Preface
This book is culmination of my research in the last 26 years at the University at
Buffalo, The State University of New York. Most of the book heavily relies on the
work of my PhD students and our joint publications.
Traditional (Newtonian) continuum mechanics portion of this book is primarily
based on the seminal textbook by Malvern (1969). Since I consider Prof. Lawrence
Malvern’s textbook one of the best ever written on continuum mechanics, I did not
find any reason to change the formulation or his presentation of the basics. Yet, when
I myself, was as a student, I found his book hard to follow because it is written at a
high level. Therefore, I have tried to simplify many of the formulae derivation steps
and made it easier for students to understand. While I did change the order of the
topics that I copied from Malvern (1969), I tried to stay true to the message Prof.
Malvern had in his formulation.
I tried to explain Unified Mechanics Theory in the simplest terms possible. In
order to accomplish this objective, I found it necessary to include the entire paper by
Sharp and Matschisky (2015), which is the English translation of Boltzmann’s
(1877) original paper. While I acknowledge that including papers from a journal
in its entirety is a very unorthodox practice, it was necessary because Boltzmann’s
original paper is misunderstood. Therefore, I had to present his entire derivation
annotated with my explanations. To this day, many physics books refer to the
equation of Boltzmann’s second law as being valid for gasses only, with no reference
to his derivation. Boltzmann did not make any such assumption in his formulation
that would invalidate the applicability of his formulation to solids. For the past
quarter century, my PhD students and I have provided in the literature the experimental proof of Boltzmann’s second law equation for solids; Sharp and Matschisky
(2015) have also addressed this validity of major misunderstanding in their paper. I
quoted them directly. The fact that Boltzmann did not consider any interaction
between the particles only increases the possible scenarios of combination. Interactions, like friction or molecular bonds, would only reduce the number of possible
combinations. Therefore, Boltzmann’s formulation can be considered an upper
bound of possible permutations. However, Boltzmann’s mathematical derivation is
vii
This book is culmination of my research in the last 26 years at the University at
Buffalo, The State University of New York. Most of the book heavily relies on the
work of my PhD students and our joint publications.
Traditional (Newtonian) continuum mechanics portion of this book is primarily
based on the seminal textbook by Malvern (1969). Since I consider Prof. Lawrence
Malvern’s textbook one of the best ever written on continuum mechanics, I did not
find any reason to change the formulation or his presentation of the basics. Yet, when
I myself, was as a student, I found his book hard to follow because it is written at a
high level. Therefore, I have tried to simplify many of the formulae derivation steps
and made it easier for students to understand. While I did change the order of the
topics that I copied from Malvern (1969), I tried to stay true to the message Prof.
Malvern had in his formulation.
I tried to explain Unified Mechanics Theory in the simplest terms possible. In
order to accomplish this objective, I found it necessary to include the entire paper by
Sharp and Matschisky (2015), which is the English translation of Boltzmann’s
(1877) original paper. While I acknowledge that including papers from a journal
in its entirety is a very unorthodox practice, it was necessary because Boltzmann’s
original paper is misunderstood. Therefore, I had to present his entire derivation
annotated with my explanations. To this day, many physics books refer to the
equation of Boltzmann’s second law as being valid for gasses only, with no reference
to his derivation. Boltzmann did not make any such assumption in his formulation
that would invalidate the applicability of his formulation to solids. For the past
quarter century, my PhD students and I have provided in the literature the experimental proof of Boltzmann’s second law equation for solids; Sharp and Matschisky
(2015) have also addressed this validity of major misunderstanding in their paper. I
quoted them directly. The fact that Boltzmann did not consider any interaction
between the particles only increases the possible scenarios of combination. Interactions, like friction or molecular bonds, would only reduce the number of possible
combinations. Therefore, Boltzmann’s formulation can be considered an upper
bound of possible permutations. However, Boltzmann’s mathematical derivation is
vii