The Resultant of a Linear Set

1944 ◽  
Vol 66 (1) ◽  
pp. 59 ◽  
Author(s):  
Ernst Snapper
Keyword(s):  
Linear Set

scholarly journals Single Step 2-Port Device De-Embedding Algorithm for Fixture-DUT-Fixture Network Assembly

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1275
Author(s):  
Simone Scafati ◽  
Enza Pellegrino ◽  
Francesco de Paulis ◽  
Carlo Olivieri ◽  
James Drewniak ◽  
...  
Keyword(s):  
Standard Technique ◽  
Single Step ◽  
Scattering Parameters ◽  
Linear Set ◽  
S Parameter ◽  
Parameter Conversion ◽  
Before And After ◽  
One Step ◽  
Typical Measurement

The de-embedding of measurement fixtures is relevant for an accurate experimental characterization of radio frequency and digital electronic devices. The standard technique consists in removing the effects of the measurement fixtures by the calculation of the transfer scattering parameters (T-parameters) from the available measured (or simulated) global scattering parameters (S-parameters). The standard de-embedding is achieved by a multiple steps process, involving the S-to-T and subsequent T-to-S parameter conversion. In a typical measurement setup, two fixtures are usually placed before and after the device under test (DUT) allowing the connection of the device to the calibrated vector network analyzer coaxial ports. An alternative method is proposed in this paper: it is based on the newly developed multi-network cascading algorithm. The matrices involved in the fixture-DUT-fixture cascading gives rise to a non-linear set of equations that is in one step analytically solved in closed form, obtaining a unique solution. The method is shown to be effective and at least as accurate as the standard multi-step de-embedding one.

scholarly journals Hydrodynamic Processes in Massive Stars

2008 ◽  
Vol 4 (S252) ◽  
pp. 439-449 ◽  
Author(s):  
Casey A. Meakin
Keyword(s):  
Stellar Evolution ◽  
Magnetized Plasma ◽  
Mixing Properties ◽  
New Era ◽  
Linear Set ◽  
Star Evolution ◽  
Hydrodynamic Processes ◽  
Stellar Interiors ◽  
Transport And Mixing ◽  
Massive Star Evolution

AbstractThe hydrodynamic processes operating within stellar interiors are far richer than represented by the best stellar evolution model available. Although it is now widely understood, through astrophysical simulation and relevant terrestrial experiment, that many of the basic assumptions which underlie our treatments of stellar evolution are flawed, we lack a suitable, comprehensive replacement. This is due to a deficiency in our fundamental understanding of the transport and mixing properties of a turbulent, reactive, magnetized plasma; a deficiency in knowledge which stems from the richness and variety of solutions which characterize the inherently non-linear set of governing equations. The exponential increase in availability of computing resources, however, is ushering in a new era of understanding complex hydrodynamic flows; and although this field is still in its formative stages, the sophistication already achieved is leading to a dramatic paradigm shift in how we model astrophysical fluid dynamics. We highlight here some recent results from a series of multi-dimensional stellar interior calculations which are part of a program designed to improve our one-dimensional treatment of massive star evolution and stellar evolution in general.

scholarly journals Low Order Harmonics Control in Stair Case Waveform by a Novel Estimation based Technique

2018 ◽  
Author(s):  
Salman Ahmad ◽  
Atif Iqbal ◽  
Imtiaz Ashraf ◽  
Sanjeevikumar Padmanaban ◽  
Mohammed Meraj
Keyword(s):  
Pulse Width Modulation ◽  
Jacobian Matrix ◽  
Initial Guess ◽  
Singularity Problem ◽  
Linear Set ◽  
Medium Voltage ◽  
Switching Losses ◽  
Voltage Application ◽  
Simulation Results ◽  
Subsequent Iteration

Few switching transitions in high power and medium voltage application of Power converters are desirable. The selective harmonics elimination (SHE) pulse width modulation offers a better quality waveform with lower switching transitions and hence lower switching losses. The SHE is a pre-programmed modulation technique where certain amounts of lower order harmonics are removed and fundamental voltage is controlled. After Fourier analysis of output waveform, a set of nonlinear transcendental equations is obtained which exhibits, multiple, unique or no solution in different range of modulation index (MI). In this paper, an iterative method based on the Jacobian estimate is proposed to solve a highly non-linear set of SHE equations. The proposed technique is easy in implementation and can solve a large number of such equations as computation of the Jacobian matrix in the subsequent iteration is estimated from the previous values.  Moreover, the proposed method also removes the singularity problem, especially for large SHE equations. High accuracy in the initial guess is also not essential for this method and can converge to the solution with any random initial guess. The computational and simulation results are given to validate the concept. The hardware result is provided to confirm the computational and simulation results.

scholarly journals Plasticity based interface model for failure modelling of unreinforced masonry under cyclic loading

2020 ◽  
Vol 42 (3) ◽  
pp. 321-338
Author(s):  
P. V. S. K. Kumar ◽  
Amirtham Rajagopal ◽  
Manoj Pandey
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Failure Modes ◽  
Back Stress ◽  
Unreinforced Masonry ◽  
Interface Model ◽  
Linear Set ◽  
Mixed Hardening ◽  
Hardening Law ◽  
Backward Integration

In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr-Coulomb criteria with a tension cut and compression cap and a back stress vector is introduced as a mixed hardening law variable  in the adopted yield surface to capture the unloading/reloading behaviour of masonry under cyclic loading. A simplified micromechanical interface modelling approach is adopted to capture all the failure modes of masonry. The integration of the differential constitutive equation is  done by using implicit Euler backward integration approach and the obtained non-linear set of equations are solved by a combined local/global Newton solver. The proposed constitutive model  is implemented in ABAQUS by writing  UMAT (user-defined subroutine) and the obtained numerical results are compared with  experimental results available in the literature.

scholarly journals On the positive linear set valued maps

2013 ◽  
Vol 14 (1) ◽  
pp. 111
Author(s):  
Anar Huseyin ◽  
Nesir Huseyin
Keyword(s):  
Linear Set

A Spherical Inclusion with Inhomogeneous Interface in Conduction

2003 ◽  
Vol 19 (1) ◽  
pp. 1-8
Author(s):  
T. Chen ◽  
C. H. Hsieh ◽  
P. C. Chuang
Keyword(s):  
Infinite Number ◽  
Effective Conductivity ◽  
Spherical Inclusion ◽  
Cone Angle ◽  
Imperfect Interface ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Legendre Series ◽  
Linear Set ◽  
The Matrix

ABSTRACTA series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

Equilibrium Thermodynamics of Combustion by Means of Genetic Algorithms

2005 ◽  
Author(s):  
S. Brusca ◽  
R. Lanzafame ◽  
M. Messina
Keyword(s):  
Equivalence Ratio ◽  
Linear Equations ◽  
Combustion Process ◽  
Genetic Approach ◽  
Equilibrium Equations ◽  
Linear Set ◽  
Wide Range ◽  
Non Linear ◽  
Release Analysis ◽  
Non Linear Equations

In order to carry out an accurate heat release analysis, it is necessary to solve a non linear set of chemical equilibrium equations to calculate concentrations of the species present in cylinder gases during the combustion process. So, the thermodynamics properties of the mixture can be evaluated. The present paper deals with the study of the thermodynamics of combustion using a genetic approach. A genetic algorithm was used to solve the set of non linear equations. The goal of this method is the possibility of solving the equations set in a wide range of pressure, temperature and equivalence ratio combinations, where more traditional methods are often found to fail.

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