scholarly journals Stability of current density impedance imaging II

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Amir Moradifam ◽  
Robert Lopez

<p style='text-indent:20px;'>This paper is a continuation of the authors earlier work on stability of Current Density Impedance Imaging (CDII) [R. Lopez, A. Moradifam, Stability of Current Density Impedance Imaging, SIAM J. Math. Anal. (2020).] We show that CDII is stable with respect to errors in both measurement of the magnitude of the current density vector field in the interior and the measurement of the voltage potential on the boundary. This completes the authors study of the stability of Current Density Independence Imaging which was previously shown only by numerical simulations.</p>

2020 ◽  
Vol 52 (5) ◽  
pp. 4506-4523
Author(s):  
Robert Lopez ◽  
Amir Moradifam

Author(s):  
Siyu Guo ◽  
Albert C. J. Luo

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.


2010 ◽  
Vol 721 (1) ◽  
pp. L58-L61 ◽  
Author(s):  
K. G. Puschmann ◽  
B. Ruiz Cobo ◽  
V. Martínez Pillet

Author(s):  
O. A. Troitskii ◽  
V. I. Stashenko

In the process of cutting of steels, high strength and heat-resistant alloys a strong warming-up of the cutting instrument takes place, necessitating its cooling by special emulsions and resulting in quick wear and increase of products cost. It was determined by experiment, that during a metal with current cutting, an electro-plastic effect arises. During the lector-plastic cutting, the plastic deformation of a metal under pulse current effect becomes easier, making the friction force between the metal chips and the cutting instrument front edge lower. The electro-plastic metal cutting method accounting the current polarity, current density vector directions, as well as pulse current parameters, can considerably improve the cut surface microstructure and increase the instrument service life. At that, the thermal regime of the cutting can be lowered due to cutting force lowering and heating zone shifting inside the piece or the instrument due to Thomson effect. It was shown, that during the electro-plastic metal cutting the friction force can decrease by 25–30% at the favorable current density vector orientation, as it takes place during electro-static metal drawing and rolling. The current plasticizing action results in decreasing friction force and the chips twisting radius, which can be confluent even for cast iron. At the example of metal drilling with the pulse current, the important current effects on the cutting mechanical parameters revealed. The conditions of metal electro-plastic cutting stated. Results of the experiment study of metal electro-plastic cutting quoted for the processes of steel and cast iron drilling.


2020 ◽  
Author(s):  
Martin Fillion ◽  
Gauthier Hulot ◽  
Patrick Alken ◽  
Arnaud Chulliat ◽  
Pierre Vigneron

&lt;p&gt;A new multi-spacecraft method to recover estimates of the average three-dimensional current density in the Earth's ionosphere is presented. It is demonstrated using the ESA's Swarm satellite constellation and by taking advantage of the favorable geometrical configurations during the early phase of the mission. The current density vector is calculated inside prisms whose vortices are defined by the satellite positions. The mathematical formalism differs from previous approaches such as the one known as the &amp;#8221;curlometer&amp;#8221;. It makes use of the well-known curl-B technique and involves an inverse problem which allows for error propagation through the calculation. Data from the vector field magnetometers of the three satellites are used and special care is taken to characterize the errors on these data. The method is applied in the low- and mid-latitude F-region on 15 February 2014. It provides latitudinal profiles of the full current density vector together with the associated error bars in the morning and evening sectors. We observe several dynamical features such as clear signatures of field-aligned interhemispheric currents, potential signatures of the wind dynamo current system as well as mid-latitude east-west currents.&lt;/p&gt;


2008 ◽  
Vol 27 (9) ◽  
pp. 1301-1309 ◽  
Author(s):  
K.F. Hasanov ◽  
A.W. Ma ◽  
A.I. Nachman ◽  
M.L.G. Joy

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