从产物通量反演反应性Boltzmann核的层析成像
Tomography of reactive Boltzmann kernels from product fluxes
- National Yang Ming Chiao Tung University（国立阳明交通大学）
- University of Duisburg-Essen（杜伊斯堡-埃森大学）
- City University of Hong Kong（香港城市大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种层析成像方法，通过测量产物通量反演可逆反应的Boltzmann碰撞核，无需对边界映射求微分，并分析了实验误差的影响。
AI中文摘要：
我们研究由Boltzmann系统描述的稀薄气体中的可逆反应$1+2\ ightleftarrows3+4$。我们证明，在规定的相对速度和出射方向的可容许集合上，一种产物物种的出射通量决定了整个定义域上的正向碰撞核。弹性碰撞定律是已知的，反向核由规定的互易关系固定。测量使用两个同步入射包，具有固定的相对速度和趋于无穷大的共同速度。在有界的角度积分碰撞率下，短的渡越时间使我们能够隔离一个正向反应的贡献，且估计在包集中时一致。对产物通量的适当测试产生核的空间线积分和傅里叶重建，而无需对非线性边界映射求微分。我们还估计了有限光束速度、包宽度、探测器分辨率和测量噪声对恢复的线积分的影响。
英文摘要：
We study the reversible reaction $1+2\rightleftarrows3+4$ 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.
