Thermal transport is a key issue limiting many important energy transfer and conversion applications such as thermoelectric energy conversion, thermal management of electronic devices, and thermal barrier coatings. Analogous to the fact that blackbody radiation comprises broad band of photons of different frequencies (colors), heat conduction in solids is also contributed by broad band of phonons (lattice vibrations) of different frequencies. This talk will cover several unusual findings on frequency-dependent (spectral) phonon transport properties in solids, based on predictive atomistic simulations including first principles calculations and molecular dynamics. The first part of the talk will cover non-linear and non-equilibrium thermal transport in graphene. We predict that asymmetric graphene nanoribbons exhibit thermal diode behavior, i.e., thermal transport is more effective in one direction than the opposite direction [1]. We also show that electrons and different phonon modes in graphene are driven out of thermal equilibrium when irradiated with laser [2-3]. Hence, the apparent thermal conductivity obtained from Raman spectroscopy and the Fourier equation can under-estimate the thermal conductivity considerably. These predictions have been confirmed by experiments. The second part of the talk will demonstrate the significance of four-phonon scattering [4]. For a long time the three-phonon scattering process has been considered to govern thermal transport in solids, while the role of higher-order four-phonon scattering has been persistently unclear and so ignored. We show that for silicon and diamond, however, the predicted thermal conductivity is reduced by 30% at 1,000 K after including four-phonon scattering, bringing prediction in excellent agreement with measurements. For the projected ultrahigh-thermal conductivity material, zincblende BAs, a competitor of diamond as a heat sink material, four-phonon scattering is found to be strikingly strong and reduces the predicted thermal conductivity from 2,200 W/m-K to 1,400 W/m-K at room temperature, and the reduction at 1,000 K is 60% [5].   References: [1] Wang, Vallabhaneni, Hu, Qiu, Chen and Ruan, Nano Lett. 14, 592 (2014).[2] Vallabhaneni, Singh, Bao, Murthy, and Ruan, Phys. Rev. B 93, 125432 (2016). [3] Sullivan, Vallabhaneni, Kholmanov, Ruan, Murthy, and Shi, Nano Lett. 17, 2049−2056 (2017). [4] Feng and Ruan, Phys. Rev. B 93, 045202 (2016). [5] Feng, Lindsay, and Ruan, submitted (2017). Dr. Xiulin Ruan is a professor in the School of Mechanical Engineering and Birck Nanotechnology Center at Purdue University.  He received his B.S. (in 2000) and M.S. (in 2002) from the Department of Engineering Mechanics at Tsinghua University. He then received another M.S. in electrical engineering (in 2006) and Ph.D. in mechanical engineering (in 2007) from the University of Michigan at Ann Arbor, before joining Purdue.  His research and teaching interests are focused on multiscale multiphysics simulations and experiments of phonon, photon, and electron transport and interactions, and he has published over 80 journal articles on these topics. He currently serves as an Editorial Board member for the journal Scientific Reports, and an associate editor for ASME Journal of Electronic Packaging.