Bibliografie tematiche / Continuous or discrete homogenization

Letteratura scientifica selezionata sul tema "Continuous or discrete homogenization"

Autore: Grafiati
Pubblicato: 8 giugno 2024

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Articoli di riviste sul tema "Continuous or discrete homogenization":

1

Gottwald, Georg A., e Ian Melbourne. "Homogenization for deterministic maps and multiplicative noise". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, n. 2156 (8 agosto 2013): 20130201. http://dx.doi.org/10.1098/rspa.2013.0201.

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A recent paper of Melbourne & Stuart (2011 A note on diffusion limits of chaotic skew product flows. Nonlinearity 24 , 1361–1367 (doi:10.1088/0951-7715/24/4/018)) gives a rigorous proof of convergence of a fast–slow deterministic system to a stochastic differential equation with additive noise. In contrast to other approaches, the assumptions on the fast flow are very mild. In this paper, we extend this result from continuous time to discrete time. Moreover, we show how to deal with one-dimensional multiplicative noise. This raises the issue of how to interpret certain stochastic integrals; it is proved that the integrals are of Stratonovich type for continuous time and neither Stratonovich nor Itô for discrete time. We also provide a rigorous derivation of super-diffusive limits where the stochastic differential equation is driven by a stable Lévy process. In the case of one-dimensional multiplicative noise, the stochastic integrals are of Marcus type both in the discrete and continuous time contexts.
2

Nassar, H., A. Lebée e L. Monasse. "Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, n. 2197 (gennaio 2017): 20160705. http://dx.doi.org/10.1098/rspa.2016.0705.

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Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.
3

Wei, Nan, Hongling Ye, Xing Zhang, Jicheng Li e Boshuai Yuan. "Vibration Characteristics Research of Sandwich Structure with Octet-truss Lattice Core". Journal of Physics: Conference Series 2125, n. 1 (1 novembre 2021): 012059. http://dx.doi.org/10.1088/1742-6596/2125/1/012059.

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Abstract Lattice sandwich beams are often subjected to vibrations when they are used. The aim of this study was to explore the vibration characteristics of the octet-truss lattice core sandwich beam by translating discrete octet-truss core to the continuous homogenization material. The natural frequencies of which are obtained by theoretical calculation and numerical simulation. The theoretical solutions are in good agreement with the numerical results. It demonstrates that the theoretical approach is effective to compute the natural frequency. Furthermore, the influences of truss member radius and thin sheets ply on the natural frequencies are also discussed. The outcomes indicate that the octet-truss lattice core sandwich beam’s natural frequencies are controlled via selecting the appropriate truss member radius and the face sheets thickness.
4

Gomes, Diogo A., e Xianjin Yang. "The Hessian Riemannian flow and Newton’s method for effective Hamiltonians and Mather measures". ESAIM: Mathematical Modelling and Numerical Analysis 54, n. 6 (16 settembre 2020): 1883–915. http://dx.doi.org/10.1051/m2an/2020036.

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Effective Hamiltonians arise in several problems, including homogenization of Hamilton–Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry–Mather theory. In Aubry–Mather theory, related objects, Mather measures, are also of great importance. Here, we combine ideas from mean-field games with the Hessian Riemannian flow to compute effective Hamiltonians and Mather measures simultaneously. We prove the convergence of the Hessian Riemannian flow in the continuous setting. For the discrete case, we give both the existence and the convergence of the Hessian Riemannian flow. In addition, we explore a variant of Newton’s method that greatly improves the performance of the Hessian Riemannian flow. In our numerical experiments, we see that our algorithms preserve the non-negativity of Mather measures and are more stable than related methods in problems that are close to singular. Furthermore, our method also provides a way to approximate stationary MFGs.
5

Josnin, Jean-Yves, Séverin Pistre e Claude Drogue. "Modélisation d'un système karstique complexe (bassin de St-Chaptes, Gard, France) : un outil de synthèse des données géologiques et hydrogéologiques". Canadian Journal of Earth Sciences 37, n. 10 (1 ottobre 2000): 1425–45. http://dx.doi.org/10.1139/e00-056.

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Numerous software packages allow the efficient modeling of the hydrodynamic behaviour of aquifers in continuous media. To study pressure transfer in discontinuous media like karsts, the black-box models are restrictive and the models that consider discrete conduit networks are unsuitable for reservoir scale. We show that the utilization of a continuous media model can lead to useful results, even in the case of complex systems, but needs to be adapted to karst specificity. The problem is approached by studying a hydrogeological system located in the Mediterranean Languedoc region: the St-Chaptes basin. This system consists of three superposed aquifers included in four different stratigraphic series. The main aquifer is a karst formation in contact with two other karst formations that belong to different hydrogeologic systems. Considering geological data in addition to hydrological data and with the hypothesis of a relative homogenization of the karst's hydraulic behaviour on a large spatial scale for daily to monthly increments, the model that takes into account the relations with the other aquifers allows (i) a preliminary identification of the main heterogeneities inside the reservoir; (ii) the location of barriers and low-permeability zones that isolate some parts of the aquifer; (iii) the observation of a curious behaviour of the piezometric levels in the confined zones of the aquifer; and (iv) the characterization of the exchanges with the other low-volume but existing aquifers.
6

Amaro-Mellado, José Lázaro, e Dieu Tien Bui. "GIS-Based Mapping of Seismic Parameters for the Pyrenees". ISPRS International Journal of Geo-Information 9, n. 7 (17 luglio 2020): 452. http://dx.doi.org/10.3390/ijgi9070452.

