Impact parameter formulation of classical finite characteristic collision time approximation

1975 ◽  
Vol 8 (13) ◽  
pp. 2249-2254 ◽  
Author(s):  
D R Bates ◽  
G N Bates
Keyword(s):  
Impact Parameter ◽  
Collision Time ◽  
Finite Characteristic ◽  
Time Approximation

scholarly journals Line Shapes in a Magnetic Field: Trajectory Modifications II: Full Collision-Time Statistics

2019 ◽  
Author(s):  
Spiros Alexiou
Keyword(s):  
Magnetic Field ◽  
Impact Parameter ◽  
Constant Magnetic Field ◽  
Larmor Radius ◽  
Collision Time ◽  
Line Broadening ◽  
Line Shapes ◽  
Low Magnetic Field

In a previous paper\cite{simplified}, a variation of the Collision-time Statistics method was applied to identify the relevant perturbers for line broadening under the action of a constant magnetic field. As discussed, that version was simplified and inadequate for low magnetic field and/or large perturber mass (ions). The purpose of the present work is to augment the previous work, so that such cases, corresponding to the Larmor radius exceeding the maximum impact parameter, can be handed efficiently. The results may also be used to construct analytic, i.e. impact/unified models under the usual assumptions in these models.

scholarly journals A note on the relations between elastic and inelastic interactions and increasing ratio σel(s)/σtot(s) at the LHC

2019 ◽  
Vol 34 (32) ◽  
pp. 1950259 ◽  
Author(s):  
S. M. Troshin ◽  
N. E. Tyurin
Keyword(s):  
Elastic Scattering ◽  
Energy Dependence ◽  
Impact Parameter ◽  
Cross Sections ◽  
Parameter Dependence ◽  
Slope Parameter ◽  
Short Notice ◽  
Inelastic Interactions ◽  
The Impact ◽  
Mode A

We comment briefly on relations between the elastic and inelastic cross-sections valid for the shadow and reflective modes of the elastic scattering. Those are based on the unitarity arguments. It is shown that the redistribution of the probabilities of the elastic and inelastic interactions (the form of the inelastic overlap function becomes peripheral) under the reflective scattering mode can lead to increasing ratio of [Formula: see text] at the LHC energies. In the shadow scattering mode, the mechanism of this increase is a different one, since the impact parameter dependence of the inelastic interactions probability is central in this mode. A short notice is also given on the slope parameter and the leading contributions to its energy dependence in both modes.

scholarly journals Distinguishing hadronic cascades from hydrodynamic models inPb(160A GeV)+Pbreactions by impact parameter variation

1999 ◽  
Vol 59 (4) ◽  
pp. R1844-R1845 ◽  
Author(s):  
M. Bleicher ◽  
M. Reiter ◽  
A. Dumitru ◽  
J. Brachmann ◽  
C. Spieles ◽  
...  
Keyword(s):  
Impact Parameter ◽  
Parameter Variation ◽  
Hydrodynamic Models

Real-time Approximation of Photometric Polygonal Lights

2020 ◽  
Vol 3 (1) ◽  
pp. 1-18
Author(s):  
Christian Luksch ◽  
Lukas Prost ◽  
Michael Wimmer
Keyword(s):  
Real Time ◽  
Specular Reflection ◽  
Near Field ◽  
Measurement Data ◽  
Data Sets ◽  
Photometric Measurement ◽  
Integration Technique ◽  
Time Approximation ◽  
Light Emitter ◽  
Selection Of

We present a real-time rendering technique for photometric polygonal lights. Our method uses a numerical integration technique based on a triangulation to calculate noise-free diffuse shading. We include a dynamic point in the triangulation that provides a continuous near-field illumination resembling the shape of the light emitter and its characteristics. We evaluate the accuracy of our approach with a diverse selection of photometric measurement data sets in a comprehensive benchmark framework. Furthermore, we provide an extension for specular reflection on surfaces with arbitrary roughness that facilitates the use of existing real-time shading techniques. Our technique is easy to integrate into real-time rendering systems and extends the range of possible applications with photometric area lights.

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

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