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Dissertations / Theses on the topic 'Homogenization'
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Yan, Chang (Karen). "On homogenization and de-homogenization of composite materials /." Philadelphia, Pa. : Drexel University, 2003. http://dspace.library.drexel.edu/handle/1860/246.
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Jennings, Theodore Lee. "Ingot homogenization." Thesis, Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/11240.
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Essel, Emmanuel Kwame. "Homogenization of Reynolds equations." Licentiate thesis, Luleå : Luleå University of Technology, 2007. http://epubl.ltu.se/1402-1757/2007/30/.
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Persson, Jens. "Selected Topics in Homogenization." Doctoral thesis, Mittuniversitetet, Institutionen för teknik och hållbar utveckling, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-16230.
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The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. In order to achieve homogenization results for these problems we study and enrich the theory of two-scale convergence and its kins. In particular the concept of very weak two-scale convergence and generalizations is developed, and we study an application of this convergence mode where it is employed to detect scales of heterogeneity.Huvudsakligt fokus i avhandlingen ligger på homogeniseringen av vissa elliptiska och paraboliska problem. Mer precist så homogeniserar vi: ickeperiodiska linjära elliptiska problem i två dimensioner med homotetisk skalning; två typer av evolutionsmultiskaliga linjära paraboliska problem, en med två mikroskopiska skalor i både rum och tid där de senare ges i form av en tvåparameterfamilj, och en med två mikroskopiska skalor i rum och tre i tid som ges i form av fixa potensfunktioner; samt, slutligen, evolutionsmultiskaliga monotona paraboliska problem med en mikroskopisk skala i rum och ett godtyckligt antal i tid som inte är begränsade till att vara givna i form av potensfunktioner. För att kunna uppnå homogeniseringsresultat för dessa problem så studerar och utvecklar vi teorin för tvåskalekonvergens och besläktade begrepp. Speciellt så utvecklar vi begreppet mycket svag tvåskalekonvergens med generaliseringar, och vi studerar en tillämpningav denna konvergenstyp där den används för att detektera förekomsten av heterogenitetsskalor.
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Manson, Charles. "Some topics in homogenization." Thesis, University of Warwick, 2010. http://wrap.warwick.ac.uk/34600/.
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This thesis is mainly concerned with solving a new type of periodic homogenization problem. A solution of removing the Diophantine hypothesis on the homogenization problem where the interface sits at an irrational angle to the period is attempted but is not yet complete. As an aside an oscillator problem is analyzed using the corrector based approach of homogenization.
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Strömqvist, Martin. "Homogenization in Perforated Domains." Doctoral thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-147702.
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Homogenization theory is the study of the asymptotic behaviour of solutionsto partial differential equations where high frequency oscillations occur.In the case of a perforated domain the oscillations are due to variations in thedomain of the equation. The four articles that constitute this thesis are devotedto obstacle problems in perforated domains. Paper A treats an optimalcontrol problem where the objective is to control the solution to the obstacleproblem by the choice of obstacle. The optimal obstacle in the perforated domain,as well as its homogenized limit, are characterized in terms of certainauxiliary problems they solve. In papers B,C and D the authors solve homogenizationproblems in a perforated domain where the perforation is definedas the intersection between a periodic perforation and a hyper plane. Thetheory of uniform distribution is an indespensible tool in the analysis of theseproblems. Paper B treats the obstacle problem for the Laplace operator andthe authors use correctors to derive a homogenized equation. Paper D is ageneralization of paper B to the p-Laplacian. The authors employ capacitytechniques which are well adapted to the problem. In Paper C the obstaclevaries on the same scale as the perforations. In this setting the authorsemploy the theory of Gamma-convergence to prove a homogenization result.QC 20140703
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Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.
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In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases.
The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales
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Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.
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Dissertation for the Degree of Doctor of Philosophy in MathematicsFundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA
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Rozehnalová, Petra. "Homogenization in Perforated Domains." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2016. http://www.nusl.cz/ntk/nusl-234696.
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Numerické řešení matematických modelů popisujících chování materiálů s jemnou strukturou (kompozitní materiály, jemně perforované materiály, atp.) obvykle vyžaduje velký výpočetní výkon. Proto se při numerickém modelování původní materiál nahrazuje ekvivalentním materiálem homogenním. V této práci je k nalezení homogenizovaného materiálu použita dvojškálová konvergence založena na tzv. rozvinovacím operátoru (anglicky unfolding operator). Tento operátor poprvé použil J. Casado-Díaz. V disertační práci je operátor definován jiným způsobem, než jak uvádí původní autor. To dovoluje pro něj dokázat některé nové vlastnosti. Analogicky je definován operátor pro funkce definované na perforovaných oblastech a jsou dokázány jeho vlastnosti. Na závěr je rozvinovací operátor použit k nalezení homogenizovaného řešení speciální skupiny diferenciálních problémů s integrální okrajovou podmínkou. Odvozené homogenizované řešení je ilustrováno na numerických experimentech.
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Hassani, B. "Homogenization and topological structural optimization." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.493797.
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Nassar, Hussein. "Elastodynamic homogenization of periodic media." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1151/document.
