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Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century

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ISBN: 9783038977469 Year: Pages: 260 DOI: 10.3390/books978-3-03897-747-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-05 11:17:10
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Entropy in Dynamic Systems

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ISBN: 9783039216161 9783039216178 Year: Pages: 172 DOI: 10.3390/books978-3-03921-617-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Advanced Numerical Methods in Applied Sciences

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ISBN: 9783038976660 9783038976677 Year: Pages: 306 DOI: 10.3390/books978-3-03897-667-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 08:44:06
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Keywords

time fractional differential equations --- mixed-index problems --- analytical solution --- asymptotic stability --- conservative problems --- Hamiltonian problems --- energy-conserving methods --- Poisson problems --- Hamiltonian Boundary Value Methods --- HBVMs --- line integral methods --- constrained Hamiltonian problems --- Hamiltonian PDEs --- highly oscillatory problems --- boundary element method --- finite difference method --- floating strike Asian options --- continuous geometric average --- barrier options --- isogeometric analysis --- adaptive methods --- hierarchical splines --- THB-splines --- local refinement --- linear systems --- preconditioners --- Cholesky factorization --- limited memory --- Volterra integral equations --- Volterra integro–differential equations --- collocation methods --- multistep methods --- convergence --- B-spline --- optimal basis --- fractional derivative --- Galerkin method --- collocation method --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- discretization of systems of differential equations --- higher-order finite element methods --- discontinuous Galerkin methods --- finite difference methods --- isogeometric analysis --- B-splines --- curl–curl operator --- time harmonic Maxwell’s equations and magnetostatic problems --- low rank completion --- matrix ODEs --- gradient system --- ordinary differential equations --- Runge–Kutta --- tree --- stump --- order --- elementary differential --- edge-histogram --- edge-preserving smoothing --- histogram specification --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods --- hyperbolic partial differential equations --- high order discontinuous Galerkin finite element schemes --- shock waves and discontinuities --- vectorization and parallelization --- high performance computing --- generalized Schur algorithm --- null-space --- displacement rank --- structured matrices --- stochastic differential equations --- stochastic multistep methods --- stochastic Volterra integral equations --- mean-square stability --- asymptotic stability --- numerical analysis --- numerical methods --- scientific computing --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods

Emergent Quantum Mechanics. David Bohm Centennial Perspectives

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ISBN: 9783038976165 Year: Pages: 544 DOI: 10.3390/books978-3-03897-617-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2019-04-05 10:34:31
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeper-level"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

Keywords

quantum foundations --- nonlocality --- retrocausality --- Bell’s theorem --- Bohmian mechanics --- quantum theory --- surrealistic trajectories --- Bell inequality --- quantum mechanics --- generalized Lagrangian paths --- covariant quantum gravity --- emergent space-time --- Gaussian-like solutions --- entropy and time evolution --- resonances in quantum systems --- the Friedrichs model --- complex entropy. --- Bell’s theorem --- the causal arrow of time --- retrocausality --- superdeterminism --- toy-models --- quantum ontology --- sub-quantum dynamics --- micro-constituents --- emergent space-time --- emergent quantum gravity --- entropic gravity --- black hole thermodynamics --- Stern-Gerlach --- trajectories --- spin --- Bell theorem --- fractal geometry --- p-adic metric --- singular limit --- gravity --- conspiracy --- free will --- number theory --- quantum potential --- Feynman paths --- weak values --- Bohm theory --- no-hidden-variables theorems --- observables --- measurement problem --- Bohmian mechanics --- primitive ontology --- Retrocausation --- weak values --- Stochastic Electrodynamics --- quantum mechanics --- decoherence --- interpretations --- pilot-wave theory --- Bohmian mechanics --- Born rule statistics --- measurement problem --- quantum thermodynamics --- strong coupling --- operator thermodynamic functions --- quantum theory --- de Broglie–Bohm theory --- contextuality --- atom-surface scattering --- bohmian mechanics --- matter-wave optics --- diffraction --- vortical dynamics --- Schrödinger equation --- de Broglie–Bohm theory --- nonequilibrium thermodynamics --- zero-point field --- de Broglie–Bohm interpretation of quantum mechanics --- pilot wave --- interior-boundary condition --- ultraviolet divergence --- quantum field theory --- Aharonov–Bohm effect --- physical ontology --- nomology --- interpretation --- gauge freedom --- Canonical Presentation --- relational space --- relational interpretation of quantum mechanics --- measurement problem --- non-locality --- discrete calculus --- iterant --- commutator --- diffusion constant --- Levi-Civita connection --- curvature tensor --- constraints --- Kilmister equation --- Bianchi identity --- stochastic differential equations --- Monte Carlo simulations --- Burgers equation --- Langevin equation --- fractional velocity --- interpretations of quantum mechanics --- David Bohm --- mind–body problem --- quantum holism --- fundamental irreversibility --- space-time fluctuations --- spontaneous state reduction --- Poincaré recurrence --- symplectic camel --- quantum mechanics --- Hamiltonian --- molecule interference --- matter-waves --- metrology --- magnetic deflectometry --- photochemistry --- past of the photon --- Mach–Zehnder interferometer --- Dove prism --- photon trajectory --- weak measurement --- transition probability amplitude --- atomic metastable states --- Bell’s theorem --- Bohmian mechanics --- nonlocality --- many interacting worlds --- wavefunction nodes --- bouncing oil droplets --- stochastic quantum dynamics --- de Broglie–Bohm theory --- quantum non-equilibrium --- H-theorem --- ergodicity --- ontological quantum mechanics --- objective non-signaling constraint --- quantum inaccessibility --- epistemic agent --- emergent quantum state --- self-referential dynamics --- dynamical chaos --- computational irreducibility --- undecidable dynamics --- Turing incomputability --- quantum ontology --- nonlocality --- time-symmetry --- retrocausality --- quantum causality --- conscious agent --- emergent quantum mechanics --- Bohmian mechanics --- de Broglie-Bohm theory

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2019 (4)