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Journal articles on the topic 'Fermi – Dirac function'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Chaudhry, M. Aslam, and Asghar Qadir. "Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–9. http://dx.doi.org/10.1155/2007/80515.

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Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einstein integral functions are expressible as operator representations in terms of themselves. Simpler derivations of previously known results of these functions are obtained by their operator representation

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2

Golovanov, R. V., and K. I. Lutskii. "Computation of the integral Fermi-Dirac function." Mathematical Models and Computer Simulations 4, no. 5 (2012): 464–70. http://dx.doi.org/10.1134/s2070048212050043.

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3

Wildberger, K., P. Lang, R. Zeller, and P. H. Dederichs. "Fermi-Dirac distribution inab initioGreen’s-function calculations." Physical Review B 52, no. 15 (1995): 11502–8. http://dx.doi.org/10.1103/physrevb.52.11502.

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4

Antia, H. M. "Rational Function Approximations for Fermi-Dirac Integrals." Astrophysical Journal Supplement Series 84 (January 1993): 101. http://dx.doi.org/10.1086/191748.

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5

Yasuda, Makoto, Takeshi Furuhashi, and Shigeru Okuma. "Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy." Journal of Advanced Computational Intelligence and Intelligent Informatics 7, no. 3 (2003): 370–76. http://dx.doi.org/10.20965/jaciii.2003.p0370.

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We studied the statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtained Fermi-Dirac distribution as a membership function by regularizing the fuzzy c-means with fuzzy entropy. We then formulated it as direct annealing clustering, and determined the meanings of the Fermi-Dirac function and fuzzy entropy from the statistical mechanical point of view, and showed that this fuzzy clustering is a part of Fermi-Dirac statistics. We also derived the critical temperature at which phase transition occurs in this fuzzy clustering. Then, with a combination of

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6

Melrose, D. B., and A. Mushtaq. "Plasma dispersion function for a Fermi–Dirac distribution." Physics of Plasmas 17, no. 12 (2010): 122103. http://dx.doi.org/10.1063/1.3528272.

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7

Aguilera‐Navarro, V. C., G. A. Estévez, and Allyn Kostecki. "A note on the Fermi–Dirac integral function." Journal of Applied Physics 63, no. 8 (1988): 2848–50. http://dx.doi.org/10.1063/1.340957.

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8

Lin, Lin, Jianfeng Lu, Lexing Ying, and E. Weinan. "Pole-Based approximation of the Fermi-Dirac function." Chinese Annals of Mathematics, Series B 30, no. 6 (2009): 729–42. http://dx.doi.org/10.1007/s11401-009-0201-7.

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9

BROWN, S. R., and M. G. HAINES. "Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators." Journal of Plasma Physics 58, no. 4 (1997): 577–600. http://dx.doi.org/10.1017/s0022377897006041.

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The quantum Boltzmann collision operator is expanded to yield a degenerate form of the Fokker–Planck collision operator. This is analysed using Rosenbluth potentials to give a degenerate analogue of the Shkarofsky operator. The distribution function is then expanded about an equilibrium Fermi–Dirac distribution function using a tensor perturbation formulation to give a zeroth-order and a first-order collision operator. These equations are shown to satisfy the relevant conservation equations. It is shown that the distribution function relaxes to a Fermi–Dirac form through electron–electron coll

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10

Srivastava, Rekha, Humera Naaz, Sabeena Kazi, and Asifa Tassaddiq. "Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions." Axioms 8, no. 2 (2019): 63. http://dx.doi.org/10.3390/axioms8020063.

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In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from ( 0 < ℜ ( s ) < 1 ) to ( 0 < ℜ ( s ) < μ ) . This leads to fresh insights for a new generalization of the Riemann zeta function. The results are validated by obtaining the classical series representation of the polylogarithm and Hurwitz–Lerch zeta functions as special cases. Fractional derivatives an

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11

MOLINARI, V., D. MOSTACCI, and F. PIZZIO. "QUANTUM–RELATIVISTIC DISTRIBUTION FUNCTION FOR BOSONS AND FERMIONS." International Journal of Modern Physics B 26, no. 12 (2012): 1241004. http://dx.doi.org/10.1142/s0217979212410044.

