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  • 1
    Publication Date: 2024-04-05
    Description: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
    Keywords: Physics ; Physics ; Quantum physics ; Quantum optics ; Statistical physics ; Machine learning ; Elementary particles (Physics) ; Quantum field theory ; thema EDItEUR::P Mathematics and Science::PH Physics::PHJ Optical physics ; thema EDItEUR::P Mathematics and Science::PH Physics::PHQ Quantum physics (quantum mechanics and quantum field theory) ; thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics ; thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics ; thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence::UYQM Machine learning ; thema EDItEUR::P Mathematics and Science::PH Physics::PHJ Optical physics ; thema EDItEUR::P Mathematics and Science::PH Physics::PHQ Quantum physics (quantum mechanics and quantum field theory) ; thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics ; thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics ; thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence::UYQM Machine learning
    Language: English
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Journal of metastable and nanocrystalline materials Vol. 23 (Jan. 2005), p. 191-194 
    ISSN: 1422-6375
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Microstructure of nickel deposit ,which was prepared with pulse-plating technology on depleted uranium surface, has been studied by X-ray diffractometry(XRD),Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM). The results indicate that the crystallographic structure of the deposit is face centered cubic; the deposit has a highly preferred orientation of (200), the relative orientation density of (200) is 3.44; the average grain size is about 45.5nm. The deposit is fine and has multi-crystal nature as well as crystallographic defects as dislocation, stacking and twin. It’s feasible to prepare nanocrystalline nickel deposit on depleted uranium surface with pulse plating technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Advanced materials research Vol. 11-12 (Feb. 2006), p. 721-724 
    ISSN: 1662-8985
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The filling process of plastic precise gear is simulated by CAE software and the factors thatinfluence injection molding accuracy in single cavity mold are discussed in this paper. With theassistant of visualization technology, the mechanism of filling unbalance which influences efficientinjection molding was especially studied. The model of filling unbalance was supposed that wasverified experimentally by visualization technique. It is clarified that the mechanism of fillingunbalance results from dissymmetrical temperature distribution on the cross-section of runner, whichis strongly influenced by the shear heat and the cooling process in the runner. At the same time, a newmethod was proposed for improving the filling imbalance by applying appropriate injection moldingprocess without any changes in runner shape of multi-cavity mold
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Key engineering materials Vol. 324-325 (Nov. 2006), p. 983-986 
    ISSN: 1013-9826
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper, the effect of imperfect inner interface on the stress fields in the coatedinclusion composite is investigated, the spring-layer of vanishing thickness model is introduced tosimulate the imperfect interface, assuming that across the interface between the inclusion and thecoating the interfacial traction is continuous while displacement discontinuities are permittedthrough interfacial traction-displacement jump relations. Numerical examples corresponding to thecomposites containing single coated spherical and fibrous inclusion, respectively, under shearloading at infinity, are calculated, which indicate that the imperfect inner interfaces havesignificant effect on stress fields of the composites
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Key engineering materials Vol. 334-335 (Mar. 2007), p. 797-800 
    ISSN: 1013-9826
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a method for chemical functionalization of CNTs through thecombined process of UV/O3 treatment and silanization process. FT-IR and TEM were employed tocharacterize the changes in surface functionalities and morphology. The results indicate improveddispersion and attachment of silane molecules on the surface of CNTs. Epoxy matrix nanocompositescontaining functionalized CNTs showed much better dispersion with associated higher mechanicalproperties than those without functionalization. These findings confirmed the improved interfacialinteractions due to covalent bonding between the functionalized CNTs and epoxy resin
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Key engineering materials Vol. 336-338 (Apr. 2007), p. 401-404 
    ISSN: 1013-9826
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The structure, thermal expansion coefficients, and electric conductivity of Ce1-xGdxO2-x/2 (x = 0~ 0.6) solid solutions, prepared by gel-combustion method, were investigated. The uniform small particlesize of the gel-combustion prepared materials allows sintering of the samples into highly dense ceramicpellets at 1300°C, a significantly lower temperature, compared to that of 1600~1650°C required for ceriasolid electrolytes prepared by traditional solid state techniques. XRD showed that single-phase solidsolutions have been formed in all investigated range. The maximum conductivity, σ600°C = 5.26×10-3S/cm,was found at x = 0.2. The thermal expansion coefficient, determined from high-temperature X-ray data is8.125×10-6 K-1 at x = 0.2
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 308-311 (May 1999), p. 995-999 
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 308-311 (May 1999), p. 1030-1034 
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Westerville, Ohio : American Ceramics Society
    Journal of the American Ceramic Society 86 (2003), S. 0 
    ISSN: 1551-2916
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Lead zirconate titanate (Pb(Zr,Ti)O3, PZT) thin films were grown on silicon 〈100〉 substrate by aerosol plasma deposition (APD) using solid-state-reacted powder containing donor oxide Nb2O5 when keeping the substrate at room temperature and 200°C. Crystalline phases of the deposited films have been analyzed via X-ray diffractometry (XRD), and microstructure via scanning and transmission electron microscopy (SEM and TEM). Cross-sectional TEM revealed that the microstructure comprised several layers including the deposited PZT film and the platinum-electrode-and-titanium-buffered layers on SiO2–Si substrate. The Pt-electrode layer contained (111)Pt twinned columnar grains with a slight misorientation and forming low-angle grain boundaries among them. The PZT layer contained randomly oriented grains embedded in an amorphous matrix. Some of the PZT grains, oriented with the zone axis Z= [[Twomacr]11]PZT parallel to Z= [111]Pt, were grown epitaxially on the Pt layer by sharing the (111)PZT plane with the (111)Pt twinned columnar Pt crystals. However, the existence of such an orientation relationship was confined to several nanosize grains at and near the PZT-Pt interface, and no gross film texture has been developed. An amorphous grain boundary phase, generated by pressure-induced amorphisation (PIA) in the solid state, was identified by high-resolution imaging. Its presence is taken to account for the densification of the PZT thin films via a sintering mechanism involving an amorphous phase on deposition at 25° and 200°C.
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  • 10
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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