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In the present paper, three of the main seismic parameters, maximum magnitude -Mmax, b-value, and annual rate -AR, have been studied for the Pyrenees range in southwest Europe by a Geographic Information System (GIS). The main aim of this work is to calculate, represent continuously, and analyze some of the most crucial seismic indicators for this belt. To this end, an updated and homogenized Poissonian earthquake catalog has been generated, where the National Geographic Institute of Spain earthquake catalog has been considered as a starting point. Herein, the details about the catalog compilation, the magnitude homogenization, the declustering of the catalog, and the analysis of the completeness, are exposed. When the catalog has been produced, a GIS tool has been used to drive the parameters’ calculations and representations properly. Different grids (0.5 × 0.5° and 1 × 1°) have been created to depict a continuous map of these parameters. The b-value and AR have been obtained that take into account different pairs of magnitude–year of completeness. Mmax has been discretely obtained (by cells). The analysis of the results shows that the Central Pyrenees (mainly from Arudy to Bagnères de Bigorre) present the most pronounced seismicity in the range.
7

Pradel, F., e K. Sab. "Homogenization of discrete media". Le Journal de Physique IV 08, PR8 (novembre 1998): Pr8–317—Pr8–324. http://dx.doi.org/10.1051/jp4:1998839.

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Etoughe, M. Betoue, e G. Panasenko. "Partial homogenization of discrete models". Applicable Analysis 87, n. 12 (dicembre 2008): 1425–42. http://dx.doi.org/10.1080/00036810802378638.

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Braides, Andrea, Valeria Chiadò Piat e Andrey Piatnitski. "Homogenization of Discrete High-Contrast Energies". SIAM Journal on Mathematical Analysis 47, n. 4 (gennaio 2015): 3064–91. http://dx.doi.org/10.1137/140975668.

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Caillerie, Denis, Ayman Mourad e Annie Raoult. "Discrete Homogenization in Graphene Sheet Modeling". Journal of Elasticity 84, n. 1 (30 marzo 2006): 33–68. http://dx.doi.org/10.1007/s10659-006-9053-5.

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Ti possono interessare anche gli elenchi estesi di opere sul tema "Continuous or discrete homogenization":
Articoli di riviste Tesi Libri

Tesi sul tema "Continuous or discrete homogenization":

1

Rizzi, Gianluca. "Strain-gradient effects in the discrete/continuum transition via homogenization". Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/369095.

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A second-gradient elastic material has been identified as the equivalent homogeneous material of an hexagonal lattice made up of three different orders of linear elastic bars (hinged at each junction). In particular, the material equivalent to the lattice exhibits: (i.) non-locality, (ii.) non-centrosymmetry, and (iii.) anisotropy (even if the hexagonal geometry leads to isotropy at first-order). A Cauchy elastic equivalent solid is only recovered in the limit of vanishing length of the lattice’s bars. The identification of the second-gradient elastic material is complemented by analyses of positive definiteness and symmetry of the constitutive operators. Solutions of specific mechanical problems in which the lattice response is compared to the corresponding response of an equivalent boundary value problem for the homogeneous second-gradient elastic material are presented. These comparisons show the efficacy of the proposed identification procedure.
2

Rizzi, Gianluca. "Strain-gradient effects in the discrete/continuum transition via homogenization". Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3552/1/Rizzi_Gianluca_PhD_thesis.pdf.

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A second-gradient elastic material has been identified as the equivalent homogeneous material of an hexagonal lattice made up of three different orders of linear elastic bars (hinged at each junction). In particular, the material equivalent to the lattice exhibits: (i.) non-locality, (ii.) non-centrosymmetry, and (iii.) anisotropy (even if the hexagonal geometry leads to isotropy at first-order). A Cauchy elastic equivalent solid is only recovered in the limit of vanishing length of the lattice’s bars. The identification of the second-gradient elastic material is complemented by analyses of positive definiteness and symmetry of the constitutive operators. Solutions of specific mechanical problems in which the lattice response is compared to the corresponding response of an equivalent boundary value problem for the homogeneous second-gradient elastic material are presented. These comparisons show the efficacy of the proposed identification procedure.
3

Lauerbach, Laura [Verfasser], Anja [Gutachter] Schlömerkemper e Martin [Gutachter] Kruzik. "Stochastic Homogenization in the Passage from Discrete to Continuous Systems - Fracture in Composite Materials / Laura Lauerbach ; Gutachter: Anja Schlömerkemper, Martin Kruzik". Würzburg : Universität Würzburg, 2020. http://d-nb.info/1220634239/34.

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Ruf, Matthias [Verfasser], Marco [Akademischer Betreuer] [Gutachter] Cicalese, Antoine [Gutachter] Gloria e Andrea [Gutachter] Braides. "Discrete-to-continuum limits and stochastic homogenization of ferromagnetic surface energies / Matthias Ruf ; Gutachter: Antoine Gloria, Marco Cicalese, Andrea Braides ; Betreuer: Marco Cicalese". München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1137323493/34.

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Alavi, Seyed Ehsan. "Homogénéisation de milieux architecturés périodiques et quasi-périodiques vers des milieux continus généralisés". Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0305.

