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Journal articles on the topic 'Continuous or discrete homogenization'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Gottwald, Georg A., and Ian Melbourne. "Homogenization for deterministic maps and multiplicative noise." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2156 (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

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2

Rasskazov, S. V., T. A. Yasnygina, I. S. Chuvashova, et al. "Pb-isotope Systematics of Bitumens, Kerogens, and Oils: from Isochronous and Discrete Sources to Extended Trends of Global Components." Geology and Environment 4, no. 4 (2024): 165–99. https://doi.org/10.26516/2541-9641.2024.4.165.

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The paper presents a review of Pb isotope data on bitumens, kerogens, and oils. The diagrams of Pb isotopes distinguish isochron families, discrete clusters, and continuous extended trends of data points. Arguments are given in favor of Pb isotopic homogenization with the output of isochron Pb–Pb dating under hydrothermal conditions during lead separation from uranium into ore minerals simultaneously with the enrichment of bitumen with uranium. From families of data points of oils and kerogen, the Pb isotope diagrams reveal discreteness of source components that have not undergone general Pb i

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3

Nassar, H., A. Lebée, and 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, no. 2197 (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 diffe

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4

Wei, Nan, Hongling Ye, Xing Zhang, Jicheng Li, and Boshuai Yuan. "Vibration Characteristics Research of Sandwich Structure with Octet-truss Lattice Core." Journal of Physics: Conference Series 2125, no. 1 (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 radiu

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5

Zona, Renato, and Vincenzo Minutolo. "Elastic to Plastic Lattice Structure Homogenization via Finite Element Limit Analysis." Symmetry 17, no. 7 (2025): 1120. https://doi.org/10.3390/sym17071120.

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This work focuses on characterizing structured metamaterials by assessing their elastic law and ultimate strength using finite elements and limit analysis applied to a representative volume element. The elastic and plastic behavior of a reference geometry—the octet truss lattice—is obtained by calculating the response of the representative volume element subjected to prescribed tensor strain bases, namely pure normal strain and pure shear, along the cube symmetry directions. The geometry of the body centered cubic and pure cubic phases of the representative volume element has been analyzed, hi

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6

Gomes, Diogo A., and Xianjin Yang. "The Hessian Riemannian flow and Newton’s method for effective Hamiltonians and Mather measures." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (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.

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7

Rallu, Antoine, and Claude Boutin. "Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions." Mathematics 12, no. 12 (2024): 1844. http://dx.doi.org/10.3390/math12121844.

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This paper deals with the long-wavelength behaviour of a Euler beam periodically supported by co-located rotation and compression springs. An asymptotic homogenization method is applied to derive the several macroscopic models according to the stiffness contrasts between the elastic supports and the beam. Effective models of differential order two or four are obtained, which can be merged into a single unified model whose dispersion relations at long and medium wavelengths fit those derived by Floquet-Bloch. Moreover, the essential role of rotation supports is clearly evidenced. A mixed "discr

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8

Josnin, Jean-Yves, Séverin Pistre, and 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, no. 10 (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-Chapt

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9

Forest, Samuel, David McDowell, Stefan Müller, and Ewald Werner. "Mechanics of Materials: Multiscale Design of Advanced Materials and Structures." Oberwolfach Reports 21, no. 1 (2024): 657–730. http://dx.doi.org/10.4171/owr/2024/11.

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Materials can now be designed and architectured like structural components for targeted mechanical and physical properties. Structures and microstructures should not be studied independently and their design will benefit from a multiscale approach combining nonlinear continuum mechanics approaches and physical descriptions of elasticity, viscoplasticity, phase transformations and damage of microstructures, at various scales. The aim of the workshop was to gather outstanding junior and senior researchers in the various branches of mathematics, physics and engineering sciences suited to address

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10

Amaro-Mellado, José Lázaro, and Dieu Tien Bui. "GIS-Based Mapping of Seismic Parameters for the Pyrenees." ISPRS International Journal of Geo-Information 9, no. 7 (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 compila

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11

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

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12

Etoughe, M. Betoue, and G. Panasenko. "Partial homogenization of discrete models." Applicable Analysis 87, no. 12 (2008): 1425–42. http://dx.doi.org/10.1080/00036810802378638.

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13

Braides, Andrea, Valeria Chiadò Piat, and Andrey Piatnitski. "Homogenization of Discrete High-Contrast Energies." SIAM Journal on Mathematical Analysis 47, no. 4 (2015): 3064–91. http://dx.doi.org/10.1137/140975668.

