Tomography of reactive Boltzmann kernels from product fluxes
Abstract
We study the reversible reaction 1+2rightleftarrows3+4 in a dilute gas described by a Boltzmann system. We prove that the outgoing flux of one product species determines the forward collision kernel throughout the domain on a prescribed admissible set of relative velocities and outgoing directions. The elastic collision laws are known, and the reverse kernel is fixed by a prescribed reciprocity relation. The measurements use two synchronized incoming packets with fixed relative velocity and a common velocity tending to infinity. Under bounded angularly integrated collision rates, the short transit time allows us to isolate the contribution of one forward reaction, with estimates uniform as the packets concentrate. Suitable tests of the product flux yield the spatial line integrals of the kernel and a Fourier reconstruction, without differentiating the nonlinear boundary map. We also estimate the effects of finite beam speed, packet width, detector resolution, and measurement noise on the recovered line integrals.
Related
- Notes on Uniform Policy Score Bounds and Lipschitz Continuity for Truncated Gaussian, Product Cauchy, Boltzmann, and Softmax Policies
- Saturation and Localization Results for Max-product Generalized Sampling Operators based on Centered Bell-shaped Kernels
- A volume-conserving ALE continuous Galerkin method with residual-based Dirichlet--Neumann fluxes for nonlinear free-surface waves
- Homogenization of degenerate parabolic Signorini problems with vanishing storage and oscillating surface fluxes
- Towards Exact Multidimensional Fluxes: A Structure-Preserving Data-Informed Framework for Riemann Solvers
BibTeX
@misc{lin2026tomography,
title = {{Tomography of reactive Boltzmann kernels from product fluxes}},
author = {Yi-Hsuan Lin and Hongyu Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39770},
eprint = {2609.39770},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39770},
}
RIS
TY - UNPB
TI - Tomography of reactive Boltzmann kernels from product fluxes
AU - Yi-Hsuan Lin
AU - Hongyu Liu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39770
UR - https://arxiv.org/abs/2609.39770
AB - We study the reversible reaction 1+2rightleftarrows3+4 in a dilute gas described by a Boltzmann system. We prove that the outgoing flux of one product species determines the forward collision kernel throughout the domain on a prescribed admissible set of relative velocities and outgoing directions. The elastic collision laws are known, and the reverse kernel is fixed by a prescribed reciprocity relation. The measurements use two synchronized incoming packets with fixed relative velocity and a common velocity tending to infinity. Under bounded angularly integrated collision rates, the short transit time allows us to isolate the contribution of one forward reaction, with estimates uniform as the packets concentrate. Suitable tests of the product flux yield the spatial line integrals of the kernel and a Fourier reconstruction, without differentiating the nonlinear boundary map. We also estimate the effects of finite beam speed, packet width, detector resolution, and measurement noise on the recovered line integrals.
ER -