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La problématique récente de la conception de métamatériaux a renouvelé l'intérêt dans les théories de l'homogénéisation en régime dynamique. En particulier, la théorie de l'homogénéisation élastodynamique initiée par J.R. Willis a reçu une attention particulière suite à des travaux sur l'invisibilité élastique. La présente thèse reformule la théorie de Willis dans le cas des milieux périodiques, examine ses implications et évalue sa pertinence physique au sens de quelques ``conditions d'homogénéisabilité'' qui sont suggérées. En se basant sur les résultats de cette première partie, des développements asymptotiques approximatifs de la théorie de Willis sont explorés en relation avec les théories à gradient. Une condition nécessaire de convergence montre alors que toutes les branches optiques de la courbe de dispersion sont omises quand des développements asymptotiques de Taylor de basse fréquence et de longue longueur d'onde sont déployés. Enfin, une nouvelle théorie de l'homogénéisation est proposée. On montre qu'elle généralise la théorie de Willis et qu'elle l'améliore en moyenne fréquence de sorte qu'on retrouve certaines branches optiques omises auparavant. On montre également que le milieu homogène effectif défini par la nouvelle théorie est un milieu généralisé dont les champs satisfont une version élastodynamique généralisée du lemme de Hill-MandelThe recent issue of metamaterials design has renewed the interest in homogenization theories under dynamic loadings. In particular, the elastodynamic homogenization theory initiated by J.R. Willis has gained special attention while studying elastic cloaking. The present thesis reformulates Willis theory for periodic media, investigates its outcome and assesses its physical suitability in the sense of a few suggested ``homogenizability conditions''. Based on the results of this first part, approximate asymptotic expansions of Willis theory are explored in connection with strain-gradient media. A necessary convergence condition then shows that all optical dispersion branches are lost when long-wavelength low-frequency Taylor asymptotic expansions are carried out. Finally, a new homogenization theory is proposed to generalize Willis theory and improve it at finite frequencies in such a way that selected optical branches, formerly lost, are recovered. It is also proven that the outcome of the new theory is an effective homogeneous generalized continuum satisfying a generalized elastodynamic version of Hill-Mandel lemma
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Zhuge, Jinping. "Boundary Layers in Periodic Homogenization." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/64.
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The boundary layer problems in periodic homogenization arise naturally from the quantitative analysis of convergence rates. Formally they are second-order linear elliptic systems with periodically oscillating coefficient matrix, subject to periodically oscillating Dirichelt or Neumann boundary data. In this dissertation, for either Dirichlet problem or Neumann problem, we establish the homogenization results and obtain the nearly sharp convergence rates, provided the domain is strictly convex. Also, we show that the homogenized boundary data is in W1,p for any p ∈ (1,∞), which implies the Cα-Hölder continuity for any α ∈ (0,1).
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Törnqvist, Julia. "Electromagnetic Homogenization-simulations of Materials." Thesis, Uppsala universitet, Elektricitetslära, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-395866.
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This thesis aims to determine the distribution of the relative permittivity for random mixtures of material using electromagnetic simulations. The algorithm used in the simulations is the FDTD method which solves Maxwell's equations numerically in the time-domain. The material is modeled as randomly shaped particles with radius 12 ± 10 micrometre in x- and y-direction and radius 3 ± 1 micrometre in zdirection. The scattering parameters from the transmitted and reflected electric field when a plane wave interacts with the material are measured. The relative permittivity is determined from the scattering parameters using the iterative Baker-Jarvis method. The simulations shows that both the distribution and the value of the relative permittivity is low when the particles have non conducting layers to force interruptions to prevent percolation, a conducting path between the particles. The most important result is of the kind where the simulations do not have any boundaries to prevent percolation. These simulations reflects how the relative permittivity distributes in real measurements. It is established that the value of the relative permittivity has a large distribution and also that percolation occurs because of the periodic structures.
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Lobkova, Tatiana. "Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains." Licentiate thesis, Mittuniversitetet, Avdelningen för kvalitetsteknik, maskinteknik och matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-30683.
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This thesis is based on four papers. The main focus is on homogenization of selected parabolic problems with time oscillations, and hyperbolic-parabolic problems without time oscillations. The approaches are prepared by means of certain methods, such as two-scale convergence, multiscale convergence and evolution multiscale convergence. We also discuss further results on homogenization of evolution problems in perforated domains.Vid tidpunkten för försvar av avhandlingen var följande delarbeten opublicerade: delarbete 1 inskickat, delarbete 2 accepterat, delarbete 4 inskickat.
At the time of the defence the following papers were unpublished: paper 1 submitted, paper 2 accepted, paper 4 submitted.
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Fabricius, John. "Homogenization theory with applications in tribology." Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25720.
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Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficents. Many important problems in physics with one or several microscopic length scales give rise to this kind of equations. Hence there is a need for methods that enable an efficient treatment of such problems. To this end several homogenization techniques exist, ranging from the fairly abstract ones to those that are more oriented towards applications. This thesis is concerned with two such methods, namely the "asymptotic expansion method", also known as the "method of multiple scales", and multiscale convergence. The former method, sometimes referred to as the "engineering approach to homogenization" has, due to its versatility and intutive appeal, gained wide acceptance and popularity in the applied fields. However, it is not rigorous by mathematical standards. Multiscale convergence, introduced by Nguetseng in 1989, is a notion of weak convergence in Lp spaces that is designed to take oscillations into account. Although not the most general method around, multiscale convergence has become widely used by homogenizers because of its simplicity. In spite of its success, the multiscale theory is not yet sufficiently developed to be used in connection with certain nonlinear problems with several microscopic scales. In Paper A we extend some previously obtained results in multiscale convergence that enable us to homogenize a nonlinear problem with three scales. In Appendix to Paper A we present in more detail some results that were used in the proof of some of the main theorems in Paper A. Tribology is the science of bodies in relative motion interacting through a mechanical contact. An important aspect of tribology is to explain the principles of friction, lubrication and wear. Tribological phenomena are encountered everywhere in nature and technology and have a huge economical impact on society. An important example is that of two sliding solid surfaces interacting through a thin film of viscous fluid (lubricant). Hydrodynamic lubrication occurs when the pressure generated within the lubricant, through the viscosity of the fluid, is able to sustain an externally applied load. Many common bearings, e.g. journal bearings or slider bearings, operate according to this principle. As a branch of fluid dynamics, the mathematical foundations of lubrication theory are given by the Navier-Stokes equations, describing the motion of a viscous fluid. Because of the thin film assumption several simplifications are possible, leading to various reduced equations named after Osborne Reynolds, the founding father of lubrication theory. The Reynolds equation is used by engineers to compute the pressure distribution in various situations of thin film lubrication. For extremely thin films, it has been observed that the surface micro topography is an important factor in hydrodynamic performance. Hence it is important to understand the influence of surface roughness with small characteristic wavelength upon the pressure solution. Since the 1980s such problems have been increasingly studied by homogenization theory. The idea is to replace the original equation with a homogenized equation where the roughness effects are "averaged out". One problem consists of finding an algorithm that gives the homogenized equation. Another problem, consists of showing, by introducing the appropriate mathematical defintions, that the homogenized equation really is the correct one. Papers B and C investigate the effects of surface roughness by means of multiscale expansion of the pressure in various situations of hydrodynamic lubrication. Paper B, for which Paper A constitutes a rigorous basis, considers homogenization of the stationary Reynolds equation and roughness with two characteristic wavelengths. This leads to a multiscale problem and adds to the complexity of the homogenization process. To compare the homogenized solution to the solution of the unaveraged Reynolds equation, some numerical examples are also included. Paper C is devoted to homogenization of a variational principle which is a generalization of the unstationary Reynolds equation (both surfaces are rough). The advantage of adopting the calculus of variations viewpoint is that the recently introduced "variational bounds" can be computed. Bounds can be seen as a "cheap" alternative to computing the realtively costly homogenized solution. Several numerical examples are included to illustrate the utility of bounds.Godkänd; 2008; 20080905 (ysko)
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Tsandzana, Afonso Fernando. "Homogenization with applications in lubrication theory." Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18727.
