References
- 1. Y. Li, X. Shen, Z. Wu, J. Huang, Y. Chen, Y. Ni, and J. Huang, Temperature-dependent transformation thermotics: From switchable thermal cloaks to macroscopic thermal diodes, Physical review letters, vol. 115, no. 19, p. 195503, 2015.
- 2. S. Narayana and Y. Sato, Heat flux manipulation with engineered thermal materials, Physical review letters, vol. 108, no. 21, p. 214303, 2012.
- 3. M. Maldovan, Sound and heat revolutions in phononics, Nature, vol. 503, no. 7475, pp. 209-217, 2013.
- 4. N. Li, J. Ren, L. Wang, G. Zhang, P. Hãnggi, and B. Li, Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond, Reviews of Modern Physics, vol. 84, no. 3, p. 1045, 2012.
- 5. C. Dames, Solid-state thermal rectification with existing bulk materials, Journal of Heat Transfer, vol. 131, no. 6, p. 061301, 2009.
- 6. D. Sawaki, W. Kobayashi, Y. Moritomo, and I. Terasaki, Thermal rectification in bulk materials with asymmetric shape, Appl. Phys. Lett., vol. 98, 2011.
- 7. W. Kobayashi, Y. Teraoka, and I. Terasaki, An oxide thermal rectifier, Applied Physics Letters, vol. 95, no. 17, p. 171905, 2009.
- 8. N. Yang, G. Zhang, and B. Li, Thermal rectification in asymmetric graphene ribbons, Applied Physics Letters, vol. 95, no. 3, p. 033107, 2009.
- 9. M. Criado-Sancho, L. F. D. Castillo, J. Casas-Vázquez, and D. Jou, Theoretical analysis of thermal rectification in a bulk Si/nanoporous Si device, Physics Letters A, vol. 376, no. 19, pp. 1641-1644, 2012.
- 10. M. Criado-Sancho, F. X. Alvarez, and D. Jou, Thermal rectification in inhomogeneous nanoporous Si devices, Journal of Applied Physics, vol. 114, no. 5, p. 053512, 2013.
- 11. E.González-Noya, D. Srivastava, and M. Menon, Heat-pulse rectification in carbon nanotube y junctions, Physical Review B, vol. 79, no. 11, p. 115432, 2009.
- 12. C. Chang, D. Okawa, A. Majumdar, and A. Zettl, Solid-state thermal rectifier, Science, vol. 314, no. 5802, pp. 1121-1124, 2006.
- 13. B. Hu, L. Yang, and Y. Zhang, Asymmetric heat conduction in nonlinear lattices, Physical review letters, vol. 97, no. 12, p. 124302, 2006.
- 14. H. Machrafi, G. Lebon, and D. Jou, Thermal rectifier efficiency of various bulk-nanoporous silicon devices, International Journal of Heat and Mass Transfer, vol. 97, pp. 603-610, 2016.
- 15. R. Scheibner, M. König, D. Reuter, A. Wieck, C. Gould, H. Buhmann, and L. Molenkamp, Quantum dot as thermal rectifier, New Journal of Physics, vol. 10, no. 8, p. 083016, 2008.
- 16. Y. C. Tseng, D. M. T. Kuo, Y. C. Chang, and L. Yan-Ting, Heat rectification effect of serially coupled quantum dots, Applied Physics Letters, vol. 103, no. 5, p. 053108, 2013.
- 17. C. F. Barenghi, L. Skrbek, and K. Sreenivasan, Introduction to quantum turbulence, Proc. NAt. Acad. Sci., PNAS-USA, vol. 111(1), pp. 4647-4652, 2014.
- 18. R. J. Donnelly, Quantized vortices in helium II. Cambridge, UK: Cambridge University Press, 1991.
- 19. C. F. Barenghi, R. J. Donnelly, and W. F.Vinen, Quantized Vortex Dynamics and Superuid Turbulence. Berlin: Springer, 2001.
- 20. S. K. Nemirovskii, Quantum turbulence: Theoretical and numerical problems, Physics Reports, vol. 524, no. 3, pp. 85-202, 2013.
- 21. M. Sciacca, D. Jou, and M. S. Mongiovì, Effective thermal conductivity of helium II: from Landau to Gorter-Mellink regimes, Zeitschrift für angewandte Mathematik und Physik, vol. 66, no. 4, pp. 1835-1851, 2015.
- 22. M. S. Mongiovì and D. Jou, Thermodynamical derivation of a hydrodynamical model of inhomogeneous superuid turbulence, Physical Review B, vol. 75, no. 2, p. 024507, 2007.
- 23. D. Jou, G. Lebon, and M. S. Mongiovì, Second sound, superuid turbulence, and intermittent effects in liquid helium II , Physical Review B, vol. 66, pp. 224509-224517, 2002.
- 24. M. Mongiovì, D. Jou, and M. Sciacca, Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superuid helium, Physics Report, vol. 726, pp. 1-71, 2018.
- 25. L. Saluto, M. S. Mongiovì, and D. Jou, Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component, Zeitschrift für angewandte Mathematik und Physik, vol. 65, pp. 531-548, 2014.
- 26. M. S. Mongiovì, Extended irreversible thermodynamics of liquid helium II, Physical Review B, vol. 48, no. 9, pp. 6276-6283, 1993.
- 27. M. S. Mongiovì, Extended irreversible thermodynamics of liquid helium II: boundary condition and propagation of fourth sound, Physica A: Statistical Mechanics and its Applications, vol. 292, no. 1, pp. 55{74, 2001.
- 28. D. Jou, J. Casas-Vázquez, and M. Criado-Sancho, Thermodynamics of Fluids Under Flow. Berlin: Springer, second ed., 2011.
- 29. L. Saluto, D. Jou, and M. S. Mongiovì, Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence, Physica A: Statistical Mechanics and its Applications, vol. 406, pp. 272-280, 2014.
- 30. L. Saluto, D. Jou, and M. S. Mongiovi, Vortex diffusion and vortex-line hysteresis in radial quantum turbulence, Physica B: Condensed Matter, vol. 440, pp. 99-103, 2014.
- 31. M. Sciacca, M. Mongiovi, and D. Jou, Alternative vinen equation and its extension to rotating counterflow, superfluid turbulence, Physica B, vol. 403, pp. 2215-2224, 2008.
- 32. K. P. Martin and J. T. Tough, Evolution of superfluid turbulence in thermal counterflow, Phys. Rev. B, vol. 27, pp. 2788-2799, 1983.
- 33. S. K. Nemirovskii, Diffusion of inhomogeneous vortex tangle and decay of superuid turbulence, Phys. Rev. B, vol. 81, pp. 64512-64521, 2010.
- 34. G. W. Stagg, N. G. Parker, and C. F. Barenghi, Superfluid boundary layer, Phys. Rev. Lett., vol. 118, p. 135301, Mar 2017.
- 35. M. L. Mantia, Particle dynamics in wall-bounded thermal counterflow of superfluid helium, Physics of Fluids, vol. 29, no. 6, p. 065102, 2017.
- 36. W. Vinen, Mutual friction in a heat current in liquid helium II. III. theory of the mutual friction, Proceedings of the Royal Society, London, vol. A240, pp. 493-515, 1957.
- 37. L. Saluto and M. S. Mongiovi, Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels, Communications in Applied and Industrial Mathematics, vol. 7, no. 2, pp. 130-149, 2016.
- 38. I. Carlomagno, V. Cimmelli, and D. Jou, Computational analysis of heat rectification in compositiongraded systems: From macro-to-nanoscale, Physica B: Condensed Matter, vol. 481, pp. 244-251, 2016.