Application of the wavelet transform to nanoscale thermal transport

Physical Review B - Condensed Matter and Materials Physics

Volumn 86, Issue 10, 2012, Pages

  Baker, Christopher H ^a   Jordan, Donald A ^a   Norris, Pamela M ^a  

^a University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866887122     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.86.104306     Document Type: Article

References (50)

1. L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.47.12727 47, 12727 (1993).
2. L. E. Bell, Science SCIEAS 0036-8075 10.1126/science.1158899 321, 1457 (2008).
3. C. J. Vineis, A. Shakouri, A. Majumdar, and M. G. Kanatzidis, Adv. Mater. ADVMEW 0935-9648 10.1002/adma.201000839 22, 3970 (2010).
4. P. Pichanusakorn and P. Bandaru, Mater. Sci. Eng., R MIGIEA 0927-796X 10.1016/j.mser.2009.10.001 67, 19 (2010).
5. A. Shakouri, Annu. Rev. Mater. Res. ARMRCU 1531-7331 10.1146/annurev- matsci-062910-100445 41, 399 (2011).
6. K. W. J. Barnham and G. Duggan, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.345339 67, 3490 (1990).
7. G. Chen, Nanoscale Energy Transport and Conversion (Oxford University Press, Oxford, UK, 2005).
8. W. A. Little, Can. J. Phys. CJPHAD 0008-4204 10.1139/p59-037 37, 334 (1959).
9. E. T. Swartz and R. O. Pohl, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.61.605 61, 605 (1989).
10. M. T. Dove, Introduction to Lattice Dynamics (Cambridge University Press, Cambridge, UK, 1993).
11. A. Ward and D. A. Broido, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.085205 81, 085205 (2010).
12. V. Narayanamurti, H. L. Störmer, M. A. Chin, A. C. Gossard, and W. Wiegmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.2012 43, 2012 (1979).
13. T. S. English, J. C. Duda, J. L. Smoyer, D. A. Jordan, P. M. Norris, and L. V. Zhigilei, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.035438 85, 035438 (2012).
14. N. Mingo and L. Yang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68. 245406 68, 245406 (2003);
15. N. Mingo and L. Yang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70. 249901 70, 249901 (E) (2004). (Pubitemid 40362508)
16. J.-S. Wang, J. Wang, and N. Zeng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.033408 74, 033408 (2006). (Pubitemid 44087226)
17. D. A. Young and H. J. Maris, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.3685 40, 3685 (1989).
18. H. Zhao and J. B. Freund, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1835565 97, 024903 (2005); (Pubitemid 40183078)
19. H. Zhao and J. B. Freund, J. Appl. Phys. 0021-8979 10.1063/1.1899761 97, 109901 (E) (2005). (Pubitemid 40866182)
20. P. K. Schelling, S. R. Phillpot, and P. Keblinski, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1465106 80, 2484 (2002). (Pubitemid 34474313)
21. L. Sun and J. Y. Murthy, J. Heat Transfer JHTRAO 0022-1481 10.1115/1.4001912 132, 102403 (2010).
22. M. Hu, P. Keblinski, J.-S. Wang, and N. Raravikar, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.3000441 104, 083503 (2008).
23. L. Hu, L. Zhang, M. Hu, J.-S. Wang, B. Li, and P. Keblinski, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.235427 81, 235427 (2010).
24. N. A. Roberts and D. G. Walker, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.3517159 108, 123515 (2010).
25. Z. T. Tian, B. E. White, Jr., and Y. Sun, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3458831 96, 263113 (2010).
26. C. Kimmer, S. Aubry, A. Skye, and P. K. Schelling, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.144105 75, 144105 (2007).
27. A. J. H. McGaughey and M. Kaviany, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.094303 69, 094303 (2004);
28. A. J. H. McGaughey and M. Kaviany, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.189901 79, 189901(E) (2009).
29. J. E. Turney, E. S. Landry, A. J. H. McGaughey, and C. H. Amon, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.064301 79, 064301 (2009).
30. J. M. Dickey and A. Paskin, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.188.1407 188, 1407 (1969).
31. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2004).
32. To be sure, the issue of locality is addressed by the short-time or windowed Fourier transform which is a modification of the Fourier transform. The focus shall remain on the wavelet transform and its contrast to the Fourier transform because (1) the Fourier transform is vastly more familiar to the nanoscale community as it is the basis of some of its most important concepts, including density of states, and (2) the wavelet transform contains additional advantages over the short-time Fourier transform. Interested readers are directed to Kaiser for a more in-depth comparison of the two techniques (Ref.).
33. M. Farge, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fl.24. 010192.002143 24, 395 (1992).
34. P. Goupillaud, A. Grossman, and J. Morlet, Geoexploration GEOXAV 0016-7142 10.1016/0016-7142(84)90025-5 23, 85 (1984). (Pubitemid 14661429)
35. S. Mallat, IEEE Trans. Pattern Anal. Mach. Intell. ITPIDJ 0162-8828 10.1109/34.192463 11, 674 (1989).
36. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, IEEE Trans. Image Process. IIPRE4 1057-7149 10.1109/83.136597 1, 205 (1992).
37. C. Torrence and G. P. Compo, Bull. Am. Meteorol. Soc. BAMIAT 0003-0007 79, 61 (1998).
38. J. Shiomi and S. Maruyama, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.205420 73, 205420 (2006). (Pubitemid 43764892)
39. G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, 1994).
40. M. Plancheral and M. Leffler, Rend. Circolo Mat. (Palermo) RCMMAR 0009-725X 10.1007/BF03014877 30, 289 (1910);
41. E. C. Titchmarsh, Proc. London Math. Soc. PLMTAL 0024-6115 10.1112/plms/s2-23.1.279 23, 279 (1925).
42. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1999).
43. D. Jordan, R. W. Miksad, and E. J. Powers, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1147636 68, 1484 (1997).
44. This result can be derived from Eqs. and.
45. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).
46. F. H. Stillinger and T. A. Weber, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.31.5262 31, 5262 (1985);
47. F. H. Stillinger and T. A. Weber, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.33.1451 33, 1451(E) (1986).
48. J. D. Gale and A. L. Rohl, Mol. Simul. MOSIEA 0892-7022 10.1080/0892702031000104887 29, 291 (2003). (Pubitemid 44115103)
49. S. Plimpton, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1995.1039 117, 1 (1995).
50. S. Sinha, P. K. Schelling, S. R. Phillpot, and K. E. Goodson, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1831549 97, 023702 (2005). (Pubitemid 40183036)