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In the present work, quantum–relativistic equilibrium distribution functions are derived for bosons above the critical temperature and for weakly degenerate fermions, extending to the relativistic case the Bose–Einstein and Fermi–Dirac distributions.

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12

Chandramohan, D., and S. Balasubramanian. "Thomas-Fermi-Dirac dielectric function for GaAs and GaP." Physical Review B 35, no. 6 (1987): 2750–54. http://dx.doi.org/10.1103/physrevb.35.2750.

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13

Tai, Yen-Ling, Shin-Jhe Huang, Chien-Chang Chen, and Henry Horng-Shing Lu. "Computational Complexity Reduction of Neural Networks of Brain Tumor Image Segmentation by Introducing Fermi–Dirac Correction Functions." Entropy 23, no. 2 (2021): 223. http://dx.doi.org/10.3390/e23020223.

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Nowadays, deep learning methods with high structural complexity and flexibility inevitably lean on the computational capability of the hardware. A platform with high-performance GPUs and large amounts of memory could support neural networks having large numbers of layers and kernels. However, naively pursuing high-cost hardware would probably drag the technical development of deep learning methods. In the article, we thus establish a new preprocessing method to reduce the computational complexity of the neural networks. Inspired by the band theory of solids in physics, we map the image space i

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14

Brunel, Vivien. "From the Fermi–Dirac distribution to PD curves." Journal of Risk Finance 20, no. 2 (2019): 138–54. http://dx.doi.org/10.1108/jrf-01-2018-0009.

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Purpose In machine learning applications, and in credit risk modeling in particular, model performance is usually measured by using cumulative accuracy profile (CAP) and receiving operating characteristic curves. The purpose of this paper is to use the statistics of the CAP curve to provide a new method for credit PD curves calibration that are not based on arbitrary choices as the ones that are used in the industry. Design/methodology/approach The author maps CAP curves to a ball–box problem and uses statistical physics techniques to compute the statistics of the CAP curve from which the auth

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15

Yeşiltaş, Özlem, and Bengü Çag̃atay. "The massless Dirac–Weyl equation with deformed extended complex potentials." Canadian Journal of Physics 96, no. 7 (2018): 770–73. http://dx.doi.org/10.1139/cjp-2017-0608.

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Basically (2 + 1)-dimensional Dirac equation with real deformed Lorentz scalar potential is investigated in this study. The position-dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein–Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Moreover, the Lie algebraic analysis is also performed.

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16

Prostko, Eric P., Hsin-I. Wu, James M. Chandler, and Scott A. Senseman. "Modeling weed emergence as influenced by burial depth using the Fermi-Dirac distribution function." Weed Science 45, no. 2 (1997): 242–48. http://dx.doi.org/10.1017/s004317450009278x.

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Research was conducted to determine the suitability of the Fermi-Dirac distribution function for modeling the seedling emergence of downy brome, johnsongrass, and round-leaved mallow, as influenced by burial depth. Six sets of previously published emergence data were used to formulate the model and test its adequacy. Two independent johnsongrass emergence data sets were used to validate the model. Constant temperature growth chamber studies were conducted to evaluate the effects of temperature and moisture on the model parameters. The Fermi-Dirac distribution function was found to adequately d

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17

TREVISAN, LUIS AUGUSTO, and CARLOS MIREZ. "A NONEXTENSIVE STATISTICAL MODEL FOR THE NUCLEON STRUCTURE FUNCTION." International Journal of Modern Physics E 22, no. 07 (2013): 1350044. http://dx.doi.org/10.1142/s0218301313500444.

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We studied an application of nonextensive thermodynamics to describe the structure function of nucleon, in a model where the usual Fermi–Dirac and Bose–Einstein energy distribution were replaced by the equivalent functions of the q-statistical. The parameters of the model are given by an effective temperature T, the q parameter (from Tsallis statistics), and two chemical potentials given by the corresponding up (u) and down (d) quark normalizations in the nucleon.

