Abstract

Metamaterials offer a powerful way to manipulate a variety of physical fields ranging from wave fields (electromagnetic field, acoustic field, elastic wave, etc.), static fields (static magnetic field, static electric field) to diffusive fields (thermal field, diffusive mass). However, the relevant reports and studies are usually limited to a single physical field or functionality. In this study, we proposed and experimentally demonstrated a bifunctional metamaterial which could manipulate thermal and electric fields simultaneously and independently. Specifically, a composite with independently controllable thermal and electric conductivity was introduced, on the basis of which a bifunctional device capable of shielding thermal flux and concentrating electric current simultaneously was designed, fabricated and characterized. This work provides an encouraging example of metamaterials transcending their natural limitations, which offers a promising future in building a broad platform for the manipulation of multi-physics fields.

© 2016 Optical Society of America

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References

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  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [Crossref] [PubMed]
  2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [Crossref] [PubMed]
  3. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [Crossref] [PubMed]
  4. S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
    [Crossref] [PubMed]
  5. M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
    [Crossref] [PubMed]
  6. S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
    [Crossref] [PubMed]
  7. S. Narayana and Y. Sato, “DC magnetic cloak,” Adv. Mater. 24(1), 71–74 (2012).
    [Crossref] [PubMed]
  8. F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
    [Crossref] [PubMed]
  9. C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
    [Crossref] [PubMed]
  10. J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
    [Crossref]
  11. F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
    [Crossref] [PubMed]
  12. T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
    [Crossref] [PubMed]
  13. W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
    [Crossref] [PubMed]
  14. S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
    [Crossref] [PubMed]
  15. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
    [Crossref] [PubMed]
  16. S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
    [Crossref] [PubMed]
  17. Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
    [Crossref]
  18. T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
    [Crossref] [PubMed]
  19. T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
    [Crossref]
  20. C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
    [Crossref] [PubMed]
  21. S. Guenneau and T. M. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10(83), 20130106 (2013).
    [Crossref] [PubMed]
  22. R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
    [Crossref] [PubMed]
  23. L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
    [Crossref] [PubMed]
  24. M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
    [Crossref]
  25. Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
    [Crossref] [PubMed]
  26. C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
    [Crossref] [PubMed]
  27. T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
    [Crossref] [PubMed]
  28. X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
    [Crossref]
  29. D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43(9), 377–407 (1978).
    [Crossref]

2016 (1)

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

2015 (3)

C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
[Crossref] [PubMed]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
[Crossref] [PubMed]

2014 (4)

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

2013 (7)

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

S. Guenneau and T. M. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10(83), 20130106 (2013).
[Crossref] [PubMed]

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
[Crossref]

2012 (7)

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

S. Narayana and Y. Sato, “DC magnetic cloak,” Adv. Mater. 24(1), 71–74 (2012).
[Crossref] [PubMed]

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

2011 (1)

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

2009 (1)

M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

2008 (2)

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

2006 (1)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

1978 (1)

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43(9), 377–407 (1978).
[Crossref]

Amra, C.

Bai, X.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Bergman, D. J.

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43(9), 377–407 (1978).
[Crossref]

Bückmann, T.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

Castaldi, G.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Cui, T. J.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Enoch, S.

M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

Fang, N.

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

Farhat, M.

M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

Galdi, V.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Gao, D.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Geng, Z.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
[Crossref] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Gömöry, F.

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

Guenneau, S.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

S. Guenneau and T. M. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10(83), 20130106 (2013).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

Han, T.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

He, S.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

He, S. L.

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Huang, J.

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Jiang, C.

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Jiang, W.

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Jiang, W. X.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

Jin, T. Y.

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Kadic, M.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Lan, C.

Lan, L.

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Lei, D. Y.

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

Li, B.

C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
[Crossref] [PubMed]

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
[Crossref] [PubMed]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

Li, Y.

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Liu, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Luo, C. Y.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

Luo, Y.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

Ma, H. F.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

Ma, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Ma, Y. G.

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Mei, Z. L.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

Moccia, M.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Narayana, S.

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

S. Narayana and Y. Sato, “DC magnetic cloak,” Adv. Mater. 24(1), 71–74 (2012).
[Crossref] [PubMed]

Navau, C.

J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
[Crossref]

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref] [PubMed]

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

Ni, Y.

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Prat-Camps, J.

J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
[Crossref]

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref] [PubMed]

Puvirajesinghe, T. M.

S. Guenneau and T. M. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10(83), 20130106 (2013).
[Crossref] [PubMed]

Qiu, C. W.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

Raza, M.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Sanchez, A.

J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
[Crossref]

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref] [PubMed]

Sato, Y.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

S. Narayana and Y. Sato, “DC magnetic cloak,” Adv. Mater. 24(1), 71–74 (2012).
[Crossref] [PubMed]

Savo, S.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Schittny, R.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Shen, X.

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Solovyov, M.

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

Song, R.

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

Souc, J.