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In this licentiate thesis we study some mathematical problems in hydrodynamic lubrication theory. It is composed of two papers (A and B) and a complementary appendix. Lubrication theory is devoted to fluid flow in thin domains. The main purpose of lubrication is to reduce friction and wear between two solid surfaces in relative motion. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation which describes the motion of viscous fluids. In thin domains several approximations are possible which leads to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict different important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field.In many practical situations the surface roughness amplitude and the film thickness are of the same order. Therefore, any realistic model should account for the effect of surface roughness. This implies that the mathematical modelling leads to partial differential equations with coefficients that will oscillate rapidly in space and time due to the relative motion of the surfaces. A direct numerical analysis is very difficult since an extremely fine mesh is required to describe the different scales. One method which has proved successful to handle such problems is to do some averaging (asymptotic analysis). The branch in mathematics which has been developed for this purpose is called homogenization.In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness ε and wavelength μ of the roughness tend to zero is analyzed and described. The results are obtained using the formal method of multiple scale expansion. The limit equation depends on how fast the two small parameters ε and μ go to zero relative to each other. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime).In paper B we present a mathematical model in hydrodynamic lubrication that takes into account cavitation (formation of air bubbles), surface roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness. A one-dimensional problem describing a step bearing is also solved explicitly and by numerical methods.Godkänd; 2014; 20140415 (afotsa); Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Afonso Fernando Tsandzana Ämne: Matematik/Mathematics Uppsats: Homogenization with Applications in Lubrication Theory Examinator: Professor Peter Wall, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Anders Holmbom, Mittuniversitetet, Östersund Tid: Onsdag den 11 juni 2014 kl 10.00 Plats: E231, Luleå tekniska universitet
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Chan, Yiu Mo Patton. "Laminated beam theory based on homogenization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0022/MQ50485.pdf.
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Ochieng, A., and MS Onyango. "Homogenization energy in a stirred tank." Elsevier, 2006. http://encore.tut.ac.za/iii/cpro/DigitalItemViewPage.external?sp=1000755.
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Mixing in stirred tanks influences conversion of reactants for fast reactions, and the efficiency of a mixing process can be determined from
the power consumption and mixing time, which are the two parameters that define homogenization energy. In this study, the computational fluid
dynamics (CFD) and laser Doppler velocimetry (LDV) techniques were employed to study the effect of the Rushton turbine bottom clearance
on the flow field, mixing time and power consumption in a stirred tank. Experimental and simulation studies were conducted in a tank with and
without a draft tube where a conductivity meter and decolourization methods were employed in validating the mixing time simulation results. A
good agreement between the experimental and simulation results for the flow field and mixing time was obtained. The results showed a reduction
in mixing time and power consumption at a low impeller clearance, with reference to the standard clearance, and a further reduction of the same
parameters was obtained for a system fitted with a draft tube. At the low clearance, there was an increase in mixing efficiency by 46%, for a system
without draft tube and 61% for that with the draft tube.
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Nguyen, Dang Van, Denis Grebenkov, Cyril Poupon, Bihan Denis Le, and Jing-Rebecca Li Li. "Effective diffusion tensor computed by homogenization." Diffusion fundamentals 18 (2013) 9, S. 1-6, 2013. https://ul.qucosa.de/id/qucosa%3A13716.
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The convergence of the long-time apparent diffusion tensor of diffusion magnetic resonance imaging (dMRI) to the effective diffusion tensor obtained by mathematical homogenization theory was considered for two-compartment geometric models containing non-elongated cells of general shapes. A numerical study was conducted in two and three dimensions to demonstrate this convergence as a function of the diffusion time.
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Onofrei, Daniel T. "Homogenization of an elastic-plastic problem." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-121632.
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Nguyen, Dang Van, Denis Grebenkov, Cyril Poupon, Bihan Denis Le, and Jing-Rebecca Li Li. "Effective diffusion tensor computed by homogenization." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184337.
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The convergence of the long-time apparent diffusion tensor of diffusion magnetic resonance imaging (dMRI) to the effective diffusion tensor obtained by mathematical homogenization theory was considered for two-compartment geometric models containing non-elongated cells of general shapes. A numerical study was conducted in two and three dimensions to demonstrate this convergence as a function of the diffusion time.
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Del, Toro Rosaria. "Dynamic homogenization of composite viscoelastic materials." Thesis, IMT Alti Studi Lucca, 2019. http://e-theses.imtlucca.it/276/1/DelToro_phdthesis.pdf.
