First-order expansion

2009 ◽  
pp. 109-118
Author(s):  
Alice Guionnet
Keyword(s):  
First Order ◽  
Order Expansion

scholarly journals Light-cone distribution amplitudes of light mesons with QED effects

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Martin Beneke ◽  
Philipp Böer ◽  
Jan-Niklas Toelstede ◽  
K. Keri Vos
Keyword(s):  
Light Cone ◽  
Electromagnetic Coupling ◽  
First Order ◽  
Order Expansion ◽  
Group Evolution ◽  
Fixed Order ◽  
Light Mesons ◽  
Charged Mesons ◽  
Qed Effects ◽  
Exclusive Processes

Abstract We discuss the generalization of the leading-twist light-cone distribution amplitude for light mesons including QED effects. This generalization was introduced to describe virtual collinear photon exchanges at the strong-interaction scale ΛQCD in the factorization of QED effects in non-leptonic B-meson decays. In this paper we study the renormalization group evolution of this non-perturbative function. For charged mesons, in particular, this exhibits qualitative differences with respect to the well-known scale evolution in QCD only, especially regarding the endpoint-behaviour. We analytically solve the evolution equation to first order in the electromagnetic coupling αem, which resums large logarithms in QCD on top of a fixed-order expansion in αem. We further provide numerical estimates for QED corrections to Gegenbauer coefficients as well as inverse moments relevant to (QED-generalized) factorization theorems for hard exclusive processes.

Second Order Perturbation Analysis of a Forced Nonlinear Mathieu Equation

2012 ◽  
Author(s):  
Venkatanarayanan Ramakrishnan ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Mathieu Equation ◽  
Second Order ◽  
Order Perturbation ◽  
Cubic Nonlinearity ◽  
First Order ◽  
Order Expansion ◽  
Direct Forcing

The present study deals with the response of a forced nonlinear Mathieu equation. The equation considered has parametric excitation at the same frequency as direct forcing and also has cubic nonlinearity and damping. A second-order perturbation analysis using the method of multiple scales unfolds numerous resonance cases and system behavior that were not uncovered using first-order expansions. All resonance cases are analyzed. We numerically plot the frequency response of the system. The existence of a superharmonic resonance at one third the natural frequency was uncovered analytically for linear system. (This had been seen previously in numerical simulations but was not captured in the first-order expansion.) The effect of different parameters on the response of the system previously investigated are revisited.

A Contour Integral and First Order Expansion Problem

1945 ◽  
Vol 20 (2) ◽  
pp. 79 ◽  
Author(s):  
H. P. Doole
Keyword(s):  
Contour Integral ◽  
First Order ◽  
Order Expansion

scholarly journals ON THE NUMBER OF LIMIT CYCLES FOR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ2n WITH TWO ZONES

2013 ◽  
Vol 23 (02) ◽  
pp. 1350024 ◽  
Author(s):  
JAUME LLIBRE ◽  
FENG RONG
Keyword(s):  
Small Parameter ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Averaging Theory ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential

We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary.

scholarly journals LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

2011 ◽  
Vol 21 (11) ◽  
pp. 3181-3194 ◽  
Author(s):  
PEDRO TONIOL CARDIN ◽  
TIAGO DE CARVALHO ◽  
JAUME LLIBRE
Keyword(s):  
Limit Cycles ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Two Dimensional ◽  
Bifurcation Of Limit Cycles ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential

We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in ℝn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed.

Perturbation analysis of functionals of random measures

1995 ◽  
Vol 27 (2) ◽  
pp. 306-325 ◽  
Author(s):  
François Baccelli ◽  
Maurice Klein ◽  
Sergei Zuyev
Keyword(s):  
Phase Space ◽  
Random Measure ◽  
Random Processes ◽  
Stationary Processes ◽  
Light Traffic ◽  
Random Measures ◽  
First Order ◽  
Order Expansion ◽  
Palm Measure ◽  
New Algorithms

We use the fact that the Palm measure of a stationary random measure is invariant to phase space change to generalize the light traffic formula initially obtained for stationary processes on a line to general spaces. This formula gives a first-order expansion for the expectation of a functional of the random measure when its intensity vanishes. This generalization leads to new algorithms for estimating gradients of functionals of geometrical random processes.

Applicability of second-order expansion in s13 to explore δCP in small and medium baseline ν experiments

2016 ◽  
Vol 31 (09) ◽  
pp. 1650037
Author(s):  
Mandip Singh
Keyword(s):  
Series Expansion ◽  
Second Order ◽  
Mixing Angle ◽  
First Order ◽  
Long Baseline ◽  
Order Expansion ◽  
Matrix Formula ◽  
Small Baseline ◽  
Reactor Mixing ◽  
Baseline Experiment

The series expansion of neutrino evolution matrix “[Formula: see text]”, up to first-order in small reactor mixing angle [Formula: see text] is very useful formalism to study experiments quantitatively. The formalism has been used especially to investigate CP-violating phase [Formula: see text]. In order to perform a broad investigation for the possible measurement of [Formula: see text] phase, we will study small baseline experiments: Chooz [Formula: see text], T2K [Formula: see text] and ESS [Formula: see text], medium baseline experiment: NO[Formula: see text]A [Formula: see text] and long baseline experiment: LBNE [Formula: see text].

The First Order Expansion of Motion Equations in the Uncalibrated Case

1996 ◽  
Vol 64 (1) ◽  
pp. 128-146 ◽  
Author(s):  
T. Viéville ◽  
O.D. Faugeras
Keyword(s):  
Motion Equations ◽  
First Order ◽  
Order Expansion
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