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Cette thèse vise à revisiter les schémas d'homogénéisation d'ordre supérieur vers des continuums d'ordre ou de gradient supérieurs, successivement pour les matériaux et composites architecturés périodiques et quasi-périodiques, en se basant sur des principes variationnels et une extension de la condition de macrohomogénéité de Hill. Les méthodes d'homogénéisation continue sont exposées dans la première partie pour les milieux micropolaires et micromorphes, suivies par une présentation de l’homogénéisation discrète, alternative de l’homogénéisation continue.Nous avons étendu ces développements théoriques à la situation des matériaux quasi-périodiques, de microstructure régulière, qui peut être transformée en une configuration périodique de référence. L'idée commune aux méthodes d'homogénéisation périodique proposées (de nature continue ou discrète) est de décomposer le déplacement microscopique en une partie homogène représentative de la cinématique du milieu continu effectif adopté, et une fluctuation évaluée à partir d'un principe variationnel. En substance, les développements théoriques permettent l'élaboration de continuums enrichis (milieux continus généralisés) de type micromorphe, et des variantes qui en découlent en utilisant des conditions de dégénérescence appropriées. Des applications numériques ont été réalisées pour des matériaux architecturés et des composites à renforts de type inclusion sujets à de tels effets d'ordre supérieur en raison de leur architecture interne. Sur le plan théorique, les développements réalisés remédient à de nombreuses limitations des schémas d'homogénéisation d'ordre supérieur existants.Dans la partie II, les propriétés mécaniques effectives classiques et d'ordre supérieur des matériaux architecturés ont été évaluées sur la base de schémas d'homogénéisation discrets. En suivant l'idée d'une approche phénoménologique, des modèles consistants de type couple de contraintes de réseaux de poutres répétitifs ont été élaborés. Des milieux de Cosserat enrichis ont été élaborés dans l'esprit de la micromécanique, en adoptant des modèles de poutre de Timoshenko à un niveau microscopique, et en appliquant une méthode de continualisation vers un milieu de substitution effectif de Cosserat. La méthode de continualisation proposée s'avère précise et efficace en termes de calcul par rapport aux schémas d'homogénéisation continus et aux simulations par éléments finis réalisés sur la microstructure initiale. Un résultat essentiel des analyses effectuées est la quantification des effets de bord.Le contexte théorique qui sous-tend l'homogénéisation asymptotique quasi-périodique dans le cadre de l'élasticité anisotrope linéarisée est abordé dans la troisième partie. Différentes méthodologies d'évaluation des propriétés effectives quasi-périodiques ont été élaborées, conduisant à l'émergence de milieux effectifs à gradient de déformation. Les transformations conformes définissent une classe spécifique de transformations géométriques permettant de concevoir des matériaux architecturés générant un gradient de porosité interne, ce qui en fait de bons candidats pour des biosubstituts en biomécanique osseuse
This thesis aims to revisit higher-order homogenization schemes towards higher-order or higher gradient continua, successively for periodic and quasi-periodic architected materials and composites, based on variational principles and an extension of Hill macrohomogeneity condition. Continuous homogenization methods are exposed in Part I for micropolar and micromorphic media, followed by an exposition of the alternative discrete homogenization method.We have extended these theoretical developments to the situation of quasi-periodic materials, which still have a regular microstructure. The common idea to the proposed periodic homogenization methods of continuous or discrete nature is to split the microscopic displacement into a homogeneous part representative of the kinematics of the adopted effective continuum and a fluctuation evaluated from a variational principle. In substance, the theoretical developments allow the elaboration of enriched continua (generalized continua) of micromorphic type and all sub continua obtained using suitable degeneration conditions. Numerical applications have been made for architected materials and inclusion-based composites prone to higher-order effects due to their inner architecture. On the theoretical framework, the performed developments remedy many existing limitations of existing higher-order homogenization schemes.In Part II, repetitive lattice materials' effective classical and higher-order mechanical properties have been evaluated based on discrete homogenization schemes. Following the idea of a phenomenological approach, consistent couple stress models of repetitive beam lattices have been elaborated. Enriched Cosserat media have been derived in the spirit of micromechanics, adopting Timoshenko beam models at a microlevel, and applying a continualization method towards a Cosserat effective substitution medium. The proposed continualization method proves to be accurate and computationally efficient compared to continuous homogenization schemes and fully resolved finite element simulations. One key outcome of the performed analyses is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition.The theoretical background underlying quasi-periodic asymptotic homogenization in the framework of linearized anisotropic elasticity deserves the development of Part III. Different methodologies for evaluating the effective quasi-periodic properties have been elaborated, leading to the emergence of strain gradient effective media. Conformal transformations define a specific class of geometrical mappings, allowing for designing compatible architected materials with inner porosity gradient, making them suitable bone biomechanics candidates
6

Baird, Graham. "Mixed discrete-continuous fragmentation equations". Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6.

