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Journal articles on the topic 'Distributions de Boltzmann'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Khamnei, Hossein Jabbari, Sajad Nikannia, Masood Fathi, and Shahryar Ghorbani. "Modeling income distribution: An econophysics approach." Mathematical Biosciences and Engineering 20, no. 7 (2023): 13171–81. http://dx.doi.org/10.3934/mbe.2023587.

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<abstract><p>This study aims to develop appropriate models for income distribution in Iran using the econophysics approach for the 2006–2018 period. For this purpose, the three improved distributions of the Pareto, Lognormal, and Gibbs-Boltzmann distributions are analyzed with the data extracted from the target household income expansion plan of the statistical centers in Iran. The research results indicate that the income distribution in Iran does not follow the Pareto and Lognormal distributions in most of the study years but follows the generalized Gibbs-Boltzmann distribution f

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2

Hornack, Fred M. "Visualizing Boltzmann-like distributions." Journal of Chemical Education 65, no. 1 (1988): 24. http://dx.doi.org/10.1021/ed065p24.

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Liu, Fu-Hu, Ya-Qin Gao, and Hua-Rong Wei. "On Descriptions of Particle Transverse Momentum Spectra in High Energy Collisions." Advances in High Energy Physics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/293873.

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The transverse momentum spectra obtained in the frame of an isotropic emission source are compared in terms of Tsallis, Boltzmann, Fermi-Dirac, and Bose-Einstein distributions and the Tsallis forms of the latter three standard distributions. It is obtained that, at a given set of parameters, the standard distributions show a narrower shape than their Tsallis forms which result in wide and/or multicomponent spectra with the Tsallis distribution in between. A comparison among the temperatures obtained from the distributions is made with a possible relation to the Boltzmann temperature. An exampl

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4

Orland, Henri. "Accelerated Sampling of Boltzmann Distributions." Journal of the Physical Society of Japan 78, no. 10 (2009): 103002. http://dx.doi.org/10.1143/jpsj.78.103002.

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5

Treumann, Rudolf A., and Wolfgang Baumjohann. "Generalised partition functions: inferences on phase space distributions." Annales Geophysicae 34, no. 6 (2016): 557–64. http://dx.doi.org/10.5194/angeo-34-557-2016.

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Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose

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6

Altun, Emrah, and Gökçen Altun. "The Maxwell-Boltzmann-Exponential distribution with regression model." Mathematica Slovaca 74, no. 4 (2024): 1011–22. http://dx.doi.org/10.1515/ms-2024-0074.

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Abstract This paper proposes a new probability model called as Maxwell-Boltzmann-Exponential (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-s

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Lin, Hejie, and Tsung-Wu Lin. "Mechanical Proof of the Maxwell-Boltzmann Speed Distribution With Analytical Integration." International Journal of Statistics and Probability 10, no. 3 (2021): 135. http://dx.doi.org/10.5539/ijsp.v10n3p135.

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The Maxwell-Boltzmann speed distribution is the probability distribution that describes the speeds of the particles of ideal gases. The Maxwell-Boltzmann speed distribution is valid for both un-mixed particles (one type of particle) and mixed particles (two types of particles). For mixed particles, both types of particles follow the Maxwell-Boltzmann speed distribution. Also, the most probable speed is inversely proportional to the square root of the mass. The Maxwell-Boltzmann speed distribution of mixed particles is based on kinetic theory; however, it has never been derived from a mechanica

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Liu, Jeremy, Ke-Thia Yao, and Federico Spedalieri. "Dynamic Topology Reconfiguration of Boltzmann Machines on Quantum Annealers." Entropy 22, no. 11 (2020): 1202. http://dx.doi.org/10.3390/e22111202.