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14

Caillerie, Denis, Ayman Mourad, and Annie Raoult. "Discrete Homogenization in Graphene Sheet Modeling." Journal of Elasticity 84, no. 1 (2006): 33–68. http://dx.doi.org/10.1007/s10659-006-9053-5.

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15

Ricker, Sarah, Andreas Menzel, and Paul Steinmann. "Towards the computational homogenization of discrete microstructures." PAMM 7, no. 1 (2007): 4080021–22. http://dx.doi.org/10.1002/pamm.200700583.

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16

Gladbach, Peter, and Eva Kopfer. "Stochastic homogenization of dynamical discrete optimal transport." Journal of Mathematical Analysis and Applications 553, no. 2 (2026): 129883. https://doi.org/10.1016/j.jmaa.2025.129883.

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17

NGUYEN, VINH PHU, MARTIJN STROEVEN, and LAMBERTUS JOHANNES SLUYS. "MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS." Journal of Multiscale Modelling 03, no. 04 (2011): 229–70. http://dx.doi.org/10.1142/s1756973711000509.

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This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are descri

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18

PANASENKO, GRIGORY. "THE PARTIAL HOMOGENIZATION: CONTINUOUS AND SEMI-DISCRETIZED VERSIONS." Mathematical Models and Methods in Applied Sciences 17, no. 08 (2007): 1183–209. http://dx.doi.org/10.1142/s0218202507002248.

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The partial homogenization is a new method for the treatment of the boundary layers in the homogenization theory. It keeps the initial formulation near the boundary, passes to the high order homogenization at some distance from the boundary and prescribes the asymptotically precise junction conditions between the homogenized and the heterogeneous models at the interface. This method is related to the method of asymptotic partial domain decomposition MAPDD (see G. Panasenko, Method of asymptotic partial decomposition of domain, Math. Mod. Meth. Appl. Sci.8 (1998) 139–156). The partial homogeniz

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19

Kwon, Y. W., and C. Manthena. "Homogenization technique of discrete atoms into smeared continuum." International Journal of Mechanical Sciences 48, no. 12 (2006): 1352–59. http://dx.doi.org/10.1016/j.ijmecsci.2006.07.014.

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20

BRAIDES, ANDREA, and MARGHERITA SOLCI. "INTERFACIAL ENERGIES ON PENROSE LATTICES." Mathematical Models and Methods in Applied Sciences 21, no. 05 (2011): 1193–210. http://dx.doi.org/10.1142/s0218202511005295.

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In this paper we prove a homogenization theorem for interfacial discrete energies defined on an a-periodic Penrose tiling in ℝ2. A general result on the homogenization of surface energies cannot be directly adapted to this case; the existence of the limit interfacial energy is therefore proved by showing some refined "quasi-periodic" properties of the tilings.

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21

Ali, Mohamad Hasan, and Julius M. Zelmanowitz. "Discrete Implies Continuous." Journal of Algebra 183, no. 1 (1996): 186–92. http://dx.doi.org/10.1006/jabr.1996.0213.

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22

STEFANOU, IOANNIS, and JEAN SULEM. "THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES." Journal of Multiscale Modelling 02, no. 03n04 (2010): 217–34. http://dx.doi.org/10.1142/s1756973710000424.

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The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogeni

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23

Tollenaere, H., and D. Caillerie. "Continuous modeling of lattice structures by homogenization." Advances in Engineering Software 29, no. 7-9 (1998): 699–705. http://dx.doi.org/10.1016/s0965-9978(98)00034-9.

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24

Neukamm, Stefan, Mathias Schäffner, and Anja Schlömerkemper. "Stochastic Homogenization of Nonconvex Discrete Energies with Degenerate Growth." SIAM Journal on Mathematical Analysis 49, no. 3 (2017): 1761–809. http://dx.doi.org/10.1137/16m1097705.

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25

Dos Reis, F., and J. F. Ganghoffer. "Equivalent mechanical properties of auxetic lattices from discrete homogenization." Computational Materials Science 51, no. 1 (2012): 314–21. http://dx.doi.org/10.1016/j.commatsci.2011.07.014.

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26

Alfaro, M. V. Cid, A. S. J. Suiker, C. V. Verhoosel, and R. de Borst. "Computational homogenization of discrete fracture in fibre-epoxy systems." International Journal of Material Forming 2, S1 (2009): 931–34. http://dx.doi.org/10.1007/s12289-009-0593-7.

