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Investigation of Microstructure and Creep Properties of Sn-xSb Solder Alloys up to Peritectic Composition
Get PDFParticle strengthening was studied in Sn-xSb (x=0.5–3.0 wt. %). Tensile deformation behavior of Sn-2.5 wt.% Sb is investigated at temperature ranging (298 - 343K) and under different constant loads ranging (5.1 - 14.0 MPa). The microstructure characteristics of the tested alloys have been obtained using x-ray diffraction. Morphological studies using optical microscope have been investigated to obtain correlation between the microstructure and mechanical behavior of the alloys. The improved strength is attributed to the uniform distribution of the SnSb intermetallic compound (IMC) inside b-Sn matrix. Based on the obtained stress exponent (n) and activation energy (Q), it is proposed that the dominant deformation mechanism is dislocation climb over the whole temperature range used
Application of the Magnus and Fer expansions to a perturbative study of the time dependent Jaynes Cummings Model
Get PDFWe apply the Magnus and Fer perturbation methods to Jaynes Cummings Model (JCM) with linear time dependence and show that the perturbation methods yield results which are appreciably close to the results obtained by Wei-Norman method, leading to exact solution when the Hamiltonian under consideration is an element of su(2), thus making the perturbation methods important for Hamiltonians for which a method of exact solution is not available
Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method
Get PDFIn this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results areshown to illustrate the efficiency and accuracy of the approximate solution
Solution of Abel Integral Equation Using Differential Transform Method
Get PDFThe application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced here. Also illustrative examples with exact solutions are considered to show the validity and applicability of the proposed method. Abel integral equation, Differential transform method, Fractional differential transform method
Further Acceleration of the Simpson Method for Solving Nonlinear Equations
Get PDFThere are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four. Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method. We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method
Regional Boundary Gradient Detectability in Distributed Parameter Systems
Get PDFThe aim of this paper is study and explore the notion of the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space, we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems
Supplement to the Collatz Conjecture
Get PDFFor any natural number was created the supplement sequence, that is convergent together with the original sequence. The parameter - index was defined, that is the same tor both sequences. This new method provides the following results:
All natural numbers were distributed into different classes according to the corresponding indexes;
The analytic formulas ( not by computer performed routine calculations) were produced, the formulas for groups of consecutive natural numbers of different lengths, having the same index;
The new algorithm to find index for any natural number was constructed and proved
Behavior of Cosmic Rays and Propellant-Free Microwave Thruster Can Support the Hypothesis of Crystalline Vacuum
Get PDFThe paper suggests an explanation of the efficiency of the EmDrive device based on the hypothesis of a crystalline vacuum, previously successfully used to explain the cutoff of the cosmic-ray spectrum. The hypothesis of crystalline vacuum enables to transform part of momentum directly to vacuum crystalline lattice giving rise to reaction force which allow to ensure the fulfillment of the momentum conservation law during EmDrive functioning. Therefore crystalline vacuum plays the role of a supporting medium for all wave vectors of electromagnetic oscillations in a conical resonator, which causes the appearance of forces and momentums of rotation, the optimization of which can open up a tempting prospect for creating of unique aircraft
Can The Spectra Of Hermitian Operator Be Invariant Under x ?? p ? :Case Study :1D General Oscillator
Get PDFWe address an intriguing question on spectral invariance in quantum mechanics on exchange of co-ordinateand momentum X<-- --> p considering general oscillator as an example
ZnS/Cu2ZnSnS4/CdTe/In Thin Film Structure for Solar Cells
Get PDFA solar cell with glass/ITO/ZnS/Cu2ZnSnS4/CdTe/In structure has been fabricated using all-electrodeposited ZnS, Cu2ZnSnS4 and CdTe thin films. The three semiconductor layers were electrodeposited using a two-electrode system for process simplification. The incorporation of a wide bandgap amorphous ZnS as a buffer/window layer to form ITO/ZnS/Cu2ZnSnS4/CdTe/In solar cell resulted in the formation of this 3-layer device structure. This has yielded corresponding improvement in all the solar cell parameters resulting in a conversion efficiency >12% under AM1.5 illumination conditions at room temperature. These results demonstrate the advantages of the multi-layer device architecture over the conventional 2-layer structure