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### Physics Literature Collection

 The World Public Library Physics Collection contains 263 conversations regarding the nature of physics.

### Chapter the Semi Discrete Approach

Physics Literature

Excerpt: One strategy for obtaining difference approximations to a PDE is to start by differencing the space derivatives only without approximating the time derivative. In the following chapters we proceed with an analysis making considerable use of this concept which we refer to as the semi discrete approach ? referencing the space derivatives converts the basic PDE into a set of coupled ODEs. In the most general notation these ODEs would be expressed in the form ...

### Chapter Finite Volume Methods

Physics Literature

Excerpt: In Chapter ?we saw how to derive difference approximations to arbitrary derivatives. In Chapter ? we saw that the application of a difference approximation to the spatial derivatives in our model PDEs produces a coupled set of ODEs. In this Chapter we will show how similar semi discrete forms can be derived using volume approximations in space. Finite volume methods have become popular in CFD as a result primarily of two advantages. First they ensure that the di...

### Chapter Time Marching Methods for Ode S

Physics Literature

Excerpt: After discretizing the spatial derivatives in the governing PDEs such as the Navier Stokes equations we obtain a coupled system of nonlinear ODEs in the form. These can be integrated in time using a time marching method to obtain a time accurate solution to an unsteady flow problem For a steady flow problem spatial discretization leads to a coupled system of nonlinear algebraic equations in the form ...

### Chapter Stability of Linear Systems

Physics Literature

Excerpt: A general definition of stability is neither simple nor universal and depends on the particular phenomenon being considered In the case of the nonlinear ODEs of interest in fluid dynamics stability is often discussed in terms of xed points and attractors In these terms a system is said to be stable in a certain domain if from within that domain some norm of its solution is always attracted to the same xed point These are important and interesting concepts but we...

### Chapter Choice of Time Marching Methods

Physics Literature

Excerpt: In this chapter we discuss considerations involved in selecting a time marching method for a specific application Examples are given showing how time marching methods can be compared in a given context An important concept underlying much of this discussion is stillness which is defined in the next section ...

### Chapter Relaxation Methods

Physics Literature

Excerpt: In the past three chapters we developed a methodology for designing analyzing and choosing time marching methods These methods can be used to compute the time accurate solution to linear and nonlinear systems of ODEs in the general form which arise after spatial discretization of a PDE Alternatively they can be used to solve for the steady solution of Eq which satisfies the following coupled system of nonlinear algebraic equations ...

### Fundamentals of Computational Fluid Dynamics

##### By: Harvard Lomax

Physics Literature

Excerpt: Motivation. The material in this book originated from attempts to understand and systemize numerical solution techniques for the partial differential equations governing the physics of fluid flow As time went on and these attempts began to crystallize underlying constraints on the nature of the material began to form The principal such constraint was the demand for unification Was there one mathematical structure which could be used to describe the behavior and ...

### Fundamentals of the Monte Carlo Method for Neutral and Charged Par...

##### By: Alex F. Bielajew

Physics Literature

Preface: This book arises out of a course I am teaching for a two-credit (26 hour) graduate-level course Monte Carlo Methods being taught at the Department of Nuclear Engineering and Radiological Sciences at the University of Michigan.

### General Relativity and Cosmology for Undergraduates

##### By: Professor John W. Norbury

Physics Literature

Introduction: Many of the modern ideas in cosmology can be explained without the need to discuss General Relativity. The present chapter represents an attempt to do this based entirely on Newtonian mechanics. The equations describing the velocity (called the Friedmann equation) and acceleration of the universe are derived from Newtonian mechanics and also the cosmological constant is introduced within a Newtonian framework. The equations of state are also derived in a ve...

### Chapter 1 : Introduction 1. 1 Geochemistry

##### By: W.M. White

Physics Literature

Excerpt: Geochemistry has flourished in the quantitative approach that has dominated earth science in the second half of the twentieth century. This quantitative approach has produced greater advances in the understanding of our planet in the last 50 years than in all of prior human history. The contributions of geochemistry to this advance have been simply enormous. Much of what we know about how the Earth and the Solar System formed has come from research on the chemis...

### Chapter 2 : Energy Entropy and Fundamental Thermodynamic Concepts

##### By: W.M. White

Physics Literature

Excerpt: The Thermodynamic Perspective. We defined geochemistry as the application of chemical knowledge and techniques to solve geological problems. It is appropriate, then, to begin our study of geochemistry with a review of physical chemistry. Our initial focus will be on thermodynamics. Strictly defined, thermodynamics is the study of energy and its transformations. Chemical reactions and changes of states of matter inevitably involve energy changes. By using thermod...

