Numerical Calculation Error of Variational Method with Dielectric Measurement Using a Coaxial-probe

2018 ◽  
Author(s):  
Kouji Shibata ◽  
Masaki Kobayashi
Keyword(s):  
Numerical Calculation ◽  
Variational Method ◽  
Dielectric Measurement ◽  
Calculation Error ◽  
Coaxial Probe

scholarly journals Numerical Calculation of Energy Eigen-values of the Hydrogen Negative Ion in the 2p^2 Configuration by Using the Variational Method

2020 ◽  
Vol 24 (1) ◽  
pp. 30
Author(s):  
Yosef Robertus Utomo ◽  
Guntur Maruto ◽  
Agung Bambang Setio Utomo ◽  
Pekik Nurwantoro ◽  
Sholihun Sholihun
Keyword(s):  
Numerical Calculation ◽  
Variational Method ◽  
Trial Function ◽  
Hydrogen Molecule ◽  
Negative Ion ◽  
Multipole Moments ◽  
A Value ◽  
Eigen Value ◽  
Eigen Values ◽  
Electric Multipole Moments

Calculation of energy eigen value of hydrogen negative ion (H − ) in 2p^2 configuration using the method of variation functions has been done. A work on H − can lead to calculations of electric multipole moments of a hydrogen molecule. The trial function is a linear combination of 8 expansion terms each of which is related to the Chandrasekhar’s basis. This work produces a series of 7 energy eigen values which converges to a value of −0.2468 whereas the value of this convergence is expected to be −0.2523. This deviation from the expected value is mainly due to the elimination of interelectronic distance (u) coordinate. The values of the exponent parameters used in this work contribute also to this deviation. This variational method will be applied to the construction of some energy eigen functions of Hv2 .

scholarly journals The Kinematic and Dynamic Modeling and Numerical Calculation of Robots with Complex Mechanisms Based on Lie Group Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-34
Author(s):  
Lu-Han Ma ◽  
Yong-Bo Zhong ◽  
Gong-Dong Wang ◽  
Nan Li
Keyword(s):  
Numerical Calculation ◽  
Lie Group ◽  
Dynamic Models ◽  
Lagrange Equation ◽  
Kinematic Parameter ◽  
Model Complexity ◽  
Calculation Error ◽  
Closed Chain ◽  
Complex Mechanisms ◽  
The Relationship

The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness.

scholarly journals Precision Permittivity Measurement for Low-Loss Thin Planar Materials Using Large Coaxial Probe from 1 to 400 MHz

2018 ◽  
Vol 2 (4) ◽  
pp. 81
Author(s):  
Kok Yeow You ◽  
Man Seng Sim
Keyword(s):  
Dielectric Constant ◽  
Dielectric Measurement ◽  
Tangent Loss ◽  
Outer Diameter ◽  
Low Loss ◽  
Probe Calibration ◽  
Lift Off ◽  
Tan Δ ◽  
Planar Materials ◽  
Coaxial Probe

This paper focuses on the non-destructive dielectric measurement for low-loss planar materials with a thickness of less than 3 mm using a large coaxial probe with an outer diameter of 48 mm. The aperture probe calibration procedure required only to make a measurement of the half-space air and three offset shorts. The reflection coefficient for the thin material is measured using a Keysight E5071C network analyzer from 0.3 MHz to 650 MHz and then converted to a relative dielectric constant, εr and tangent loss, tan δ via closed form capacitance model and lift-off calibration process. Average measurement error of dielectric constant, Δεr is less than 6% from 1 MHz to 400 MHz and the resolution of loss tangent, tan δ measurement is capable of achieving 10−3.

scholarly journals Effect of Open-Ended Coaxial Probe-to-Tissue Contact Pressure on Dielectric Measurements

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 2060 ◽  
Author(s):  
Gertjan Maenhout ◽  
Tomislav Markovic ◽  
Ilja Ocket ◽  
Bart Nauwelaers
Keyword(s):  
Contact Pressure ◽  
Tissue Sample ◽  
Extracellular Fluid ◽  
Biological Tissues ◽  
Dielectric Measurement ◽  
Uncertainty Interval ◽  
Dielectric Data ◽  
Coaxial Probes ◽  
Coaxial Probe ◽  
Cellular Organelles