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The work contained in this thesis concerns the development, and the mathematical and numerical analysis, of a new class of hybrid discrete-continuous fragmentation model. The framework is introduced as a potential answer to the occurrence of 'shattering' mass loss, commonly observed in purely continuous fragmentation models. Initially, the study begins by introducing the model, which takes the form of an integro-differential equation, coupled with a system of ordinary differential equations. Once the model has been established, it is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato-Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve non-negativity and conserve mass. Having determined the existence of a solution, the work continues with the development of a numerical scheme for the approximate solution of the modelling equations. Considering a truncated version of the equations, rewritten in an alternative conservative form, the scheme is built around a finite volume discretisation. Using a standard weak compactness argument, the approximations generated by the numerical scheme are shown to converge (weakly) to a weak solution of the truncated equations. By relating this weak solution to the strong solutions provided by the earlier semigroup analysis, the weak solution is found to be unique and as a consequence, differentiable, non-negative and mass-conserving. The theoretical study is completed with an examination of the effect of varying the truncation point. In particular, establishing that as the length of the truncated interval is increased, in the limit, the original solution to the full model is obtained. Finally, the thesis is completed with a numerical investigation, seeking to experimentally confirm the assertions of the earlier theoretical work and assess the performance of the numerical scheme for a suite of test models.
7

Silva, Pedro André Arroyo. "Modelo matemático com parâmetros que dependem da discretização: aplicação ao estudo de fenômenos de propagação discreta em meios excitáveis". Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7194.

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A formação de padrões espaço-temporais são observados em processos químicos e bio-lógicos. Apesar dos sistemas bioquímicos serem altamente heterogêneos, aproximações homogenizadas contínuas formadas por equações diferenciais parciais são utilizadas fre-quentemente. Estas aproximações são usualmente justificadas pela diferença de escalas entre as heterogeneidades e o tamanho da característica espacial dos padrões. Em certas condições do meio, por exemplo, quando há um acoplamento fraco entre as células car-díacas, os modelos homogenizados discretos são mais adequados. Entretanto, os modelos discretos são menos manejáveis, por exemplo, na geração de malha para 2D e 3D, se comparado com os modelos contínuos. Aqui estudamos um modelo matemático homoge-nizado contínuo que se aproxima do modelo homogenizado. Este modelo é dado a partir de equações diferencias parciais com um parâmetro que depende da discretização da ma-lha. Dessa maneira nos referimos a este por um modelo matemático com parâmetros que dependem da discretização. Validamos nossa aproximação em um meio excitável genérico que simula três fenômenos em 1D: a propagação do potencial de ação transmembrânico no tecido cardíaco, a propagação do potencial de ação em filamentos de axônios cobertos por bainhas de mielina e a propagação do ativador e inibidor em microemulsões químicas. Para o caso 2D desenvolvemos uma versão da nossa aproximação que reproduz ondas espirais em um meio com acoplamento fraco.
The spatio-temporal patterns formations are observed in chemical and biological pro-cesses. Although biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. These approaches are usually justified by the difference scales between the characteristic spatial size of the patterns. Under some conditions of the medium, for instance, under weak coupling between cardiac cells, discrete models are more adequate. On the other hand discrete models may be less manageable, for instance, in terms of mesh generation, com-pared to the continuum models. Here we study a mathematical model to approach the discreteness which permits the computer implementation on non-uniform meshes. The model is cast as a partial differential equation but with a parameter that depends on the discretization mesh. Therefore we refer to it as a mathematical model with parameters dependent of discretization. We validate the approach in a generic excitable media that simulates three different phenomena in 1D: the propagation of action potential in car-diac tissue, the propation of the action potentialin filaments of axons wrapped by myelin sheaths, and the propagation of the activator/inhibitor in chemical microemulsions. For the 2D case we develop a version to this approach in microemulsions where it was possible to reproduce spiral waves with weak coupling of the medium.
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ElNady, Khaled. "Modèles de comportement non linéaire des matériaux architecturés par des méthodes d'homogénéisation discrètes en grandes déformations. Application à des biomembranes et des textiles". Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0032/document.