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Boltzmann machines have useful roles in deep learning applications, such as generative data modeling, initializing weights for other types of networks, or extracting efficient representations from high-dimensional data. Most Boltzmann machines use restricted topologies that exclude looping connectivity, as such connectivity creates complex distributions that are difficult to sample. We have used an open-system quantum annealer to sample from complex distributions and implement Boltzmann machines with looping connectivity. Further, we have created policies mapping Boltzmann machine variables to

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KANIADAKIS, G. "PHYSICAL ORIGIN OF THE POWER-LAW TAILED STATISTICAL DISTRIBUTIONS." Modern Physics Letters B 26, no. 10 (2012): 1250061. http://dx.doi.org/10.1142/s0217984912500613.

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Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the statistical mechanics presented in [Phys. Rev. E66 (2002) 056125] and [Phys. Rev. E72 (2005) 036108]. The a

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10

White, J. R., W. Johns, C. J. Fontes, N. M. Gill, N. R. Shaffer, and C. E. Starrett. "Charge state distributions in dense plasmas." Physics of Plasmas 29, no. 4 (2022): 043301. http://dx.doi.org/10.1063/5.0084109.

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Charge state distributions in hot, dense plasmas are a key ingredient in the calculation of spectral quantities like the opacity. However, they are challenging to calculate, as models like Saha–Boltzmann become unreliable for dense, quantum plasmas. Here, we present a new variational model for the charge state distribution, along with a simple model for the energy of the configurations that includes the orbital relaxation effect. Comparison with other methods reveals generally good agreement with average atom-based calculations, the breakdown of the Saha–Boltzmann method, and mixed agreement w

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11

Castillo, Jaime S., Katherine P. Gaete, Héctor A. Muñoz, et al. "Scale Mixture of Maxwell-Boltzmann Distribution." Mathematics 11, no. 3 (2023): 529. http://dx.doi.org/10.3390/math11030529.

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This paper presents a new distribution, the product of the mixture between Maxwell-Boltzmann and a particular case of the generalized gamma distributions. The resulting distribution, called the Scale Mixture Maxwell-Boltzmann, presents greater kurtosis than the recently introduced slash Maxwell-Boltzmann distribution. We obtained closed-form expressions for its probability density and cumulative distribution functions. We studied some of its properties and moments, as well as its skewness and kurtosis coefficients. Parameters were estimated by the moments and maximum likelihood methods, via th

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12

Frausto-Solis, Juan, Ernesto Liñán-García, Juan Paulo Sánchez-Hernández, J. Javier González-Barbosa, Carlos González-Flores, and Guadalupe Castilla-Valdez. "Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem." Advances in Bioinformatics 2016 (June 20, 2016): 1–16. http://dx.doi.org/10.1155/2016/7357123.

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A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the fina

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13

Gomez, Ignacio S., Bruno G. da Costa, and Maike A. F. dos Santos. "Majorization and Dynamics of Continuous Distributions." Entropy 21, no. 6 (2019): 590. http://dx.doi.org/10.3390/e21060590.

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In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions ϕ for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker–Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics

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14

Haubold, Hans J., Dilip Kumar, and Ashik A. Kabeer. "Fox’s H-Functions: A Gentle Introduction to Astrophysical Thermonuclear Functions." Axioms 13, no. 8 (2024): 532. http://dx.doi.org/10.3390/axioms13080532.

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Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely the Maxwell–Boltzmann distribution, the pathway distribution, and the Mittag-Leffler distribution. Moreover, a natural generalization of the Maxwell–Boltzmann velocity distribution is discussed. Furthermore, an explicit evaluation of the reaction rate integral in the high-energy cut-off case is carried out. Generalized special functions of mathemat

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15

LEVY, MOSHE, and SORIN SOLOMON. "POWER LAWS ARE LOGARITHMIC BOLTZMANN LAWS." International Journal of Modern Physics C 07, no. 04 (1996): 595–601. http://dx.doi.org/10.1142/s0129183196000491.

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Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative d

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16

Liu, Fu-Hu, Ya-Hui Chen, Hua-Rong Wei, and Bao-Chun Li. "Transverse Momentum Distributions of Final-State Particles Produced in Soft Excitation Process in High Energy Collisions." Advances in High Energy Physics 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/965735.

