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Boltzmann Statistic

The Experts below are selected from a list of 54 Experts worldwide ranked by ideXlab platform

A. Ibragimov – 1st expert on this subject based on the ideXlab platform

  • Semi-analytical model for the Seebeck coefficient in semiconductors with isotropic DOS given by a power function
    The European Physical Journal B, 2012
    Co-Authors: A. Ibragimov

    Abstract:

    The relations for the Seebeck coefficient in a semiconductor with the isotropic density of states given by a power function are introduced within the scope of a semi-analytical model, which is based on the theoretical relations given by the foundations of the semiconductor physics as well as on experimentally defined temperature dependences of various semiconductor characteristics, but does not include any adjustable parameters. Between those characteristics the major role plays the intrinsic carrier concentration. It was demonstrated that although the introduced model is based on the simplified Maxwell-Boltzmann Statistic, it is not compromised by this choice. A comparison with experimental data for five different semiconductors proves its ability to provide reliable predictions over a wide range of parameters (temperature, dopant type and concentration) not only for non-degenerated wide bandgap semiconductors (Si, Ge) but also for InAs, which represents partly degenerated narrow bandgap semiconductors with a non-parabolic density of states. Even in the case of a HgCdTe, with its extremely narrow bandgap and complex temperature dependence of the carrier concentration, the model is in good agreement with experimental data. The semi-analytical nature of the introduced model and its dependence on the abundance and reliability of the used experimental data were discussed on the example of Bi_2Te_3. Although the relative deficiency and controversy of the experimental results in this case significantly impede the model’s applicability, it is still able to give at least qualitative predictions, which are nevertheless better than the results of the calculation of the thermopower from first principles. Being primarily addressed to the experimental community, the model provides simple relations in the case of the parabolic non-intrinsic semiconductor for thermoelectric voltage and for optimal dopant concentration for the thermogenerator within the known working temperature range, which can be useful in real-life ‘energy harvesting’ applications.

  • Semi-analytical model for the Seebeck coefficient in semiconductors with isotropic DOS given by a power function
    European Physical Journal B, 2012
    Co-Authors: A. Ibragimov

    Abstract:

    The relations for the Seebeck coefficient in a semiconductor with the isotropic density of states given by a power function are introduced within the scope of a semi-analytical model, which is based on the theoretical relations given by the foundations of the semiconductor physics as well as on experimentally defined temperature dependences of various semiconductor characteristics, but does not include any adjustable parameters. Between those characteristics the major role plays the intrinsic carrier concentration. It was demonstrated that although the introduced model is based on the simplified Maxwell-Boltzmann Statistic, it is not compromised by this choice. A comparison with experimental data for five different semiconductors proves its ability to provide reliable predictions over a wide range of parameters (temperature, dopant type and concentration) not only for non-degenerated wide bandgap semiconductors (Si, Ge) but also for InAs, which represents partly degenerated narrow bandgap semiconductors with a non-parabolic density of states. Even in the case of a HgCdTe, with its extremely narrow bandgap and complex temperature dependence of the carrier concentration, the model is in good agreement with experimental data. The semi-analytical nature of the introduced model and its dependence on the abundance and reliability of the used experimental data were discussed on the example of Bi 2 Te 3 . Although the relative deficiency and controversy of the experimental results in this case significantly impede the model’s applicability, it is still able to give at least qualitative predictions, which are nevertheless better than the results of the calculation of the thermopower from first principles. Being primarily addressed to the experimental community, the model provides simple relations in the case of the parabolic non-intrinsic semiconductor for thermoelectric voltage and for optimal dopant concentration for the thermogenerator within the known working temperature range, which can be useful in real-life ‘energy harvesting’ applications. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Kingsley E. Haynes – 2nd expert on this subject based on the ideXlab platform

  • SPIN GLASS AND THE INTERACTIONS OF CONGESTION AND EMISSIONS: AN EXPLORATORY STEP. IN: TRANSPORT AND INFORMATION SYSTEMS
    Classics in Transport Analysis, 2020
    Co-Authors: Rajendra Kulkarni, Roger R. Stough, Kingsley E. Haynes

    Abstract:

    Traffic congestion formation on roadways s modeled by recognition of the centrality of dynamical systems and by using concepts from complexity theory as imbedded in the spin glass analogue. It also explores the concept of how an increase in air pollution caused by vehicle exhaust emission can be traced to traffic congestion, specifically to the acceleration/deceleration of vehicles on the road. Spin glass is first introduced and then by applying the 2-D x-y Ising model and defining a Hamiltonian for a system of vehicles on the road, derivations are made of the specific friction of congestion and the bulk modulus of congestion using the Gibbs-Boltzmann Statistic. Similarly, using the interactions of vehicles with each other and the resulting accelerations and decelerations of vehicles as the basis for exhaust emissions, derivations are made of a specificity of exhaust emissions. These are analogs to the entropy models of thermodynamics. This series of derivations serves as an analytical model for detecting incidents of congestion and increase in air pollution due to exhaust emissions in transportation systems.

