scholarly journals Renormalization group in the infinite-dimensional turbulence: determination of the RG-functions without renormalization constants

2015 ◽  
pp. 461-469 ◽  
Author(s):  
L.Ts. Adzhemyan ◽  
T.L. Kim ◽  
M.V. Kompaniets ◽  
V.K. Sazonov
Keyword(s):  
Renormalization Group ◽  
Infinite Dimensional ◽  
Renormalization Constants

RENORMALIZATION CONSTANTS IN QUANTUM CHROMODYNAMICS

1998 ◽  
Vol 13 (09) ◽  
pp. 1507-1513
Author(s):  
KAZUHIKO NISHIJIMA ◽  
IZURU DEMIZU
Keyword(s):  
Renormalization Group ◽  
Renormalization Constant ◽  
Qualitative Evaluation ◽  
Group Method ◽  
Renormalization Group Method ◽  
Sum Rule ◽  
Gauge Dependence ◽  
Quark Field ◽  
Exact Evaluation ◽  
Renormalization Constants

The gauge dependence of the renormalization constant of the quark field has been studied with the help of the renormalization group method. In the case of the color gauge field an exact evaluation of the renormalization constant is feasible because of the presence of a sum rule, but in the absence of the corresponding sum rule, only a qualitative evaluation is possible for the quark field.

Determination of Hydraulic Permeability Based on the Measurements of Outflow

2015 ◽  
Vol 3 ◽  
pp. 105-116
Author(s):  
Jozef Kačur ◽  
Jozef Minár
Keyword(s):  
Unsaturated Flow ◽  
Dimensional Space ◽  
A Priori ◽  
Hydraulic Permeability ◽  
Infinite Dimensional ◽  
Tuning Parameters ◽  
Finite Dimensional ◽  
Partially Saturated Porous Media ◽  
The Cost

In this paper we present a method for the determination of the hydraulic permeability for flow in partially saturated porous media. The dependence of hydraulic permeability on effective saturation is not assumed to be a member of any specific finite dimensional class of functions (e.g. vanGenuchten-Mualem, Burdin-Mualem, Brook-Corey). Instead, an infinite dimensional space of functions with limited a priori assumptions (e.g. smoothness, monotonicity) is considered. Consequently, we face a more challenging problem compared to the finite-dimensional case, in which only few tuning parameters need to be determined. We consider the case of 1D unsaturated flow and assume that the data are collected at the outflow of the sample. The hydraulic permeability is determined in an iterative way. We minimize the cost functional reflecting the discrepancy between the measured and computed data. In doing so, we use the Gateaux differential to obtain the direction of the descent.

Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework

2015 ◽  
Vol 18 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Francesco Cordoni ◽  
Luca Di Persio
Keyword(s):  
Invariant Measure ◽  
Stochastic Partial Differential Equation ◽  
Forward Rate ◽  
Infinite Dimensional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Unique Invariant Measure

In this paper we study a particular class of forward rate problems, related to the Vasicek model, where the driving equation is a linear Gaussian stochastic partial differential equation. We first give an existence and uniqueness results of the related mild solution in infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroup with respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.

scholarly journals Effective viscosity of puller-like microswimmers: a renormalization approach

2013 ◽  
Vol 10 (89) ◽  
pp. 20130720 ◽  
Author(s):  
Simon Gluzman ◽  
Dmitry A. Karpeev ◽  
Leonid V. Berlyand
Keyword(s):  
Renormalization Group ◽  
Critical Point ◽  
Effective Viscosity ◽  
Collective Motion ◽  
Analytical Determination ◽  
Renormalization Approach ◽  
Theoretical Results ◽  
Better Than ◽  
Passive Suspensions

Effective viscosity (EV) of suspensions of puller-like microswimmers (pullers), for example Chlamydamonas algae, is difficult to measure or simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytical determination of the passive EV for all concentrations remains unsatisfactory. At the same time, the EV of bacterial suspensions is closely linked to collective motion in these systems and is biologically significant. We develop an approach for determining analytical EV estimates at all concentrations for suspensions of pullers as well as for passive suspensions. The proposed methods are based on the ideas of renormalization group (RG) theory and construct the EV formula based on the known asymptotics for small concentrations and near the critical point (i.e. approaching dense packing). For passive suspensions, the method is verified by comparison against known theoretical results. We find that the method performs much better than an earlier RG-based technique. For pullers, the validation is done by comparing them to experiments conducted on Chlamydamonas suspensions.

Renormalization Group: From a general concept to numbers

2019 ◽  
pp. 69-80
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
General Concept ◽  
Quantum Field ◽  
Fixed Dimension ◽  
Perturbative Renormalization ◽  
Borel Transformation

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

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