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Transverse momentum distributions of final-state particles produced in soft process in proton-proton (pp) and nucleus-nucleus (AA) collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies are studied by using a multisource thermal model. Each source in the model is treated as a relativistic and quantum ideal gas. Because the quantum effect can be neglected in investigation on the transverse momentum distribution in high energy collisions, we consider only the relativistic effect. The concerned distribution is finally described by the Boltzmann or two-compon

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17

Sebastian, Nicy, Arak M. Mathai, and Hans J. Haubold. "Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions." Entropy 23, no. 6 (2021): 754. http://dx.doi.org/10.3390/e23060754.

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In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densitie

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18

Qian, Hong, and John A. Schellman. "Transformed Poisson−Boltzmann Relations and Ionic Distributions†." Journal of Physical Chemistry B 104, no. 48 (2000): 11528–40. http://dx.doi.org/10.1021/jp994168m.

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19

Zaninetti, Lorenzo. "New Probability Distributions in Astrophysics: III. The Truncated Maxwell-Boltzmann Distribution." International Journal of Astronomy and Astrophysics 10, no. 03 (2020): 191–202. http://dx.doi.org/10.4236/ijaa.2020.103010.

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20

Zaninetti, Lorenzo. "New Probability Distributions in Astrophysics: IV. The Relativistic Maxwell-Boltzmann Distribution." International Journal of Astronomy and Astrophysics 10, no. 04 (2020): 302–18. http://dx.doi.org/10.4236/ijaa.2020.104016.

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21

Belgacem, Chokri Hadj. "Comparative study between exponential Boltzmann and Lambert Boltzmann distributions for heat capacity calculation." International Journal of Modern Physics B 33, no. 14 (2019): 1950140. http://dx.doi.org/10.1142/s0217979219501406.

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The Stirling’s estimation to [Formula: see text](N!) is typically introduced to students as a step in the derivation of the statistical expression for the heat capacity. However, naïve application of this estimation leads to wrong conclusions. In this paper, firstly, the heat capacity of some semiconductor compounds was calculated using exponential Boltzmann distribution and compared with experimental data. It has shown a disagreement between experimental results and those calculated. Secondly, by applying the more exact Stirling formula, an analytical formulation of Boltzmann statistics using

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22

SUZUKI, N., and M. BIYAJIMA. "TRANSVERSE MOMENTUM DISTRIBUTION WITH RADIAL FLOW IN RELATIVISTIC DIFFUSION MODEL." International Journal of Modern Physics E 16, no. 01 (2007): 133–47. http://dx.doi.org/10.1142/s0218301307005582.

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Large transverse momentum distributions of identified particles observed at the Relativistic Heavy Ion Collider (RHIC) are analyzed by a relativistic stochastic model in the three dimensional (non-Euclidean) rapidity space. A distribution function obtained from the model is Gaussian-like in radial rapidity. It can well describe observed transverse momentum pT distributions. Estimation of radial flow is made from the analysis of pT distributions for [Formula: see text] in Au + Au Collisions. Temperatures are estimated from observed large pT distributions under the assumption that the distributi

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23

Corral, Álvaro, and Montserrat García del Muro. "From Boltzmann to Zipf through Shannon and Jaynes." Entropy 22, no. 2 (2020): 179. http://dx.doi.org/10.3390/e22020179.

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The word-frequency distribution provides the fundamental building blocks that generate discourse in natural language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf’s law, at least approximately. Following Stephens and Bialek (2010), we interpret the frequency of any word as arising from the interaction potentials between its constituent letters. Indeed, Jaynes’ maximum-entropy principle, with the constrains given by every empirical two-letter marginal distribution, leads to a Boltzmann distribution for word probabilities

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24

Pavlov, A. V., and K. I. Oyama. "The role of vibrationally excited nitrogen and oxygen in the ionosphere over Millstone Hill during 16-23 March, 1990." Annales Geophysicae 18, no. 8 (2000): 957–66. http://dx.doi.org/10.1007/s00585-000-0957-2.

