Size Effects on Nanowire Phonon Thermal Conductivity: a Numerical Investigation Using the Boltzmann Equation
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Analytical solution of the Boltzmann transport equation for phonon transport in Bi 0.95 Sb 0.05 nanowire is obtained.Thermal conductivity was calculated from the analytical solution of the Boltzmann transport equation.We calculate the lattice thermal conductivity of Bi 0.95 Sb 0.05 nanowire as a function of temperature for different wire thicknesses.The results show that thermal conductivity of nanowire can be significantly smaller than the bulk thermal conductivity.We show that low thermal conductivity Bi 0.95 Sb 0.05 nanowire for thermoelectric applications would have a small diameter.Keywords:
Lattice Boltzmann methods
Boltzmann constant
In this paper, the lattice vehicular model, which is in the form the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. A 3-bit approximation, which describe uncongested traffic flow, for the discretization of the Boltzmann equation in both time and phase space is discussed in detail. The lattice vehicular Boltzmann model ensures vehicles would not travel backward. A general procedure to derive the vehicular lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly.
Lattice Boltzmann methods
Bhatnagar–Gross–Krook operator
Lattice gas automaton
Boltzmann relation
Boltzmann constant
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It is well known that the lattice Boltzmann Method (LBM) has been very successful in many computational physics fields. In contrast, numerical theory in the lattice Boltzmann method has made little headway. In order to solve a 2D Burgers equation, a lattice Boltzmann scheme with a BGK model is constructed. The maximum value principle is proved and stability is also obtained. Numerical experiments show the second order convergent accuracy of the scheme.
Lattice Boltzmann methods
Bhatnagar–Gross–Krook operator
Lattice gas automaton
Lattice (music)
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Abstract The Boltzmann equation is at the heart of the semiclassical Bloch–Boltzmann theory of electronic transport in solids. The kinetic theory of gases based on the Boltzmann equation, originally developed for dilute classical gases, has since been applied successfully to the electron gas in metals and in semiconductors, despite of the fact that this latter gas is neither classical (except in non-degenerate semiconductors) nor dilute.
Semiclassical physics
Boltzmann constant
Kinetic Theory
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This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients by using two-term approximation of Boltzmann equation. But there is difference between the result of the two-term approximation of the Boltzmann equation and experiments in pure CF$_4$ molecular gas and in CF$_4$ +Ar gas mixture. Therefore, In this paper, we calculated the electron drift velocity (W) in pure CF$_4$ molecular gas and CF$_4$ +Ar gas mixture (1 %, 5 %, 10 %) for range of E/N values from 0.17～300 Td at the temperature was 300 K and pressure was 1 Torr by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation have been compared with each other for a range of E/N.
Boltzmann constant
Torr
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Abstract In Chapter 4, we examined the classical and quantum mechanical generalizations of the Boltzmann equation needed for the treatment of transport and relaxation phenomena in a gas of rotating molecules.
Boltzmann constant
Lattice Boltzmann methods
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We present a direct solution method to the Bloch‐Boltzmann‐Peierls equations governing the transport of carriers and optical phonons in semiconductors. This approach is based on a multigroup formulation of the original equations, which still contains both the full quantum statistics of carriers and phonons and a very general description of the carrier band structure. It allows the investigation of the particle distributions of arbitrary anisotropies with respect to a main direction. Concerning the mathematical properties of the deduced transport model, we prove a Boltzmann H‐theorem for the obtained evolution equations. The equilibrium solution of the multigroup model is compared with that of the original Bloch‐Boltzmann‐Peierls equations. Numerical results are given for relaxation processes of hot electrons and hot phonons.
Boltzmann constant
Convection–diffusion equation
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We present numerical calculations of quantum transport in perfect octagonal approximants. These calculations include a Boltzmann (intra-band) contribution and a non-Boltzmann (inter-band) contribution. When the unit cell size of the approximant increases, the magnitude of the Boltzmann terms decreases, whereas the magnitude of the non-Boltzmann terms increases. This shows that, in large approximants, the non-Boltzmann contributions should dominate the transport properties of electrons. This confirms the breakdown of the Bloch–Boltzmann theory for understanding the transport properties in approximants with very large unit cells, and then in quasicrystals, as found in actual Al-based approximants.
Boltzmann constant
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In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.
Lattice Boltzmann methods
Bhatnagar–Gross–Krook operator
Lattice gas automaton
Boltzmann relation
Boltzmann's entropy formula
Boltzmann constant
Boltzmann distribution
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We celebrate Boltzmann on the occasion of his 150th birthday as a pioneer of many-body theory. Of special importance for many-body physics is Boltzmann's transport equation which he introduced in order to describe the macroscopic behavior of gases in terms of the microscopic motion of interacting atoms. One might say, using a more modern language, that Boltzmann's equation solved the many-body problem of a dilute gas of classical atoms with strong short range interactions. It was realized later that this equation is a very fundamental equation of many-body statistics. For example, the Boltzmann equation is established today as one of the basic equations of the physics of gases, plasma physics, neutron transport, radiative transfer, the theory of semiconductors and metals, the theory of quantum liquids, and other fields of physics.
Boltzmann constant
Many-body theory
Classical physics
Convection–diffusion equation
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