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18

Arjona, Vicente, Juan Borge, and María A. H. Vozmediano. "Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals." Symmetry 12, no. 5 (2020): 814. http://dx.doi.org/10.3390/sym12050814.

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Dirac and Weyl semimetals are three-dimensional electronic systems with the Fermi level at or near a band crossing. Their low energy quasi-particles are described by a relativistic Dirac Hamiltonian with zero effective mass, challenging the standard Fermi liquid (FL) description of metals. In FL systems, electrical and thermo–electric transport coefficient are linked by very robust relations. The Mott relation links the thermoelectric and conductivity transport coefficients. In a previous publication, the thermoelectric coefficient was found to have an anomalous behavior originating in the qua

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19

Kim, Bum-Kyu, Eun-Kyoung Jeon, Ju-Jin Kim, and Jeong-O. Lee. "Positioning of the Fermi Level in Graphene Devices with Asymmetric Metal Electrodes." Journal of Nanomaterials 2010 (2010): 1–5. http://dx.doi.org/10.1155/2010/575472.

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To elucidate the effect of the work function on the position of the Dirac point, we fabricated graphene devices with asymmetric metal contacts. By measuring the peak position of the resistance for each pair of metal electrodes, we obtained the voltage of the Dirac pointVgDirac(V) from the gate response. We found that the position ofVgDirac(V) in the hybrid devices was significantly influenced by the type of metal electrode. The measured shifts inVgDirac(V) were closely related to the modified work functions of the metal-graphene complexes. Within a certain bias range, the Fermi level of one of

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20

Kluszczyński, K., and M. Kciuk. "Analytical Description of SMA Actuator Dynamics based on Fermi-Dirac Function." Acta Physica Polonica A 131, no. 5 (2017): 1274–79. http://dx.doi.org/10.12693/aphyspola.131.1274.

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21

Johari, Zaharah, Mohammad Taghi Ahmadi, Desmond Chang Yih Chek, N. Aziziah Amin, and Razali Ismail. "Modelling of Graphene Nanoribbon Fermi Energy." Journal of Nanomaterials 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/909347.

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Graphene nanoribbon (GNR) is a promising alternative to carbon nanotube (CNT) to overcome the chirality challenge as a nanoscale device channel. Due to the one-dimensional behavior of plane GNR, the carrier statistic study is attractive. Research works have been done on carrier statistic study of GNR especially in the parabolic part of the band structure using Boltzmann approximation (nondegenerate regime). Based on the quantum confinement effect, we have improved the fundamental study in degenerate regime for both the parabolic and nonparabolic parts of GNR band energy. Our results demonstrat

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22

Vinh, Pham Nguyen Thanh. "ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP." Hue University Journal of Science: Natural Science 126, no. 1B (2017): 117. http://dx.doi.org/10.26459/hueuni-jns.v126i1b.4116.

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In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.

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23

SRIRAMKUMAR, L. "ODD STATISTICS IN ODD DIMENSIONS FOR ODD COUPLINGS." Modern Physics Letters A 17, no. 15n17 (2002): 1059–66. http://dx.doi.org/10.1142/s0217732302007545.

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We consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D + 1)-dimensional flat spacetime. We show that, when (D + 1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D + 1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even. We emphasize the point that, since, along the accelerated trajectory, the Wightman function and, as a result, the

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24

Ahmadi, Mohammad Taghi, Zaharah Johari, N. Aziziah Amin, Amir Hossein Fallahpour, and Razali Ismail. "Graphene Nanoribbon Conductance Model in Parabolic Band Structure." Journal of Nanomaterials 2010 (2010): 1–4. http://dx.doi.org/10.1155/2010/753738.