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Ce travail porte sur le développement de modèles micromécaniques pour le calcul de la réponse homogénéisée de matériaux architecturés, en particulier des matériaux se présentant sous forme de treillis répétitifs. Les matériaux architecturés et micro-architecturés couvrent un domaine très large de de propriétés mécaniques, selon la connectivité nodale, la disposition géométrique des éléments structuraux, leurs propriétés mécaniques, et l'existence d'une possible hiérarchie structurale. L'objectif principal de la thèse est la prise en compte des nonlinéarités géométriques résultant des évolutions importantes de la géométrie initiale du treillis, causée par une rigidité de flexion des éléments structuraux faible en regard de leur rigidité en extension. La méthode dite d'homogénéisation discrète est développée pour prendre en compte les non linéarités géométriques pour des treillis quais périodiques; des schémas incrémentaux sont construits qui reposent sur la résolution incrémentale et séquentielle des problèmes de localisation - homogénéisation posés sur une cellule de base identifiée, soumise à un chargement contrôlé en déformation. Le milieu continu effectif obtenu est en général un milieu micropolaire anisotrope, dont les propriétés effectives reflètent la disposition des éléments structuraux et leurs propriétés mécaniques. La réponse non affine des treillis conduit à des effets de taille qui sont pris en compte soit par un enrichissement de la cinématique par des variables de microrotation ou par la prise en compte des seconds gradients du déplacement. La construction de milieux effectifs du second gradient est faite dans un formalisme de petites perturbations. Il est montré que ces deux types de milieu effectif sont complémentaires en raison de l'analogie existant lors de la construction théorique des réponses homogénéisées, et par le fait qu'ils fournissent des longueurs internes en extension, flexion et torsion. Des applications à des structures tissées et des membranes biologiques décrites comme des réseaux de filaments quais-périodiques ont été faites. Les réponses homogénéisées obtenues sont validées par des comparaisons avec des simulations par éléments finis réalisées sur un volume élémentaire représentatif de la structure. Les schémas d'homogénéisation ont été implémentés dans un code de calcul dédié, alimenté par un fichier de données d'entrée de la géométrie du treillis et de ses propriétés mécaniques. Les modèles micromécaniques développés laissent envisager du fait de leur caractère prédictif la conception de nouveaux matériaux architecturés permettant d'élargir les frontières de l'espace 'matériaux-propriétés'
The present thesis deals with the development of micromechanical schemes for the computation of the homogenized response of architectured materials, focusing on periodical lattice materials. Architectured and micro-architectured materials cover a wide range of mechanical properties according to the nodal connectivity, geometrical arrangement of the structural elements, their moduli, and a possible structural hierarchy. The principal objective of the thesis is the consideration of geometrical nonlinearities accounting for the large changes of the initial lattice geometry, due to the small bending stiffness of the structural elements, in comparison to their tensile rigidity. The so-called discrete homogenization method is extended to the geometrically nonlinear setting for periodical lattices; incremental schemes are constructed based on a staggered localization-homogenization computation of the lattice response over a repetitive unit cell submitted to a controlled deformation loading. The obtained effective medium is a micropolar anisotropic continuum, the effective properties of which accounting for the geometrical arrangement of the structural elements within the lattice and their mechanical properties. The non affine response of the lattice leads to possible size effects which can be captured by an enrichment of the classical Cauchy continuum either by adding rotational degrees of freedom as for the micropolar effective continuum, or by considering second order gradients of the displacement field. Both strategies are followed in this work, the construction of second order grade continua by discrete homogenization being done in a small perturbations framework. We show that both strategies for the enrichment of the effective continuum are complementary due to the existing analogy in the construction of the micropolar and second order grade continua by homogenization. The combination of both schemes further delivers tension, bending and torsion internal lengths, which reflect the lattice topology and the mechanical properties of its structural elements. Applications to textiles and biological membranes described as quasi periodical networks of filaments are considered. The computed effective response is validated by comparison with FE simulations performed over a representative unit cell of the lattice. The homogenization schemes have been implemented in a dedicated code written in combined symbolic and numerical language, and using as an input the lattice geometry and microstructural mechanical properties. The developed predictive micromechanical schemes offer a design tool to conceive new architectured materials to expand the boundaries of the 'material-property' space
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Schlömerkemper, Anja. "Magnetic forces in discrete and continuous systems". Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37349.

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The topic of this thesis is a mathematically rigorous derivation of formulae for the magnetic force which is exerted on a part of a bounded magnetized body by its surrounding. Firstly, the magnetic force is considered within a continuous system based on macroscopic magnetostatics. The force formula in this setting is called Brown's force formula referring to W. F. Brown, who gave a mainly physically motivated discussion of it. This formula contains a surface integral which shows a nonlinear dependence on the normal. Brown assumes the existence of an additional term in the surface force which cancels the nonlinearity to allow an application of Cauchy's theorem in continuum mechanics to a magnetoelastic material. The proof of Brown's formula which is given in this work involves a suitable regularization of a hypersingular kernel and uses singular integral methods. Secondly, we consider a discrete, periodic setting of magnetic dipoles and formulate the force between a part of a bounded set and its surrounding. In order to pass to the continuum limit we start from the usual force formula for interacting magnetic dipoles. It turns out that the limit of the discrete force is different from Brown's force formula. One obtains an additional nonlinear surface term which allows one to regard Brown's assumption on the surface force as a consequence of the atomistic approach. Due to short range effects one obtains moreover an additional linear surface term in the continuum limit of the discrete force. This term contains a certain lattice sum which depends on a hypersingular kernel and the underlying lattice structure
Das Thema dieser Arbeit ist eine mathematisch strenge Herleitung von Formeln für die magnetische Kraft, die auf einen Teil eines beschränkten, magnetischen Körpers durch seine Umgebung ausgeübt wird. Zunächst wird die magnetische Kraft in einem kontinuierlichen System auf Grundlage der makroskopischen Magnetostatik betrachtet. Mit Bezug auf W. F. Brown, der eine vor allem physikalisch motivierte Herleitung der Kraftformel gegeben hat, wird diese auch Brownsche Kraftformel genannt. Das Oberflächenintegral in dieser Formel zeigt eine nichtlineare Abhängigkeit von der Normalen. Um Cauchys Theorem aus der Kontinuumsmechanik in einem magnetoelastischen Material anwenden zu können, nimmt Brown an, dass die Oberflächenkraft einen zusäatzlichen Term enthält, der den nichtlinearen Ausdruck aufhebt. Der Beweis der Brownschen Kraftformel in dieser Arbeit beruht auf einer geeigneten Regularisierung eines hypersingulären Kerns und benutzt Methoden für singuläre Integrale. Danach gehen wir von einem diskreten, periodischen System von magnetischen Dipolen aus und betrachten die Kraft zwischen einem Teil einer beschränkten Menge und der Umgebung. Um zum Kontinuumslimes überzugehen, starten wir von der üblichen Kraftformel für wechselwirkende magnetische Dipole. Es zeigt sich, dass sich der Limes der diskreten Kraft von der Brownschen Kraftformel unterscheidet. Man erhält einen zusätzlichen nichtlinearen Oberflächenterm, der es ermöglicht, Browns Annahme als Konsequenz des atomistischen Zugangs zu sehen. Kurzreichweitige Effekte führen zudem zu einem linearen Oberflächenterm im Kontinuumlimes der diskreten Kraft. Dieser Zusatzterm enthält eine gewisse Gittersumme, die von einem hypersingulären Kern und der Struktur des zugrundeliegenden Gitters abhängt
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Kimia, Behjoo. "Deblurring Gaussian blur : continuous and discrete approaches". Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=65339.

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Libri sul tema "Continuous or discrete homogenization":

1

Neal, Katherine. From Discrete to Continuous. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-0077-1.

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Mohamed, Saad H. Continuous and discrete modules. Cambridge ; New York: Cambridge University Press, 1990.

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Miller, Boris M., e Evgeny Ya Rubinovich. Impulsive Control in Continuous and Discrete-Continuous Systems. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0095-7.

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Miller, B. Impulsive control in continuous and discrete-continuous systems. New York: Kluwer Academic/Plenum Publishers, 2003.

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Miller, Boris M. Impulsive control in continuous and discrete-continuous systems. New York, NY: Kluwer Academic/Plenum Publishers, 2003.

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Miller, B. Impulsive Control in Continuous and Discrete-Continuous Systems. Boston, MA: Springer US, 2003.

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Neff, Herbert P. Continuous and discrete linear systems. Malabar, Fla: Krieger Pub. Co., 1991.

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Dougherty, Edward R. Image processing: Continuous to discrete. Englewood Cliffs, NJ: Prentice-Hall, 1987.

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Bucek, Victor J. Control systems: Continuous and discrete. Englewood Cliffs, N.J: Prentice Hall, 1989.

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Chu, Eleanor Chin-hwa. Discrete and Continuous Fourier Transforms. London: Taylor and Francis, 2008.

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Capitoli di libri sul tema "Continuous or discrete homogenization":

1

Berlyand, Leonid, e Volodymyr Rybalko. "Continuum Limits for Discrete Problems with Fine Scales". In Getting Acquainted with Homogenization and Multiscale, 139–68. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01777-4_11.

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Ryvkin, Michael, Moshe Fuchs, Fabian Lipperman e Eyal Moses. "Non-Homogenization Approach to the Analysis of Periodic Elastic Systems: Applications to Fracture Mechanics and Topological Optimization". In Continuum Models and Discrete Systems, 129–34. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2316-3_21.

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Awrejcewicz, Jan, Igor V. Andrianov e Leonid I. Manevitch. "Discrete—Continuous Systems". In Springer Series in Synergetics, 253–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-72079-6_4.

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Eisner, Tanja. "Discrete vs. continuous". In Stability of Operators and Operator Semigroups, 163–82. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0195-5_5.

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Stabel, Aaron, Kimberly Kroeger-Geoppinger, Jennifer McCullagh, Deborah Weiss, Jennifer McCullagh, Naomi Schneider, Diana B. Newman et al. "Discrete Versus Continuous". In Encyclopedia of Autism Spectrum Disorders, 983. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-1698-3_100464.

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Andrew, Alex M. "Continuous versus Discrete". In IFSR International Series on Systems Science and Engineering, 37–55. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-75164-1_3.

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Artiba, A., V. V. Emelyanov e S. I. Iassinovski. "Modelling Discrete/Continuous Systems". In Introduction to Intelligent Simulation: The RAO Language, 397–414. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5709-8_15.

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Stremersch, Geert. "Continuous Versus Discrete Events". In Supervision of Petri Nets, 149–74. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1537-1_7.

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Skakovski, Aleksander. "Discrete-Continuous Scheduling Problem". In Population-Based Approaches to the Resource-Constrained and Discrete-Continuous Scheduling, 107–24. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62893-6_8.

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Lyche, Tom, e Jean-Louis Merrien. "Continuous and Discrete Approximations". In Exercises in Computational Mathematics with MATLAB, 249–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43511-3_11.

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Atti di convegni sul tema "Continuous or discrete homogenization":

1

Gazzo, S. "Anisotropic behaviours and strain concentration in lattice material evaluated by means of discrete homogenization". In AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-84.

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Abstract. Lattice fibre materials are challenging the standard modelling approaches due to their specific nature that results in peculiar effective behaviours such as extremely anisotropic materials or generalized continuum media. In this context, the aim of this paper is to the determine qualitatively and quantitatively the role of the morphological and mechanical parameters by investigating simple archetypical microstructures. The study is conducted through an up-scaling approach making use of the Homogenization method of discrete periodic media in the framework of a variational approach. The results of the homogenization have been validated comparing the response of the continuum with the response of discrete models.
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Gonella, Stefano, e Massimo Ruzzene. "Homogenization of Vibrating Periodic Lattice Structures". In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84428.

