scholarly journals Bounds for the electrical resistance for homogeneous conducting body of rotation

2021 ◽  
Vol 11 (5) ◽  
pp. 104-122
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel ◽  
Attila Baksa ◽  
Dávid Gönczi
Keyword(s):  
Steady State ◽  
Lower Bound ◽  
Electric Current ◽  
Electrical Resistance ◽  
Current Flow ◽  
Electrical Conductance ◽  
Upper Bounds ◽  
The Body ◽  
Lower And Upper Bounds ◽  
Electric Current Flow

A mathematical model is developed for the steady-state electric current flow through in a homogeneous isotropic conductor whose shape is a body of rotation. The body of rotation considered is bounded by the coordinate surfaces of an orthogonal curvilinear coordinate system. The equations of the Maxwell’s theory of electric current flow in a homogeneous solid conductor body are used to formulate the corresponding electric boundary value problem. The studied steady-state conduction problem is axisymmetric. The determination of the steady motion of charges is based on the concept of the electrical conductance of the conductors the inverse of which is the electrical resistance. The exact (strict) value of the electrical resistance is known only for bodies with very simple shapes, therefore, the principles and the methods that can be used for creating lower and upper bounds to the numerical value of electrical resistance (electrical conductance) are important. The derivation of the upper and lower bound formulae for the electrical conductance of axisymmetric ring-like conductor is based on the two types of Cauchy–Schwarz inequality. The condition of equality of the derived lower and upper bounds is examined. Several examples illustrate the applications of the derived upper and lower bound formulae.

scholarly journals Full-Duplex Relay with Delayed CSI Elevates the SDoF of the MIMO X Channel

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1484
Author(s):  
Tong Zhang ◽  
Gaojie Chen ◽  
Shuai Wang ◽  
Rui Wang
Keyword(s):  
Lower Bound ◽  
Channel State Information ◽  
Interference Alignment ◽  
Upper Bounds ◽  
Full Duplex ◽  
Multiple Antenna ◽  
Lower And Upper Bounds ◽  
Channel State ◽  
State Information ◽  
Full Duplex Relay

In this article, the sum secure degrees-of-freedom (SDoF) of the multiple-input multiple-output (MIMO) X channel with confidential messages (XCCM) and arbitrary antenna configurations is studied, where there is no channel state information (CSI) at two transmitters and only delayed CSI at a multiple-antenna, full-duplex, and decode-and-forward relay. We aim at establishing the sum-SDoF lower and upper bounds. For the sum-SDoF lower bound, we design three relay-aided transmission schemes, namely, the relay-aided jamming scheme, the relay-aided jamming and one-receiver interference alignment scheme, and the relay-aided jamming and two-receiver interference alignment scheme, each corresponding to one case of antenna configurations. Moreover, the security and decoding of each scheme are analyzed. The sum-SDoF upper bound is proposed by means of the existing SDoF region of two-user MIMO broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). As a result, the sum-SDoF lower and upper bounds are derived, and the sum-SDoF is characterized when the relay has sufficiently large antennas. Furthermore, even assuming no CSI at two transmitters, our results show that a multiple-antenna full-duplex relay with delayed CSI can elevate the sum-SDoF of the MIMO XCCM. This is corroborated by the fact that the derived sum-SDoF lower bound can be greater than the sum-SDoF of the MIMO XCCM with output feedback and delayed CSIT.

scholarly journals AN EXPERIMENTAL STUDY OF DIATHERMY

1927 ◽  
Vol 46 (5) ◽  
pp. 715-734 ◽  
Author(s):  
Ronald V. Christie ◽  
Carl A. L. Binger
Keyword(s):  
Electrical Resistance ◽  
High Frequency ◽  
Skin Effect ◽  
Current Flow ◽  
Homogeneous Medium ◽  
Local Heat ◽  
The Body ◽  
Technical Error ◽  
Theoretical Considerations ◽  
Maximal Heating