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Many experimental measurements have been done on GNR conductance. In this paper, analytical model of GNR conductance is presented. Moreover, comparison with published data which illustrates good agreement between them is studied. Conductance of GNR as a one-dimensional device channel with parabolic band structures near the charge neutrality point is improved. Based on quantum confinement effect, the conductance of GNR in parabolic part of the band structure, also the temperature-dependent conductance which displays minimum conductance near the charge neutrality point are calculated. Graphene n

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25

Chakraborty, P. K., S. K. Biswas, and K. P. Ghatak. "On the modification of the Fermi–Dirac distribution function in degenerate semiconductors." Physica B: Condensed Matter 352, no. 1-4 (2004): 111–17. http://dx.doi.org/10.1016/j.physb.2004.06.062.

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26

Mamedov, B. A. "Analytical evaluation of the plasma dispersion function for a Fermi Dirac distribution." Chinese Physics B 21, no. 5 (2012): 055204. http://dx.doi.org/10.1088/1674-1056/21/5/055204.

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27

Anandaram, Mandyam N. "On the Adaptive Quadrature of Fermi-Dirac Functions and their Derivatives." Mapana - Journal of Sciences 18, no. 1 (2019): 1–20. http://dx.doi.org/10.12723/mjs.48.1.

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In this paper, using the Python SciPy module “quad”, a fast auto-adaptive quadrature solver based on the pre-compiled QUADPACK Fortran package, computational research is undertaken to accurately integrate the generalised Fermi-Dirac function and all its partial derivatives up to the third order. The numerical results obtained with quad method when combined with optimised break points achieve an excellent accuracy comparable to that obtained by other publications using fixed-order quadratures.

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28

BUCCELLA, FRANCO, OFELIA PISANTI, LUIGI ROSA, ILYA DORSNER, and PIETRO SANTORELLI. "A POSITIVE TEST FOR FERMI–DIRAC DISTRIBUTIONS OF QUARK–PARTONS." Modern Physics Letters A 13, no. 06 (1998): 441–51. http://dx.doi.org/10.1142/s0217732398000516.

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By describing a large class of deep inelastic processes with standard parametrization for the different parton species, we check the characteristic relationship dictated by Pauli principle: broader shapes for higher first moments. Indeed, the ratios between the second and the first moments and the one between the third and the second moments for the valence partons is an increasing function of the first moment and agrees quantitatively with the values found with Fermi–Dirac distributions.

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29

Callelero, Marcielow J., and Danilo M. Yanga. "Mobility of spin polarons with vertex corrections." International Journal of Modern Physics B 33, no. 18 (2019): 1950195. http://dx.doi.org/10.1142/s0217979219501959.

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The mobility of holes in the spin polaron theory is discussed in this paper using a representation where holes are described as spinless fermions and spins as normal bosons. The hard-core bosonic operator is introduced through the Holstein–Primakoff transformation. Mathematically, the theory is implemented in the finite temperature (Matsubara) Green’s function method. The expressions for the zeroth-order term of the hole mobility is determined explicitly for hole occupation factor taking the form of Fermi–Dirac distribution and the classical Maxwell–Boltzmann distribution function. These are p

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30

Barbier, Michaël, Panagiotis Vasilopoulos, and François M. Peeters. "Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1932 (2010): 5499–524. http://dx.doi.org/10.1098/rsta.2010.0218.

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We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In

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31

Gurumurugan, K., and D. Chandramohan. "Analytic form of Thomas-Fermi-Dirac dielectric function for III-V compound semiconductors." International Journal of Quantum Chemistry 40, no. 5 (1991): 695–702. http://dx.doi.org/10.1002/qua.560400511.

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32

Sidje, Roger B., and Yousef Saad. "Rational approximation to the Fermi–Dirac function with applications in density functional theory." Numerical Algorithms 56, no. 3 (2010): 455–79. http://dx.doi.org/10.1007/s11075-010-9397-6.

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33

Ali, Mazhar N., Leslie M. Schoop, Chirag Garg, et al. "Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS." Science Advances 2, no. 12 (2016): e1601742. http://dx.doi.org/10.1126/sciadv.1601742.

