Use Of Complex Functions Research Articles

On the use of complex functions in solving non-stationary problems of heat conductivity in a multilayered medium by the Fourier method

The article shows that the difficulties encountered in solving thermal conductivity problems in a multilayer medium by the Fourier analytic method can be overcome by using the apparatus of complex functions. These are the problems of finding the eigenvalues, normalizing the basis functions and finding the expansion coefficients in a Fourier series. The results can be used to solve other non-stationary problems of transport theory.

Stability of stiffened cruciform steel columns under shear and compression by the complex finite strip method

This paper focuses on the stability of steel columns with cruciform section under uniform compressive and shear stresses. The complex finite strip method (CFSM) is employed to solve the buckling of open thin-walled steel columns. CFSM results are validated against other numerical techniques. CFSM has high convergence, accuracy and superior computational efficiency. Due to the use of complex functions, it can also capture shear buckling. The influence of longitudinal stiffeners and section geometry on the buckling behavior of stiffened cruciform sections is investigated. The buckling behavior of cruciform sections is compared against U, I, and T section steel columns.

The Post–Winternitz system on spherical and hyperbolic spaces: A proof of the superintegrability making use of complex functions and a curvature-dependent formalism

Two important advances in integrability have been the recent discovery of the higher-order superintegrability of the Tremblay–Turbiner–Winternitz system (related to the harmonic oscillator) and the Post–Winternitz system (related to the Kepler problem). The properties of the TTW system have been recently studied on the two-dimensional spherical Sκ2 (κ>0) and hyperbolic Hκ2 (κ<0) spaces by making use of a curvature-dependent formalism and the existence of a complex factorization for the higher-order constant of motion. Now in this Letter we prove that a similar technique can also be applied for the study of the PW system.

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.

Testing Ourselves

Those of you who have already downloaded the MATLABbased ComplexGUI virtual tool, made available after the publication of its tutorial, please note that we have just prepared its Web-based version, which is ready for you at DOGUS MODSIM lab [see ibid., vol 53, no 4, August 2011, pp 252-260]. One does not need to have a MATLAB compiler anymore: all you need to do is to connect http:// modsim.dogus.edu.tr and remotely run the package. In the author's tutorial he omitted mentioning a wonderful feature article by Prof. Juan R. Mosig (2003) that is reference herein. If you are interested in the use of complex functions and their mappings in electromagnetics (EM), you should read Prof. Mosig's feature article fi rst, and then play with our ComplexGUI package, either remotely at DOGUS MODSIM lab or locally in your com puter with the downloaded package. Also in this issue, the author introduces a canonical structure, with both funda mental analytical and numerical methods, and supply several MATLAB codes. This is an absolute requirement towards using commercial packages, and discussing their pros and cons [see L. Sevgi, "Complex Electromagnetic Problems and Numerical Simulation Approaches," Piscataway, NJ, IEEE Press/Wiley, 2003].

Spatial prediction of soil properties in temperate mountain regions using support vector regression

Digital soil mapping in mountain areas faces two major limitations: the small number of available observations and the non-linearity of the relations between environmental variables and soil properties. A possible approach to deal with these limitations involves the use of non-parametric models to interpolate soil properties of interest. Among the different approaches currently available, Support Vector Regression (SVR) seems to have several advantages over other techniques. SVR is a set of techniques in which model complexity is limited by the learning algorithm itself, which prevents overfitting. Moreover, the non-linear approximation of SVR is based on a kernel transformation of the data, which avoids the use of complex functions and is computationally feasible; while the resulting projection in feature space is especially suited for sparse datasets. A brief introduction to this methodology, a comparison with other popular methodologies and a framework for the application of this approach to a study site in the Italian Alps is discussed.

Basics of Modelling IEC 61499 Function Blocks with Integer-Valued Data Types

The best way to prove the correct behaviour of a distributed control system in any case is to do a closed-loop verification of the control system connected with the plant. As formal model we will use the known Net Condition/Event Systems (NCES) and extend the rule-based transformation of the IEC 61499 control system from former publications to the use of complex function blocks interfaces and integer-valued data types. To use variables of these data types at the condition of ECTransitions, the connecting rules between the interface and the Execution Control Chart are expanded. The modelling of the plant as well as the analysis of the reachability graph are presented using a real manufacturing system.