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Sun, C.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Sun, F.

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Teng, J.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

Thong, J. T.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Veynante, D.

Wang, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Wegener, M.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Wu, L.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Xia, C.

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

Yang, F.

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

Yang, T.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Yang, Y.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
[Crossref] [PubMed]

Ye, H.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

Yeo, S. P.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

Yuan, T.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

Zeng, L.

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

Zhang, S.

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhao, J.

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

Zhou, J.

Adv. Mater. (3)

S. Narayana and Y. Sato, “DC magnetic cloak,” Adv. Mater. 24(1), 71–74 (2012).
[Crossref] [PubMed]

T. Han, H. Ye, Y. Luo, S. P. Yeo, J. Teng, S. Zhang, and C. W. Qiu, “Manipulating DC currents with bilayer bulk natural materials,” Adv. Mater. 26(21), 3478–3483 (2014).
[Crossref] [PubMed]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

X. Shen, Y. Li, C. Jiang, Y. Ni, and J. Huang, “Thermal cloak-concentrator,” Appl. Phys. Lett. 109(3), 031907 (2016).
[Crossref]

Energy Environ. Sci. (1)

T. Han, J. Zhao, T. Yuan, D. Y. Lei, B. Li, and C. W. Qiu, “Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials,” Energy Environ. Sci. 6(12), 3537 (2013).
[Crossref]

J. R. Soc. Interface (1)

S. Guenneau and T. M. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10(83), 20130106 (2013).
[Crossref] [PubMed]

NPG Asia Mater. (1)

Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5(11), e73 (2013).
[Crossref]

Opt. Express (2)

Phys. Rep. (1)

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43(9), 377–407 (1978).
[Crossref]

Phys. Rev. Lett. (9)

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

F. Yang, Z. L. Mei, T. Y. Jin, and T. J. Cui, “dc electric invisibility cloak,” Phys. Rev. Lett. 109(5), 053902 (2012).
[Crossref] [PubMed]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Sci. Rep. (4)

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3, 1593 (2013).
[Crossref] [PubMed]

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic field invisibility cloak,” Sci. Rep. 5, 16416 (2015).
[Crossref] [PubMed]

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
[Crossref] [PubMed]

Science (4)

F. Gömöry, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental realization of a magnetic cloak,” Science 335(6075), 1466–1468 (2012).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

Supercond. Sci. Technol. (1)

J. Prat-Camps, A. Sanchez, and C. Navau, “Superconductor–ferromagnetic metamaterials for magnetic cloaking and concentration,” Supercond. Sci. Technol. 26(7), 074001 (2013).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) The proposed bifunctional metamaterial with independently controllable thermal and electric conductivity in the associated (ρ, ϕ, z) cylindrical coordinate system.The unit cell is composed of severial fanlike inclusions made ofmaterial A, B, C, and D.The thermal and electric conductivity for materials A, B, C, and D are (κA, σA), (κB, σB), (κC, σC) and (κD, σD) respectively. The corresponding geometrical parameters can be seen in the insert. The principle for bifunctional device behaving as thermal cloak and electric concentrator: (b) The corresponding physical model. the space is divided into three parts: interior region (ρ<R1), shell (R1<ρ<R2), and exterior region (ρ>R2) (see Fig. 1(b)). The thermal and electric conductivity for background medium (interior and external regions) is κ0, σ0, while the one for the bifunctional shell is κ1, σ1, respectively.(c) The bifunctional device applied with temperature gradient and electric potential gradient. (d) The thermal flux distribution. (e) The current distribution.
Fig. 2
Fig. 2 (a) The schematic illustration for practical realization of bifunctional device. the corresponding geometry parameters are optimized as follow: Δρ=4mm , Δϕ=40° , a=3mm , α=20° . (b) The photogragh for the fabricated sample.
Fig. 3
Fig. 3 Thermal simulation results for background material: a) temperature profile. c) thermal flux distribution. Thermal simulation results for bifunctional device: b) temperature profile. d) thermal flux distribution. Electric simulation results for background material: e) electric potential distribution. g) current density. Electric simulation results for bifunctional device: f) electric potential distribution. h) current density.
Fig. 4
Fig. 4 (a) Measured temperature profile for background material. (b) Measured temperature profile for bifunctional device. (c) The corresponding simulated temperature profile for background material. (d) The simulated corresponding temperature profile for bifunctional device.
Fig. 5
Fig. 5 The simulation and experiment results for background material and the one with electric concentrator: simulated electric potential values for the different cases at corresponding positions: (a) x = −20mm, (b) x = 20mm and (c) y = 0mm. d, e, f) Corresponding experimental potential values, respectively. The white lines in inserts represent observed lines.

Equations (4)

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κ ϕ = Δϕ κ C κ D (Δϕα) κ C +α κ D a Δρ
κ ρ 0
σ ϕ 0
σ ρ = Δρ σ B σ D (Δρa) σ B +a σ D α Δϕ

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