The Evolution of the Two-Dimensional Maxwell-Boltzmann Distribution

Novak, John; Bortz, Alfred B.

doi:10.1119/1.1976147

Cited by 16 publications

(5 citation statements)

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“…With the help of the concept of probability and statistics, we sought numerous statistical distribution patterns and found that the Boltzmann equation and distribution were widely used in gas kinetics. As early as in 1970, Novak et al 22 simulated a twodimensional ideal gas by a computer to observe the speed distribution function. Results indicated that the Maxwell− Boltzmann distribution indeed occurs in nature.…”

Section: Resultsmentioning

confidence: 99%

Novel Kinetic Model for Petcoke Gasification at High Temperature

et al. 2019

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Gasification kinetic parameters are valuable for designing a gasifier and optimizing operation conditions. In this work, a novel kinetic model named the apparent kinetic model (AKM) is presented and used for kinetic modeling of petcoke gasification under CO2 or steam atmospheres at high temperatures. The AKM was obtained from the Boltzmann equation distribution, which was consistent with the simplified gasification mechanism of petcoke at high temperature. The AKM was used for modeling petcoke gasification at various conditions to verify the applicability of the model. The kinetic modeling results of AKM and three common models were also compared in detail. The fitting results showed that the AKM prediction agrees very well with the gasification experimental results under two atmospheres at high temperature. It was amazing to find that the fitting values, such as t 0.5, were close to the experimental values, with a very limited deviation. The fitting-corresponding R 2 values of AKM were above 0.99 for most conditions, which indicated that AKM was suitable for petcoke gasification at high temperature with high accuracy. It was found that the gasification profile can be described well by AKM, whereas the other three common models showed great deviations in both low and high carbon conversion ranges. It can be concluded that the results of AKM are the best when used to simulate petcoke gasification at high temperature. The kinetic parameters obtained by AKM were accurate and conformed with the gasification reactivity of petcoke, which indicated that the AKM was an appropriate kinetic model for modeling the gasification of petcoke at high temperature.

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Section: Resultsmentioning

confidence: 99%

Novel Kinetic Model for Petcoke Gasification at High Temperature

et al. 2019

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“…Although discussions of exact molecular dynamics simulations have appeared in the research literature for over thirty years (2), there has been little discussion of them in the pedagogic literature. usual approach has been programs based on random simulations of collisions, as opposed to actually following particles (3,4), Such simulations run very quickly; no time is wasted in determining which particles are actually colliding or in updating positions. However, information regarding true time and distance scales for the gases modeled cannot be inferred.…”

Section: Acknowledgmentmentioning

confidence: 99%

“…x cos q>(rl;cos 02 -u2icos 02) + sin 02 -t>2lsin 02) (3) from which final speeds and angles can be computed.…”

Section: Dynamics Of Hard-disk Collisionsmentioning

confidence: 99%

Deterministic simulations of two-dimensional hard-disk gases

Reed¹

1993

J. Chem. Educ.

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“…Also it appears that essentially the same stochastic algorithms for a homogenous gas were invented independently by people interested in using them as a pedagogical tool to demonstrate evolution of a gas toward Maxwell-Boltzmann(MB) distribution. [4] [5] [6]. In order to represent time evolution of the real gas such methods should converge to the true solution of the Boltzmann equation in the limit of N → ∞, V k → 0, ∆t → 0.…”

Section: Introductionmentioning

confidence: 99%

Theory of direct simulation Monte Carlo method

Karabulut,

Karabulut

2007

Preprint

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A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N → ∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang-Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogenous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N → ∞, V k → 0, ∆t → 0 where V k is the volume k th cell. We also show that

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The Evolution of the Two-Dimensional Maxwell-Boltzmann Distribution

Cited by 16 publications

References 0 publications

Novel Kinetic Model for Petcoke Gasification at High Temperature

Novel Kinetic Model for Petcoke Gasification at High Temperature

Deterministic simulations of two-dimensional hard-disk gases

Theory of direct simulation Monte Carlo method

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