Synthesis of spatial coherence

The mutual intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We propose to use the mutual intensity as a carrier of information to avoid speckle noise in coherent illumination systems and to permit the use of complex functions that are prohibited spatially incoherent sources. To do this we require methods for encoding the information as a coherence function. An optical system for synthesizing a beam with a given mutual intensity function is proposed. The optical system permits the synthesis of any desired mutual intensity function. The illumination is supplied by a quasi-monochromatic, spatially incoherent source. Experimental results demonstrate the performance of this system for several cases.

Design of a general-purpose radioisotopic meter

The design of a general-purpose (wide range and independent of the properties of a specific material) radioisotopic instrument capable of high-accuracy measurement of a certain physical parameter would make it possible to dispense with the expensive practice of designing local narrow-range meters. Unfortunately, until recently the design of such an instrument was impossible. This situation has now changed mainly because of the availability of program-controlled facilities (single-board, mini-, and personal computers) for processing measuring, control, and providing auxiliary information; advances in the production of radionuclides with specified properties (mass, size, radiation intensity and energy, etc.); and the design of x-ray tubes with controlled high-voltage sources, development of metrological support especially in the field of equivalent standards and procedures for automatic plotting of transition functions and calibration curves (CCs). The use of program-controlled facilities in RMIs provided a way to overcome many problems associated with increase the accuracy and quality of instruments that were impossible to solve by hardware only because of the required increase of weight, size, power consumption, and associated deterioration of other RIP characteristics. Among others, these problems include the use of complex functions for smoothing experimental data for plotting CCs and transition functions (in laboratory investigations and in operation), more accurate correction of RMI readings depending on the combined effect of influencing factors, varying the measurement time as a function of count rate for a given RMI error level, determination of the effect of the most influencing impurity on the results of measurement of a given parameter with the aid of a spectrometric detector, programmed control of scanners and other auxiliary devices during measurement, determination of scanner accuracy over the entire scanning range, etc. Application of equivalent standards (ESs) in plotting calibration curves and transition functions [i] makes it possible to design an instrument for measuring a certain physical parameter in any specific material in which the measured parameter lies within the instrument range. Equivalent standards are fabricated from inexpensive and readily available materials (e.g., aluminum, dacron, etc., can be used to calibrate thickness meters for flat materials) that possess long-term stability, are not affected by changes of atmospheric parameters (temperature, humidity, pressure), and are resistant to common reagents. Equivalent standards also are used as a reference for correction of instrument readings during measurements. Equivalent standards are useful for the following reasons:

The use of complex valued functions for the solution of three-dimensional elasticity problems

For the treatment of plane elasticity problems the use of complex functions has turned out to be an elegant and effective method. The complex formulation of stresses and displacements resulted from the introduction of a real stress function which has to satisfy the 2-dimensional biharmonic equation. It can be expressed therefore with the aid of complex functions. In this paper the fundamental idea of characterizing the elasticity problem in the case of zero body forces by a biharmonic stress function represented by complex valued functions is extended to 3-dimensional problems. The complex formulas are derived in such a way that the Muskhelishvili formulation for plane strain is included as a special case. As in the plane case, arbitrary complex valued functions can be used to ensure the satisfaction of the governing equations. Within the solution of an analytical example some advantages of the presented method are illustrated.

Derivation of the near-tip stress and displacement fields for a moving crack without using complex functions

This note presents a mathematically simple approach to deriving the equations for the mixed-mode stress and displacement fields near the tip of a moving crack. Coordinate transformations allow the results to be derived without the use of complex functions.

An alternative method for solving the elementary equation for damped oscillation (teaching)

A method is introduced by which the general and complete (i.e. periodic and aperiodic) solutions of the differential equation describing free damped oscillators can be obtained in a mathematically satisfying way, solely on the basis of elementary satisfying way, solely on the basis of elementary knowledge of differential and integral calculus and avoiding the use of complex functions. This direct and brief method has certain didactic advantages: it leads quite naturally to the classification of undamped, underdamped, critically damped and overdamped linear systems; it also yields in a straightforward way the general solution in the case of critical damping.

Die Stufenversetzung im elastisch isotropen Halbraum

The elastic displacement functions of dislocations in limited bodies are of increasing interest with regard to the computation of the electron-microscopic contrast. This paper deals with straight dislocations running parallel to the surface of a semi-infinite region of elastically isotropic material. The linear theory of elasticity is employed. The use of complex functions makes it possible to calculate in closed form the displacement functions of dislocations with various orientations of the BURGERS vector. The symmetries of the displacement functions in infinite and semi-infinite regions are compared. The electron diffraction contrast of dislocations in finite bodies is treated briefly.