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## Nonlinear Finite-Amplitude Dynamics

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After ... More

## Postprocessing

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ... More

## Internal Gravity Waves

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on internal gravity waves in a stable thermal stratification. When the amplitude of the fluid velocity is small relative to the amplitude of the phase velocity, a linear ... More

## Double-Diffusive Convection

*Gary A. Glatzmaier*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then ... More

## Magnetic Field

*Gary A. Glatzmaier*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0011
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first ... More

## Density Stratification

*Gary A. Glatzmaier*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the effects of large variations in density with depth, that is, density stratification. It first describes anelastic models for 2D cartesian box and 2D cylindrical annulus ... More

## An Archaeology Of Artificial Life, Underwater

*Stefan Helmreich, Sophia Roosth, and Michele Friedner*

### in Sounding the Limits of Life: Essays in the Anthropology of Biology and Beyond

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164809
- eISBN:
- 9781400873869
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164809.003.0003
- Subject:
- Anthropology, Social and Cultural Anthropology

This chapter examines how scientists working on Artificial Life have understood their practices as situated historically. It first considers the practice of finding genealogies for Artificial Life, ... More

## Deterministic Models

*N. Thompson Hobbs and Mevin B. Hooten*

### in Bayesian Models: A Statistical Primer for Ecologists

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0002
- Subject:
- Biology, Ecology

This chapter talks about deterministic models as expressions of ecological hypotheses. These models are based on a deterministic equation or equations making predictions that can be compared with ... More

## Mathematics and Narrative: A Narratological Perspective

*Uri Margolin*

*Apostolos Doxiadis and Barry Mazur (eds)*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0014
- Subject:
- Mathematics, History of Mathematics

This chapter examines the manifold relations between narrative and mathematics from the point of view of narratology. In particular, it considers some of the ways in which we can speak of mathematics ... More

## Perturbations and generalized solutions

*Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel*

### in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153896
- eISBN:
- 9781400842636
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153896.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the effect of state perturbations on solutions to a hybrid system. It shows that state perturbations, of arbitrarily small size, can dramatically change the behavior of ... More

## Introduction to Probability and Random Variables

*M. Vidyasagar*

### in Hidden Markov Processes: Theory and Applications to Biology

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0001
- Subject:
- Mathematics, Probability / Statistics

This chapter provides an introduction to probability and random variables. Probability theory is an attempt to formalize the notion of uncertainty in the outcome of an experiment. For instance, ... More

## Systematically Interrogating Agent-Based Models

*Michael Laver and Ernest Sergenti*

### in Party Competition: An Agent-Based Model

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691139036
- eISBN:
- 9781400840328
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691139036.003.0004
- Subject:
- Political Science, Comparative Politics

This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the ... More

## Nonlinear Structure and Halo Formation

*Abraham Loeb and Steven R. Furlanetto*

### in The First Galaxies in the Universe

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691144917
- eISBN:
- 9781400845606
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144917.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter studies the evolution of perturbations in the nonlinear regime. It focuses for the most part on analytic models that shed light on the physical processes involved. The advent of computer ... More

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