  • Spin glass and the interactions of congestion and emissions: An exploratory step
    Transportation Research Part C-emerging Technologies, 1996
    Co-Authors: Rajendra Kulkarni, Roger R. Stough, Kingsley E. Haynes

    Abstract:

    Abstract This paper models traffic congestion formation on highways and roads by recognizing the centrality of dynamical systems and using concepts from complexity theory as imbedded in the spin glasses analogue. Further, it explores the concept of how an increase in air pollution caused by vehicle exhaust emission can be traced to traffic congestion, specifically to the acceleration/deceleration of vehicles on the roads. First, spin glass is introduced and then by applying the two-dimensional x − y Ising model and defining a Hamiltonian (based on Edwards-Anderson and Mattis models of spin glass systems) for a system of vehicles on the road, derivations are made of the specific friction of congestion and the bulk modulus of congestion using the Gibbs-Boltzmann Statistic. Similarly using the interactions of vehicles with each other and the resulting accelerations and decelerations of vehicles as the basis for exhaust emissions, derivations are made of a specificity of exhaust emissions . These are analogues to the entropy models of thermodynamics. This series of derivations serves as an analytical model for detecting incidents of congestion and increase in air pollution due to exhaust emissions in transportation systems.

Rajendra Kulkarni – 3rd expert on this subject based on the ideXlab platform

  • SPIN GLASS AND THE INTERACTIONS OF CONGESTION AND EMISSIONS: AN EXPLORATORY STEP. IN: TRANSPORT AND INFORMATION SYSTEMS
    Classics in Transport Analysis, 2020
    Co-Authors: Rajendra Kulkarni, Roger R. Stough, Kingsley E. Haynes

    Abstract:

    Traffic congestion formation on roadways s modeled by recognition of the centrality of dynamical systems and by using concepts from complexity theory as imbedded in the spin glass analogue. It also explores the concept of how an increase in air pollution caused by vehicle exhaust emission can be traced to traffic congestion, specifically to the acceleration/deceleration of vehicles on the road. Spin glass is first introduced and then by applying the 2-D x-y Ising model and defining a Hamiltonian for a system of vehicles on the road, derivations are made of the specific friction of congestion and the bulk modulus of congestion using the Gibbs-Boltzmann Statistic. Similarly, using the interactions of vehicles with each other and the resulting accelerations and decelerations of vehicles as the basis for exhaust emissions, derivations are made of a specificity of exhaust emissions. These are analogs to the entropy models of thermodynamics. This series of derivations serves as an analytical model for detecting incidents of congestion and increase in air pollution due to exhaust emissions in transportation systems.

  • Spin glass and the interactions of congestion and emissions: An exploratory step
    Transportation Research Part C-emerging Technologies, 1996
    Co-Authors: Rajendra Kulkarni, Roger R. Stough, Kingsley E. Haynes

    Abstract:

    Abstract This paper models traffic congestion formation on highways and roads by recognizing the centrality of dynamical systems and using concepts from complexity theory as imbedded in the spin glasses analogue. Further, it explores the concept of how an increase in air pollution caused by vehicle exhaust emission can be traced to traffic congestion, specifically to the acceleration/deceleration of vehicles on the roads. First, spin glass is introduced and then by applying the two-dimensional x − y Ising model and defining a Hamiltonian (based on Edwards-Anderson and Mattis models of spin glass systems) for a system of vehicles on the road, derivations are made of the specific friction of congestion and the bulk modulus of congestion using the Gibbs-Boltzmann Statistic. Similarly using the interactions of vehicles with each other and the resulting accelerations and decelerations of vehicles as the basis for exhaust emissions, derivations are made of a specificity of exhaust emissions . These are analogues to the entropy models of thermodynamics. This series of derivations serves as an analytical model for detecting incidents of congestion and increase in air pollution due to exhaust emissions in transportation systems.