A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases

Hu, Jingwei; Ma, Zheng

doi:10.1016/j.jcp.2019.01.049

“…Moreover, the moments propagation property is shown by taking the similar strategy as the elastic case; and the energy dissipation feature, which is distinct for the inelastic model, is also justified by the delicate analysis. At last, the additional reason that motivates us to study the existence theory for the inelastic model is our recent progress [14][15][16] in the numerical approximation of Boltzmann collision operator; having the existence results in hand, we can further logically and heuristically apply them in the numerical simulation as well as the stability analysis of corresponded numerical solution.…”

Section: Motivationmentioning

confidence: 99%

On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

Qi

¹

2021

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…What's more, the moments propagation property is shown by taking the similar strategy as the elastic case; and the energy dissipation feature, which is distinct for the inelastic model, is also justified by the delicate analysis. At last, the additional reason that motivates us to study the existence theory for the inelastic model is our recent progress [14][15][16] in the numerical approximation of Boltzmann collision operator; having the existence results in hand, we can further logically and heuristically apply them in the numerical simulation as well as the stability analysis of corresponded numerical solution.…”

Section: Motivationmentioning

confidence: 99%

On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

Qi

2020

Preprint

0

Get access via publisher Add to dashboard Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…In this section, we review the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation. The presentation follows the formulation originally proposed in [19] which is the basis for many fast algorithms developed recently [9,12,13]. Here we limit the description to the extent that is sufficient for the following proof.…”

Section: Introductionmentioning

confidence: 99%

A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation

Hu

¹

,

Qi

²

,

Yang

³

2020

Preprint

Self Cite

Get access via publisher Add to dashboard Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

show abstract

A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases

Cited by 17 publications

References 25 publications

On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation

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