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Magnetoresistance (MR), the change of a material’s electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual “butterfly”-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 105percent at 9 T and 2 K at a 45° angle between the applied current

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34

Changshi, Liu. "More precise determination of work function based on Fermi–Dirac distribution and Fowler formula." Physica B: Condensed Matter 444 (July 2014): 44–48. http://dx.doi.org/10.1016/j.physb.2014.03.037.

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35

Kim, Heung Soo, Anindya Ghoshal, Jaehwan Kim, and Seung-Bok Choi. "Transient analysis of delaminated smart composite structures by incorporating the Fermi–Dirac distribution function." Smart Materials and Structures 15, no. 2 (2006): 221–31. http://dx.doi.org/10.1088/0964-1726/15/2/001.

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36

Rossani, A. "Semiconductor spintronics: The full matrix approach." Modern Physics Letters B 29, no. 35n36 (2015): 1550243. http://dx.doi.org/10.1142/s0217984915502437.

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A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi–Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.

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37

Van Mieghem, P., and S. Tang. "WEIGHT OF THE SHORTEST PATH TO THE FIRST ENCOUNTERED PEER IN A PEER GROUP OF SIZE m." Probability in the Engineering and Informational Sciences 22, no. 1 (2007): 37–52. http://dx.doi.org/10.1017/s026996480800003x.

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We model the weight (e.g., delay, distance, or cost) from an arbitrary node to the nearest (in weight) peer in a peer-to-peer (P2P) network. The exact probability generating function and an asymptotic analysis is presented for a random graph with independent and identically distributed exponential link weights. The asymptotic distribution function is a Fermi–Dirac distribution that frequently appears in statistical physics. The good agreement with simulation results for relatively small P2P networks makes the asymptotic formula for the probability density function useful for estimating the min

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38

Matsushita, Kenji, Makoto Fukuda, and Kouich Hamanaka. "Filter Circuit with Periodically Arranged Nonuniform Microstriplines Having Linewidths Determined by Fermi-Dirac Distribution Function." IEEJ Transactions on Electronics, Information and Systems 129, no. 12 (2009): 2241–42. http://dx.doi.org/10.1541/ieejeiss.129.2241.

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39

HAAS, F., P. K. SHUKLA, and B. ELIASSON. "Nonlinear saturation of the Weibel instability in a dense Fermi plasma." Journal of Plasma Physics 75, no. 2 (2009): 251–58. http://dx.doi.org/10.1017/s0022377808007368.

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AbstractWe present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi–Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner–Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields ar

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40

SYROS, C. "ON THE RANDOM QFT FOUNDATIONS OF STATISTICAL MECHANICS." International Journal of Modern Physics B 05, no. 18 (1991): 2909–34. http://dx.doi.org/10.1142/s0217979291001139.

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The Statistical Mechanics of the N-particle system is derived from Quantum Random Field Theory. An asymptotically measure preserving, flow operator has been obtained from the QFT evolution operator. A basic assumption is that the field Lagrangian is a generalized, infinitely divisible random field, and the interaction Hamiltonian varies in time in a step-wise manner at the transition lattice space-time points. Macroscopic boundary conditions are imposed on the wave functions. The density matrix, the partition function, the Bose-Einstein, the Fermi-Dirac distributions and the thermodynamic temp

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41

Ghoshal, Anindya, Heung Soo Kim, Jaehwan Kim, Seung-Bok Choi, William H. Prosser, and Hsiang Tai. "Modeling delamination in composite structures by incorporating the Fermi–Dirac distribution function and hybrid damage indicators." Finite Elements in Analysis and Design 42, no. 8-9 (2006): 715–25. http://dx.doi.org/10.1016/j.finel.2005.10.008.

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42

Nahir, Tal M. "On the calculation of rate constants by approximating the Fermi–Dirac distribution with a step function." Journal of Electroanalytical Chemistry 518, no. 1 (2002): 47–50. http://dx.doi.org/10.1016/s0022-0728(01)00688-x.

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43

Chandramohan, D., and S. Balasubramanian. "Analytic form of Thomas-Fermi-Dirac dielectric function for Si, Ge and diamond by variational method." Zeitschrift f�r Physik B Condensed Matter 79, no. 2 (1990): 181–84. http://dx.doi.org/10.1007/bf01406582.