The principles governing the passage of high frequency currents through various conductors have been discussed and exemplified in experiments done on both non-living and living bodies. In Part I it was shown: (1) That the current takes the path of least electrical resistance rather than the shortest path; (2) that maximal heating occurs at the point of greatest concentration of the lines of current flow. In a homogeneous medium with parallel electrodes maximal heat production occurs in those portions of the medium adjoining the electrodes and the heat gradient is from without inward. Under these circumstances maximal heating never occurs at the center. In discussing the localization of heat not only the electrical resistance and current concentration, but also the cooling effect, must be considered. In experiments on the dog's cadaver no evidence of the so called "skin effect" could be demonstrated. This is in contradistinction to the findings of Bettman and Crohn, but the discrepancy is explained on the basis of what we believe to be a technical error in their work. The finding of no "skin effect" is in agreement with the conclusions of Dowse and Iredell, based on both experimental and theoretical considerations. In Part II three types of experiments were performed on the anesthetized dog. The conclusions to be derived from them are these: (1) The heat gradient of the body is reversed during diathermy and heating occurs from without inward; (2) deep heating during diathermy is greater than that which results from the application of local heat to the skin; (3) the lung can be heated by diathermy in spite of simultaneous cooling of the chest wall. These experiments we regard as satisfactory evidence of the passage of the current through the interior of the body.

Simulation of the Electric Current Flow in Amorphous-Crystalline Ti2NiCu Alloy with Shape Memory Effect

2016 ◽  
Vol 845 ◽  
pp. 146-149
Author(s):  
Dmitriy S. Kuchin ◽  
Victor V. Koledov ◽  
Pavel V. Bogun ◽  
Peter V. Lega ◽  
Vedamanickam Sampath ◽  
...  
Keyword(s):  
Electric Current ◽  
Current Flow ◽  
Amorphous Matrix ◽  
Volume Fraction ◽  
Current Density Distribution ◽  
Heat Evolution ◽  
Equatorial Region ◽  
Joule Heat ◽  
Electric Pulses ◽  
Electric Current Flow

A new technique for the production of nanograined alloys from rapidly quenched amorphous ribbons by serial electric pulses has been proposed recently [1]. The present work involves a theoretical study of electric current flow in a nonhomogeneous Ti2NiCu alloy consisting of an amorphous matrix with a crystalline phase of spherical morphology embedded in it. The electric current density distribution was calculated in the vicinity of a spherical nucleus, which has an electrical resistance that is only 0.4 times that of the amorphous matrix. The calculation of Joule heat density was done in the nucleus and in the amorphous volume surrounding it. It was shown that during the current pulse the Joule heat evolution in nucleus exceeds one in equatorial region in matrix, but less than near the poles. The dependence of relative resistivity of nonhomogeneous amorphous-crystalline alloy on volume fraction of spherical crystalline nuclei was calculated

scholarly journals A Computational Perspective on Network Coding

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Qin Guo ◽  
Mingxing Luo ◽  
Lixiang Li ◽  
Yixian Yang
Keyword(s):  
Graph Theory ◽  
Computational Complexity ◽  
Lower Bound ◽  
Network Coding ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Multicast Networks ◽  
Computational Perspective ◽  
Source Rate

From the perspectives of graph theory and combinatorics theory we obtain some new upper bounds on the number of encoding nodes, which can characterize the coding complexity of the network coding, both in feasible acyclic and cyclic multicast networks. In contrast to previous work, during our analysis we first investigate the simple multicast network with source rateh=2, and thenh≥2. We find that for feasible acyclic multicast networks our upper bound is exactly the lower bound given by M. Langberg et al. in 2006. So the gap between their lower and upper bounds for feasible acyclic multicast networks does not exist. Based on the new upper bound, we improve the computational complexity given by M. Langberg et al. in 2009. Moreover, these results further support the feasibility of signatures for network coding.

Minimization of Bounded Cable Tensions in Cable-Based Parallel Manipulators

2007 ◽  
Author(s):  
Mahir Hassan ◽  
Amir Khajepour
Keyword(s):  
Lower Bound ◽  
Numerical Method ◽  
Upper Bound ◽  
Task Force ◽  
Parallel Manipulators ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Cable Forces

In this work, the application of the Dykstra’s alternating projection method to find the minimum-2-norm solution for actuator forces is discussed in the case when lower and upper bounds are imposed on the actuator forces. The lower bound is due to specified pretension desired in the cables and the upper bound is due to the maximum allowable forces in the cables. This algorithm presents a systematic numerical method to determine whether or not a solution exists to the cable forces within these bounds and, if it does exist, calculate the minimum-2-norm solution for the cable forces for a given task force. This method is applied to an example 2-DOF translational cable-driven manipulator and a geometrical demonstration is presented.

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