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27

Xia, Yuanqing, Zhihong Deng, Li Li, and Xiumei Geng. "A new continuous-discrete particle filter for continuous-discrete nonlinear systems." Information Sciences 242 (September 2013): 64–75. http://dx.doi.org/10.1016/j.ins.2013.04.030.

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28

Bryantsev, P. Yu, V. S. Zolotorevskiy, and V. K. Portnoy. "The Effect of Heat Treatment and Mn, Cu and Cr Additions on the Structure of Ingots of Al-Mg-Si-Fe Alloys." Materials Science Forum 519-521 (July 2006): 401–6. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.401.

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Phase transformations in 6XXX alloys with Mn, Cu and Cr additions have been studied in the process of homogenization annealing at different temperatures. The continuous cooling transformation diagrams of decomposition of solid solution during the cooling of ingots from the homogenization temperature have been plotted. The effect of the cooling rate after homogenization on the properties of ingots during extrusion has been studied.

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29

Fichtner, Andreas, and Shravan M. Hanasoge. "Discrete wave equation upscaling." Geophysical Journal International 209, no. 1 (2017): 353–57. http://dx.doi.org/10.1093/gji/ggx016.

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Abstract We present homogenization technique for the uniformly discretized wave equation, based on the derivation of an effective equation for the low-wavenumber component of the solution. The method produces a down-sampled, effective medium, thus making the solution of the effective equation less computationally expensive. Advantages of the method include its conceptual simplicity and ease of implementation, the applicability to any uniformly discretized wave equation in 1-D, 2-D or 3-D, and the absence of any constraints on the medium properties. We illustrate our method with a numerical exa

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30

Morduchow, Morris. "Discrete and Continuous Compounding." American Mathematical Monthly 92, no. 10 (1985): 734. http://dx.doi.org/10.2307/2323232.

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31

Maksimov, Vladimir Petrovich. "Continuous-discrete dynamic models." Ufimskii Matematicheskii Zhurnal 13, no. 3 (2021): 95–103. http://dx.doi.org/10.13108/2021-13-3-95.

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32

AKATSUKA, Takeaki, Nobuo FURUMATSU, and Hirokazu NISHITANI. "Combined Continuous-Discrete Simulation." Transactions of the Society of Instrument and Control Engineers 34, no. 3 (1998): 247–53. http://dx.doi.org/10.9746/sicetr1965.34.247.

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33

Morduchow, Morris. "Discrete and Continuous Compounding." American Mathematical Monthly 92, no. 10 (1985): 734–35. http://dx.doi.org/10.1080/00029890.1985.11971726.

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34

Bowins, Brad. "Depression: Discrete or Continuous?" Psychopathology 48, no. 2 (2014): 69–78. http://dx.doi.org/10.1159/000366504.

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35

Böckenholt, Ulf, Eric Bradlow, Wes Hutchinson, et al. "Continuous and Discrete Variables." Journal of Consumer Psychology 10, no. 1-2 (2001): 37–53. http://dx.doi.org/10.1207/s15327663jcp1001&2_04.

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36

Hall, Randolph W. "Discrete models/continuous models." Omega 14, no. 3 (1986): 213–20. http://dx.doi.org/10.1016/0305-0483(86)90040-x.

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37

Droździel, Paweł, Tetiana Vitenko, Viktor Voroshchuk, Sergiy Narizhnyy, and Olha Snizhko. "Discrete-Impulse Energy Supply in Milk and Dairy Product Processing." Materials 14, no. 15 (2021): 4181. http://dx.doi.org/10.3390/ma14154181.

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The efficient use of supplied energy is the basis of the discrete-impulse energy supply (DIES) concept. In order to explore the possibility of using DIES to intensify the hydromechanical processes, the emulsification of milk fat (homogenization of milk, preparation of spreads) and, in particular, the processing of cream cheese masses, were studied. Whole non-homogenized milk, fat emulsions, and cream cheese mass were the object of investigation. To evaluate the efficiency of milk homogenization, the homogenization coefficient change was studied, which was determined by using the centrifugation

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38

Tassa, Tamir. "Homogenization with multiple scales." Asymptotic Analysis 20, no. 1 (1999): 61–96. https://doi.org/10.3233/asy-1999-344.

