American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Homogenization of the Neumann problem for a quasilinear elliptic equation in a perforated domain
  • NHM Home
  • This Issue
  • Next Article
    Spectrum and dynamical behavior of a kind of planar network of non-uniform strings with non-collocated feedbacks
June  2010, 5(2): 335-360. doi: 10.3934/nhm.2010.5.335

Electromagnetic circuits

Graeme W. Milton 1, and  Pierre Seppecher 2,

1. 

Department of Mathematics, University of Utah, Salt Lake City UT 84112, United States
2. 

Institut de Mathématiques de Toulon, Université de Toulon et du Var, BP 132-83957 La Garde Cedex, France

Received  May 2009 Revised  February 2010 Published  May 2010

The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of them. The electromagnetic circuits consist of thin triangular magnetic components joined at the edges by cylindrical dielectric components. Some of the edges can be terminal edges to which electric fields are applied. The response is measured in terms of the real or virtual free currents that are associated with the terminal edges. The relation between the terminal electric fields and the terminal free currents is governed by a symmetric complex matrix $\W$. In the case where all the terminal edges are disjoint, and the frequency is fixed, a complete characterization is obtained of all possible response matrices $\W$ both in the lossless and lossy cases. This is done by introducing a subclass of electromagnetic circuits, called electromagnetic ladder networks, which can realize the response matrix $\W$ of any other type of electromagnetic circuit with disjoint terminal edges. It is sketched how an electromagnetic ladder network, structured as a cubic network, can have a macroscopic electromagnetic continuum response which is non-Maxwellian, and novel.
Keywords: Electromagnetism, Circuits, Metamaterials., Networks.
Mathematics Subject Classification: Primary: 35Q60, 78A48, 94C0.
Citation: Graeme W. Milton, Pierre Seppecher. Electromagnetic circuits. Networks & Heterogeneous Media, 2010, 5 (2) : 335-360. doi: 10.3934/nhm.2010.5.335
[1]

Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials. Electronic Research Archive, 2020, 28 (2) : 961-976. doi: 10.3934/era.2020051
[2]

Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems & Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297
[3]

Michel Lenczner. Homogenization of linear spatially periodic electronic circuits. Networks & Heterogeneous Media, 2006, 1 (3) : 467-494. doi: 10.3934/nhm.2006.1.467
[4]

Ignacio García de la Vega, Ricardo Riaza. Bifurcation without parameters in circuits with memristors: A DAE approach. Conference Publications, 2015, 2015 (special) : 340-348. doi: 10.3934/proc.2015.0340
[5]

Frank Jochmann. A singular limit in a nonlinear problem arising in electromagnetism. Communications on Pure & Applied Analysis, 2011, 10 (2) : 541-559. doi: 10.3934/cpaa.2011.10.541
[6]

Denis Serre. Non-linear electromagnetism and special relativity. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 435-454. doi: 10.3934/dcds.2009.23.435
[7]

Fernando Miranda, José-Francisco Rodrigues, Lisa Santos. On a p-curl system arising in electromagnetism. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 605-629. doi: 10.3934/dcdss.2012.5.605
[8]

Flaviano Battelli, Michal Fečkan. On the existence of solutions connecting IK singularities and impasse points in fully nonlinear RLC circuits. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3043-3061. doi: 10.3934/dcdsb.2017162
[9]

Mapundi K. Banda, Michael Herty, Axel Klar. Gas flow in pipeline networks. Networks & Heterogeneous Media, 2006, 1 (1) : 41-56. doi: 10.3934/nhm.2006.1.41
[10]

Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo. Flow optimization in vascular networks. Mathematical Biosciences & Engineering, 2017, 14 (3) : 607-624. doi: 10.3934/mbe.2017035
[11]

Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano. Dragging in mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37
[12]

A. Marigo. Robustness of square networks. Networks & Heterogeneous Media, 2009, 4 (3) : 537-575. doi: 10.3934/nhm.2009.4.537
[13]

Manisha Pujari, Rushed Kanawati. Link prediction in multiplex networks. Networks & Heterogeneous Media, 2015, 10 (1) : 17-35. doi: 10.3934/nhm.2015.10.17
[14]

Yi Ming Zou. Dynamics of boolean networks. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1629-1640. doi: 10.3934/dcdss.2011.4.1629
[15]

H. N. Mhaskar, T. Poggio. Function approximation by deep networks. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4085-4095. doi: 10.3934/cpaa.2020181
[16]

Jesse Collingwood, Robert D. Foley, David R. McDonald. Networks with cascading overloads. Journal of Industrial & Management Optimization, 2012, 8 (4) : 877-894. doi: 10.3934/jimo.2012.8.877
[17]

Werner Creixell, Juan Carlos Losada, Tomás Arredondo, Patricio Olivares, Rosa María Benito. Serendipity in social networks. Networks & Heterogeneous Media, 2012, 7 (3) : 363-371. doi: 10.3934/nhm.2012.7.363
[18]

Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565
[19]

Yuki Kumagai. Social networks and global transactions. Journal of Dynamics & Games, 2019, 6 (3) : 211-219. doi: 10.3934/jdg.2019015
[20]

Xiaoxian Tang, Jie Wang. Bistability of sequestration networks. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020165

2019 Impact Factor: 1.053

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences