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"Soft condensed matter physics relies on a fundamental understanding at the interface between physics, chemistry, biology, and engineering for a host of materials and circumstances that are related to, but outside, the traditional definition of condensed matter physics. Featuring contributions from leading researchers in the field, this book uniquely discusses both the contemporary experimental and computational manifestations of soft condensed matter systems. From particle tracking and image analysis, novel materials and computational methods, to confocal microscopy and bacterial assays, this book will equip the reader for collaborative and interdisciplinary research efforts relating to a range of modern problems in nonlinear and non-equilibrium systems. It will enable both graduate students and experienced researchers to supplement a more traditional understanding of thermodynamics and statistical systems with knowledge of the techniques used in contemporary investigations. Color versions of a selection of the figures are available at www.cambridge.org/9780521115902"-- "Soft condensed matter physics relies on a fundamental understanding at the interface between physics, chemistry, biology, and engineering for a host of materials and circumstances that are related to, but outside, the traditional definition of condensed matter physics. Featuring contributions from leading researchers in the field, this book uniquely discusses both the contemporary experimental and computational manifestations of soft condensed matter systems. From particle tracking and image analysis, novel materials and computational methods, to confocal microscopy and bacterial assays, this book will equip the reader for collaborative and interdisciplinary research efforts relating to a range of modern problems in nonlinear and non-equilibrium systems. It will enable both graduate students and experienced researchers to supplement a more traditional understanding of thermodynamics and statistical systems with knowledge of the techniques used in contemporary investigations"--

Experimental mathematics. --- Soft condensed matter --- Mathematics.

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Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Mathematical physics. --- Diffusion. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Gases --- Liquids --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Physical mathematics --- Diffusion --- Properties --- Mathematics --- Affine space. --- Algebra. --- Axiom. --- Bell's theorem. --- Brownian motion. --- Central limit theorem. --- Classical mathematics. --- Classical mechanics. --- Clifford algebra. --- Combinatorial proof. --- Commutative property. --- Constructive quantum field theory. --- Continuum hypothesis. --- David Hilbert. --- Dimension (vector space). --- Discrete mathematics. --- Distribution (mathematics). --- Eigenfunction. --- Equation. --- Euclidean space. --- Experimental mathematics. --- Fermi–Dirac statistics. --- Feynman–Kac formula. --- First-order logic. --- Fokker–Planck equation. --- Foundations of mathematics. --- Fractal dimension. --- Gaussian process. --- Girsanov theorem. --- Gödel's incompleteness theorems. --- Hilbert space. --- Hilbert's program. --- Holomorphic function. --- Infinitesimal. --- Integer. --- Internal set theory. --- Interval (mathematics). --- Limit (mathematics). --- Mathematical induction. --- Mathematical optimization. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Measurable function. --- Measure (mathematics). --- Minkowski space. --- Natural number. --- Neo-Riemannian theory. --- Non-standard analysis. --- Number theory. --- Operator algebra. --- Ornstein–Uhlenbeck process. --- Orthonormal basis. --- Perturbation theory (quantum mechanics). --- Philosophy of mathematics. --- Predicate (mathematical logic). --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Projection (linear algebra). --- Pure mathematics. --- Pythagorean theorem. --- Quantum field theory. --- Quantum fluctuation. --- Quantum gravity. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Quantum system. --- Quantum teleportation. --- Random variable. --- Real number. --- Renormalization group. --- Renormalization. --- Riemann mapping theorem. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schrödinger equation. --- Scientific notation. --- Set (mathematics). --- Sign (mathematics). --- Sobolev inequality. --- Special relativity. --- Spectral theorem. --- Spin (physics). --- Statistical mechanics. --- Stochastic calculus. --- Stochastic differential equation. --- Tensor algebra. --- Theorem. --- Theoretical physics. --- Theory. --- Turing machine. --- Variable (mathematics). --- Von Neumann algebra. --- Wiener process. --- Wightman axioms. --- Zermelo–Fraenkel set theory.