Observation of second sound in graphite over 200 K

Second sound refers to the phenomenon of heat propagation as temperature waves in the phonon hydrodynamic transport regime. We directly observe second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique. The experimentally determined dispersion relation of the thermal-wave velocity increases with decreasing grating period, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation. Through simulation, we reveal this increase as a result of thermal zero sound—the thermal waves due to ballistic phonons. Our experimental findings are well explained with the interplay among three groups of phonons: ballistic, diffusive, and hydrodynamic phonons. Our ab initio calculations further predict a large isotope effect on the properties of thermal waves and the existence of second sound at room temperature in isotopically pure graphite.

The Irradiation Instability of Protoplanetary Disks

The temperature in most parts of a protoplanetary disk is determined by irradiation from the central star. Numerical experiments of Watanabe and Lin suggested that such disks, also called “passive disks,” suffer from a thermal instability. Here we use analytical and numerical tools to elucidate the nature of this instability. We find that it is related to the flaring of the optical surface, the layer at which starlight is intercepted by the disk. Whenever a disk annulus is perturbed thermally and acquires a larger scale height, disk flaring becomes steeper in the inner part and flatter in the outer part. Starlight now shines more overhead for the inner part and so can penetrate into deeper layers; conversely, it is absorbed more shallowly in the outer part. These geometric changes allow the annulus to intercept more starlight, and the perturbation grows. We call this the irradiation instability. It requires only ingredients known to exist in realistic disks and operates best in parts that are both optically thick and geometrically thin (inside 30 au, but can extend to further reaches when, e.g., dust settling is considered). An unstable disk develops traveling thermal waves that reach order unity in amplitude. In thermal radiation, such a disk should appear as a series of bright rings interleaved with dark shadowed gaps, while in scattered light it resembles a moving staircase. Depending on the gas and dust responses, this instability could lead to a wide range of consequences, such as ALMA rings and gaps, dust traps, vertical circulation, vortices, and turbulence.

Bragg Mirrors for Thermal Waves

We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier’s law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation’s solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved (>90%). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier’s law.

Bragg Mirrors for Thermal Waves

We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier's law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation's solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved ($>90\%$). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier's law.

High-order fluxes in heat transfer with phonons and electrons: application towavepropagation

We propose a theoretical model to study heat transfer at the nanoscale by means of high-order thermodynamic fluxes. The model is fully compatible with the model of heat transfer of extended irreversible thermodynamics, represents a generalization of the Guyer–Krumhansl proposal (Guyer & Krumhansl 1966 Phys. Rev. 148 ) and is able to deal with relaxational and non-local effects. It also accounts for the role played by the different heat carriers (electrons and/or lattice vibrations) and captures different heat-carrier temperatures. The proposed model is hyperbolic and is used to investigate the propagation of thermal waves.

Thermal Oscillations in Sea Ice and Soils

<p><b>We present mathematical analysis of temperature oscillations in depth-dependent media by investigating the thermodynamics of sea ice and of soils. Time-series temperature measurements from thermistor strings are common in both sea ice and soils and are used to study their properties, evolution, seepage flux and a host of interactions with their environment. We use numerical tools and perturbation theory to study the propagation of high frequency, small amplitude temperature oscillations through the in-homogeneous media using one dimensional models. Analytical tools for studying such thermal waves are derived.</b></p> <p>In sea ice the absorption of solar radiation and oscillating air temperatures result in two distinct thermal wave propagation behaviours. At depths, stationary waves associated with in place solar heating are observed, whereas near the surface, travelling thermal waves are present due to the quick decay in the absorbed solar radiation and the oscillatory air temperatures. These are observed in thermistor string data taken in McMurdo Sound, Antarctica between 1996-2003. Using a variety of mathematical tools, the leading order behaviour of the diurnal temperature oscillation is approximated in terms of elementary functions and is compared with results from numerical simulations.</p> <p>The thermodynamics of soils differ from sea ice in that all the solar radiation is absorbed at the upper boundary and water movement within the soil carries heat. Macroscale in-homogeneity in the advection-diffusion equation is considered and the thermal wave propagation characteristics are studied using a WKB approximation. The leading order behaviour is shown to reduce exactly to the Stallman equations, being the solution to the thermal wave propagation in a homogeneous soil with constant, uniform water flow. We use the leading order WKB expansion to estimate errors in the homogeneous soil assumption commonly made to estimate the seepage velocity and soil diffusivity. It is shown that the diffusivity estimations are relatively stable and provide reasonably accurate results, but the seepage velocity estimations incur significant errors that should be considered. A frequency dependence in the error leads us to suggest multi-frequency analysis for detection and further studies of the effects of in-homogeneous soil thermodynamics.</p>

Thermal Oscillations in Sea Ice and Soils

<p><b>We present mathematical analysis of temperature oscillations in depth-dependent media by investigating the thermodynamics of sea ice and of soils. Time-series temperature measurements from thermistor strings are common in both sea ice and soils and are used to study their properties, evolution, seepage flux and a host of interactions with their environment. We use numerical tools and perturbation theory to study the propagation of high frequency, small amplitude temperature oscillations through the in-homogeneous media using one dimensional models. Analytical tools for studying such thermal waves are derived.</b></p> <p>In sea ice the absorption of solar radiation and oscillating air temperatures result in two distinct thermal wave propagation behaviours. At depths, stationary waves associated with in place solar heating are observed, whereas near the surface, travelling thermal waves are present due to the quick decay in the absorbed solar radiation and the oscillatory air temperatures. These are observed in thermistor string data taken in McMurdo Sound, Antarctica between 1996-2003. Using a variety of mathematical tools, the leading order behaviour of the diurnal temperature oscillation is approximated in terms of elementary functions and is compared with results from numerical simulations.</p> <p>The thermodynamics of soils differ from sea ice in that all the solar radiation is absorbed at the upper boundary and water movement within the soil carries heat. Macroscale in-homogeneity in the advection-diffusion equation is considered and the thermal wave propagation characteristics are studied using a WKB approximation. The leading order behaviour is shown to reduce exactly to the Stallman equations, being the solution to the thermal wave propagation in a homogeneous soil with constant, uniform water flow. We use the leading order WKB expansion to estimate errors in the homogeneous soil assumption commonly made to estimate the seepage velocity and soil diffusivity. It is shown that the diffusivity estimations are relatively stable and provide reasonably accurate results, but the seepage velocity estimations incur significant errors that should be considered. A frequency dependence in the error leads us to suggest multi-frequency analysis for detection and further studies of the effects of in-homogeneous soil thermodynamics.</p>