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Abstract. We present a comparison of the observed behavior of the F region ionosphere over Millstone Hill during the geomagnetically quiet and storm period on 16-23 March, 1990, with numerical model calculations from the time-dependent mathematical model of the Earth's ionosphere and plasmasphere. The effects of vibrationally excited N2(v) and O2(v) on the electron density and temperature are studied using the N2(v) and O2(v) Boltzmann and non-Boltzmann distribution assumptions. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calcula

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25

Flannigan, David J., and Kenneth S. Suslick. "Non-Boltzmann Population Distributions during Single-Bubble Sonoluminescence." Journal of Physical Chemistry B 117, no. 49 (2013): 15886–93. http://dx.doi.org/10.1021/jp409222x.

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26

Baker, Nathan A., and J. Andrew McCammon. "Non-Boltzmann Rate Distributions in Stochastically Gated Reactions." Journal of Physical Chemistry B 103, no. 4 (1999): 615–17. http://dx.doi.org/10.1021/jp984151o.

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27

Visscher, P. B., and D. M. Apalkov. "Non-Boltzmann energy distributions in spin-torque devices." Journal of Applied Physics 99, no. 8 (2006): 08G513. http://dx.doi.org/10.1063/1.2165785.

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28

Kugel, Roger W., and Paul A. Weiner. "Energy Distributions in Small Populations: Pascal versus Boltzmann." Journal of Chemical Education 87, no. 11 (2010): 1200–1205. http://dx.doi.org/10.1021/ed1003838.

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29

Mathai, A. M., and Serge B. Provost. "Generalized Boltzmann factors induced by Weibull-type distributions." Physica A: Statistical Mechanics and its Applications 392, no. 4 (2013): 545–51. http://dx.doi.org/10.1016/j.physa.2012.10.030.

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30

Smaal, Nicholas, and José Roberto C. Piqueira. "Complexity Measures for Maxwell–Boltzmann Distribution." Complexity 2021 (January 23, 2021): 1–6. http://dx.doi.org/10.1155/2021/9646713.

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This work presents a discussion about the application of the Kolmogorov; López-Ruiz, Mancini, and Calbet (LMC); and Shiner, Davison, and Landsberg (SDL) complexity measures to a common situation in physics described by the Maxwell–Boltzmann distribution. The first idea about complexity measure started in computer science and was proposed by Kolmogorov, calculated similarly to the informational entropy. Kolmogorov measure when applied to natural phenomena, presents higher values associated with disorder and lower to order. However, it is considered that high complexity must be associated to int

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31

Bulso, Nicola, and Yasser Roudi. "Restricted Boltzmann Machines as Models of Interacting Variables." Neural Computation 33, no. 10 (2021): 2646–81. http://dx.doi.org/10.1162/neco_a_01420.

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Abstract We study the type of distributions that restricted Boltzmann machines (RBMs) with different activation functions can express by investigating the effect of the activation function of the hidden nodes on the marginal distribution they impose on observed binary nodes. We report an exact expression for these marginals in the form of a model of interacting binary variables with the explicit form of the interactions depending on the hidden node activation function. We study the properties of these interactions in detail and evaluate how the accuracy with which the RBM approximates distribu

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32

Meir, Ronny. "ON DERIVING DETERMINISTIC LEARNING RULES FROM STOCHASTIC SYSTEMS." International Journal of Neural Systems 02, no. 04 (1991): 283–89. http://dx.doi.org/10.1142/s012906579100025x.

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We discuss the derivation of deterministic learning rules from an underlying stochastic system. We focus on the symmetrically connected Boltzmann machine and show how various approximations give rise to different learning algorithms. In particular, we show how to derive a symmetrized form of the recurrent back propagation learning algorithm from the Boltzmann machine. We also discuss the connection between the different deterministic learning algorithms focusing on the probability distributions from which they originate. It will also be shown that inspite of the fact that two probability distr

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Landsman, Zinoviy, Udi Makov, and Tomer Shushi. "A New Class of Distributions Based on Hurwitz Zeta Function with Applications for Risk Management." Open Statistics & Probability Journal 7, no. 1 (2016): 53–62. http://dx.doi.org/10.2174/1876527001607010053.

