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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

Numerical Analysis or Numerical Method in Symmetry

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ISBN: 9783039283729 9783039283736 Year: Pages: 194 DOI: 10.3390/books978-3-03928-373-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:08
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This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Keywords

risk assessment --- numerical analysis --- ignition hazard --- effective field strength --- offshore plant --- Hamiltonian system --- complex Lagrangian --- Noether symmetries --- first integrals --- symplectic Runge–Kutta methods --- effective order --- partitioned runge-kutta methods --- symplecticity --- hamiltonian systems --- Runge-Kutta type methods --- fourth-order ODEs --- order conditions --- B-series --- quad-colored trees --- k-hypergeometric differential equations --- non-homogeneous --- k-hypergeometric series --- special function --- general solution --- Frobenius method --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- recurrence relations --- differential equations --- composition properties --- orthogonality properties --- numerical analysis --- heat generation --- chemical reaction --- thin needle --- nanofluid --- fourth-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- particle accelerator --- coupling impedance --- dual integral equations --- Clenshaw-Curtis quadrature --- steepest descent method --- logarithmic singularities --- Cauchy singularity --- highly oscillatory integrals --- second-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- Fredholm integral equations --- multiresolution analysis --- unitary extension principle --- oblique extension principle --- B-splines --- wavelets --- tight framelets --- Swift–Hohenberg type of equation --- surfaces --- narrow band domain --- closest point method --- operator splitting method

Molecular Magnets

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ISBN: 9783038977100 Year: Pages: 166 DOI: 10.3390/books978-3-03897-711-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Chemistry (General)
Added to DOAB on : 2019-03-21 14:08:22
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Molecular magnets show many properties not met in conventional metallic magnetic materials, i.e. low density, transparency to electromagnetic radiation, sensitivity to external stimuli such as light, pressure, temperature, chemical modification or magnetic/electric fields, and others. They can serve as “functional” materials in sensors of different types or be applied in high-density magnetic storage or nanoscale devices. Research into molecule-based materials became more intense at the end of the 20th century and is now an important branch of modern science. The articles in this Special Issue, written by physicists and chemists, reflect the current work on molecular magnets being carried out in several research centers. Theoretical papers in the issue concern the influence of spin anisotropy in the low dimensional lattice of the resulting type of magnet, as well as thermodynamics and magnetic excitations in spin trimers. The impact of external pressure on structural and magnetic properties and its underlying mechanisms is described using the example of Prussian blue analogue data. The other functionality discussed is the magnetocaloric effect, investigated in coordination polymers and high spin clusters. In this issue, new molecular magnets are presented: (i) ferromagnetic high-spin [Mn6] single-molecule magnets, (ii) solvatomagnetic compounds changing their structure and magnetism dependent on water content, and (iii) a family of purely organic magnetic materials. Finally, an advanced calorimetric study of anisotropy in magnetic molecular superconductors is reviewed.

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

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ISBN: 9783039214099 9783039214105 Year: Pages: 254 DOI: 10.3390/books978-3-03921-410-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:15
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The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Keywords

parameter-dependent model --- surrogate modeling --- tensor-train decomposition --- gappy POD --- heterogeneous data --- elasto-viscoplasticity --- archive --- model reduction --- 3D reconstruction --- inverse problem plasticity --- data science --- model order reduction --- POD --- DEIM --- gappy POD --- GNAT --- ECSW --- empirical cubature --- hyper-reduction --- reduced integration domain --- computational homogenisation --- model order reduction (MOR) --- low-rank approximation --- proper generalised decomposition (PGD) --- PGD compression --- randomised SVD --- nonlinear material behaviour --- machine learning --- artificial neural networks --- computational homogenization --- nonlinear reduced order model --- elastoviscoplastic behavior --- nonlinear structural mechanics --- proper orthogonal decomposition --- empirical cubature method --- error indicator --- symplectic model order reduction --- proper symplectic decomposition (PSD) --- structure preservation of symplecticity --- Hamiltonian system --- reduced order modeling (ROM) --- proper orthogonal decomposition (POD) --- enhanced POD --- a priori enrichment --- modal analysis --- stabilization --- dynamic extrapolation --- computational homogenization --- large strain --- finite deformation --- geometric nonlinearity --- reduced basis --- reduced-order model --- sampling --- Hencky strain --- microstructure property linkage --- unsupervised machine learning --- supervised machine learning --- neural network --- snapshot proper orthogonal decomposition

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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