Diffusion

Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes (Springer Series in Solid-State Sciences)
$219.00
Diffusion is a vital topic in solid-state physics and chemistry, physical metallurgy and materials science. Diffusion processes are ubiquitous in solids at elevated temperatures. A thorough understanding of diffusion in materials is crucial for materials development and engineering. This book first gives an account of the central aspects of diffusion in solids, for which the necessary background is a course in solid state physics. It then provides easy access to important information about diffuson in metals, alloys, semiconductors, ion-conducting materials, glasses and nanomaterials. Several diffusion-controlled phenomena, including ionic conduction, grain-boundary and dislocation pipe diffusion, are considered as well. Graduate students in solid-state physics, physical metallurgy, materials science, physical and inorganic chemistry or geophysics will benefit from this book as will physicists, chemists, metallurgists, materials engineers in academic and industrial research laboratories.

Diffusions, Markov Processes, and Martingales: Volume 1, Foundations (Cambridge Mathematical Library)
$66.00
The authors have compiled an excellent text which introduces the reader to the fundamental theory of Brownian motion from the point of view of modern martingale and Markov process theory. I highly recommend this book for anyone who wants to acquire and in-depth understanding of Brownian motion and stochastic calculus.

The book is fairly self-contained, although the reader should prepare herself with some prerequisite material. Rudin's Real and Complex Analysis and Norris' Markov Chains provide a good basis. You'll also need a solid understanding of the basic properties of Laplace transforms as is covered in an undergraduate course on differential equations (e.g. Schiff's The Laplace Transform: Theory and Applications).

Rogers and Williams begin Chapter 1 of the 2nd edition of their first volume 'Foundations' by exploring Brownian motion from several different modern viewpoints. This is intended to help the reader develop an intuition about Brownian motion and related diffusions. They then move on to explore the well-known features of Brownian motion, including the strong Markov property, the Reflection principle, the Blumenthal Zero-One Law and the Law of the Iterated Logarithm.

The section on Brownian motion in higher dimensions is very nice and I enjoyed the applications of Brownian motion to complex analysis. I particularly liked the Ito's Rule-style proof of the Maximum Modulus Principle.
The authors close out Chapter 1 with detailed introductions of Gaussian and Levy Processes.

In the chapter on Brownian motion, the authors make several forward references to Chapter 2, which covers the prerequisite material from measure theory, probability theory, and stochastic processes needed for both volume I and II. If you found these forward references a bit unsettling, it is quite reasonable to first read Chapter 2 (sections 1-5), then read Chapter 1, and then finish up with canonical Brownian motion section at the end of Chapter 2.

Chapter 3 is a wonderful treatment of Markov processes and requires that the reader have an appreciation of the classical theory of Markov chains. In the first section of Chapter 3, the basic theory of operator semigroups is covered and the authors prove the famous Hille-Yosida Theorem.

The next section covers the 'base case' of operator semigroups. Rogers and Williams refer to these as Feller-Dynkin semigroups. (Ethier and Kurtz simply call these Feller semigroups in their book Markov Processes: Characterization and Convergence.) Each Feller-Dynkin semigroup is shown to be realized by strong Markov process. Continuous Levy processes are then characterized as a nice application of the Feller-Dynkin theory.

The highlight of the next section is the Feynmac-Kac formulas. These are presented from the Markov process point of view (computing generators of transformed Markov processes), not from the usual PDEs point of view. Since the authors don't have Ito's Rule available in this first volume, they establish Feynman-Kac using the theory of additive functionals.

The final sections of the book deal with Markov processes with values in a countable state space. Ray processes and the Martin boundary are introduced, however as I began read this material, I felt that the authors believed that I already knew why Ray Theory is so important. I felt this last material would have been a bit better motivated with more of a tie-in to the theory of harmonic functions and the Dirichlet problem. However, the proof of Ray's Theorem is very elegant and really solidifies the reader's understanding of the Hille-Yosida Theorem.

Several of the sections wrap up with a small set of exercises. There are also exercises sprinkled throughout the text (several of which the authors plead with you to work through). The exercises have been thoughtfully selected and reinforce the material.

DP5 5 In. Diffusion Screen
$22.50
I'm only using it with a 250w bulb primarily to light my backdrops and haven't had any problems. I was considering moving up to a higher powered bulb but I think I'll figure something else out there.

Diffusion in Solids: Field Theory, Solid-State Principles, and Applications
$151.50
To the curious minds of today and tomorrow:

I've recently gotten this book as a present and read a few chapters of it to date. As I am well versed in diffusion, I presume it's ok for me to comment on the book without having fully read it.

After reading a few chapters, and perusing over the entire volume, I was most impressed with Dr. Glickman's text. He's to be commended for having done a very fine job.

Diffusion is inherently a very mathematical subject. Yet, without a proper presentation of the important aspects of the physical phenomena it is barrren and simply reduced to solving partial differential equations. Glickman's book, seems to succeed at providing the physical picture of diffusion with utmost clarity, while maintaining mathematical rigor. Furthermore, it is up to date and exposes the reader to recent developments in the study of diffusion phenomena. The treatment is primarily on the phenomenology of diffusion. If you fancy to learn more about diffusion kinetics, I recommend the book by Khachaturyan (Theory of Structural Phase Transformations in Solids).

As someone who learned diffusion from Physical Metallurgy books, Shewmon's and Carslaw's books, I find Glickman's very refreshing for it's modern, rigorous and comprehensive.

I highly recommend it.

Cheers,

Dr. E.
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