Synchrotron Self‐Comptonization in a Relativistic Collision Front Model

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

scholarly journals On the Determinant Problem for the Relativistic Boltzmann Equation

2021 ◽  
Author(s):  
James Chapman ◽  
Jin Woo Jang ◽  
Robert M. Strain
Keyword(s):  
Boltzmann Equation ◽  
Upper Bound ◽  
Numerical Study ◽  
Jacobian Determinant ◽  
Large Role ◽  
Relativistic Boltzmann Equation ◽  
Relativistic Analog ◽  
Relativistic Collision ◽  
Pointwise Limit ◽  
Open Question

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.

Relativistic collision operators for modeling noninductive current drive by waves

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

scholarly journals In-medium pion valence distributions in a light-front model

2017 ◽  
Vol 766 ◽  
pp. 125-131 ◽  
Author(s):  
J.P.B.C. de Melo ◽  
K. Tsushima ◽  
I. Ahmed
Keyword(s):  
Light Front ◽  
Front Model

Capillary water absorption by a porous cylinder

2017 ◽  
Vol 42 (2) ◽  
pp. 120-124 ◽  
Author(s):  
Christopher Hall
Keyword(s):  
Radial Flow ◽  
Effective Porosity ◽  
Capillary Absorption ◽  
Porous Cylinder ◽  
Capillary Water ◽  
Cylinder Axis ◽  
Flow Through ◽  
Front Model ◽  
Sharp Front ◽  
Good Agreement

Capillary absorption (imbibition) of water by a porous cylinder is described by means of a Sharp-Front model. The cumulative absorption increases as (time)1/2 at early times, but more slowly as the wet front approaches the cylinder axis. Results are given in terms of dimensionless variables. Experimental data on plaster cylinders are in good agreement with theory. Estimates of the sorptivity and effective porosity of the material can be obtained. The model may be useful in testing drilled cores and may also be applied to radial flow through the wall of a porous tube (hence to conduits and arches).

Scaling for deuteron structure functions in a relativistic light-front model

1996 ◽  
Vol 53 (6) ◽  
pp. 3111-3130 ◽  
Author(s):  
W. N. Polyzou ◽  
W. Glöckle
Keyword(s):  
Structure Functions ◽  
Light Front ◽  
Front Model

scholarly journals Tree crowns grow into self-similar shapes controlled by gravity and light sensing

2018 ◽  
Vol 15 (142) ◽  
pp. 20170976 ◽  
Author(s):  
Laurent Duchemin ◽  
Christophe Eloy ◽  
Eric Badel ◽  
Bruno Moulia
Keyword(s):  
Tree Growth ◽  
Initial Conditions ◽  
Tree Crown ◽  
Tree Crowns ◽  
Light Sensing ◽  
The Core ◽  
Long Period ◽  
Self Similar ◽  
Similar Solutions ◽  
Front Model

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

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