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A non-local dynamic homogenization technique for the analysis
of a viscoelastic heterogeneous material which displays
a periodic microstructure is herein proposed. The asymptotic
expansion of the micro-displacement field in the transformed
Laplace domain allows obtaining, from the expression
of the micro-scale field equations, a set of recursive differential
problems defined over the periodic unit cell. Consequently,
the cell problems are derived in terms of perturbation
functions depending on the geometrical and physicalmechanical
properties of the material and its microstructural
heterogeneities. A down-scaling relation is formulated in a
consistent form, which correlates the microscopic to the macroscopic
transformed displacement field and its gradients through
the perturbation functions. Average field equations of infinite
order are determined by substituting the down-scale relation
into the micro-field equation. Based on a variational
approach, the macroscopic field equations of a non-local continuum
is delivered and the local and non-local overall constitutive
and inertial tensors of the homogenized continuum
are determined. The problem of wave propagation in case of
a bi-phase layered material with orthotropic phases and axis
of orthotropy parallel to the direction of layers is investigated
as an example. In such a case, the local and non-local overall
constitutive and inertial tensors are determined analytically
and the dispersion curves obtained from the non-local
homogenized model are analysed.
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Adegoke, Olutayo. "Homogenization of Precipitation Hardening Nickel Based Superalloys." Thesis, Högskolan Dalarna, Materialvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:du-11135.
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Allvac 718 Plus and Haynes 282 are relatively new precipitation hardening nickel based superalloys with good high temperature mechanical properties. In addition, the weldability of these superalloys enhances easy fabrication. The combination of high temperature capabilities and superior weldability is unmatched by other precipitation hardening superalloys and linked to the amount of the γ’ hardening precipitates in the materials. Hence, it is these properties that make Allvac 718 Plus and Haynes 282 desirable in the manufacture of hot sections of aero engine components. Studies show that cast products are less weldable than wrought products. Segregation of elements in the cast results in inhomogeneous composition which consequently diminishes weldability. Segregation during solidification of the cast products results in dendritic microstructure with the segregating elements occupying interdendritic regions. These segregating elements are trapped in secondary phases present alongside γ matrix. Studies show that in Allvac 718Plus, the segregating phase is Laves while in Haynes 282 the segregating phase is not yet fully determined. Thus, the present study investigated the effects of homogenization heat treatments in eliminating segregation in cast Allvac 718 Plus and Haynes 282. Paramount to the study was the effect of different homogenization temperatures and dwell time in the removal of the segregating phases. Experimental methods used to both qualify and quantify the segregating phases included SEM, EDX analysis, manual point count and macro Vickers hardness tests. Main results show that there is a reduction in the segregating phases in both materials as homogenization proceeds hence a disappearance of the dendritic structure. In Allvac 718 Plus, plate like structures is observed to be closely associated with the Laves phase at low temperatures and dwell times. In addition, Nb is found to be segregating in the interdendritic areas. The expected trend of increase in Laves as a result of the dissolution of the plate like structures at the initial stage of homogenization is only detectable for few cases. In Haynes 282, white and grey phases are clearly distinguished and Mo is observed to be segregating in interdendritic areas.
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Gloria, Antoine. "Qualitative and quantitative results in stochastic homogenization." Habilitation à diriger des recherches, Université des Sciences et Technologie de Lille - Lille I, 2012. http://tel.archives-ouvertes.fr/tel-00779306.
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The issue of establishing the status of nonlinear elasticity theory for rubber with respect to the point of view of polymer physics is at the heart of this manuscript. Our aim is to develop mathematical methods to describe, understand, and solve this multiscale problem. At the level of the polymer chains, rubber can be described as a network whose nodes represent the cross-links between the polymer chains. This network can be considered as the realization of some stochastic process. Given the free energy of the polymer network, we'd like to derive a continuum model as the characteristic length of the polymer chains vanishes. In mathematical terms, this process can be viewed as a hydrodynamic limit or as a discrete homogenization, depending on the nature of the free energy of the network. In view of the works by Treloar, by Flory, and by Rubinstein and Colby on polymer physics, and in view of the stochastic nature of the network, stochastic discrete homogenization seems to be the right tool for the analysis. Hence, in order to complete our program we need to understand the stochastic homogenization of discrete systems. Two features make the analysis rich and challenging from a mathematical perspective: the randomness and the nonlinearity of the problem. The achievement of this manuscript is twofold: - a complete and sharp quantitative theory for the approximation of homogenized coefficients in stochastic homogenization of discrete linear elliptic equations; - the first rigorous and global picture on the status of nonlinear elasticity theory with respect to polymer physics, which partially answers the question raised by Ball in his review paper on open problems in elasticity. Although the emphasis of this manuscript is put on discrete models for rubber, and more generally on the homogenization of discrete elliptic equations, we have also extended most of the results to the case of elliptic partial differential equations --- some of the results being even more striking in that case.
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Cui, Jiajia. "Nonzero depolarization volumes in electromagnetic homogenization studies." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/2437.
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The work of this thesis concerns depolarization regions in the homogenization of random, particulate composites. In conventional approaches to homogenization, the depolarization dyadics which represent the component phase particles are provided by the singularity of the corresponding dyadic Green function. Thereby, the component particles are effectively treated as vanishingly small, point-like entities. However, through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. In this thesis, depolarization regions of nonzero volume are considered. In order to estimate the constitutive parameters of homogenized composite materials (HCMs), the strong-property-fluctuation theory (SPFT) is implemented. This is done through a standard procedure involving the calculation of successive corrections to a preliminary ansatz, in terms of statistical cumulants of the spatial distribution of the component phase particles. The influence of depolarization regions of nonzero volume on the zeroth (and first), second and third order SPFT estimates of HCM constitutive parameters is investigated. Both linear and weakly nonlinear HCMs are considered.
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Kooreman, Gabriel. "Consistent hybrid diffusion-transport spatial homogenization method." Thesis, Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52950.
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Recent work by Yasseri and Rahnema has introduced a consistent spatial homogenization (CSH) method completely in transport theory. The CSH method can very accurately reproduce the heterogeneous flux shape and eigenvalue of a reactor, but at high computational cost. Other recent works for homogenization in diffusion or quasi-diffusion theory are accurate for problems with low heterogeneity, such as PWRs, but are not proven for more heterogeneous reactors such as BWRs or GCRs.