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44

Kim, Heung Soo, Jae Hwan Kim, and Seung Bok Choi. "Characterization of Delamination in Laminated Composites Based on Damage Indices." Key Engineering Materials 321-323 (October 2006): 925–29. http://dx.doi.org/10.4028/www.scientific.net/kem.321-323.925.

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A modal strain based damage index is proposed to investigate the damage effects of discrete delaminations in a laminated composite structure. The Fermi-Dirac distribution function is incorporated with an improved layerwise laminate theory to model smooth transition of the displacement and the strain fields at the delaminated interfaces. Modal analysis is conducted to investigate dynamic effects of delamination in a laminated structure and to obtain modal strains. The damage index is calculated based on fundamental modal strains of laminated structures. The damage effects of laminated structure

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45

Kaiblinger-Grujin, G., and H. Kosina. "An Improved Ionized Impurity Scattering Model for Monte Carlo Calculations." VLSI Design 6, no. 1-4 (1998): 209–12. http://dx.doi.org/10.1155/1998/87014.

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The well known Brooks-Herring (BH) formula for charged-impurity (CI) scattering overestimates the mobility of electrons in highly doped semiconductors. The BH approach relies on a static, single-site description of the carrier-impurity interactions neglecting many-particle effects. We propose a physically based charged-impurity scattering model including Fermi- Dirac statistics, dispersive screening, and two-ion scattering. An approximation for the dielectric function is made to avoid numerical integrations. The resulting scattering rate formulas are analytical. Monte Carlo calculations were p

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46

Kim, Heung Soo, Seung Bok Choi, and Jae Hwan Kim. "Damage Characterization of Delamination in Smart Composite Laminates Based on Smooth Transition of Displacement Field." Key Engineering Materials 306-308 (March 2006): 375–80. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.375.

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A dynamic analysis method has been developed to investigate and characterize the effect due to the presence of discrete single and multiple delaminations of composite laminated structures. The Fermi-Dirac distribution function is combined with an improved layerwise laminate theory to model a smooth transition in the displacement and the strain fields of the delaminated interfaces. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Based on the developed model, the effects of discrete delaminations

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47

Sari, R. Yosi Aprian, and W. S. B. Dwandaru. "DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES." Jurnal Sains Dasar 4, no. 2 (2016): 179. http://dx.doi.org/10.21831/jsd.v4i2.9096.

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This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple therm

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Pan, Chengsheng, Suting Chen, Luyao Wang, and Yanyan Zhang. "Anisotropic diffusion based on Fermi-Dirac distribution function and its application in the Shack-Hartman wavefront sensor." International Journal of Sensor Networks 34, no. 2 (2020): 95. http://dx.doi.org/10.1504/ijsnet.2020.10032762.

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49

Zhang, Yanyan, Chengsheng Pan, Luyao Wang, and Suting Chen. "Anisotropic diffusion based on Fermi-Dirac distribution function and its application in the Shack-Hartman wavefront sensor." International Journal of Sensor Networks 34, no. 2 (2020): 95. http://dx.doi.org/10.1504/ijsnet.2020.110462.

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50

Reynolds, Robert, and Allan Stauffer. "A Note on Some Definite Integrals of Arthur Erdélyi and George Watson." Mathematics 9, no. 6 (2021): 674. http://dx.doi.org/10.3390/math9060674.

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Abstract:

This manuscript concerns two definite integrals that could be connected to the Bose-Einstein and the Fermi-Dirac functions in the integrands, separately, with numerators slightly modified with a difference in two expressions that contain the Fourier kernel multiplied by a polynomial and its complex conjugate. In this work, we use our contour integral method to derive these definite integrals, which are given by ∫0∞ie−imx(log(a)−ix)k−eimx(log(a)+ix)k2eαx−1dx and ∫0∞ie−imx(log(a)−ix)k−eimx(log(a)+ix)k2eαx+1dx in terms of the Lerch function. We use these two definite integrals to derive formulae

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