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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

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/9780691141725.003.0007
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

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/9780691141725.003.0011
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

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/9780691141725.003.0012
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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