To address these issues, a consistent hybrid diffusion-transport spatial homogenization (CHSH) method is developed as an extension of the CSH method that uses conventional flux weighted homogenized cross sections to calculate the heterogeneous solution. The whole-core homogenized transport calculation step of the CSH method has been replaced with a whole- core homogenized diffusion calculation. A whole-core diffusion calculation is a reasonable replacement for transport because the homogenization procedure tends to smear out transport effects at the core level. The CHSH solution procedure is to solve a core-level homogenized diffusion equation with the auxiliary source term and then to apply an on-the-fly transport-based re-homogenization at the assembly level to correct the homogenized and auxiliary cross sections. The method has been derived in general geometry with continuous energy, and it is implemented and tested in fine group, 1-D slab geometry on controlled and uncontrolled BWR and HTTR benchmark problems. The method converges to within 2% mean relative error for all four configurations tested and has computational efficiency 2 to 4 times faster than the reference calculation.
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Gathier, Benjamin. "Multiscale strength homogenization : application to shale nanoindentation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43049.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2008.Includes bibliographical references (p. 236-246).
Shales are one of the most encountered materials in sedimentary basins. Because of their highly heterogeneous nature, their strength prediction for oil and gas exploitation engineering has long time been an enigma. In this thesis, we propose a two-scale non-linear procedure for the homogenization of their yield design strength properties, based on the Linear Comparison Composite Theory. At Level 0, the intrinsic friction of shales is captured via a cohesive-frictional strength criterion for the clay particles (Drucker-Prager). Level I is composed of a porous clay phase and Level II incorporates silt and quartz grains. Homogenization yields either an elliptical or an hyperbolc strength criterion, depending on the packing density of the porous clay phase. These criteria are employed in an original reverse algorithm of indentation hardness to develop hardness-packing density scaling relations that allow a separation of constituent properties and volume fraction and morphology parameters, including interface conditions between the porous clay matrix and the (rigid) silt inclusions. The application of this algorithm to 11 shale samples from the GeoGenome project data base allows us to identify: (i) an invariant value of the solid hardness of clay particles, which is independent of clay mineralogy, porosity, etc.; and (ii) shale independent scaling relations of the cohesion and of the friction coefficient with the mean clay packing density, which provides some evidence that the elementary building block of shale is a clay polycrystal. The use of these scaling relations in the Level II-homogenization provides a first-order model for the prediction of the macroscopic strength properties of shale, based on only two parameters that delineate shale's macroscopic diversity: clay packing density and silt inclusion volume fraction.
by Benjamin Gathier.
S.M.
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Chen, Ying Ph D. Massachusetts Institute of Technology. "Percolation and homogenization theories for heterogeneous materials." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44389.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008.Includes bibliographical references (p. 139-145).
Most materials produced by Nature and by human beings are heterogeneous. They contain domains of different states, structures, compositions, or material phases. How these different domains are distributed in space, or in other words, how they connect to one another, determines their macroscopic properties to a large degree, making the simple rule-of-mixtures ineffective in most cases. This thesis studies the macroscopic effective diffusion, diffusional creep, and elastic properties of heterogeneous grain boundary networks and composite solids, both theoretically and numerically, and explores the microstructure-property correlations focusing on the effects of microstructural connectivity (topology). We have found that the effects of connectivity can be effectively captured by a percolation threshold, a case-specific volume fraction at which the macroscopic effective property undergoes a critical transition, and a set of critical scaling exponents, which also reflect the universality class that the property belongs to. Using these percolation quantities together with the generalized effective medium theory, we are able to directly predict the effective diffusivity and effective diffusional creep viscosity of heterogeneous grain boundary networks to a fairly accurate degree. Diffusion in composite solids exhibits different percolation threshold and scaling behaviors due to interconnectivity at both edges and corners. Continuum elasticity suffers from this complexity as well, in addition to the complicating factor that each phase is always characterized by several independent elastic constants. These issues are each addressed in detail. In addition to studying all the above properties for a random distribution of grain boundaries or phases, we have also studied the effects of correlations in spatial distributions.
(cont.) This topic is especially important in materials science, because virtually no materials exhibit random phase distributions. We have examined the percolation of effective properties for correlated microstructures spanning between the random distribution and the perfectly periodic distribution. An important result of this work is new understanding about what correlations may be considered small, or inconsequential, to the percolation scaling behavior, and which are large or long-range, and lead to a loss of universality. Finally, a rigorous, and easy-to-use, analytical homogenization method is developed for periodic composite materials.
by Ying Chen.
Ph.D.
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Yan, Bing. "High Pressure Homogenization of Selected Liquid Beverages." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1471376403.
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Alkes, Helen. "Inverse Problem in Porous Medium Using Homogenization." DigitalCommons@USU, 1992. https://digitalcommons.usu.edu/etd/7127.
Full textAbstract:
The problem under consideration is that of obtaining a representation of the permeability of a porous medium which is heterogeneous and anisotropic from limited information. To solve this inverse problem we propose the use of two different pieces that work together. A simulated annealing algorithm is presented and coupled with an homogenization technique; together these solve the problem which was posed. Further, numerical simulation results are presented illustrating the use of the simulated annealing algorithm as well as a coupling with the homoginization technique. This study illustrates that the performance of the annealing algorithm is enhanced with usage of homogenization.
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Covezzi, Federica <1990>. "Homogenization of nonlinear composites for multiscale analysis." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8608/1/covezzi_federica_tesi.pdf.
Full textAbstract:
A composite is a material made out of two or more constituents
(phases) combined together in order to achieve desirable mechanical
or thermal properties. Such innovative materials have been widely
used in a large variety of engineering fields in the past decades. The
design of a composite structure requires the resolution of a multiscale
problem that involves a macroscale (i.e. the structural scale)
and a microscale. The latter plays a crucial role in the determination
of the material behavior at the macroscale, especially when dealing
with constituents characterized by nonlinearities. For this reason, numerical
tools are required in order to design composite structures by
taking into account of their microstructure. These tools need to provide
an accurate yet efficient solution in terms of time and memory
requirements, due to the large number of internal variables of the
problem. This issue is addressed by different methods that overcome
this problem by reducing the number of internal variables. Within
this framework, this thesis focuses on the development of a new
homogenization technique named Mixed TFA (MxTFA) in order to
solve the homogenization problem for nonlinear composites. This
technique is based on a mixed-stress variational approach involving
self-equilibrated stresses and plastic multiplier as independent
variables on the Reference Volume Element (RVE). The MxTFA is developed
for the case of elastoplasticity and viscoplasticity, and it is
implemented into a multiscale analysis for nonlinear composites. Numerical
results show the efficiency of the presented techniques, both
at microscale and at macroscale level.
