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This book presents the theory of soft matter to students at the
advanced undergraduate or beginning graduate level. It provides a
basic introduction to theoretical physics as applied to soft
matter, explaining the concepts of symmetry, broken symmetry, and
order parameters; phases and phase transitions; mean-field theory;
and the mathematics of variational calculus and tensors. It is
written in an informal, conversational style, which is accessible
to students from a diverse range of backgrounds. The book begins
with a simple "toy model" to demonstrate the physical significance
of free energy. It then introduces two standard theories of phase
transitions-the Ising model for ferromagnetism and van der Waals
theory of gases and liquids-and uses them to illustrate principles
of statistical mechanics. From those examples, it moves on to
discuss order, disorder, and broken symmetry in many states of
matter, and to explain the theoretical methods that are used to
model the phenomena. It concludes with a chapter on liquid
crystals, which brings together all of these physical and
mathematical concepts. The book is accompanied online by a set of
"interactive figures"-some allow readers to change parameters and
see what happens to a graph, some allow readers to rotate a plot or
other graphics in 3D, and some do both. These interactive figures
help students to develop their intuition for the physical meaning
of equations. This book will prepare advanced undergraduate or
early graduate students to go into more advanced theoretical
studies. It will also equip students going into experimental soft
matter science to be fully conversant with the theoretical aspects
and have effective collaborations with theorists.
This book presents the theory of soft matter to students at the
advanced undergraduate or beginning graduate level. It provides a
basic introduction to theoretical physics as applied to soft
matter, explaining the concepts of symmetry, broken symmetry, and
order parameters; phases and phase transitions; mean-field theory;
and the mathematics of variational calculus and tensors. It is
written in an informal, conversational style, which is accessible
to students from a diverse range of backgrounds. The book begins
with a simple "toy model" to demonstrate the physical significance
of free energy. It then introduces two standard theories of phase
transitions-the Ising model for ferromagnetism and van der Waals
theory of gases and liquids-and uses them to illustrate principles
of statistical mechanics. From those examples, it moves on to
discuss order, disorder, and broken symmetry in many states of
matter, and to explain the theoretical methods that are used to
model the phenomena. It concludes with a chapter on liquid
crystals, which brings together all of these physical and
mathematical concepts. The book is accompanied online by a set of
"interactive figures"-some allow readers to change parameters and
see what happens to a graph, some allow readers to rotate a plot or
other graphics in 3D, and some do both. These interactive figures
help students to develop their intuition for the physical meaning
of equations. This book will prepare advanced undergraduate or
early graduate students to go into more advanced theoretical
studies. It will also equip students going into experimental soft
matter science to be fully conversant with the theoretical aspects
and have effective collaborations with theorists.
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