A Discrete-Ordinates Solution for the Strong Evaporation Problem in Rarefied Gas Dynamics

Scherer, C. S.

doi:10.5540/tcam.2021.022.02.00201

TCAM

2021

DOI: 10.5540/tcam.2021.022.02.00201

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A Discrete-Ordinates Solution for the Strong Evaporation Problem in Rarefied Gas Dynamics

C. S. Scherer

Abstract: In this work we solve the nonlinear strong evaporation problem in rarefied gas dynamics. The analysis is based on the BGK model, with three dimensional velocity vector, derived from the Boltzmann equation. We present the complete development of a closed form solution for evaluating density, velocity, temperature perturbations and the heat flux of a gas. Numerical results are presented and discussed.

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Fock-space approach to stochastic susceptible-infected-recovered models

Souza

Araújo²,

Duarte-Filho³

et al. 2022

Phys. Rev. E

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We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system's states defined by SIR occupation numbers. In the Fock space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N . We present small and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.

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Fock-space approach to stochastic susceptible-infected-recovered models

Souza

Araújo²,

Duarte-Filho³

et al. 2022

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

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A Discrete-Ordinates Solution for the Strong Evaporation Problem in Rarefied Gas Dynamics

Cited by 1 publication

References 12 publications

Fock-space approach to stochastic susceptible-infected-recovered models

Fock-space approach to stochastic susceptible-infected-recovered models

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