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This paper constructs a new family of distributions, which is based on the Hurwitz zeta function, which includes novel distributions as well important known distributions such as the normal, gamma, Weibull, Maxwell-Boltzmann and the exponential power distributions. We provide the n-th moment, the Esscher transform and premium and the tail conditional moments for this family.

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Jang, Dukjae, Youngshin Kwon, Kyujin Kwak, and Myung-Ki Cheoun. "Big Bang nucleosynthesis in a weakly non-ideal plasma." Astronomy & Astrophysics 650 (June 2021): A121. http://dx.doi.org/10.1051/0004-6361/202038478.

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We propose a correction of the standard Big Bang nucleosynthesis (BBN) scenario to resolve the primordial lithium problem by considering a possibility that the primordial plasma can deviate from the ideal state. In the standard BBN, the primordial plasma is assumed to be ideal, with particles and photons satisfying the Maxwell-Boltzmann and Planck distribution, respectively. We suggest that this assumption of the primordial plasma being ideal might oversimplify the early Universe and cause the lithium problem. We find that a deviation of photon distribution from the Planck distribution, which

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35

Rafik, Zeraoulia, Alvaro H. Salas, and David L. Ocampo. "A New Special Function and Its Application in Probability." International Journal of Mathematics and Mathematical Sciences 2018 (November 1, 2018): 1–12. http://dx.doi.org/10.1155/2018/5146794.

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In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chèbyshev polynomials of the first kind and the error function. Also we provide its series representation using Padé approximant. We show a convincing numerical evidence about an accuracy of 10-6 for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions, for example, Maxwell–Boltzmann distribution and normal distribution, such that we show its application usin

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Lin, Hejie, and Tsung-Wu Lin. "Mechanical Proof of the Maxwell-Boltzmann Speed Distribution With Numerical Iterations." International Journal of Statistics and Probability 10, no. 4 (2021): 21. http://dx.doi.org/10.5539/ijsp.v10n4p21.

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The Maxwell-Boltzmann speed distribution is the probability distribution that describes the speeds of the particles of ideal gases. The Maxwell-Boltzmann speed distribution is valid for both un-mixed particles (one type of particle) and mixed particles (two types of particles). For mixed particles, both types of particles follow the Maxwell-Boltzmann speed distribution. Also, the most probable speed is inversely proportional to the square root of the mass.  This paper proves the Maxwell-Boltzmann speed distribution and the speed ratio of mixed particles using computer-generated dat

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Quevedo Cubillos, Hernando, and María N. Quevedo. "Income distribution in the Colombian economy from an econophysics perspective." Cuadernos de Economía 35, no. 69 (2016): 691–707. http://dx.doi.org/10.15446/cuad.econ.v35n69.44876.

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Recently, in econophysics, it has been shown that it is possible to analyze economic systems as equilibrium thermodynamic models. We apply statistical thermodynamics methods to analyze income distribution in the Colombian economic system. Using the data obtained in random polls, we show that income distribution in the Colombian economic system is characterized by two specific phases. The first includes about 90% of the interviewed individuals, and is characterized by an exponential Boltzmann-Gibbs distribution. The second phase, which contains the individuals with the highest incomes, can be d

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HUBA, J. D., and J. G. LYON. "A new 3D MHD algorithm: the distribution function method." Journal of Plasma Physics 61, no. 3 (1999): 391–405. http://dx.doi.org/10.1017/s0022377899007503.

