RENORMALIZATION GROUP IN MODERN PHYSICS

1988 ◽  
Vol 03 (06) ◽  
pp. 1321-1341 ◽  
Author(s):  
D.V. SHIRKOV
Keyword(s):  
Ultra Violet ◽  
Point Of View ◽  
Theoretical Physics ◽  
Self Similarity ◽  
Simple Derivation ◽  
Renormalization Groups ◽  
Functional Formulation ◽  
Modern Physics ◽  
Similarity Laws ◽  
General Method

Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view we present a simple derivation of the renorm-group (RG) in QFT “liberated” from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare “different” RG’s.

Adjustable wetting of Liquid Flame Spray (LFS) TiO2-nanoparticle coated board: Batch-type versus roll-to-roll stimulation methods

2014 ◽  
Vol 29 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Mikko Tuominen ◽  
Hannu Teisala ◽  
Janne Haapanen ◽  
Mikko Aromaa ◽  
Jyrki M. Mäkelä ◽  
...  
Keyword(s):  
Argon Plasma ◽  
Ultra Violet ◽  
High Volume ◽  
Point Of View ◽  
Flame Spray ◽  
Ambient Conditions ◽  
Batch Type ◽  
Roll To Roll ◽  
Long Time ◽  
Liquid Flame Spray

Abstract Superhydrophobic nanoparticle coating was created on the surface of board using liquid flame spray (LFS). The LFS coating was carried out continuously in ambient conditions without any additional hydrophobization steps. The contact angle of water (CAW) of ZrO2, Al2O3 and TiO2 coating was adjusted reversibly from >150° down to ~10−20° using different stimulation methods. From industrial point of view, the controlled surface wetting has been in focus for a long time because it defines the liquid-solid contact area, and furthermore can enhance the mechanical and chemical bonding on the interface between the liquid and the solid. The used stimulation methods included batch-type methods: artificial daylight illumination and heat treatment and roll-to-roll methods: corona, argon plasma, IR (infra red)- and UV (ultra violet)-treatments. On the contrary to batch-type methods, the adjustment and switching of wetting was done only in seconds or fraction of seconds using roll-to-roll stimulation methods. This is significant in the converting processes of board since they are usually continuous, high volume operations. In addition, the creation of microfluidic patterns on the surface of TiO2 coated board using simple photomasking and surface stimulation was demonstrated. This provides new advantages and possibilities, especially in the field of intelligent printing. Limited durability and poor repellency against low surface tension liquids are presently the main limitations of LFS coatings.

A solution of the time paradox of physics

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Grit Kalies
Keyword(s):  
Laws Of Nature ◽  
Theoretical Physics ◽  
Quantum Level ◽  
Energy Equivalence ◽  
Time Arrow ◽  
Laws Of Thermodynamics ◽  
Time Concepts ◽  
Modern Physics ◽  
The One ◽  
Matter Energy

AbstractQuantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.

Covariant Physics

2021 ◽  
Author(s):  
Moataz H. Emam
Keyword(s):  
Point Of View ◽  
Theoretical Physics ◽  
Newtonian Mechanics ◽  
Theory Of Relativity ◽  
College Physics ◽  
Introductory Courses ◽  
Tensor Calculus ◽  
Research Papers ◽  
Intended Reader ◽  
Theory Of Fields

This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics oriented topics rarely discussed at the level of the intended reader (mid-college physics major). It does so from the point of view of the so-called principle of covariance; a symmetry that underlies most of physics, including such familiar branches as Newtonian mechanics and electricity and magnetism. The book is written from a minimalist perspective, providing the reader with only the most basic of notions; just enough to be able to read, and hopefully comprehend, modern research papers on these subjects. In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds. The hope is that students with a minimal mathematical background in calculus and only some introductory courses in physics may be able to study this book and benefit from it.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

scholarly journals Limits of Predictability of a Global Self-Similar Routing Model in a Local Self-Similar Environment

