relativistic collision
Recently Published Documents


TOTAL DOCUMENTS

19
(FIVE YEARS 2)

H-INDEX

6
(FIVE YEARS 0)

2021 ◽  
pp. 2100245
Author(s):  
Felix M. Kröger ◽  
Günter Weber ◽  
Simon Hirlaender ◽  
Reyes Alemany‐Fernandez ◽  
Mieczyslaw W. Krasny ◽  
...  

Author(s):  
James Chapman ◽  
Jin Woo Jang ◽  
Robert M. Strain

AbstractThis article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Newtonian Boltzmann equation, the center-of-momentum coordinates have played a large role in the study of the Newtonian non-cutoff Boltzmann equation, in particular we mention the widely used cancellation lemma [1]. In this article we calculate specifically the very complicated Jacobian determinant, in ten variables, for the relativistic collision map from the momentum p to the post collisional momentum $$p'$$ p ′ ; specifically we calculate the determinant for $$p\mapsto u = \theta p'+\left( 1-\theta \right) p$$ p ↦ u = θ p ′ + 1 - θ p for $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] . Afterwards we give an upper-bound for this determinant that has no singularity in both p and q variables. Next we give an example where we prove that the Jacobian goes to zero in a specific pointwise limit. We further explain the results of our numerical study which shows that the Jacobian determinant has a very large number of distinct points at which it is machine zero. This generalizes the work of Glassey-Strauss (1991) [8] and Guo-Strain (2012) [12]. These conclusions make it difficult to envision a direct relativistic analog of the Newtonian cancellation lemma in the center-of-momentum coordinates.


Author(s):  
Yi-Lun Du ◽  
Kai Zhou ◽  
Jan Steinheimer ◽  
Long-Gang Pang ◽  
Anton Motornenko ◽  
...  

2012 ◽  
Vol 19 (10) ◽  
pp. 103109 ◽  
Author(s):  
Ying Wang ◽  
Chengxun Yuan ◽  
Ruilin Gao ◽  
Zhongxiang Zhou

2011 ◽  
Vol 18 (2) ◽  
pp. 022504 ◽  
Author(s):  
Y. J. Hu ◽  
Y. M. Hu ◽  
Y. R. Lin-Liu

2005 ◽  
Vol 627 (1) ◽  
pp. 62-74 ◽  
Author(s):  
C. Arbeiter ◽  
M. Pohl ◽  
R. Schlickeiser

Sign in / Sign up

Export Citation Format

Share Document