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Marcolini, Giorgia. "Homogenization and analysis of hydrological time series." Doctoral thesis, Università degli studi di Trento, 2017. https://hdl.handle.net/11572/367910.
Full textAbstract:
In hydrological studies, it is very important to properly analyze the relationship among the different components of the water cycle, due to the complex feedback mechanisms typical of this system. The analysis of available time series is hence a fundamental step, which has to be performed before any modeling activity. Moreover, time series analysis can shed light over the spatial and temporal dynamics of correlated hydrological and climatological processes. In this work, we focus on three tools applied for time series analysis: homogeneity tests, wavelet analysis and copula analysis. Homogeneity tests allow to identify a first important kind of variability in the time series, which is not due to climate nor seasonal variability. Testing for inhomogeneities is therefore an important step that should be always performed on a time series before using it for any application. The homogenization of snow depth data, in particular, is a challenging task. Up to now, it has been performed analyzing available metadata, which often present contradictions and are rarely complete. In this work, we present a procedure to test the homogeneity of snow depth time series based on the Standard Normal Homogeneity Test (SNHT). The performance of the SNHT for the detection of inhomogeneities in snow depth data is further investigated with a comparison experiment, in which a dataset of snow depth time series relative to Austrian stations has been analyzed with both the SNHT and the HOMOP algorithm. The intercomparison study indicates that the two algorithms show comparable performance.
The wavelet transform analysis allows to obtain a different kind of information about the variability of a time series. In fact, it determines the different frequency content of a signal in different time intervals. Moreover, the wavelet coherence analysis allows to identify periods where two time series are correlated and their phase shift. We apply the wavelet transform to a dataset of snow depth time series of stations distributed in the Adige catchment and on a dataset of 16 discharge time series located in the Adige and in the Inn catchments. The same datasets are used to perform a wavelet coherence analysis considering the Mediterranean Oscillation Index (MOI) and the North Atlantic Oscillation Index (NAOI). This analysis highlights a difference in the behavior of the snow time series collected below and above 1650 m a.s.l.. We also observe a difference between low and high elevation sites in the amount of mean seasonal snow depth and snow cover duration. More interestingly, snow time series collected at different elevations respond differently to temperature and more in general to climate changes. The wavelet analysis allows us also to distinguish between gauging stations belonging to different catchments, while the wavelet coherence analysis revealed non-stationary correlations with the MOI and NAOI, indicating a very complex relation between the measured quantities and climatic indexes. Finally the application of copulas allows modeling the marginal of each variable and their dependence structure independently. We apply this technique to two relevant cases. First we study snow related variables in relation with temperature, the NAOI and the MOI, which we already investigated with the wavelet coherence analysis. Then we model flood events registered at two stations of the Inn river: Wasserburg and Passau. This last analysis is performed with the goal of predicting future flood events and derive construction parameters for retention basins. We test three different combinations of variables (direct peak discharge-direct volume, direct peak discharge-direct volume-rising time-base flow, direct peak discharge-direct volume-rising time-moving threshold) describing the flood events and compare the results. The consistency in the results indicates that the proposed methodology is robust and reliable. This study shows the importance of approaching the analysis to hydrological time series from several points of view: quality of the data, variability of the time series and relation between different variables. Moreover, it shows that integrating the use of various time series analysis methods can greatly improve our understanding of the system behavior.
33
Marcolini, Giorgia. "Homogenization and analysis of hydrological time series." Doctoral thesis, University of Trento, 2017. http://eprints-phd.biblio.unitn.it/2636/1/Disclaimer_Marcolini.pdf.
Full textAbstract:
In hydrological studies, it is very important to properly analyze the relationship among the different components of the water cycle, due to the complex feedback mechanisms typical of this system. The analysis of available time series is hence a fundamental step, which has to be performed before any modeling activity. Moreover, time series analysis can shed light over the spatial and temporal dynamics of correlated hydrological and climatological processes. In this work, we focus on three tools applied for time series analysis: homogeneity tests, wavelet analysis and copula analysis. Homogeneity tests allow to identify a first important kind of variability in the time series, which is not due to climate nor seasonal variability. Testing for inhomogeneities is therefore an important step that should be always performed on a time series before using it for any application. The homogenization of snow depth data, in particular, is a challenging task. Up to now, it has been performed analyzing available metadata, which often present contradictions and are rarely complete. In this work, we present a procedure to test the homogeneity of snow depth time series based on the Standard Normal Homogeneity Test (SNHT). The performance of the SNHT for the detection of inhomogeneities in snow depth data is further investigated with a comparison experiment, in which a dataset of snow depth time series relative to Austrian stations has been analyzed with both the SNHT and the HOMOP algorithm. The intercomparison study indicates that the two algorithms show comparable performance.