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The paper describes a homogenization technique for periodic lattice structures. The analysis is performed by considering the irreducible unit cell as a building block that defines the periodic pattern. In particular, the continuum equivalent representation for the discrete structure is sought with the objective of retaining information regarding the local properties of the lattice, while condensing its global behavior into a set of differential equations. These equations can then be solved either analytically or numerically, thus providing a model which involves a significantly lower number of variables than those required for the detailed model of the assembly. The methodology is first tested by comparing the dispersion relations obtained through homogenization with those corresponding to the detailed model of the unit cells and then extended to the comparison of exact and approximate harmonic responses. This comparison is carried out for both one-dimensional and two-dimensional assemblies. The application to three-dimensional structures is not attempted in this work and will be approached in the future without the need for substantial conceptual changes in the theoretical procedure. Hence the presented technique is expected to be applicable to a wide range of periodic structures, with applications ranging from the design of structural elements of mechanical and aerospace interest to the optimization of smart materials with attractive mechanical, thermal or electrical properties.
3

Pekmezi, Gerald, David Littlefield e Bruno Chareyre. "Statistical Distributions of the Elastic Moduli of Particle Aggregates at the Mesoscale". In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-052.

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Abstract The current work is part of an ongoing effort to couple the Discrete Element Method (DEM), used as a mesoscale method, with Statistical Mechanics in order to construct a framework for the modeling, homogenization, and uncertainty quantification of particulate geomaterials. The aspect of the framework tackled in this work, is the quantification of stress and deformation of heterogenous DE models. Such quantification is necessary to allow DEM to “speak continuum”. DEM is a discrete particle method, wherein the concept of “stress” does not fit naturally, but where each particle pair is considered to interact through discrete forces. Additionally, DEM is an explicit method, and equivalent continuum deformation must be defined in the context of particle kinematics.
4

Gonella, Stefano, e Massimo Ruzzene. "Homogenization and Equivalent In-Plane Properties of Hexagonal and Re-Entrant Honeycombs". In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42400.

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The investigation of equivalent in-plane properties for hexagonal and re-entrant (auxetic) lattices can be carried out through the analysis of the partial differential equations associated with their homogenized continuum models. A homogenization technique is adopted based on the approximation of the discrete lattice equations according to the finite differences formalism. The technique can be used in conjunction with a finite element (FE) description of the lattice unit cell and therefore allows handling structures with different levels of complexity and various internal geometries within a general and compact framework that can be easily implemented in a numerical code. The in-plane wave propagation characteristics of honeycombs can be investigated with the proposed approach: approximate phase velocities can be calculated from the equations of motion for the low-frequency modes and compared with the exact values obtained through a Fourier analysis of the unit cell.
5

Starosvetsky, Yuli, e Alexander F. Vakakis. "Nonlinear Dynamics of Granular Chains". In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29208.

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We study strongly nonlinear traveling waves in one-dimensional granular chains with no pre-compression. We directly study the discrete, strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multi-hump traveling wave solutions with arbitrary wavelengths. We develop systematic semi–analytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wavenumber) and energy. Our findings indicate that homogeneous granular chains possess complex nonlinear dynamics, including the capacity for intrinsic nonlinear energy transfer.
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LIU, XIN, BO PENG e WENBIN YU. "MULTISCALE MODELING OF THE EFFECTIVE THERMAL CONDUCTIVITY OF 2D WOVEN COMPOSITES BY MECHANICS OF STRUCTURE GENOME AND NEURAL NETWORKS". In Thirty-sixth Technical Conference. Destech Publications, Inc., 2021. http://dx.doi.org/10.12783/asc36/35936.

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A data-driven multiscale modeling approach is developed to predict the effective thermal conductivity of two-dimensional (2D) woven composites. First, a two-step homogenization approach based on mechanics of structure genome (MSG) is developed to predict effective thermal conductivity. The accuracy and efficiency of the MSG model are compared with the representative volume element (RVE) model based on three-dimensional (3D) finite element analysis (FEA). Then, the simulation data is generated by the MSG model to train neural network models to predict the effective thermal conductivity of three 2D woven composites. The neural network models have mixed input features: continuous input (e.g., fiber volume fraction and yarn geometries) and discrete input (e.g., weave patterns). Moreover, the neural network models are trained with the normalized features to enable reusability. The results show that the developed data-driven models provide an ultra-efficient yet accurate approach for the thermal design and analysis of 2D woven composites.
7

D'Addetta, Gian Antonio, Ekkehard Ramm, Stefan Diebels e Wolfgang Ehlers. "Homogenization for Particle Assemblies". In Third International Conference on Discrete Element Methods. Reston, VA: American Society of Civil Engineers, 2002. http://dx.doi.org/10.1061/40647(259)46.

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Eliáš, J., e G. Cusatis. "Homogenization of mesoscale discrete model for poroelasticity". In 16th edition of the International Conference on Computational Plasticity. CIMNE, 2021. http://dx.doi.org/10.23967/complas.2021.037.

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Pucillo, Giovanni Pio, Antonio De Iorio, Stefano Rossi e Mario Testa. "On the Effects of the USP on the Lateral Resistance of Ballasted Railway Tracks". In 2018 Joint Rail Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/jrc2018-6204.

