problem for a linear ordinary differential equation
Analytical Solution for the Change in Impedance of a Coil Situated above a Moving Conducting Medium
No full textAnalytical solution of eddy current testing problem is obtained for the case of a moving two-layer medium. The electrical conductivity and magnetic permeability of the upper layer are exponential functions of the vertical coordinate. The solution is found by the method of a double Fourier transform. The change in impedance is expressed in closed form as a double integral. Solution can be generalized for the case of a multilayer medium with arbitrary number of layers
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