Boltzmann Statistic

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A. Ibragimov - One of the best experts 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 - One of the best experts 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 - One of the best experts 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.

Razali Ismail - One of the best experts on this subject based on the ideXlab platform.

  • Analysis and simulation of carriers Statistic for semiconducting single wall carbon nanotube
    Materials Research Innovations, 2020
    Co-Authors: J. Karamdel, Mohammad Taghi Ahmadi, Mitra Damghanian, Burhanuddin Yeop Majlis, Razali Ismail
    Abstract:

    AbstractIn scaling down to 10 nm, the electron transportation is predominantly ballistic. Moreover, in most of the doped nanoscale devices, the carrier density is in the degenerate regime. In these cases the failure of Boltzmann Statistic has led the research to new explanations. In this paper the authors formulate and simulate the carrier concentration in a semiconducting single wall carbon nanotube using the Fermi-Dirac distribution function. It was shown that the band structure of semiconducting single wall carbon nanotube nearby the minimum energy is parabolic and density of state is proportional to the Fermi-Dirac distribution. In the non-degenerate regime, Fermi energy is a weak logarithmic function of carrier concentration and varies linearly with temperature, but for strongly degenerate Statistics, the Fermi energy is a strong function of carrier concentration and is independent of temperature.

  • Numerical Study of Carrier Velocity for P-type Strained Silicon MOSFET
    2009
    Co-Authors: Yau Wei Heong, Mohammad Taghi Ahmadi, Jatmiko Endro Suseno, Razali Ismail
    Abstract:

    Strained induced in the silicon channel layer provides lower effective mass and suppresses intervalley scattering. In this paper, a numerical study of carrier concentration for P-type strained Silicon MOS is presented. Density of state proportion of Fermi-Dirac integral that covers the carrier Statistics to all degenerate level is studied and its limits are obtained. In the nondegenerate regime the results replicate Boltzmann Statistic and its result is vary in degenerate regime. The Fermi energy with respect to the transformed band edge is a function of carrier concentration for quasi two dimensional strained Silicon PMOS. Based on the Fermi - Dirac Statistic, density of state the carrier concentration is obtained. Fermi energy is a function of temperature that independent of the carrier concentration in the nondegenrate regime. In the other strongly degenerate, the Fermi energy is a function of carrier concentration appropriate for given dimensionality, but is independent of temperature. The limitations on carrier drift due to high-field streamlining of otherwise randomly velocity vector in equilibrium is reported. The results are based on asymmetrical distribution function that converts randomness in zero-field to streamlined one in a very high electric field. The ultimate drift velocity is found to be appropriate thermal velocity for a given dimensionality for non- degenerately doped nanostructure. However, the ultimate drift velocity is the Fermi velocity for degenerately doped nanostructures.

Ziyad Abdalrahman - One of the best experts on this subject based on the ideXlab platform.

  • Simulated Annealing : Simulated Annealing for Large Scale Optimization in Wireless Communications
    2020
    Co-Authors: Tamim Sakhavat, Haithem Grissa, Ziyad Abdalrahman
    Abstract:

    In this thesis a simulated annealing algorithm is employed as an optimization tool for a large scale optimization problem in wireless communication. In this application, we have 100 places for transition antennas and 100 places for receivers, and also a channel between each position in both areas. Our aim is to nd, say the best 3 positions there, in a way that the channel capacity is maximized.The number of possible combinations is huge. Hence, nding the best channel will take a very long time using an exhaustive search. To solve this problem, we use a simulated annealing algorithm and estimate the best answer. The simulated annealing algorithm chooses a random element, and then from the local search algorithm, compares the selected element with its neighbourhood. If the selected element is the maximum among its neighbours, it is a local maximum. The strength of the simulated annealing algorithm is its ability to escape from local maximum by using a random mechanism that mimics the Boltzmann Statistic.