Introduction
to the Calculus of Variations
Chaire d'Analyse Appliquée
Introduction
to the Calculus of Variationssummary: A textbook on foundations
of the problems of calculus of variations and its many methods and techniques.
Calculus
of Variationssummary: An introduction, translated from the Russian by R. A. Silverman, to the calculus of variations, with special attention to applications of the theory to mechanics and physics.
The behavior of the total twist and self-linking number of a closed space curve under inversionssummary: A research paper
Understanding
DNA, The molecule & how it worksummary: Understanding DNA explains, step by step, why DNA forms specific structures, the form of these structures and how they fundamentally affect the biological processes of transcription and replication.
Unravelling
DNAsummary: A curious blend of history, biographical details to cover the development of molecular biology from the influence of physicists earlier in the century, through the central dogma of molecular biology to discussion of social issues raised by genetic engineering.
DNA topologysummary: A clear, concise explanation of the relevance of supercoiling and catenation in the context of biological activity of the DNA molecule.
DNA structure
and Functionsummary: a timely and comprehensive resource, that provides a simple yet comprehensive introduction to nearly all aspects of DNA structure. It also explains current ideas on the biological significance of classic and alternative DNA conformations.
The theory
of Polymer Dynamicssummary: a comprehensive account of the modern theory for the dynamical properties of polymer solutions, including viscoelasticity(non linear too, based on molecular dynamical models), diffusion, dynamic light scattering, flow, and electric birefringence.
Nonlinear
Problems of Elasticitysummary: a manual which covers the
equations of motion for extensible and elastic strings and rods, bifurcation
theory, variational methods, the special Cosserat theory of rods, 3D continuum
mechanics, general theories of rods and shells, non-linear plasticity,
and dynamical problems as well. The bible of rodlike continuum approaches.
Statistical
Physics of Macromoleculessummary: A contemporary textbook on statistics of chain models of polymer solutions and melts, liquid crystals, polyelectrolyte chains, also featuring dynamic viscoelasticity behavior of polymer systems, with some specific attention towards biopolymers DNA and proteins. Some recent advances in statistical theory of DNA gel electrophoresis, polymers at interfaces, and dynamics of concentrated solutions of branched polymers, are also covered.
Dynamics
of proteins and nucleic acidssummary: a self-contained introduction to the theory of atomic motion in proteins and nucleic acids. An understanding of such motion is essential because it plaus a crucially important role in biological activity. A variety of theoretical and experimental studies is described and these are critically analyzed to provide a comprehensive picture of dynamic aspects of biomolecular structure and function.
Mathematical
Approaches to Biomolecular Structure and Dynamics1996 Springer, ISBN 0-38-794838-4
summary: Interdisciplinary research in mathematics and molecular biology is driven by ever-growing experimental, theoretical and computational power. This volume consists of a representative sample of papers presented during the month-long IMA Summer Program in Molecular Biology and covers the spectrum from experiment to computation to simulation to theory.
Calculating
the Secrets of Lifesummary: explores how differential
geometry, topology, and differential mechanics have allowed researchers
to wind and unwind DNA's double helix to understand the phenomenon of supercoiling.
The book describes the role of mathematics in researching the origin, structure
and function of life by applying stochastic and statistical theory to the
study of DNA sequences.
Modeling
Superhelical DNA: Recent Analytical and Dynamical Approachessummary: a review paper about analytical and kinetic approaches spanning molecular, Langevin and Brownian dynamics, as well as dynamical theories of elastic rods.
Simulating
DNA at low resolutionsummary: another review paper about the modeling of local and global structural changes induced by the binding of various proteins to DNA, sequence-specific and environmental (salt) effects.