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This book entitled “Chemical Symmetry Breaking” is a collective volume of state-of-the-art reports on unique nonlinear chemical and physical symmetry-breaking phenomena that were experimentally observed upon a thermally or photochemically induced phase transition in various organic condensed phases, such as metastable liquid crystals, crystals, amorphous solids, and colloidal polymer materials, only under nonequilibrium conditions. Each author summarizes the introductory section in simple terms but in detail for beginners in this field. We wish that many readers familiarize themselves with the general concepts and features of nonlinear and nonequilibrium (or out of equilibrium) complexity theory, which govern a variety of unique dynamic behaviors observed in chemistry, physics, life science and other fields, so that they may discover novel symmetry-breaking phenomena in their own research areas.
Research & information: general --- amplification of chirality --- dynamic crystallization --- Diels–Alder reaction --- absolute asymmetric synthesis --- conglomerate --- racemization --- attrition-enhanced deracemization --- Viedma ripening --- reversible reaction --- enantiomorphic crystal --- polymorphism --- off-shell quantum field --- space-like momentum --- dressed photon --- micro-macro duality --- Clebsch dual field --- Majorana fermion --- the cosmological term --- Weyl tensor --- dark energy --- dark matter --- photomechanical --- crystal --- right–left symmetry breaking --- chiral symmetry breaking --- dissipative structure --- energy conversion --- mechanical work --- self-oscillation --- collective dynamics --- autonomous motion --- self-replication --- autocatalysis --- molecular motor --- molecular robot --- amorphous-to-crystal phase transformation --- detection of real-time symmetry breaking --- mechanofluorochromism --- fluorescence spectroscopy --- liquid-like cluster --- evaporative crystallization --- quartz crystal microbalance --- two-step nucleation model --- chiral --- circularly polarized luminescence (CPL) --- magnetic circularly polarized luminescence (MCPL) --- spontaneous resolution --- chirality --- deracemization --- preferential enrichment --- thermodynamics --- phase diagrams --- kinetics --- symmetry breaking --- ferroelectricity --- antiferrolelectricity --- subphases --- resonant X-ray scattering --- vapochromism --- fluorescence --- macrocycles --- inclusion crystals --- host–guest chemistry --- spin symmetry breaking --- magnetic liquid crystals --- magneto-LC effect --- nitroxide radicals --- superparamagnetic domain --- spin glass state --- elastic organic crystals --- mechanical deformation --- π-conjugated molecules --- photoluminescence --- deformation-induced photoluminescence changes --- biomolecular handedness --- circular dichroism --- circularly polarized luminescence --- non-equilibrium --- colloid --- conjugated polymer --- amplification of chirality --- dynamic crystallization --- Diels–Alder reaction --- absolute asymmetric synthesis --- conglomerate --- racemization --- attrition-enhanced deracemization --- Viedma ripening --- reversible reaction --- enantiomorphic crystal --- polymorphism --- off-shell quantum field --- space-like momentum --- dressed photon --- micro-macro duality --- Clebsch dual field --- Majorana fermion --- the cosmological term --- Weyl tensor --- dark energy --- dark matter --- photomechanical --- crystal --- right–left symmetry breaking --- chiral symmetry breaking --- dissipative structure --- energy conversion --- mechanical work --- self-oscillation --- collective dynamics --- autonomous motion --- self-replication --- autocatalysis --- molecular motor --- molecular robot --- amorphous-to-crystal phase transformation --- detection of real-time symmetry breaking --- mechanofluorochromism --- fluorescence spectroscopy --- liquid-like cluster --- evaporative crystallization --- quartz crystal microbalance --- two-step nucleation model --- chiral --- circularly polarized luminescence (CPL) --- magnetic circularly polarized luminescence (MCPL) --- spontaneous resolution --- chirality --- deracemization --- preferential enrichment --- thermodynamics --- phase diagrams --- kinetics --- symmetry breaking --- ferroelectricity --- antiferrolelectricity --- subphases --- resonant X-ray scattering --- vapochromism --- fluorescence --- macrocycles --- inclusion crystals --- host–guest chemistry --- spin symmetry breaking --- magnetic liquid crystals --- magneto-LC effect --- nitroxide radicals --- superparamagnetic domain --- spin glass state --- elastic organic crystals --- mechanical deformation --- π-conjugated molecules --- photoluminescence --- deformation-induced photoluminescence changes --- biomolecular handedness --- circular dichroism --- circularly polarized luminescence --- non-equilibrium --- colloid --- conjugated polymer
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This book entitled “Chemical Symmetry Breaking” is a collective volume of state-of-the-art reports on unique nonlinear chemical and physical symmetry-breaking phenomena that were experimentally observed upon a thermally or photochemically induced phase transition in various organic condensed phases, such as metastable liquid crystals, crystals, amorphous solids, and colloidal polymer materials, only under nonequilibrium conditions. Each author summarizes the introductory section in simple terms but in detail for beginners in this field. We wish that many readers familiarize themselves with the general concepts and features of nonlinear and nonequilibrium (or out of equilibrium) complexity theory, which govern a variety of unique dynamic behaviors observed in chemistry, physics, life science and other fields, so that they may discover novel symmetry-breaking phenomena in their own research areas.