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We study the homogenization of oscillatory solutions of partial differential equations with a multiple number of small scales. We consider a variety of problems – nonlinear convection–diffusion equations with oscillatory initial and forcing data, the Carleman model for the discrete Boltzman equations, and two‐dimensional linear transport equations with oscillatory coefficients. In these problems, the initial values, force terms or coefficients are oscillatory functions with a multiple number of small scales – $f(x,{x}/{{\varepsilon}_1},\ldots,{x}/{{\varepsilon}_n})$ . The essential question in

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39

Stein, Oliver, Jan Oldenburg, and Wolfgang Marquardt. "Continuous reformulations of discrete–continuous optimization problems." Computers & Chemical Engineering 28, no. 10 (2004): 1951–66. http://dx.doi.org/10.1016/j.compchemeng.2004.03.011.

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40

Damlamian, Alain, and Klas Pettersson. "Homogenization of oscillating boundaries." Discrete and Continuous Dynamical Systems 23, no. 1/2 (2008): 197–219. http://dx.doi.org/10.3934/dcds.2009.23.197.

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41

Frénod, Emmanuel. "Homogenization-based numerical methods." Discrete and Continuous Dynamical Systems - Series S 9, no. 5 (2016): i—ix. http://dx.doi.org/10.3934/dcdss.201605i.

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42

Braides, Andrea, Marco Cicalese, and Matthias Ruf. "Continuum limit and stochastic homogenization of discrete ferromagnetic thin films." Analysis & PDE 11, no. 2 (2018): 499–553. http://dx.doi.org/10.2140/apde.2018.11.499.

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43

OKUMURA, Dai, Nobutada OHNO, and Yoshihiro KATAGIRI. "Formulation of a Homogenization Theory for Discrete Dislocation Dynamics Analysis." Journal of the Society of Materials Science, Japan 59, no. 2 (2010): 149–56. http://dx.doi.org/10.2472/jsms.59.149.

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44

Lemarchand, C., B. Devincre, and L. P. Kubin. "Homogenization method for a discrete-continuum simulation of dislocation dynamics." Journal of the Mechanics and Physics of Solids 49, no. 9 (2001): 1969–82. http://dx.doi.org/10.1016/s0022-5096(01)00026-6.

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45

Goda, Ibrahim, Mohamed Assidi, and Jean-François Ganghoffer. "Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization." Journal of the Mechanics and Physics of Solids 61, no. 12 (2013): 2537–65. http://dx.doi.org/10.1016/j.jmps.2013.07.014.

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46

Arenz, Christian, Daniel Burgarth, and Robin Hillier. "Dynamical decoupling and homogenization of continuous variable systems." Journal of Physics A: Mathematical and Theoretical 50, no. 13 (2017): 135303. http://dx.doi.org/10.1088/1751-8121/aa6017.

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47

Zhao, Hongwei, Kai Long, and Z. D. Ma. "Homogenization Topology Optimization Method Based on Continuous Field." Advances in Mechanical Engineering 2 (January 2010): 528397. http://dx.doi.org/10.1155/2010/528397.

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48

Mazzola, Claudio. "Can discrete time make continuous space look discrete?" European Journal for Philosophy of Science 4, no. 1 (2013): 19–30. http://dx.doi.org/10.1007/s13194-013-0072-3.

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49

Zengin, Huseyin, Yunus Turen, Hayrettin Ahlatci, Yavuz Sun, and Ismail Hakkı Kara. "Microstructure and Corrosion Properties of Homogenized Mg-4Zn-1La Magnesium Alloy." Key Engineering Materials 750 (August 2017): 118–23. http://dx.doi.org/10.4028/www.scientific.net/kem.750.118.

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In this study, microstructure and corrosion behaviour of homogenized Mg-4Zn-1La magnesium alloy was investigated. Mg-4Zn-1La alloy was produced by low-pressure die casting method. Homogenization treatments were performed at 350 °C and 400 °C for 12, 18, 24 and 48 hours, followed by rapid cooling in water at room temperature. Microstructure characterizations showed that La addition led to a formation of semi-continuous network structure and islands of second phases which identified as T-phase (Mg7Zn3RE). A significant amount of second phase dissolution and an increase in a-Mg grain size with in

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50

Wang, Jiaolong, Dexin Zhang, and Xiaowei Shao. "New version of continuous–discrete cubature Kalman filtering for nonlinear continuous–discrete systems." ISA Transactions 91 (August 2019): 174–83. http://dx.doi.org/10.1016/j.isatra.2019.01.016.

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