View:

- no detail
- some detail
- full detail

## Hierarchies, Complex Fractal Dimensions, and Log-Periodicity

*Didier Sornette*

### in Why Stock Markets Crash: Critical Events in Complex Financial Systems

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175959
- eISBN:
- 9781400885091
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175959.003.0006
- Subject:
- Business and Management, Finance, Accounting, and Banking

This chapter describes the concept of fractals and their self-similarity, including fractals with complex dimensions. It shows how these geometric and mathematical objects enable one to codify the ... More

## Hydrodynamics

*Stefano Atzeni and JÜrgen Meyer-Ter-Vehn*

### in The Physics of Inertial Fusion: BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter

- Published in print:
- 2004
- Published Online:
- January 2008
- ISBN:
- 9780198562641
- eISBN:
- 9780191714030
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198562641.003.0006
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter is devoted to hydrodynamic concentration of energy, in particular to cold isentropic compression of matter by converging hydrodynamic flows. The discussion is restricted to ... More

## Scale-invariance

*Guido Caldarelli*

### in Scale-Free Networks: Complex Webs in Nature and Technology

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199211517
- eISBN:
- 9780191705984
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211517.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents an overview of self-similar phenomena in nature and why they are so important and how this applies to complex networks.

## Scale-, Base-, and Sum-lnvariance

*Arno Berger and Theodore P. Hill*

### in An Introduction to Benford's Law

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691163062
- eISBN:
- 9781400866588
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691163062.003.0005
- Subject:
- Mathematics, Probability / Statistics

This chapter establishes and illustrates three basic invariance properties of the Benford distribution that are instrumental in demonstrating whether or not certain datasets are Benford, and that ... More

## Effective Field Theories for Nuclear and (Some) Atomic Physics

*U. van Kolck*

### in Effective Field Theory in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School: Volume 108, July 2017

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198855743
- eISBN:
- 9780191889370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198855743.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

These lectures are a pedagogical—not comprehensive—introduction to the applications of effective field theory (EFT) in the context of nuclear and atomic physics. A common feature of these ... More

## Kolmogorov’s (1941) theory revisited

*W. David McComb*

### in Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199689385
- eISBN:
- 9780191768255
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199689385.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

By restricting our attention in this book to HIT, we have ruled out effects due to mean shear, system rotation, density stratification; and so on. This leaves us with a stark choice: deviation from ... More

## Aggregation

*Paul Charbonneau*

### in Natural Complexity: A Modeling Handbook

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691176840
- eISBN:
- 9781400885497
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691176840.003.0003
- Subject:
- Computer Science, Programming Languages

This chapter explores how naturally occurring inanimate structures grow by accretion of smaller-sized components, focusing on one specific accretion process: diffusion-limited aggregation (DLA). In ... More

## Benfordʼs Law in the Natural Sciences

*David Hoyle*

### in Benford's Law: Theory and Applications

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691147611
- eISBN:
- 9781400866595
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147611.003.0016
- Subject:
- Mathematics, Probability / Statistics

This chapter focuses on the occurrence of Benford's law within the natural sciences, emphasizing that Benford's law is to be expected within many scientific data sets. This is a consequence of the ... More

## A First Glance at Renormalisation and Symmetry

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0017
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The fate of the classical symmetries in a quantum field theory after renormalisation. Global symmetries versus gaugec symmetries. The Adler–Bell–Jackiw anomaly. The breaking of scale invariance and ... More

## It Must Be Beautiful

*Roger Arditi and Lev R. Ginzburg*

### in How Species Interact: Altering the Standard View on Trophic Ecology

- Published in print:
- 2012
- Published Online:
- May 2015
- ISBN:
- 9780199913831
- eISBN:
- 9780190267902
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199913831.003.0007
- Subject:
- Biology, Ecology

This chapter explains the role of ratio-dependence as an invariance in ecology. It analyzes the importance of using scaling invariance in mathematics and proposes that all models of interacting ... More

## Hadrons, partons and QCD

*Michael Kachelriess*

### in Quantum Fields: From the Hubble to the Planck Scale

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198802877
- eISBN:
- 9780191841330
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802877.003.0018
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter first discusses the breaking of scale invariance of QCD with massless quarks by quantum corrections and explains that this effect is responsible for the bulk of hadron masses. Then the ... More

## Percolation

*Paul Charbonneau*

### in Natural Complexity: A Modeling Handbook

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691176840
- eISBN:
- 9781400885497
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691176840.003.0004
- Subject:
- Computer Science, Programming Languages

This chapter explores a lattice-based system where complex structures can arise from pure randomness: percolation, typically described as the passage of liquid through a porous or granular medium. In ... More

## Epidemics

*Paul Charbonneau*

### in Natural Complexity: A Modeling Handbook

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691176840
- eISBN:
- 9781400885497
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691176840.003.0009
- Subject:
- Computer Science, Programming Languages

This chapter examines the complex nature of the epidemic spread of contagious diseases. It first describes the model of epidemic spread constructed by adding random walks on a lattice to the ... More

## Earthquakes

*Paul Charbonneau*

### in Natural Complexity: A Modeling Handbook

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691176840
- eISBN:
- 9781400885497
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691176840.003.0008
- Subject:
- Computer Science, Programming Languages

This chapter examines the natural complexity of earthquakes. Earthquakes release energy that is quantified by their magnitude m, a logarithmic measure of seismic wave amplitudes. The number N of ... More

## Complexity and Criticality

*Helmut Satz*

### in The Rules of the Flock: Self-Organization and Swarm Structure in Animal Societies

- Published in print:
- 2020
- Published Online:
- March 2020
- ISBN:
- 9780198853398
- eISBN:
- 9780191888052
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853398.003.0007
- Subject:
- Physics, Soft Matter / Biological Physics, Particle Physics / Astrophysics / Cosmology

Complex systems and critical behavior in complex system are defined in terms of correlation between constituents in the medium, subject to screening by intermediate constituents. At a critical point, ... More

## The Navier–Stokes Equations

*S. G. Rajeev*

### in Fluid Mechanics: A Geometrical Point of View

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805021
- eISBN:
- 9780191843136
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805021.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

When different layers of a fluid move at different velocities, there is some friction which results in loss of energy and momentum to molecular degrees of freedom. This dissipation is measured by a ... More

## Singularities

*S. G. Rajeev*

### in Fluid Mechanics: A Geometrical Point of View

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805021
- eISBN:
- 9780191843136
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805021.003.0012
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

The initial value problem of the incompressible Navier–Stokes equations is explained. Leray’s classic study of it (using Picard iteration) is simplified and described in the language of physics. The ... More

View:

- no detail
- some detail
- full detail