Synthesis of an Eight-Link Mechanism for Varieties of Motion Programs

1973 ◽  
Vol 95 (3) ◽  
pp. 744-750 ◽  
Author(s):  
S. Hamid ◽  
A. H. Soni
Keyword(s):  
Numerical Approach ◽  
Matrix Approach ◽  
Synthesis Technique ◽  
Link Mechanism ◽  
The Matrix

Using the matrix approach, synthesis equations are derived for eight types of synthesis problems for an eight-link mechanism having five links in each of its three loops. A numerical approach due to Marquardt is applied to illustrate the synthesis technique for the varieties of motion programs.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

scholarly journals Anisotropic Metamaterials Filled Rectangular Metallic Waveguides Propagation Study and Analysis

2021 ◽  
pp. 34-43
Author(s):  
Nizar Tahri
Keyword(s):  
Control Strategy ◽  
Orthonormal Basis ◽  
Matrix Approach ◽  
Transmission Coefficients ◽  
Anisotropic Metamaterials ◽  
Waveguide Filters ◽  
S Matrix ◽  
The Matrix ◽  
The Galerkin Method ◽  
Transverse Fields

In this paper, we propose a novel generalized S-matrix characterization approach. The goal is to keep track of all observed discontinuities as efficiently as possible. In terms of reflection value, the proposed control strategy is based on transmission coefficients and one-axis rectangular guides. We successfully manipulate metal rectangular waveguide filters with both geometrical and physical discontinuity. Lossless discontinuity is depicted as a periodic structure that contains Metamaterials. The modal development of transverse fields provides the basis for the generalized S-matrix approach. The approach works by breaking down electromagnetic fields for each of the guides that make up the discontinuity on an orthonormal basis. When the Galerkin method is used, the matrix of diffraction of the junction is obtained directly.

scholarly journals The Lynden-Bell bar formation mechanism in simple and realistic galactic models

2020 ◽  
Vol 498 (3) ◽  
pp. 3368-3373
Author(s):  
E V Polyachenko ◽  
I G Shukhman
Keyword(s):  
Perturbation Theory ◽  
Angular Momentum ◽  
Formation Mechanism ◽  
Linear Perturbation ◽  
Matrix Approach ◽  
Precession Rate ◽  
Secular Evolution ◽  
The Matrix ◽  
Linear Perturbation Theory ◽  
Bar Formation

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

scholarly journals Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Matrix Method ◽  
Numerical Approach ◽  
Duffing Equation ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Solution Function ◽  
Numerical Examples ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
The Matrix

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

Energy Spectrum of a Particle Within a Confined Double Well Potential

2006 ◽  
Vol 3 (2) ◽  
pp. 257-262
Author(s):  
J. L. Marin ◽  
G. Campoy ◽  
R. Riera
Keyword(s):  
Energy Levels ◽  
Numerical Approach ◽  
Symmetric Case ◽  
Basis Functions ◽  
Hidden Symmetry ◽  
The Matrix ◽  
Jahn Teller ◽  
Free Case ◽  
Jahn Teller Effect ◽  
Double Well Potential

The energy levels of a particle within a confined double well potential are studied in this work. The spectrum of the particle can be obtained by solving the corresponding Schrödinger equation but, for practical purposes, we have used a numerical approach based in the diagonalization of the matrix related to the Hamiltonian when the wavefunction is represented as an expansion in terms of "a particle-in-a-box" basis functions. The results show that, in the symmetric confining case, the energy levels are degenerate and a regular pairwise association between them is observed, similarly as it occurs in the free case. Moreover, when the confining is asymmetric, the degeneration is partially lifted but the pairwise association of the energy levels becomes irregular. The lifting of the degeneration in the latter case is addressed to the lack of symmetry or distortion of the system, namely, to a sort of Jahn-Teller effect which is common in the energy levels of diatomic molecules, to which a double well potential can be crudely associated. In the symmetric case, the states with nodes at the origin are recognized to be the same as those of the harmonic oscillator confined by two impenetrable walls, in such a way that the system presented in this work would be interpreted as half the solution of the problem of a particle within a confined four well potential. The latter suggests the existence of a sort of hidden symmetry which remains to be studied in a more detailed way.

ERROR PROPAGATION OF THE UNCERTAINTY IN VARIOUS PARAMETERS TO THE UNCERTAINTY IN THE PRIMARY PIXE YIELD AND SECONDARY FLUORESCENCE YIELD

1993 ◽  
Vol 03 (02) ◽  
pp. 145-176 ◽  
Author(s):  
F. MUNNIK ◽  
P.H.A. MUTSAERS ◽  
E. ROKITA ◽  
M.J.A. de VOIGT
Keyword(s):  
Relative Error ◽  
Numerical Approach ◽  
Fluorescence Yield ◽  
Matrix Composition ◽  
X Ray ◽  
Propagation Factor ◽  
Proton Beam Energy ◽  
Primary Yield ◽  
The Matrix ◽  
Secondary Fluorescence

In this article the uncertainty in the PIXE yield due to the uncertainty in various parameters such as the ionization cross section, the stopping power, the X-ray attenuation coefficient, the matrix composition and the proton beam energy, is discussed. This is done for both the primary PIXE and the secondary fluorescence yield. A numerical approach to the propagation of an uncertainty in a parameter to the uncertainty in the yield is given. For this a new parameter, the propagation factor, which is the partial relative error in the yield due to the error in a parameter divided by the relative error in the parameter, is introduced. The dependence of the propagation factor on the X-ray and proton energies and or the matrix composition is investigated for the above named parameters. The physical background of these dependencies is explained; this also makes it possible to obtain a better physical insight in the formulas for the primary yield and the secondary fluorescence yield.

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