Atmosphere ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 791
Author(s):  
Nicolas Velasquez ◽  
Ricardo Mantilla
Keyword(s):  
Scaling Laws ◽  
Hydraulic Geometry ◽  
Distributed Hydrological Model ◽  
Self Similarity ◽  
Cross Sectional ◽  
Actual Observation ◽  
Scaling Parameters ◽  
Self Similar ◽  
Distributed Hydrological Models ◽  
Similarity Laws

Regional Distributed Hydrological models are being adopted around the world for prediction of streamflow fluctuations and floods. However, the details of the hydraulic geometry of the channels in the river network (cross sectional geometry, slope, drag coefficients, etc.) are not always known, which imposes the need for simplifications based on scaling laws and their prescription. We use a distributed hydrological model forced with radar-derived rainfall fields to test the effect of spatial variations in the scaling parameters of Hydraulic Geometric (HG) relationships used to simplify routing equations. For our experimental setup, we create a virtual watershed that obeys local self-similarity laws for HG and attempt to predict the resulting hydrographs using a global self-similar HG parameterization. We find that the errors in the peak flow value and timing are consistent with the errors that are observed when trying to replicate actual observation of streamflow. Our results provide evidence that local self-similarity can be a more appropriate simplification of HG scaling laws than global self-similarity.

scholarly journals Bianchi I in scalar and scalar-tensor cosmologies

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
José Belinchón
Keyword(s):  
Perfect Fluid ◽  
Theoretical Models ◽  
Point Of View ◽  
Time Varying ◽  
Self Similarity ◽  
Bianchi I ◽  
Exact Power ◽  
Varying Constants ◽  
Time Varying Constants ◽  
Matter Fields

AbstractWe study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.

scholarly journals The birth of E 8 out of the spinors of the icosahedron

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150504 ◽  
Author(s):  
Pierre-Philippe Dechant
Keyword(s):  
Clifford Algebra ◽  
Root System ◽  
Automorphism Groups ◽  
Root Systems ◽  
Double Cover ◽  
Point Of View ◽  
Three Dimensions ◽  
Theoretical Physics ◽  
Superstring Theory ◽  
3D Space

E 8 is prominent in mathematics and theoretical physics, and is generally viewed as an exceptional symmetry in an eight-dimensional (8D) space very different from the space we inhabit; for instance, the Lie group E 8 features heavily in 10D superstring theory. Contrary to that point of view, here we show that the E 8 root system can in fact be constructed from the icosahedron alone and can thus be viewed purely in terms of 3D geometry. The 240 roots of E 8 arise in the 8D Clifford algebra of 3D space as a double cover of the 120 elements of the icosahedral group, generated by the root system H 3 . As a by-product, by restricting to even products of root vectors (spinors) in the 4D even subalgebra of the Clifford algebra, one can show that each 3D root system induces a root system in 4D, which turn out to also be exactly the exceptional 4D root systems. The spinorial point of view explains their existence as well as their unusual automorphism groups. This spinorial approach thus in fact allows one to construct all exceptional root systems within the geometry of three dimensions, which opens up a novel interpretation of these phenomena in terms of spinorial geometry.

A Possible Role of Universal Length in the Theory of Weak Interactions

1973 ◽  
Vol 51 (14) ◽  
pp. 1577-1581 ◽  
Author(s):  
D. Y. Kim
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Weak Interactions ◽  
Relativistic Quantum ◽  
Universal Constant ◽  
Point Of View ◽  
Quantum Field ◽  
Elementary Length ◽  
Modern Physics

The discovery and role of already existing universal constants h and c in modern physics have been reviewed from a particular point of view. This viewpoint is characterized by a pattern of logic in terms of which one may possibly find a new universal constant, i.e. the elementary length. One of the main objectives of this paper is to find out whether the elementary length introduced this way would resolve inherent difficulties in relativistic quantum field theory. This has been explicitly studied in terms of the nonlocal field theory in connection with the CP violating kaon decay. This produced a relation [Formula: see text] which leads, on the one hand, to a consistent explanation of the possible mechanism of CP violation and, on the other hand, gives a result which is most probably the first direct link between the elementary length (nonlocality) and an experiment without having the inherent disorder in the small distance behavior in quantum field theory.

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