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In this paper, we present the results of theoretical studies of the possible mechanism of energy dissipation that takes place in the experiments with vibrating quartz fork in superfluid 3He–4He mixtures with high concentration. The possibility and efficiency of the tuning fork radiation of both the second sound wave and the diffusion dissipative wave were investigated. The relationships between the amplitudes of temperature and concentration oscillations in these waves were found and the relative wave intensities were determined. This allowed us to give a possible explanation for observed additional mechanisms of tuning fork attenuation in helium solutions. [ABSTRACT FROM AUTHOR]

We present a theoretical study of heat transfer properties in three-dimensional cylindrical conductors of finite lengths in the ballistic regime of phonon propagation. The phonon emission is considered to be radiative and its interactions with the lateral boundary is assumed to be completely diffusive. The main goal of this study is to determine the temperature profile and the features of its formation for the generalized case of a conductor of finite length. A matrix numerical solution of the integral equation for the particle energy flux is obtained and an approximate analytical solution of this equation is proposed. The heat flux and thermal conductivity coefficient are determined; and the significant difference between our results and those of the generally accepted formulation in the Knudsen regime and the Casimir model is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the phonon heat transfer in two-dimensional conductors with different types of phonon reflection from the boundaries is examined. Heat conductors with arbitrary ratios of width W to length L are studied assuming that the mean free path between phonon-phonon collisions is infinite. The integral equations for the angular distribution functions of the incident and reflected phonons at a specific point on the conductor boundary were proposed. To solve these integral equations a new iterative method is proposed. The proposed iterative approach formally corresponds to taking into account subsequent collisions of phonons with the edges of the conductor. It ensures the convergence of the desired solution for any W/L ratio and for any value of the specularity coefficient p. Interpolation formulae are found to describe with sufficient accuracy the solution of the system of integral equations in the entire region of the specularity coefficient p from 0 to 1, and the W/L ratios ranging from 10 to 0.01. These formulae allow the construction of the isolines of the thermal conductance coefficient values, from which it is possible to determine the necessary values of W/L and parameter p to get the desired value of the thermal conductance. [ABSTRACT FROM AUTHOR]

Within the framework of the theory of random walks, we present an analytical study of one-dimensional ballistic flux of quasiparticles in the presence of scattering centers (SCs) such as defects or dopants. An explicit analytical expression is derived for the quasiparticle flux and the associated heat flux carried by phonons as a function of the number of SCs and the probabilities of (i) forward and backward scattering at SCs and (ii) absorption of quasiparticles by the SCs and in the conductor between SCs. The practical application of our model to one-dimensional nanostructures and to quasi-one-dimensional heat-conducting systems such as linear polycrystals is discussed. Various limiting cases are also considered. We demonstrate that our model is in excellent agreement with experimental data on the thermal conductance of Si nanowires having geometrically modified S-shaped extremities that act as SCs to the phonon flux. [ABSTRACT FROM AUTHOR]

When modeling heat transfer in nanoribbons, an unusually sharp dependence of the heat flux, and, consequently, the thermal conductivity coefficient, on the degree of specularity of phonon reflection from the lateral boundaries was found. From numerical calculations, it followed that the addition of minimally diffuse scattering should lead to an abrupt increase in the thermal resistance of the conductor. Given the importance of selecting optimal thermal parameters in nanotechnology, this short paper provides an analysis of the found dependencies, discusses the physical reasons for this anomalous behavior, and draws conclusions about the importance of achieving the quality of the nanoconductor interface to create thermal contacts with a given or optimal thermal conductivity. [ABSTRACT FROM AUTHOR]

Phonon transport in square-cross-section nanowires is studied using spectral Monte Carlo simulations. Our results show the evolution of the different transport regimes described by Lévy statistics as a function of the surface roughness-to-thermal wavelength ratio σ/λ. More precisely, the relationship between the Lévy index γ describing the mean free path distribution Ψ(Λ) and σ/λ is established for the classical diffusive regime, the superdiffusive regime, and the ballistic regime in the nanowire. Besides the conventional superdiffusive regime that is marked by Ψ(Λ) with a single heavy-tailed peak, we reveal an unconventional superdiffusive subregime featuring Ψ(Λ) with sawtooth oscillations when σ/λ∼0.01. Investigation of the direction of propagation of phonons shows a significant narrowing of the angular distribution around the long axis of the nanowire due to the diffuse scattering at rough boundaries when σ/λ>0.1. These results shed light on the transport mechanisms of quasiballistic phonons and will help in nanowire design for specific applications.