This NATO Advanced Study Institute centered on large-scale molecular systems: Quantum mechanics, although providing a general framework for the description of matter, is not easily applicable to many concrete systems of interest; classical statistical methods, on the other hand, allow only a partial picture of the behaviour of large systems. The aim of the ASI was to present both aspects of the subject matter and to foster interaction between the scientists working in these important areas of theoretical physics and theoretical chemistry. The quantum-mechanical part was mostly based on the operator-algebraic formulation of quantum mechanics and comprised quantum statistics of infinite systems with special em phasis on macroscopic observables, equilibrium conditions, irreversibility on the one hand, symmetry breaking for molecules in the radiation field and macroscopic quantum phenomena in the theory of superconductivity (BCS-theory) on the other hand. In addition, phase-space methods for many-body systems were also presented. Statistical physics was the main topic in the other lectures of the School; much emphasis was put on the statistical features of macros copic ("large") systems, the lectures dealt with mass and energy transport im polymers, in gels and in microemulsions, with aggregation and growth phenomena, with relaxation in complex, correlated systems, with conduction and optical properties of polymers, and with the means of describing disordered systems, above all fractals and related hierarchical models.

Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.

The latest developments in quantum and classical molecular dynamics, related techniques, and their applications to several fields of science and engineering. Molecular simulations include a broad range of methodologies such as Monte Carlo, Brownian dynamics, lattice dynamics, and molecular dynamics (MD).Features of this book:• Presents advances in methodologies, introduces quantum methods and lists new techniques for classical MD• Deals with complex systems: biomolecules, aqueous solutions, ice and clathrates, liquid crystals, polymers• Provides chemical reactions, interfaces, catalysis, surface phenomena and solidsAlthough the book is not formally divided into methods and applications, the chapters are arranged starting with those that discuss new algorithms, methods and techniques, followed by several important applications.

This book examines detailed experimental and computational approaches for the analysis of many aspects vital to the understanding of membrane protein structure and function. Readers will receive guidance on the selection and use of methods for over-expression and purification, tools to characterize membrane proteins within different phospholipid bilayers, direction on functional studies, and approaches to determine the structures of membrane proteins. Detailed experimental steps for specific membrane proteins with critical notes allow the protocols to be modified to different systems. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of practical information and implementation advice that leads to excellent, reproducible results. Authoritative and up-to-date, Structure and Function Studies of Membrane Proteins serves as an ideal guide for biologists, biochemists, and biophysicists striving to further understand these essential proteins and their many biological roles.

This book covers recent advances of the fragment molecular orbital (FMO) method, consisting of 5 parts and a total of 30 chapters written by FMO experts. The FMO method is a promising way to calculate large-scale molecular systems such as proteins in a quantum mechanical framework. The highly efficient parallelism deserves being considered the principal advantage of FMO calculations. Additionally, the FMO method can be employed as an analysis tool by using the inter-fragment (pairwise) interaction energies, among others, and this feature has been utilized well in biophysical and pharmaceutical chemistry. In recent years, the methodological developments of FMO have been remarkable, and both reliability and applicability have been enhanced, in particular, for non-bio problems. The current trend of the parallel computing facility is of the many-core type, and adaptation to modern computer environments has been explored as well. In this book, a historical review of FMO and comparison to other methods are provided in Part I (two chapters) and major FMO programs (GAMESS-US, ABINIT-MP, PAICS and OpenFMO) are described in Part II (four chapters). dedicated to pharmaceutical activities (twelve chapters). A variety of new applications with methodological breakthroughs are introduced in Part IV (six chapters). Finally, computer and information science-oriented topics including massively parallel computation and machine learning are addressed in Part V (six chapters). Many color figures and illustrations are included. Readers can refer to this book in its entirety as a practical textbook of the FMO method or read only the chapters of greatest interest to them.

Exploring recent developments in the field, Coarse-Graining of Condensed Phase and Biomolecular Systems examines systematic ways of constructing coarse-grained representations for complex systems. It explains how this approach can be used in the simulation and modeling of condensed phase and biomolecular systems. Assembling some of the most influential, world-renowned researchers in the field, this book covers the latest developments in the coarse-grained molecular dynamics simulation and modeling of condensed phase and biomolecular systems. Each chapter focuses on specific examples of evolving coarse-graining methodologies and presents results for a variety of complex systems. The contributors discuss the minimalist, inversion, and multiscale approaches to coarse-graining, along with the emerging challenges of coarse-graining. They also connect atomic-level information with new coarse-grained representations of complex systems, such as lipid bilayers, proteins, peptides, and DNA.

This multi-author contributed volume includes methodological advances and original applications to actual chemical or biochemical phenomena which were not possible before the increased sophistication of modern computers. The chapters contain detailed reviews of the developments of various computational techniques, used to study complex molecular systems such as molecular liquids and solutions (particularly aqueous solutions), liquid-gas, solid-gas interphase and biomacromolecular systems. Quantum modeling of complex molecular systems is a useful resource for graduate students and fledgling researchers and is also an excellent companion for research professionals engaged in computational chemistry, material science, nanotechnology, physics, drug design, and molecular biochemistry.