### Chapter 3 : Solutions and Thermodynamics of Multi Component Systems

##### By: W.M. White

Physics Literature

Excerpt: The previous chapter, we introduced thermodynamic tools that allow us to predict the equilibrium mineral assemblage under a given set of conditions. For example, having specified temperature, we were able to determine the pressure at which the assemblage anorthite+forsterite is in equilibrium with the assemblage diopside+spinel+enstatite. In that reaction the minerals had unique and invariant compositions. In the Earth, things are not quite so simple: these mine...

### Chapter 4 : Applications of Thermodynamics to the Earth

##### By: W.M. White

Physics Literature

Introduction: In the previous 2 chapters, we developed the fundamental thermodynamic relationships and saw how they are applied to geochemical problems. The tools now in our thermodynamic toolbox are sufficient to deal with most of the phenomena we will encounter in the second half of this book. They are not sufficient, however, to deal with all geochemical problems. In this chapter, will add a final few thermodynamic tools. These allow us to deal with non-ideal behavior...

### Chapter 5 : Kinetics : The Pace of Things

##### By: W.M. White

Physics Literature

Introduction: Hermodynamics concerns itself with the distribution of components among the various phases and species of a system at equilibrium. Kinetics concerns itself with the path the system takes in achieving equilibrium. Thermodynamics allows us to predict the equilibrium state of a system. Kinetics, on the other hand, tells us how and how fast equilibrium will be attained. Though thermodynamics is a macroscopic science, we found it often useful to consider the mic...

### Chapter 6 : Aquatic Chemistry

##### By: W.M. White

Physics Literature

Introduction: Continually transforming the surface of the Earth, through interaction with the solid surface and transport of dissolved and suspended matter. Beyond that, water is essential to life and central to human activity. Thus as a society, we are naturally very concerned with water quality, which in essence means water chemistry. Aquatic chemistry is therefore the principal concern of many geochemists ...

### Chapter 7 : Trace Elements in Igneous Processes

##### By: W.M. White

Physics Literature

Introduction: In this chapter we will consider the behavior of trace elements, particularly in magmas, and introduce methods to model this behavior. Though trace elements, by definition, constitute only a small fraction of a system of interest, they provide geochemical and geological information out of proportion to their abundance. There are several reasons for this. First, variations in the concentrations of many trace elements are much larger than variations in the co...

### Chapter 8 : Radiogenic Isotope Geochemistry

##### By: W.M. White

Physics Literature

Introduction: Radiogenic isotope geochemistry has had an enormous influence on geologic thinking in the twentieth century. The story begins, however, in the latter half of the nineteenth century. At that time Lord Kelvin (who profoundly influenced the development of physics and thermodynamics in the 19th century), estimated the age of the solar system to be about 100 million years, based on the assumption that the Sun?s energy was derived from gravitational collapse. In ...

### Chapter 9 : Stable Isotope Geochemistry

##### By: W.M. White

Physics Literature

Introduction: Table isotope geochemistry is concerned with variations of the isotopic compositions of elements arising from physicochemical processes rather than nuclear processes. Fractionation of the isotopes on an element might at first seem to be an oxymoron. After all, in the last chapter we saw that some of the value of radiogenic isotopes was that the various isotopes of an element had identical chemical properties and therefore that isotope ratios such as 87Sr/86...

### Chapter 10 : The Big Picture : Cosmo Chemistry

##### By: W.M. White

Physics Literature

Introduction: In the previous eight chapters we acquired a full set of geochemical tools. In this and subsequent chapters, we will apply these tools to understanding the Earth. Certainly any full understanding of the Earth includes an understanding of its origin and it relationship to its neighboring celestial bodies. That is our focus in this chapter. The question of the origin of the Earth is closely tied to that of the composition of the Earth, and certainly the latte...

### Chapter 11 : Geochemistry of the Solid Earth I : The Mantle and Core

##### By: W.M. White

Physics Literature

Introduction: Though sizable pieces of mantle occasionally crop out on the Earth?s surface as alpine massifs or ophiolites, and small pieces, xenoliths, are occasionally brought to the surface by volcanic eruptions, much of what we know about the mantle has been deduced indirectly. Indirect methods of study include determination of geophysical properties such as heat flow, density and seismic velocity. Another indirect method of study is examination of volcanic rocks pro...

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