Research & information: general --- amplification of chirality --- dynamic crystallization --- Diels–Alder reaction --- absolute asymmetric synthesis --- conglomerate --- racemization --- attrition-enhanced deracemization --- Viedma ripening --- reversible reaction --- enantiomorphic crystal --- polymorphism --- off-shell quantum field --- space-like momentum --- dressed photon --- micro-macro duality --- Clebsch dual field --- Majorana fermion --- the cosmological term --- Weyl tensor --- dark energy --- dark matter --- photomechanical --- crystal --- right–left symmetry breaking --- chiral symmetry breaking --- dissipative structure --- energy conversion --- mechanical work --- self-oscillation --- collective dynamics --- autonomous motion --- self-replication --- autocatalysis --- molecular motor --- molecular robot --- amorphous-to-crystal phase transformation --- detection of real-time symmetry breaking --- mechanofluorochromism --- fluorescence spectroscopy --- liquid-like cluster --- evaporative crystallization --- quartz crystal microbalance --- two-step nucleation model --- chiral --- circularly polarized luminescence (CPL) --- magnetic circularly polarized luminescence (MCPL) --- spontaneous resolution --- chirality --- deracemization --- preferential enrichment --- thermodynamics --- phase diagrams --- kinetics --- symmetry breaking --- ferroelectricity --- antiferrolelectricity --- subphases --- resonant X-ray scattering --- vapochromism --- fluorescence --- macrocycles --- inclusion crystals --- host–guest chemistry --- spin symmetry breaking --- magnetic liquid crystals --- magneto-LC effect --- nitroxide radicals --- superparamagnetic domain --- spin glass state --- elastic organic crystals --- mechanical deformation --- π-conjugated molecules --- photoluminescence --- deformation-induced photoluminescence changes --- biomolecular handedness --- circular dichroism --- circularly polarized luminescence --- non-equilibrium --- colloid --- conjugated polymer
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This book entitled “Chemical Symmetry Breaking” is a collective volume of state-of-the-art reports on unique nonlinear chemical and physical symmetry-breaking phenomena that were experimentally observed upon a thermally or photochemically induced phase transition in various organic condensed phases, such as metastable liquid crystals, crystals, amorphous solids, and colloidal polymer materials, only under nonequilibrium conditions. Each author summarizes the introductory section in simple terms but in detail for beginners in this field. We wish that many readers familiarize themselves with the general concepts and features of nonlinear and nonequilibrium (or out of equilibrium) complexity theory, which govern a variety of unique dynamic behaviors observed in chemistry, physics, life science and other fields, so that they may discover novel symmetry-breaking phenomena in their own research areas.