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From the advent of high-speed (HS) railways and with increasing traffic-induced loads transmitted to the superstructure, maintenance costs due to track geometry degradation have become a crucial problem for researchers and railway administrations. Moreover, the operations of ballast renewal, track tamping, and track re-alignment, that are indispensable to guarantee a good track geometry, have dramatic effects on the tie-ballast lateral resistance, which in turn reduce the track flexural strength in the lateral plane and increase the proneness of railway tracks made of continuous welded rails (CWR) to experience either progressive lateral shift of the track panel or thermal track buckling phenomena. To restore proper values of the tie-ballast lateral resistance, railway technicians either impose a speed reduction or compact the ballast bed mechanically by mean of the dynamic track stabilizing machines. Recently, elastic elements in railway tracks are receiving more and more attention due to their ability to reduce track geometry degradation and to attenuate noise and vibrations. Under Tie Pads, or Under Sleeper Pads (USP), guarantee better homogenization of the track vertical stiffness and have received more attention due to their ability to reduce maintenance costs. Most published studies focused their attention to USPs’ attitude to improve track performances in terms of dynamic impact force mitigation and track quality improvement; however, with few exceptions, no available literature exists on lateral resistance of ballasted track with USP, and some question still remains whether or not the lateral resistance is improved by USP. In this study, the experimental results of about 40 lateral resistance tests carried out in situ are reported and discussed. The tests were performed with the Discrete Cut Panel Pull Test (DCPPT) technique on three type of concrete ties, with and without USP; each type of tie and the related track conditions (ballast thickness, subgrade thickness and composition, shoulder width, ballast wall, etc.) were representative of specific track conditions, namely traditional tracks, high-speed lines and gallery. The tests were carried out in loaded and unloaded track conditions, in compacted and just-laid track conditions. In compacted ballast conditions the peak lateral resistance due to USPs can increase up to 20% — depending on the material used — and this variation is almost constant in the bedding modulus range considered in this study, which was quite well representative of typical static bedding modulus values of actual USPs. Even higher advantages seem to be achievable with softer USPs in weak or just-tamped ballast conditions.
10

Cellier, François E. "Combined continuous/discrete simulation". In the 18th conference. New York, New York, USA: ACM Press, 1986. http://dx.doi.org/10.1145/318242.318256.

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Rapporti di organizzazioni sul tema "Continuous or discrete homogenization":

1

De Alfaro, Luca, e Zohar Manna. Continuous Verification by Discrete Reasoning,. Fort Belvoir, VA: Defense Technical Information Center, settembre 1994. http://dx.doi.org/10.21236/ada324421.

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Kaliski, Martin E. Asynchronous Discrete Control of Continuous Processes. Fort Belvoir, VA: Defense Technical Information Center, febbraio 1986. http://dx.doi.org/10.21236/ada174525.

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Greenberg, J. M. Discrete and continuous models of conservation laws. Office of Scientific and Technical Information (OSTI), agosto 1996. http://dx.doi.org/10.2172/286179.

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Swiler, Laura Painton, Patricia Diane Hough, Peter Qian, Xu Xu, Curtis B. Storlie e Herbert K. H. Lee. Surrogate models for mixed discrete-continuous variables. Office of Scientific and Technical Information (OSTI), agosto 2012. http://dx.doi.org/10.2172/1055621.

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Lee, Edward A. Constructive Models of Discrete and Continuous Physical Phenomena. Fort Belvoir, VA: Defense Technical Information Center, febbraio 2014. http://dx.doi.org/10.21236/ada604845.

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Bilovska, Natalia. HYPERTEXT: SYNTHESIS OF DISCRETE AND CONTINUOUS MEDIA MESSAGE. Ivan Franko National University of Lviv, marzo 2021. http://dx.doi.org/10.30970/vjo.2021.50.11104.

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In the article we interpret discrete and continuous message as interrupted and constant, limited and continual text, which has specific features and a number of differences between traditional (one-dimensional) text and hypertext (multidimensional). The purpose of this study is to define the concept of “hypertext”, consideration of its characteristics and features of the structure, similarities and differences with the traditional text, including the message in the media and communication. To achieve the goal of the study, we used a number of methods typical of journalism. Empirical analysis enabled a generalized description of the subject of study, which allowed to know it as a phenomenon. With the help of generalization the characteristic and specific regularities and principles of hypertext were studied. The system method is used to identify the dependence of each element of hypertext on its place in the text system as a whole. The retrospective method helped to understand the preconditions for the emergence of hypertext, to trace the dynamics of its development. General scientific methods (analysis, synthesis, induction, deduction) made it possible to formulate the conclusions of the study. Thanks to hypertext and the hypertext systems, the concept of virtual reality has gained tangible meaning. In hypertext space, virtuality organically complements reality. The state of virtuality, in this case, becomes the concept of hyperreality, and all this merges into a single whole in the space of computer text. Due to its volume and multidimensionality, hypertext can arouse scientific interest as an interdisciplinary discipline. In today’s world, the phenomenon of hypertext has been the subject of numerous discussions, conferences and research in the field of social communications, linguistics and psychology. Today, a significant number of organizations conduct large-scale research based on the concepts of hypertext associations and associative navigation.
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Parzen, Emanuel. Unification of Statistical Methods for Continuous and Discrete Data. Fort Belvoir, VA: Defense Technical Information Center, maggio 1990. http://dx.doi.org/10.21236/ada224307.

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Cambanis, Stamatis, e Elias Masry. Performance of Discrete-Time Predictors of Continuous-Time Stationary Processes. Fort Belvoir, VA: Defense Technical Information Center, dicembre 1985. http://dx.doi.org/10.21236/ada166231.

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Bauman, Lara. New methods of uncertainty quantification for mixed discrete-continuous variable models. Office of Scientific and Technical Information (OSTI), giugno 2013. http://dx.doi.org/10.2172/1090213.

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Morrison, W. N., e R. Mendelsohn. A discrete-continuous choice model of climate change impacts on energy. Office of Scientific and Technical Information (OSTI), settembre 1998. http://dx.doi.org/10.2172/656514.

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