Open-ended coaxial probes are widely used to gather dielectric properties of biological tissues. Due to the lack of an agreed data acquisition protocol, several environmental conditions can cause inaccuracies when comparing dielectric data. In this work, the effect of a different measurement probe-to-tissue contact pressure was monitored in the frequency range from 0.5 to 20 GHz. Therefore, we constructed a controlled lifting platform with an integrated pressure sensor to exert a constant pressure on the tissue sample during the dielectric measurement. In the pressure range from 7.74 kPa to 77.4 kPa, we observed a linear correlation of − 0.31 ± 0.09 % and − 0.32 ± 0.14 % per kPa for, respectively, the relative real and imaginary complex permittivity. These values are statistically significant compared with the reported measurement uncertainty. Following the literature in different biology-related disciplines regarding pressure-induced variability in measurements, we hypothesize that these changes originate from squeezing out the interstitial and extracellular fluid. This process locally increases the concentration of membranes, cellular organelles, and proteins in the sensed volume. Finally, we suggest moving towards a standardized probe-to-tissue contact pressure, since the literature has already demonstrated that reprobing at the same pressure can produce repeatable data within a 1% uncertainty interval.

scholarly journals Deviation Effect of Coaxiality on the Rock Brazilian Split

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Zenghui Zhao ◽  
Mingzhong Zhang ◽  
Qing Ma ◽  
Baosen Chen
Keyword(s):  
Tensile Strength ◽  
Numerical Calculation ◽  
Stress Distribution ◽  
Rock Fracture ◽  
Splitting Method ◽  
Maximum Tensile Stress ◽  
Analytic Solutions ◽  
Calculation Error ◽  
Splitting Test ◽  
Variable Function

Tension failure is one of the main forms of instability in geotechnical engineering. Aiming at the calculation error caused by the loading direction deviation of the Brazilian disc splitting method, a mechanical model of a disc under chord loading was constructed firstly. Based on the theory of complex variable function, the analytic solutions of stresses in a circular disc were deduced, and the calculation error of the tensile strength under chord loading was characterized by defining the error impact rate. And the stress distribution of a disc and the law of rock fracture under chord loading were detailed analyzed through numerical calculation. Through numerical calculation, the stress distribution of the disc and rock failure law under chordwise loading are discussed in detail. The results show that the stress concentration near the loading point is stronger under the chordwise loading comparing with the radial loading, which makes the disc more vulnerable to produce compression failure near the loading point. The disc exhibits a maximum tensile stress and a minimum compressive stress at the intersection of the loaded string and the horizontal diameter, so that tensile rupture damage is likely to occur here. With the increase of deviation angle, the tensile strength measured by the Brazilian splitting test decreases gradually, and the influence rate of error increases significantly. The proposed analytical solution under chord loading provides theoretical guiding significance for nonradial splitting failure of a disc.

scholarly journals Evaluation of a Reflection Method on an Open-Ended Coaxial Line and its Use in Dielectric Measurements

10.14311/882 ◽  
2006 ◽  
Vol 46 (5) ◽  
Author(s):  
R. Zajíček ◽  
J. Vrba ◽  
K. Novotný
Keyword(s):  
Biological Tissue ◽  
Tissue Sample ◽  
Coaxial Line ◽  
Dielectric Measurement ◽  
Network Analyzer ◽  
Reflection Method ◽  
Frequency Range ◽  
Discrete Elements ◽  
Biological Substance ◽  
Coaxial Probe

This paper describes a method for determining the dielectric constant of a biological tissue. A suitable way to make a dielectric measurement that is nondestructive and noninvasive for the biological substance and broadband at the frequency range of the network analyzer is to use a reflection method on an open ended coaxial line. A coaxial probe in the frequency range of the network analyzer from 17 MHz to 2 GHz is under investigation and also a calibration technique and the behavior of discrete elements in an equivalent circuit of an open ended coaxial line. Information about the magnitude and phase of the reflection coefficient on the interface between a biological tissue sample and a measurement probe is modeled with the aid of an electromagnetic field simulator. The numerical modeling is compared with real measurements, and a comparison is presented. 

Broad Band Microwave Dielectric Measurement of Liquids with an Open-Ended Coaxial Probe

2013 ◽  
Vol 333-335 ◽  
pp. 191-198
Author(s):  
Jia Ming Shi ◽  
Quirino Balzano ◽  
Christopher C. Davis
Keyword(s):  
Dielectric Properties ◽  
Broad Band ◽  
Dielectric Measurement ◽  
Network Analyzer ◽  
Frequency Range ◽  
Probe Technique ◽  
Microwave Dielectric ◽  
Coaxial Probe

The principles of the open-ended coaxial probe technique for the measurement of permittivity are described. Measurements of dielectric properties are carried out over a frequency range from 300MHz to 50GHz, with a system comprising an Agilent E8364B network analyzer and a connected 2.2mm diameter open-ended coaxial probe. Water, methanol and salines of 0.1M, 0.2M, 0.6M are used as calibration liquids or liquids to be measured. Measured permittivities are presented and compared with those calculated from the Cole-Cole equation. It is shown that, in order to get good results, the calibration liquid should be similar to the liquid being measured in dielectric properties.

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