The wavelet transform analysis allows to obtain a different kind of information about the variability of a time series. In fact, it determines the different frequency content of a signal in different time intervals. Moreover, the wavelet coherence analysis allows to identify periods where two time series are correlated and their phase shift. We apply the wavelet transform to a dataset of snow depth time series of stations distributed in the Adige catchment and on a dataset of 16 discharge time series located in the Adige and in the Inn catchments. The same datasets are used to perform a wavelet coherence analysis considering the Mediterranean Oscillation Index (MOI) and the North Atlantic Oscillation Index (NAOI). This analysis highlights a difference in the behavior of the snow time series collected below and above 1650 m a.s.l.. We also observe a difference between low and high elevation sites in the amount of mean seasonal snow depth and snow cover duration. More interestingly, snow time series collected at different elevations respond differently to temperature and more in general to climate changes. The wavelet analysis allows us also to distinguish between gauging stations belonging to different catchments, while the wavelet coherence analysis revealed non-stationary correlations with the MOI and NAOI, indicating a very complex relation between the measured quantities and climatic indexes. Finally the application of copulas allows modeling the marginal of each variable and their dependence structure independently. We apply this technique to two relevant cases. First we study snow related variables in relation with temperature, the NAOI and the MOI, which we already investigated with the wavelet coherence analysis. Then we model flood events registered at two stations of the Inn river: Wasserburg and Passau. This last analysis is performed with the goal of predicting future flood events and derive construction parameters for retention basins. We test three different combinations of variables (direct peak discharge-direct volume, direct peak discharge-direct volume-rising time-base flow, direct peak discharge-direct volume-rising time-moving threshold) describing the flood events and compare the results. The consistency in the results indicates that the proposed methodology is robust and reliable. This study shows the importance of approaching the analysis to hydrological time series from several points of view: quality of the data, variability of the time series and relation between different variables. Moreover, it shows that integrating the use of various time series analysis methods can greatly improve our understanding of the system behavior.
34
Hirschberger, Claudia Britta. "A treatise on micromorphic continua theory, homogenization, computation." Kaiserslautern Techn. Univ., Lehrstuhl für Techn. Mechanik, 2008. http://d-nb.info/99795261X/34.
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Lallemant, Lucas. "Numerical homogenization of a rough bi-material interface." Thesis, Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41111.
Full textAbstract:
The mechanical reliability of electronic components has become harder and harder to predict due to the use of composite materials. One of the key issues is creating an accurate model of the delamination mechanism, which consists in the separation of two different bounded materials. This phenomenon is a very challenging issue that is investigated in the Nano Interface Project (NIP), in which this thesis is involved.
The macroscopic adhesion force is governed by several parameters described at different length scales. Among these parameters, the roughness profile of the interface has a pronounced influence. The main difficulty for an accurate delamination characterization is then investigating the effects of this roughness profile and the modifications it implies for the overall cohesion.
The objective of the NIP is to develop an interface model for the numerical testing of electronic components in a finite element software. The problem is that a direct modeling of all the mechanisms described previously is really expensive in term of computation time, if possible at all. This difficulty is increased by the huge mismatch of the mechanical properties of the materials in contact. A scale transition method is therefore required, which is provided by homogenization. The idea is to consider the delamination at a wider scale. Rather than modeling the whole roughness profile, the adhesion at the interface will be described by homogenized, or macroscopic, parameters extracted from a representative model at the micro-scale, the RVE. This thesis will deal with the determination of these homogenized parameters.
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Dasht, Johan. "Some developments of homogenization theory and Rothe's method /." Luleå : Dept. of Mathematics, Univ, 2005. http://epubl.luth.se/1402-1757/2005/05/LTU-LIC-0505-SE.pdf.
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Olsson, Marianne. "G-Convergence and Homogenization of some Monotone Operators." Doctoral thesis, Östersund : Department of Engineering, Physics and Mathematics, Mid Sweden University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-94.
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Zarate, Ramon Saiz. "Inverse and homogenization problems for maximal monotone operators." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/26229.
Full textAbstract:
We apply self-dual variational calculus to inverse problems, optimal control problems and homogenization problems in partial differential equations.
Self-dual variational calculus allows for the variational formulation of equations which do not have to be of Euler-Lagrange type. Instead, a monotonicity condition permits the construction of a self-dual Lagrangian. This Lagrangian then permits the construction of a non-negative functional whose minimum value is zero, and its minimizer is a solution to the corresponding equation.
In the case of inverse and optimal control problems, we use the variational functional given by the self-dual Lagrangian as a penalization functional, which naturally possesses the ideal qualities for such a role. This allows for the application of standard variational techniques in a convex setting, as opposed to working with more complex constrained optimization problems. This extends work pioneered by Barbu and Kunisch.
In the case of homogenization problems, we recover existing results by dal Maso, Piat, Murat and Tartar with the use of simpler machinery. In this context self-dual variational calculus permits one to study the asymptotic properties of the potential functional using classical Gamma-convergence techniques which are simpler to handle than the direct techniques required to study the asymptotic properties of the equation itself. The approach also allows for the seamless handling of multivalued equations.
The study of such problems introduces naturally the study of the topological structures of the spaces of maximal monotone operators and their corresponding self-dual potentials. We use classical tools such as Gamma-convergence, Mosco convergence and Kuratowski-Painlevé convergence and show that these tools are well suited for the task. Results from convex analysis regarding these topologies are extended to the more general case of maximal monotone operators in a natural way. Of particular interest is that the Gamma-convergence of self-dual Lagrangians is equivalent to the Mosco convergence, and this in turn implies the Kuratowski-Painlevé convergence of their corresponding maximal monotone operators; this partially extends a classical result by Attouch relating the convergence of convex functions to the convergence of their corresponding subdifferentials.
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Clayton, John D. "Homogenization and incompatibility fields in finite strain elastoplasticity." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/17666.
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Costaouec, Ronan, and Ronan Costaouec. "Numerical methods for homogenization : applications to random media." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00674957.
Full textAbstract:
In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
41
Gallican, Valentin. "Homogenization estimates for polymer-based viscoelastic composite materials." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS543.
