scholarly journals Heat conduction on the ring: Interface problems with periodic boundary conditions

2014 ◽  
Vol 37 ◽  
pp. 107-111 ◽  
Author(s):  
Natalie E. Sheils ◽  
Bernard Deconinck
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Interface Problems

Heat Conduction of a Porous Material

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Koji Miyazaki ◽  
Saburo Tanaka ◽  
Daisuke Nagai
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Porous Material ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Phonon Dispersion ◽  
Bulk Material ◽  
Periodic Boundary Conditions ◽  
Boltzmann Transport ◽  
Time Space

In this study, we introduce our numerical and experimental works for the thermal conductivity reduction by using a porous material. Recently thermal conductivity reduction has been one of the key technologies to enhance the figure of merit (ZT) of a thermoelectric material. We carry out numerical calculations of heat conduction in porous materials, such as phonon Boltzmann transport (BTE) and molecular dynamics (MD) simulations, in order to investigate the mechanism of the thermal conductivity reduction of a porous material. In the BTE, we applied the periodic boundary conditions with constant heat flux to calculate the effective thermal conductivity of porous materials.In the MD simulation, we calculated the phonon properties of Si by using the Stillinger–Weber potential at constant temperature with periodic boundary conditions in the x, y, and z directions. Phonon dispersion curves of single crystal of Si calculated from MD results by time-space 2D FFT are agreed well with reference data. Moreover, the effects of nanoporous structures on both the phonon group velocity and the phonon density of states (DOS) are discussed. At last, we made a porous p-type Bi2Te3 by nanoparticles prepared by a beads milling method. The thermal conductivity is one-fifth of that of a bulk material as well as keeping the same Seebeck coefficient as the bulk value. However, electrical conductivity was much reduced, and the ZT was only 0.048.

Heat Conduction of a Porous Material

2009 ◽  
Author(s):  
Koji Miyazaki
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Porous Material ◽  
Boundary Conditions ◽  
Porous Materials ◽  
Periodic Boundary ◽  
Phonon Dispersion ◽  
Periodic Boundary Conditions ◽  
Nano Particles ◽  
Time Space

In this study we introduce our numerical and experimental works for the thermal conductivity reduction by using a porous material. Recently thermal conductivity reduction has been one of the key technologies to enhance the figure of merit (ZT) of a thermoelectric material. We carry out numerical calculations of heat conduction in porous materials, such as, phonon Boltzmann transport (BTE), molecular dynamics simulations (MD), in order to investigate the mechanism of the thermal conductivity reduction of a porous material. In the BTE, we applied the periodic boundary conditions with constant heat flux to calculate the effective thermal conductivity of porous materials. In the MD simulation, we calculated phonon properties of Si by using the Stillinger-Weber potential at constant temperature with periodic boundary conditions in the x, y and z directions. Phonon dispersion curves of single crystal of Si calculated from MD results by time-space 2D FFT are agreed well with reference data. Moreover, the effects of nano-porous structures on both the phonon group velocity and the phonon density of states (DOS) are discussed. At last, we made a porous p-type Bi2Te3 by nano-particles prepared by a beads milling method. The thermal conductivity is one-fifth of that of a bulk material as well as keeping the same Seebeck coefficient as the bulk value. However electrical conductivity was much reduced, and the ZT was only 0.048.

Heat Conduction in a Nano-Porous Material and Its Application

2011 ◽  
Author(s):  
Koji Miyazaki
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Porous Material ◽  
Boundary Conditions ◽  
Porous Materials ◽  
Figure Of Merit ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Time Space

In this study we introduce our numerical and experimental works for the thermal conductivity reduction by using a porous material. Recently thermal conductivity reduction has been one of the key technologies to enhance the figure of merit (ZT) of a thermoelectric material. We carry out numerical calculations of heat conduction in porous materials, such as, phonon Boltzmann transport (BTE), molecular dynamics simulations (MD), in order to investigate the mechanism of the thermal conductivity reduction of a porous material. In the BTE, we applied the periodic boundary conditions with constant heat flux to calculate the effective thermal conductivity of porous materials. In the MD simulation, we calculated phonon properties of Si by using the Stillinger-Weber potential at constant temperature with periodic boundary conditions in the x,y and z directions. Phonon dispersion curves of single crystal of Si calculated from MD results by time-space 2D FFT are agreed well with reference data. Moreover, the effects of nano-porous structures on both the phonon group velocity and the phonon density of states (DOS) are discussed. At last, we made a porous p-type Bi2Te3 by using self-assembly. The average diameter of the holes was 20 nm, and the average pitch of the hexagonally arranged holes was 50 nm. The measured cross-plane thermal conductivity is 0.25W/(m·K). The thermal conductivity of the thin film is extremely lower than that of the bulk material without any major decrease in the electrical conductivity. The figure of merit of Bi0.4Te3Sb1.6 is enhanced to 1.8 at room temperature (300K) by the formation of a porous thin film.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

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