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Scientists from the UGR provide new data on the famous law of heat conduction

Spanish version: http://sl.ugr.es/09GN

French version: http://sl.ugr.es/09Ir

The law of heat conduction, also known as Fourier’s law, establishes the proportionality between the heat current and the local temperature gradient in a material

Researchers from the University of Granada (UGR) contributed new data on Fourier’s law, the law of heat conduction that establishes the proportionality between the heat current and the local temperature gradient in a material.

Their work, titled A violation of universality in anomalous Fourier’s law and recently published in the prestigious journal Scientific Reports, from the Nature group, showed that the anomaly of thermal conductivity in low dimension materials is not universal as has been believed until now, but rather depends on certain microscopic details of the material.

Jean-Baptiste Joseph Fourier formulated his famous law of heat conduction in his book, Théorie Analytique de la Chaleur, a law that has been widely studied and used over the last 200 years. Now, Pablo Hurtado and Pedro L. Garrido, professors in the Department of Electromagnetism and Material Physics and members of the Carlos I Institute for Theoretical and Computational Physics of the UGR, have contributed new information on this law.

For some years it has been known that low dimensional materials (1d or 2d) present an anomaly in their thermal conductivity, which grows without limits with the size of the system, implying a super-efficient transport of energy, and brings with it a myriad of applications. The current explication for this anomaly suggests that it is universal, that is, that its physics are independent of details, depending only on small global system characteristics. This property is one of the most powerful and fertile ideas in theoretical physics, since it explains why apparently different phenomena show the same physics and can be understood within the same theoretical framework. For example, the anomaly in thermal conductivity can be related to another apparently very different problem: the growth of rough surfaces, described by the Kardar-Parisi-Zhang equation.

However, this UGR-led study demonstrated that the anomaly in thermal conductivity in low dimensional materials is not universal since it depends on certain details in the material that cause this phenomenon. To reach this conclusion, the researchers developed a novel scaling method that shows that, despite the observed violation of universality, a generalization in Fourier’s law exists for low dimensional materials, called anomalous Fourier’s law, that precisely describes energy transport in these systems, including in highly non-linear systems and regardless of the system’s size.

The issue raises a double interest for the researchers: on one hand, it allows an understanding of the anomaly and violation of Fourier’s law both at a fundamental and a microscopic level. On the other hand, it is of great technological interest for the various possibilities presented for its application in low dimensional materials.

The most noteworthy example is graphene, a two-dimensional material formed by mono-atomic crystalline carbon sheets, although there are several interesting examples ranging from molecular chains and carbon nanotubes to polymer fibers and nanowires, and even biological examples such as spider silk. All of these materials show anomalous thermal conductivity because of their effective low dimensionality and their applications are innumerable (phononic, transistors, diodes and thermal switches, etc.).

The researchers pointed out that these results are important because, on one hand, they question the current theory based on fluctuating hydrodynamics, indicating the existence of new physics, but at the same time they lead the way, without a doubt more complicated than originally thought, to solve this bicentennial problem.

The text of this article can be downloaded free of charge from the Nature website: http://www.nature.com/articles/srep38823

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Contact:

Pablo Ignacio Hurtado Fernández
Department of Electromagnetism and Material Physics at UGR
Telephones: (+34) 958 241 000 Ext. 20189;  (+34) 958 244 014
E-mail:  phurtado@ugr.es