scholarly journals ON THE STANDARD APPROACH TO RENORMALIZATION GROUP IMPROVEMENT

2007 ◽  
Vol 16 (06) ◽  
pp. 1681-1685 ◽  
Author(s):  
F. A. CHISHTIE ◽  
V. ELIAS ◽  
R. B. MANN ◽  
D. G. C. MCKEON ◽  
T. G. STEELE
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Detailed Comparison ◽  
Standard Approach ◽  
Loop Order ◽  
Made In

Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing Nn-1LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless λϕ4 model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

scholarly journals In-Depth Verification of a Numerical Model for an Axisymmetric RC Dome

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2152
Author(s):  
Przemysław Czumaj ◽  
Sławomir Dudziak ◽  
Zbigniew Kacprzyk
Keyword(s):  
Three Dimensional ◽  
Spatial Models ◽  
Detailed Comparison ◽  
The Finite Element Method ◽  
Robot System ◽  
Engineering Structures ◽  
Computational Analyses ◽  
Computational Systems ◽  
Good Agreement ◽  
Made In

The designers of civil engineering structures often have to face the problem of the reliability of complex computational analyses performed most often with the Finite Element Method (FEM). Any assessment of reliability of such analyses is difficult and can only be approximate. The present paper puts forward a new method of verification and validation of the structural analyses upon an illustrative example of a dome strengthened by circumferential ribs along the upper and lower edges. Four computational systems were used, namely Abaqus, Autodesk Robot, Dlubal RFEM, and FEAS. Different models were also analyzed—two-dimensional (2D) and three-dimensional (3D) ones using continuum, bar, and shell finite elements. The results of the static (with two kinds of load—self-weight and load distributed along the upper ring) and modal analyses are presented. A detailed comparison between the systems’ and models’ predictions was made. In general, the spatial models predicted a less stiff behavior of the analyzed dome than the planar models. The good agreement between different models and systems was obtained for the first natural frequency with axisymmetric eigenmodes (except from the Autodesk Robot system). The presented approach to the verification of complex shell–bar models can be effectively applied by structural designers.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

Operator regularization and the renormalization group to two-loop order in φ63

1990 ◽  
Vol 197 (1) ◽  
pp. 94-118 ◽  
Author(s):  
L Culumovic ◽  
D.G.C McKeon ◽  
T.N Sherry
Keyword(s):  
Renormalization Group ◽  
Loop Order

scholarly journals Renormalization-group-improved effective potential for the MSSM Higgs sector with explicit CP violation

2000 ◽  
Vol 586 (1-2) ◽  
pp. 92-140 ◽  
Author(s):  
M. Carena ◽  
J. Ellis ◽  
A. Pilaftsis ◽  
C.E.M. Wagner
Keyword(s):  
Renormalization Group ◽  
Cp Violation ◽  
Effective Potential ◽  
Higgs Sector

scholarly journals Multiple flux rope events at the magnetopause observations by TC-1 on 18 March 2004

2005 ◽  
Vol 23 (8) ◽  
pp. 2897-2901 ◽  
Author(s):  
C. J. Xiao ◽  
Z. Y. Pu ◽  
Y. Wei ◽  
Z. X. Liu ◽  
C. M. Carr ◽  
...  
Keyword(s):  
Flux Rope ◽  
Detailed Comparison ◽  
Dominant Negative ◽  
Time Interval ◽  
Low Latitude ◽  
Guide Field ◽  
Flux Ropes ◽  
The Mean ◽  
Mean Time ◽  
Made In

Abstract. From 23:10 to 23:50 UT on 18 March 2004, the Double Star TC-1 spacecraft detected eight flux ropes at the outbound crossing of the southern dawnside magnetopause. A notable guide field existed inside all ropes. In the mean time the Cluster spacecraft were staying in the magnetosheath and found that the events occurred under the condition of southward IMF Bz and dominant negative IMF By. There are six ropes that appeared quasi-periodically, with a repeated period being approximately 1-4 min. The last flux rope lasts for a longer time interval with a larger peak in the BN variations; it can thus be referred to as a typical FTE. The 18 March 2004 event is quite similar to the multiple flux rope event observed by Cluster on 26 January 2001 at the northern duskside high-latitude magnetopause. A detailed comparison of these two events is made in the paper. Preliminary studies imply that both of these multiple flux ropes events seem to be produced by component reconnection at the dayside low-latitude magnetopause.

The renormalization group in curved space

2021 ◽  
pp. 388-396
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Effective Action ◽  
Finite Part ◽  
Minimal Subtraction ◽  
Essential Information ◽  
Curved Space ◽  
Scaling Anomaly

As the main purpose of renormalization is not to remove divergences but to get essential information about the finite part of effective action, this chapter discusses some of the existing methods of solving this problem; such methods can be denoted the renormalization group. First, the minimal subtraction renormalization group in curved space is formulated. Next, the chapter shows how the overall μ‎-independence of the effective action enables one to interpret μ‎-dependence in some situations. As an example, the effective potential is restored from the renormalization group and compared with the expression calculated directly in chapter 13. In addition, the global conformal (scaling) anomaly is derived from the renormalization group.

Dynamic choice

2020 ◽  
pp. 133-148
Author(s):  
David M. Kreps
Keyword(s):  
Standard Approach ◽  
Dynamic Choice ◽  
Knowing That ◽  
Dynamic Strategy ◽  
Optimal Dynamic ◽  
Made In

This chapter investigates the issue of dynamic choice. Many important choices made in economic contexts are made through time. The consumer takes some action today, knowing that subsequent choices will be required tomorrow and the day following and so on. And today's choice has impact on either how the consumer views later choices or what choices will later be available or both. This can be referred to as a situation of dynamic choice. The chapter discusses how economists model the process of dynamic choice. In microeconomics, the issue of dynamic choice is usually dealt with by reducing dynamic choice to the static choice of an optimal dynamic strategy which is then carried out. The chapter examines this standard approach before considering a pair of alternatives.

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