amplification of chirality --- dynamic crystallization --- Diels–Alder reaction --- absolute asymmetric synthesis --- conglomerate --- racemization --- attrition-enhanced deracemization --- Viedma ripening --- reversible reaction --- enantiomorphic crystal --- polymorphism --- off-shell quantum field --- space-like momentum --- dressed photon --- micro-macro duality --- Clebsch dual field --- Majorana fermion --- the cosmological term --- Weyl tensor --- dark energy --- dark matter --- photomechanical --- crystal --- right–left symmetry breaking --- chiral symmetry breaking --- dissipative structure --- energy conversion --- mechanical work --- self-oscillation --- collective dynamics --- autonomous motion --- self-replication --- autocatalysis --- molecular motor --- molecular robot --- amorphous-to-crystal phase transformation --- detection of real-time symmetry breaking --- mechanofluorochromism --- fluorescence spectroscopy --- liquid-like cluster --- evaporative crystallization --- quartz crystal microbalance --- two-step nucleation model --- chiral --- circularly polarized luminescence (CPL) --- magnetic circularly polarized luminescence (MCPL) --- spontaneous resolution --- chirality --- deracemization --- preferential enrichment --- thermodynamics --- phase diagrams --- kinetics --- symmetry breaking --- ferroelectricity --- antiferrolelectricity --- subphases --- resonant X-ray scattering --- vapochromism --- fluorescence --- macrocycles --- inclusion crystals --- host–guest chemistry --- spin symmetry breaking --- magnetic liquid crystals --- magneto-LC effect --- nitroxide radicals --- superparamagnetic domain --- spin glass state --- elastic organic crystals --- mechanical deformation --- π-conjugated molecules --- photoluminescence --- deformation-induced photoluminescence changes --- biomolecular handedness --- circular dichroism --- circularly polarized luminescence --- non-equilibrium --- colloid --- conjugated polymer
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The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter.Originally published in 1994.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Space and time --- Generalized spaces --- Nonlinear theories --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Mathematics --- Angular momentum operator. --- Asymptotic analysis. --- Asymptotic expansion. --- Big O notation. --- Boundary value problem. --- Cauchy–Riemann equations. --- Coarea formula. --- Coefficient. --- Compactification (mathematics). --- Comparison theorem. --- Corollary. --- Covariant derivative. --- Curvature tensor. --- Curvature. --- Cut locus (Riemannian manifold). --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Derivative. --- Diffeomorphism. --- Differentiable function. --- Eigenvalues and eigenvectors. --- Eikonal equation. --- Einstein field equations. --- Equation. --- Error term. --- Estimation. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Exponential map (Lie theory). --- Exponential map (Riemannian geometry). --- Exterior (topology). --- Foliation. --- Fréchet derivative. --- Geodesic curvature. --- Geodesic. --- Geodesics in general relativity. --- Geometry. --- Hodge dual. --- Homotopy. --- Hyperbolic partial differential equation. --- Hypersurface. --- Hölder's inequality. --- Identity (mathematics). --- Infinitesimal generator (stochastic processes). --- Integral curve. --- Intersection (set theory). --- Isoperimetric inequality. --- Laplace's equation. --- Lie algebra. --- Lie derivative. --- Linear equation. --- Linear map. --- Logarithm. --- Lorentz group. --- Lp space. --- Mass formula. --- Mean curvature. --- Metric tensor. --- Minkowski space. --- Nonlinear system. --- Normal (geometry). --- Null hypersurface. --- Orthonormal basis. --- Partial derivative. --- Poisson's equation. --- Projection (linear algebra). --- Quantity. --- Radial function. --- Ricci curvature. --- Riemann curvature tensor. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Sard's theorem. --- Scalar (physics). --- Scalar curvature. --- Scale invariance. --- Schwarzschild metric. --- Second derivative. --- Second fundamental form. --- Sobolev inequality. --- Sobolev space. --- Stokes formula. --- Stokes' theorem. --- Stress–energy tensor. --- Symmetric tensor. --- Symmetrization. --- Tangent space. --- Tensor product. --- Theorem. --- Trace (linear algebra). --- Transversal (geometry). --- Triangle inequality. --- Uniformization theorem. --- Unit sphere. --- Vector field. --- Volume element. --- Wave equation. --- Weyl tensor.
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