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Nonlocal, Gradient and Local Models of Elastic Media: 1D Case
Published in Igor V. Andrianov, Vladyslav Danishevskyy, Jan Awrejcewicz, Linear and Nonlinear Waves in Microstructured Solids, 2021
Igor V. Andrianov, Vladyslav Danishevskyy, Jan Awrejcewicz
It is interesting to mention, that the Einstein theory of the heat capacity of solids used the so far presented conception of π-mode. The Einstein solid is a model of a solid based on two assumptions: each atom in the lattice is an independent 3D quantum harmonic oscillator and all atoms oscillate with the same frequency (in contrast to the Debye model).
Modeling Thermal Effects in Nano-Devices
Published in Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck, Computational Electronics, 2017
Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck
where CLO is the specific heat capacity for optical phonons, which can be estimated from the Einstein model, while CA (the specific heat capacity for acoustic phonons) is taken from the Debye model. Next, the collision terms are expressed using the relaxation time approximation (RTA)
Modeling Self-Heating Effects in Nanoscale Devices
Published in Zlatan Aksamija, Nanophononics, 2017
Katerina Raleva, Abdul Rawoof Shaik, Suleman Sami Qazi, Robin Daugherty, Akash Laturia, Ben Kaczer, Eric Bury, Dragica Vasileska
where CLO (specific heat capacity for optical phonons) can be estimated using the Einstein model, while CA (specific heat capacity for acoustic phonons) from the Debye model. Next, the collision terms are expressed using RTA: () (∂We∂t)coll=n⋅32kBTe+12m*vd2−32kBTphτe−ph
Identification of invisible fatigue damage of thermosetting epoxy resin by non-destructive thermal measurement using entropy generation
Published in Advanced Composite Materials, 2023
Natsuko Kudo, Ryohei Fujita, Yutaka Oya, Takenobu Sakai, Hosei Nagano, Jun Koyanagi
where is the heat capacity of the epoxy resin. The temperature dependence of specific heat capacity over a wide temperature range is necessary to determine thermal entropy generation. It is well known that the Debye model can represent the temperature dependence of solid materials; that is, the specific heat capacity is proportional to the cube of the temperature in the low-temperature region and is constant in the high-temperature region [50]. However, previous experiments have demonstrated that thermoplastic polymers, such as PA6, have a specific heat capacity that increases with temperature at approximately room temperature [42]. One of the primary factors causing the difference in the temperature dependence of specific heat capacity is the arrangement of atoms constituting a molecule. The Debye model assumes that the atoms are arranged in a regular lattice. By contrast, the thermosetting polymer used in this study has an amorphous structure in which atoms are arranged randomly in a system similar to that of a thermoplastic polymer. To capture the temperature dependence resulting from the irregular arrangement of atoms, we propose the following equation:
Pressure dependence of the electronic, optical, thermoelectric, thermodynamic properties of CsVO3: first-principles study
Published in Philosophical Magazine, 2022
S. Sâad Essaoud, A. Bouhemadou, S. Maabed, S. Bin-Omran, R. Khenata
According to the Debye model, which describes the vibration of atoms at certain frequencies, the Debye temperature θD expresses the highest temperature value that the system can reach due to a single normal vibration. From Figure 8, one notes the direct proportionality of Debye temperature with pressure and its inverse proportionality with temperature. At zero pressure and 300 K, Debye temperature of CsVO3 is equal to 402.8 K.