Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T12:24:24.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Fluxon Centering in Josephson Junctions with Exponentially Varying Width

Published online by Cambridge University Press:  28 May 2015

E. G. Semerdjieva  and
M. D. Todorov
E. G. Semerdjieva*
Affiliation:
Paisii Hilendarski University of Plovdiv, 24 Tsar Assen str., 4000 Plovdiv, Bulgaria
M. D. Todorov*
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Sofia, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria
*
Corresponding author. Email: elisaveta_s@abv.bg
Corresponding author. Email: mtod@tu-sofia.bg
Get access

Abstract

Nonlinear eigenvalue problems for fluxons in long Josephson junctions with exponentially varying width are treated. Appropriate algorithms are created and realized numerically. The results obtained concern the stability of the fluxons, the centering both magnetic field and current for the magnetic flux quanta in the Josephson junction as well as the ascertaining of the impact of the geometric and physical parameters on these quantities. Each static solution of the nonlinear boundary-value problem is identified as stable or unstable in dependence on the eigenvalues of associated Sturm-Liouville problem. The above compound problem is linearized and solved by using of the reliable Continuous analogue of Newton method.

Keywords

34L1634K1065D3065N1265N2565F15Fluxonstabilitybifurcationcritical curvecentering magnetic fieldcentering current
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 3 , August 2012 , pp. 204 - 213
Copyright
Copyright © Global-Science Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Abrashkevich, A. and Puzynin, I. V., CANM, a program for numerical solution of a system of nonlinear equations using the continuous analog of Newton's method, Comp. Phys. Commun., 156 (2004), pp. 154–170.Google Scholar
[2]Barone, A. and Paterno, G., Physics and Applications of Josephson Effect, Wiley New York, 1982.CrossRefGoogle Scholar
[3]Benabdallah, A., Caputo, J. G. and Scott, A. C., Exponentially trapped Josephson flux-flow oscillator, Phys. Rev. B, 54(2) (1996), pp. 16139–16146.Google Scholar
[4]Boyadjiev, T. L., Spline-collocation scheme of higher order, Report JINR, R2-2002-101, Dubna, 2002 (in Russian).Google Scholar
[5]Boyadjiev, T. L., Andreeva, O. Y., Semerdjieva, E. G. and Shukrinov, Y. M., Created-by-current states in long Josephson junctions, Eur. Phys. Lett., 83 (2008), 47008.Google Scholar
[6]Boyadjiev, T. L., Todorov, M. D., Fiziev, P. P. and Yazadjiev, S. S., Mathematical modeling of boson-fermion stars in the generalized scalar-tensor theory of gravity, J. Comp. Phys., 166(2) (2001), pp. 253–270.Google Scholar
[7]Boyadjiev, T. L. and Todorov, M. D., Minimal length of Josephson junctions with stable fluxon bound states, Superconductor Science and Technology, 15(1) (2002), pp. 1–7.Google Scholar
[8]Carapella, G., Martucciello, N. and Costabile, G., Experimental investigation of flux motion in exponentially shaped Josephson junctions, Phys. Rev. B, 66 (2002), 134531.Google Scholar
[9]Gal'perin, Y. S. and Filippov, A. T., Bound states of solitons in inhomogeneous Josephson transitions, Zhurnal Eksperimental'noj i Teoreticheskoj Fiziki, 86(4) (1984). [In Russian].Google Scholar
[10]Khaire, T. S., Khasawneh, M. A., Pratt, W. P. Jr and Birge, N. O., Observation of spin-triplet superconductivity in co-based Josephson junctions, Phys. Rev. Lett., 104 (2010), 137002.CrossRefGoogle ScholarPubMed
[11]Ota, Y., Machida, M., Koyama, T. and Matsumoto, H., Theory of vortex structure in Josephson junctions with multiple tunneling channels: Vortex enlargement as a probe of ±s-wave superconductivity, Phys. Rev. B, 81 (2010), 014502.CrossRefGoogle Scholar
[12]Puzynin, I. V, Amirkhanov, I. V., Zemlyanaya, E. V., Pervushin, V. N., Puzynina, T. P. and Strizh, T. A., The generalized continuous analog of Newton's method for the numerical study of some nonlinear quantum-field models, Phys. Part. Nucl., 30 (1) (1999), pp. 87–110.CrossRefGoogle Scholar
[13]Semerdjieva, E. G., Boyadjiev, T. L. and Shukrinov, Y. M., Static vortices in long Josephson contacts of exponentiallyvarying width, Low Temp. Phys., 30(6) (2004), pp. 610–618.Google Scholar
[14]Semerdjieva, E. G. and Todorov, M. D., Bifurcation curves of Josephson vortices in inhomogeneous junctions, Physica D: Nonlinear Phenomena, under review.Google Scholar
[15]Tikhonov, A. N. and Samarskii, A. A., Equations of the Mathematical Physics, Dover New York, 1990.Google Scholar
[16]Ustinov, A. V., Solitons in Josephson junctions, Physica D: Nonlinear Phenomena, 123(1-4) (1998), pp. 315–329.CrossRefGoogle Scholar
[17]Zhidkov, E. P., Makarenko, G. I. and Puzynin, I. V., Continuous analog of the Newton method in non-linear physical problems, Sov. J. Particles Nucl., 4(1) (1973).Google Scholar