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A new three-dimensional (3D) magnetohydrodynamic (MHD) algorithm is described. The 3D MHD equations are solved in conservative form using a finite-volume scheme. The hydrodynamic variables in a cell are updated by calculating fluxes across the cell interfaces. The fluxes of mass, momentum and energy across cell interfaces are calculated by integrating a Boltzmann-like distribution function over velocity space. The novel feature of the method is that the distribution function incorporates most of the electromagnetic terms. In addition, the electric field along cell edges, which is used to updat

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Cushman, Samuel A. "Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics." Entropy 23, no. 12 (2021): 1616. http://dx.doi.org/10.3390/e23121616.

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Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral mod

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Kryvdyk, V. "Particle Acceleration and Radiation in Magnetospheres of Collapsing Stars." Symposium - International Astronomical Union 195 (2000): 403–6. http://dx.doi.org/10.1017/s0074180900163296.

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Particle dynamics and nonthermal emission therefrom in the magnetospheres of collapsing stars with initial dipole magnetic fields and a certain initial energy distribution of charged particles (power-law, relativistic Maxwell, and Boltzmann distributions) are considered. The radiation fluxes are calculated for various collapsing stars with initial dipole magnetic fields and an initial power-law particle energy distribution in the magnetosphere. The effects can be observed by means of modern instruments.

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SHIDA, CLAUDIO S., and VERA B. HENRIQUES. "SMART AND WRONG VERSUS CORRECT MONTE CARLO SIMULATIONS OF KAWASAKI–ISING MODEL." International Journal of Modern Physics C 11, no. 05 (2000): 1033–36. http://dx.doi.org/10.1142/s0129183100000870.

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Wright, Sam O. M., Stevanus K. Nugroho, Matteo Brogi, et al. "A Spectroscopic Thermometer: Individual Vibrational Band Spectroscopy with the Example of OH in the Atmosphere of WASP-33b." Astronomical Journal 166, no. 2 (2023): 41. http://dx.doi.org/10.3847/1538-3881/acdb75.

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Abstract Individual vibrational band spectroscopy presents an opportunity to examine exoplanet atmospheres in detail, by distinguishing where the vibrational state populations of molecules differ from the current assumption of a Boltzmann distribution. Here, retrieving vibrational bands of OH in exoplanet atmospheres is explored using the hot Jupiter WASP-33b as an example. We simulate low-resolution spectroscopic data for observations with the JWST's NIRSpec instrument and use high-resolution observational data obtained from the Subaru InfraRed Doppler instrument (IRD). Vibrational band–speci

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MAYER, GUSZTÁV, GÁBOR HÁZI, JÓZSEF PÁLES, ATTILA R. IMRE, BJÖRN FISCHER, and THOMAS KRASKA. "ON THE SYSTEM SIZE OF LATTICE BOLTZMANN SIMULATIONS." International Journal of Modern Physics C 15, no. 08 (2004): 1049–60. http://dx.doi.org/10.1142/s0129183104006492.

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In lattice Boltzmann simulations particle groups — represented by scalar velocity distributions — are moved on a finite lattice. The size of these particle groups is not well-defined although it is crucial to assume that they should be big enough for using a continuous distribution. Here we propose to use the liquid–vapor interface as an internal yardstick to scale the system. Comparison with existing experimental data and with molecular dynamics simulation of Lennard–Jones-argon shows that the number of atoms located on one lattice site is in the order of few atoms. This contradicts the initi

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44

DeSalvo, Stephen. "Improvements to exact Boltzmann sampling using probabilistic divide-and-conquer and the recursive method." Pure Mathematics and Applications 26, no. 1 (2017): 22–45. http://dx.doi.org/10.1515/puma-2015-0020.

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Abstract We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to exact Boltzmann sampling in the trivial setting, and specializes to PDC deterministic second half in the first non-trivial application. A large class of examples is given for which this method broadly applies, and several examples are worked out explicitly.

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Cotăescu, Ion I. "Collective classical motion on hyperbolic spacetimes of any dimensions." Modern Physics Letters A 34, no. 21 (2019): 1950165. http://dx.doi.org/10.1142/s0217732319501657.

