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Axon Models

W. Otto Friesen and Jonathon A. Friesen

in NeuroDynamix II: Concepts of Neurophysiology Illustrated by Computer Simulations

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195371833
eISBN:
9780199865178
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195371833.003.0011
Subject:
Psychology, Cognitive Neuroscience

The Axon model simulates the equations and parameters derived from experiments by Hodgkin and Huxley on the squid giant axon. Because of the exact correspondence between the equations incorporated ... More


Equations Underlying the Axon Models

W. Otto Friesen and Jonathon A. Friesen

in NeuroDynamix II: Concepts of Neurophysiology Illustrated by Computer Simulations

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195371833
eISBN:
9780199865178
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195371833.003.0019
Subject:
Psychology, Cognitive Neuroscience

The Axon models present the fundamental concepts that underlie the generation and propagation of the nerve impulses. This chapter includes a complete list of the equations that describe the ... More


Ions and electrons in liquid helium

Armando Francesco Borghesani

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell ... More


ALGORITHMS FOR INCOMPRESSIBLE FLOWS

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/9780198528692.003.0008
Subject:
Mathematics, Numerical Analysis

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. ... More


Kinetic Theory of Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ... More


High-Energy Tail of the Velocity Distribution Function

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

The velocity distribution function of particles whose velocities exceed the thermal velocity cannot be described by a Maxwell distribution. This chapter shows that this part of the velocity ... More


Diffusion and Self-Diffusion

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the basic concepts of diffusion and self-diffusion. It derives relations between the mean square displacement of a diffusing particle, the diffusion coefficient, and the ... More


Two-Dimensional Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0016
Subject:
Physics, Condensed Matter Physics / Materials

It has been shown for molecular fluids that the velocity-time correlation function in ddimensions exhibits a power-law dependence for t >> 1. This function reveals a long time tail compared with an ... More


Kinetic Coefficients and Velocity Distribution for Gases of Elastic Particles

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0019
Subject:
Physics, Condensed Matter Physics / Materials

This chapter applies the Chapman–Enskog approach to an inhomogeneous gas of elastic particles. It derives the coefficients of viscosity, thermal conductivity, and velocity distribution function.


Chapman-Enskog Method for the Self-Diffusion Coefficient

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0022
Subject:
Physics, Condensed Matter Physics / Materials

The coefficient of self-diffusion was previously derived using the velocity-time correlation function. This chapter derives this coefficient using the Chapman–Enskog approach.


Cooling Granular Gas — Haff's Law

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses cooling granular gas. During the first stage of its evolution, a force-free, initially uniform granular gas remains homogeneous, while the mean velocity of its particles ... More


Sonine Polynomials Expansion of The Velocity Distribution Function

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

The velocity distribution of function of a granular gas is different from the Maxwell distribution. It may be represented in the form of a Sonine polynomials expansion. This chapter shows that the ... More


Numerical Method

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/9780691141725.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. ... More


Time-harmonic fields

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter reviews balance laws and relevant solutions to Maxwell’s equations in connection with the time-harmonic dependence. The wave equation becomes the Helmholtz equation and, for it, Green’s ... More


MULTIPLE SPECIES OF POSITIVE IONS IN NORMAL LIQUID 3HE

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0023
Subject:
Physics, Condensed Matter Physics / Materials

The realization that ions of different size are produced in liquid 3He with different concentrations of 4He isotopic impurities has allowed researchers to select the ion to be studied just by ... More


Thoracic Dermatomes

Jay A. Liveson and Dong M. Ma

in Laboratory Reference for Clinical Neurophysiology

Published in print:
1999
Published Online:
March 2012
ISBN:
9780195129243
eISBN:
9780199847792
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195129243.003.0005
Subject:
Neuroscience, Techniques

The twelve pairs of intercostal nerves consist of the anterior rami supplying the sensation of the trunk. The nerves can be divided into those running a thoracic course (T2 through T6), and those ... More


Combining Image Signals before Three-Dimensional Reconstruction: The Intrinsic Constraint Model of Cue Integration

Fulvio Domini and Corrado Caudek

in Sensory Cue Integration

Published in print:
2011
Published Online:
September 2012
ISBN:
9780195387247
eISBN:
9780199918379
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195387247.003.0007
Subject:
Psychology, Cognitive Neuroscience, Cognitive Psychology

This chapter examines the possibility that the visual system is unable to generate unbiased estimates of world properties from any single depth cue. The first part shows that retinal disparities and ... More


Basis of the Nerve Impulse

W. Otto Friesen and Jonathon A. Friesen

in NeuroDynamix II: Concepts of Neurophysiology Illustrated by Computer Simulations

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195371833
eISBN:
9780199865178
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195371833.003.0004
Subject:
Psychology, Cognitive Neuroscience

The rapid conduction of signals by neurons over distances greater than about 1 mm occurs almost exclusively by electrical impulses. This chapter presents the fundamental concepts that underlie the ... More


Some Applications

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0009
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter ... More


Motoneurones: morphology, cytology, and topographical organization

Daniel Kernell

in The Motoneurone and its Muscle Fibres

Published in print:
2006
Published Online:
September 2009
ISBN:
9780198526551
eISBN:
9780191723896
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526551.003.0005
Subject:
Neuroscience, Molecular and Cellular Systems

This chapter describes the morphology of individual gamma and (mainly) alpha motoneurones as well as the composition and localization of motoneuronal populations (pools) innervating different muscles ... More


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