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Register a new userTemperature gradient and thermal conductivity in superdiffusive materials
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Thermal conductivities are routinely calculated in molecular dynamics simulations by keeping the boundaries at different temperatures and measuring the slope of the temperature profile in the bulk of the material, explicitly using Fouriers law of heat conduction. Substantiated by the observation of a distinct linear profile at the center of the material, this approach has also been frequently used in superdiffusive materials, such as nanotubes or polymer chains, which do not satisfy Fouriers law at the system sizes considered. It has been recently argued that this temperature gradient procedure yields worse results when compared with a method based on the temperature difference at the boundaries -- thus taking into account the regions near the boundaries where the temperature profile is not linear. We study a realistic example, nanocomposites formed by adding boron nitride nanotubes to a polymer matrix of amorphous polyethylene, to show that in superdiffusive materials, despite the appearance of a central region with a linear profile, the temperature gradient method is actually inconsistent with a conductivity that depends on the system size, and, thus, it should be only used in normal diffusive systems.
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We study the effects of scattering lengths on Levy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensions
We demonstrate that a high-dimensional neural network potential (HDNNP) can predict the lattice thermal conductivity of semiconducting materials with an accuracy comparable to that of density functional theory (DFT) calculation. After a training procedure based on the force, the root mean square error between the forces predicted by the HDNNP and DFT is less than 40 meV/{AA}. As typical examples, we present the results for Si and GaN bulk crystals. The deviation from the thermal conductivity calculated using DFT is within 1% at 200 to 500 K for Si and within 5.4% at 200 to 1000 K for GaN.
We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed Levy glasses. We introduce a geometric parameter $alpha$ which plays a role analogous to the exponent characterizing the step length distribution in random systems. We study the large-time behavior of both local and average observables; for the latter case, we distinguish two different types of averages, respectively over the set of all initial sites and over the scattering sites only. The single long jump approximation is applied to analytically determine the different asymptotic behaviours as a function of $alpha$ and to understand their origin. We also discuss the possibility that the root of the mean square displacement and the characteristic length of the walker distribution may grow according to different power laws; this anomalous behaviour is typical of processes characterized by Levy statistics and here, in particular, it is shown to influence average quantities.
We report a new approach to the thermal conductivity manipulation -- substrate coupling. Generally, the phonon scattering with substrates can decrease the thermal conductivity, as observed in recent experiments. However, we find that at certain regions, the coupling to substrates can increase the thermal conductivity due to a reduction of anharmonic phonon scattering induced by shift of the phonon band to the low wave vector. In this way, the thermal conductivity can be efficiently manipulated via coupling to different substrates, without changing or destroying the material structures. This idea is demonstrated by calculating the thermal conductivity of modified double-walled carbon nanotubes and also by the ice nanotubes coupled within carbon nanotubes.
Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a long-standing problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence of a medium-range order (MRO) has been intensively discussed. However, the specific atomic arrangement corresponding to the MRO and its relationship with physical properties, such as thermal conductivity, remain elusive. Here, we solve this problem by combining topological data analysis, machine learning, and molecular dynamics simulations. By using persistent homology, we constructed a topological descriptor that can predict the thermal conductivity. Moreover, from the inverse analysis of the descriptor, we determined the typical ring features that correlated with both the thermal conductivity and MRO. The results provide an avenue for controlling the material characteristics through the topology of nanostructures.
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