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The geodesics equations on de Sitter (dS) and anti-de Sitter (AdS) spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the non-equilibrium Marle and Anderson–Witting models are derived and the distributions of the Boltzmann–Marle model on these manifolds are written down first in terms of conserved quantities and then as functions of canonical variables.

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Bernegger, Stefan. "The Swiss Re Exposure Curves and the MBBEFD Distribution Class." ASTIN Bulletin 27, no. 1 (1997): 99–111. http://dx.doi.org/10.2143/ast.27.1.563208.

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AbstractA new two-parameter family of analytical functions will be introduced for the modelling of loss distributions and exposure curves. The curve family contains the Maxwell-Boltzmann, the Bose-Einstein and the Fermi-Dirac distributions, which are well known in statistical mechanics. The functions can be used for the modelling of loss distributions on the finite interval [0, 1] as well as on the interval [0, ∞]. The functions defined on the interval [0, 1] are discussed in detail and related to several Swiss Re exposure curves used in practice. The curves can be fitted to the first two mome

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Fleitz, P. A., and C. J. Seliskar. "Characterization of OH Radical 306.4 nm Emission in Argon and Helium Reduced-Pressure ICPs." Applied Spectroscopy 41, no. 4 (1987): 679–82. http://dx.doi.org/10.1366/0003702874448760.

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The A → X emission of OH at 306.4 nm has been studied in reduced-pressure inductively coupled argon and helium plasmas. Under a variety of conditions of power and flow rate, a comparison of the A state rotational level distributions shows significant differences in the two plasmas. The rotational level distributions are generally nonlinear but can be quantitatively described as the sum of two separate Boltzmann distributions.

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Bahou, Mohammed, and Yuan-Pern Lee. "Photodissociation Dynamics of Vinyl Chloride Investigated with a Pulsed Slit-Jet and Time-Resolved Fourier-Transform Spectroscopy." Australian Journal of Chemistry 57, no. 12 (2004): 1161. http://dx.doi.org/10.1071/ch04117.

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Following photodissociation of vinyl chloride seeded in a He supersonic jet at 193 nm, rotationally resolved infrared emission of HCl (v) are recorded to yield nascent rotational and vibrational distributions. Preliminary results show that the rotational distribution of HCl free from rotational quenching deviates slightly from Boltzmann-type distribution and agrees well with trajectory calculations; a portion of the low-J component observed previously in a flow system is attributed to quenching. The implications for photodissociation dynamics are discussed.

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McComas, David J., George Livadiotis, and Nicholas V. Sarlis. "Correlations and Kappa Distributions: Numerical Experiment and Physical Understanding." Entropy 27, no. 4 (2025): 375. https://doi.org/10.3390/e27040375.

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Kappa distributions, their statistical framework, and their thermodynamic origin describe systems with correlations among their particle energies, residing in stationary states out of classical thermal equilibrium/space plasmas, from solar wind to the outer heliosphere, are such systems. We show how correlations from long-range interactions compete with collisions to define the specific shape of particle velocity distributions, using a simple numerical experiment with collisions and a variable amount of correlation among the particles. When the correlations are turned off, collisions drive any

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Pavlov, A. V. "Subauroral red arcs as a conjugate phenomenon: comparison of OV1-10 satellite data with numerical calculations." Annales Geophysicae 15, no. 8 (1997): 984–98. http://dx.doi.org/10.1007/s00585-997-0984-3.

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Abstract. This study compares the OV1-10 satellite measurements of the integral airglow intensities at 630 nm in the SAR arc regions observed in the northern and southern hemisphere as a conjugate phenomenon, with the model results obtained using the time-dependent one-dimensional mathematical model of the Earth ionosphere and plasmasphere (the IZMIRAN model) during the geomagnetic storm of the period 15–17 February 1967. The major enhancements to the IZMIRAN model developed in this study are the inclusion of He+ ions (three major ions: O+, H+, and He+, and three ion temperatures), the updated

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