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Polymers occur in many different states and their physical
properties are strongly correlated with their conformations. The
theoretical investigation of the conformational properties of
polymers is a difficult task and numerical methods play an
important role in this field. This book contains contributions from
a workshop on numerical methods for polymeric systems, held at the
IMA in May 1996, which brought together chemists, physicists,
mathematicians, computer scientists and statisticians with a common
interest in numerical methods. The two major approaches used in the
field are molecular dynamics and Monte Carlo methods, and the book
includes reviews of both approaches as well as applications to
particular polymeric systems. The molecular dynamics approach
solves the Newtonian equations of motion of the polymer, giving
direct information about the polymer dynamics as well as about
static properties. The Monte Carlo approaches discussed in this
book all involve sampling along a Markov chain defined on the
configuration space of the system. An important feature of the book
is the treatment of Monte Carlo methods, including umbrella
sampling and multiple Markov chain methods, which are useful for
strongly interacting systems such as polymers at low temperatures
and in compact phases. The book is of interest to workers in
polymer statistical mechanics and also to a wider audience
interested in numerical methods and their application in polymeric
systems.
This book contains contributions from a workshop on topology and
geometry of polymers, held at the IMA in June 1996, which brought
together topologists, combinatorialists, theoretical physicists and
polymer scientists, with a common interest in polymer topology.
Polymers can be highly self-entangled even in dilute solution. In
the melt the inter- and intra-chain entanglements can dominate the
rheological properties of these phenomena. Although the possibility
of knotting in ring polymers has been recognized for more than
thirty years it is only recently that the powerful methods of
algebraic topology have been used in treating models of polymers.
This book contains a series of chapters which review the current
state of the field and give an up to date account of what is known
and perhaps more importantly, what is still unknown. The field
abounds with open problems. The book is of interest to workers in
polymer statistical mechanics but will also be useful as an
introduction to topological methods for polymer scientists, and
will introduce mathematicians to an area of science where
topological approaches are making a substantial contribution.
Polymers occur in many different states and their physical
properties are strongly correlated with their conformations. The
theoretical investigation of the conformational properties of
polymers is a difficult task and numerical methods play an
important role in this field. This book contains contributions from
a workshop on numerical methods for polymeric systems, held at the
IMA in May 1996, which brought together chemists, physicists,
mathematicians, computer scientists and statisticians with a common
interest in numerical methods. The two major approaches used in the
field are molecular dynamics and Monte Carlo methods, and the book
includes reviews of both approaches as well as applications to
particular polymeric systems. The molecular dynamics approach
solves the Newtonian equations of motion of the polymer, giving
direct information about the polymer dynamics as well as about
static properties. The Monte Carlo approaches discussed in this
book all involve sampling along a Markov chain defined on the
configuration space of the system. An important feature of the book
is the treatment of Monte Carlo methods, including umbrella
sampling and multiple Markov chain methods, which are useful for
strongly interacting systems such as polymers at low temperatures
and in compact phases. The book is of interest to workers in
polymer statistical mechanics and also to a wider audience
interested in numerical methods and their application in polymeric
systems.
This book contains contributions from a workshop on topology and
geometry of polymers, held at the IMA in June 1996, which brought
together topologists, combinatorialists, theoretical physicists and
polymer scientists, with a common interest in polymer topology.
Polymers can be highly self-entangled even in dilute solution. In
the melt the inter- and intra-chain entanglements can dominate the
rheological properties of these phenomena. Although the possibility
of knotting in ring polymers has been recognized for more than
thirty years it is only recently that the powerful methods of
algebraic topology have been used in treating models of polymers.
This book contains a series of chapters which review the current
state of the field and give an up to date account of what is known
and perhaps more importantly, what is still unknown. The field
abounds with open problems. The book is of interest to workers in
polymer statistical mechanics but will also be useful as an
introduction to topological methods for polymer scientists, and
will introduce mathematicians to an area of science where
topological approaches are making a substantial contribution.
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