73,488 research outputs found
Carbon Nanotube Thermal Transport: Ballistic to Diffusive
We propose to use l_0/(l_0+L) for the energy transmission covering both
ballistic and diffusive regimes, where l_0 is mean free path and L is system
length. This formula is applied to heat conduction in carbon nanotubes (CNTs).
Calculations of thermal conduction show: (1) Thermal conductance at room
temperature is proportional to the diameter of CNTs for single-walled CNTs
(SWCNTs) and to the square of diameter for multi-walled CNTs (MWCNTs). (2)
Interfaces play an important role in thermal conduction in CNTs due to the
symmetry of CNTs vibrational modes. (3) When the phonon mean free path is
comparable with the length L of CNTs in ballistic-diffusive regime, thermal
conductivity \kappa goes as L^{\alpha} . The effective exponent \alpha is
numerically found to decrease with increasing temperature and is insensitive to
the diameter of SWCNTs for Umklapp scattering process. For short SWCNTs (<0.1
\mu m) we find \alpha \approx 0.8 at room temperature. These results are
consistent with recent experimental findings.Comment: 4 pages, two figure
Dimensional crossover of thermal conductance in nanowires
Dimensional dependence of thermal conductance at low temperatures in
nanowires is studied using the nonequilibrium Green's function (NEGF) method.
Our calculation shows a smooth dimensional crossover of thermal conductance in
nanowire from one-dimensional to three-dimensional behavior with the increase
of diameters. The results are consistent with the experimental findings that
the temperature dependence of thermal conductance at low temperature for
diameters from tens to hundreds nanometers will be close to Debye law. The
calculation also suggests that universal thermal conductance is only observable
in nanowires with small diameters. We also find that the interfacial thermal
conductance across Si and Ge nanowire is much lower than the corresponding
value in bulk materials.Comment: 4 figure
Tuning thermal transport in nanotubes with topological defects
Using the atomistic nonequilibrium Green's function, we find that thermal
conductance of carbon nanotubes with presence of topological lattice imperfects
is remarkably reduced, due to the strong Rayleigh scattering of high-frequency
phonons. Phonon transmission across multiple defects behaves as a cascade
scattering based with the random phase approximation. We elucidate that phonon
scattering by structural defects is related to the spatial fluctuations of
local vibrational density of states (LVDOS). An effective method of tuning
thermal transport in low-dimensional systems through the modulation of LVDOS
has been proposed. Our findings provide insights into experimentally
controlling thermal transport in nanoscale devicesComment: 10 pages, 3 figure
A Simple Approach to Functional Inequalities for Non-local Dirichlet Forms
With direct and simple proofs, we establish Poincar\'{e} type inequalities
(including Poincar\'{e} inequalities, weak Poincar\'{e} inequalities and super
Poincar\'{e} inequalities), entropy inequalities and Beckner-type inequalities
for non-local Dirichlet forms. The proofs are efficient for non-local Dirichlet
forms with general jump kernel, and also work for settings. Our
results yield a new sufficient condition for fractional Poincar\'{e}
inequalities, which were recently studied in \cite{MRS,Gre}. To our knowledge
this is the first result providing entropy inequalities and Beckner-type
inequalities for measures more general than L\'{e}vy measures.Comment: 12 page
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