## NON-PARAMETRIC IMAGE REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces non-parametric registrations. The idea behind this type of registration is to come up with an appropriate measure both for the similarity as well as for the likelihood of a ... More

## HYPERBOLIC CONSERVATION LAWS

*George Em Karniadakis and Spencer J. Sherwin*

### in Spectral/hp Element Methods for Computational Fluid Dynamics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0010
- Subject:
- Mathematics, Numerical Analysis

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the ... More

## Relativistic Fluids

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. ... More

## RELATIVISTIC HYDRODYNAMICS

*Miguel Alcubierre*

### in Introduction to 3+1 Numerical Relativity

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the derivation of dynamical equations governing the motion of a perfect fluid, known as the Euler equations, both in the special and general relativistic cases. It considers ... More

## ELASTIC REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces elastic registration using the general framework introduced in Chapter 8. A physical motivation for this particular regularizer is given. The two images are viewed as two ... More

## Equilibrium and Non-Equilibrium Collisional Regimes

*Raymond Brun*

### in Introduction to Reactive Gas Dynamics

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199552689
- eISBN:
- 9780191720277
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199552689.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter defines collisional regimes of gaseous flows, including equilibrium and non-equilibrium situations which are described with Euler equations. It examines monatomic and diatomic gas flows, ... More

## Partial differential equations for fluids

*Bijan Mohammadi and Olivier Pironneau*

### in Applied Shape Optimization for Fluids

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0003
- Subject:
- Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ... More

## The Euler-Reynolds System

*Philip Isett*

### in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691174822
- eISBN:
- 9781400885428
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174822.003.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter provides a background on the Euler-Reynolds system, starting with some of the underlying philosophy behind the argument. It describes low frequency parts and ensemble averages of Euler ... More

## Introduction: From Pipeline Economics to Computational Economics

*Ramon Marimon and Andrew Scott*

### in Computational Methods for the Study of Dynamic Economies

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.003.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics

Starts by looking at the advances in macroeconomics that have been made since A. W. Phillips's 1958 Economica paper and his physical economic model (made of piping and valves) designed to teach ... More

## Formulations of the Einstein–Euler Equations

*Luciano Rezzolla and Olindo Zanotti*

### in Relativistic Hydrodynamics

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter, which opens the second part of the book devoted to the numerical solution of the relativistic-hydrodynamics equations, presents in a concise, yet complete, way the several formulations ... More

## Notes on Agents’ Behavioural Rules under Adaptive Learning and Studies of Monetary Policy *

*Seppo Honkapohja, Kaushik Mitra, and George W. Evans*

### in Macroeconomics at the Service of Public Policy

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199666126
- eISBN:
- 9780191749278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666126.003.0005
- Subject:
- Economics and Finance, Macro- and Monetary Economics

This chapter tries to clarify some discussions on the formulation of individual intertemporal behaviour under adaptive learning in representative agent models. The authors first discuss two suggested ... More

## The Main Iteration Lemma

*Philip Isett*

### in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691174822
- eISBN:
- 9781400885428
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174822.003.0010
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter properly formalizes the Main Lemma, first by discussing the frequency energy levels for the Euler-Reynolds equations. Here the bounds are all consistent with the symmetries of the Euler ... More

## Inviscid Incompressible Flows

*Anatoly I. Ruban and Jitesh S. B. Gajjar*

### in Fluid Dynamics: Part 1: Classical Fluid Dynamics

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199681730
- eISBN:
- 9780191761607
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681730.003.0004
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter starts by formulating the Euler equations and the boundary condition for inviscid flow, namely the impermeability condition on a rigid-body surface. The Bernoulli integral for ... More

## The Consequences of Extensivity

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials

Although extensivity is not an essential property of thermodynamic systems, it is a very useful concept for analysing the properties of materials when we can ignore surface and boundary effects. This ... More

## The Stationary Action Principle

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse ... More

## The Consequences of Extensivity

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2019
- Published Online:
- February 2020
- ISBN:
- 9780198853237
- eISBN:
- 9780191887703
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853237.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the ... More

## A Main Lemma for Continuous Solutions

*Philip Isett*

### in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691174822
- eISBN:
- 9781400885428
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174822.003.0005
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter introduces the Main Lemma that implies the existence of continuous solutions. According to this lemma, there exist constants K and C such that the following holds: Let ϵ > 0, and ... More

## Euler’s 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/9780198805021.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the ... More

## Lagrangian Mechanics

*David D. Nolte*

### in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198844624
- eISBN:
- 9780191880216
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198844624.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and ... More

## Two-Dimensional and Geophysical Fluid Mechanics

*A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo*

### in Physics of Long-Range Interacting Systems

- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780199581931
- eISBN:
- 9780191787140
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581931.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this Chapter the statistical mechanics theory of long-range interactions is applied to hydrodynamics problems. The Euler equation is derived as a limiting case of the two dimensional Navier-Stokes ... More