Full textAbstract:
Cette thèse porte sur l’étude de la réponse harmonique macroscopique de matériaux composites viscoélastiques à base polymère. Nous nous intéressons tout d’abord à l’étude de matériaux composites à renforts particulaires dont la matrice est modélisée à partir de modèles de Zener fractionnaires et contient des particules sphériques élastiques. Le comportement asymptotique du module complexe macroscopique est étudié à l’aide de principes de stationnarité appliqués à la viscoélasticité complexe. Il est à noter que quatre conditions exactes sont obtenues sur les modules de stockage et de perte. Les deux premières correspondent aux réponses élastiques découplées à haute et basse fréquences, tandis que les deux autres résultent du couplage viscoélastique caractérisant la phase de transition vitreuse. A partir de celles-ci, nous développons des modèles micromécaniques viscoélastiques approchés sur toute la gamme de fréquences. Les modèles approchés font intervenir des développements en séries de Dirichlet-Prony afin d’estimer le comportement viscoélastique macroscopique. Ces derniers sont présentés à l’aide du schéma GSC dans le cas de constituants isotropes et comparés à des simulations FFT réalisées sur des microstructures périodiques pour différentes fractions volumiques de particules. Nous nous attachons ensuite à modéliser la réponse d’explosifs composés de poudres de TATB avec adjonction d’une phase polymère par une approche micromécanique en deux étapes. Nous commençons par étudier l’élasticité effective de polycristaux de TATB sans liant en fonction de nombreux paramètres morphologiques. Le comportement viscoélastique macroscopique est ensuite approché par des modèles micromécaniques et comparé à des simulations FFT et des données expérimentalesThis Ph.D. work deals with the description of the time harmonic response of polymer-based viscoelastic composite materials. On the one hand, the emphasis is put on particulate-reinforced composite materials whose matrix is defined by fractional Zener models containing elastic spherical particles. The asymptotic behaviour of the overall complex moduli is studied by resorting to stationary principles for complex viscoelasticity. Four exact conditions on the storage and loss moduli are obtained. Two of them classically correspond to the uncoupled elastic responses at low and high frequencies while the two others result from the viscoelastic coupling in the transient regime. These conditions only involve the strain fields solutions of asymptotic elastic problems. Based on these conditions, we propose to develop approximate viscoelastic homogenization models for the whole frequency range. They classically make use of Dirichlet-Prony series to estimate the overall viscoelastic behaviour. Such models are presented by means of the GSC scheme for isotropic constituents and compared to FFT full-field computations carried out on periodic microstructures with various volume fractions of particles. On the other hand, we focus on the modeling of TATB-based pressed polymer-bonded explosives seen as jointed polycrystals by means of two-step multiscale modeling. We first investigate the effective elasticity of binder-free TATB-based polycrystals with respect to various morphological parameters. Afterwards, the overall viscoelastic behaviour is assessed by making use of mean-field schemes and compared to FFT full-field computations and experimental data
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Hossain, A. N. M. Shahriyar. "Metamaterials: 3-D Homogenization and Dynamic Beam Steering." University of Akron / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1574430585435814.
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Costaouec, Ronan. "Numerical methods for homogenization : applications to random media." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1012/document.
Full textAbstract:
Le travail de cette thèse a porté sur le développement de techniques numériques pour l'homogénéisation de matériaux présentant à une petite échelle des hétérogénéités aléatoires. Sous certaines hypothèses, la théorie mathématique de l'homogénéisation stochastique permet d'expliciter les propriétés effectives de tels matériaux. Néanmoins, en pratique, la détermination de ces propriétés demeure difficile. En effet, celle-ci requiert la résolution d'équations aux dérivées partielles stochastiques posées sur l'espace tout entier. Dans cette thèse, cette difficulté est abordée de deux manières différentes. Les méthodes classiques d'approximation conduisent à approcher les propriétés effectives par des quantités aléatoires. Réduire la variance de ces quantités est l'objectif des travaux de la Partie I. On montre ainsi comment adapter au cadre de l'homogénéisation stochastique une technique de réduction de variance déjà éprouvée dans d'autres domaines. Les travaux de la Partie II s'intéressent à des cas pour lesquels le matériau d'intérêt est considéré comme une petite perturbation aléatoire d'un matériau de référence. On montre alors numériquement et théoriquement que cette simplification de la modélisation permet effectivement une réduction très importante du coût calculIn this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
44
Lorenzani, Silvia. "Homogenization of the Smoluchowski equation in perforated domains." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5704/.
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Carneiro, Molina Arturo Jose. "Computational homogenization for multi scale finite element simulation." Thesis, Swansea University, 2007. https://cronfa.swan.ac.uk/Record/cronfa42431.
Full textAbstract:
This work presents a general formulation of small and large strain multiscale solid constitutive models based on the volume averaging of the microscopic strain (deformation gradient under large strain) and stress fields over a locally attached microstructure Representative Volume Element (RVE). Both elasto-plastic and hyperelastic behaviour are considered in the modelling of the RVE. A multiscale first-order computational homogenization method for modelling nonlinear deformation processes of evolving multi-phase materials is developed based on the Finite Element discretisation of both macro- and micro-structure. The approach consist of suitably imposing the macroscopic strain on the RVE and then computing the macroscopic stress as the volume average of the microscopic stress field obtained by solving numerically the local (initial) boundary value problem. In this context, the effective (homogenized) tangent modulus is obtained as a function of microstructure stiffness matrix which, in turn, depends upon the material properties and geometrical distribution of the micro-constituents in the RVE. The multiscale material presented here is restricted to two-dimensional problems, however we remark that the extension to three dimensions is trivial. The effectiveness of the proposed strategies is is demonstrated by means of numerical examples.
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Russell, Brandon C. "HOMOGENIZATION IN PERFORATED DOMAINS AND WITH SOFT INCLUSIONS." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/55.
Full textAbstract:
In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, we connect these large-scale estimates with local regulartity results at the microscopic-level to achieve interior Lipschitz regularity at every scale.
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Stelzig, Philipp Emanuel. "On problems in homogenization and two-scale convergence." Doctoral thesis, Università degli studi di Trento, 2012. https://hdl.handle.net/11572/368072.
Full textAbstract:
This thesis addresses two problems from the theory of periodic homogenization and the related notion of two-scale convergence. Its main focus rests on the derivation of equivalent transmission conditions for the interaction of two adjacent bodies which are connected by a thin layer of interface material being perforated by identically shaped voids. Herein, the voids recur periodically in interface direction and shall in size be of the same order as the interface thickness. Moreover, the constitutive properties of the material occupying the bodies adjacent to the interface are assumed to be described by some convex energy densities of quadratic growth. In contrast, the interface material is supposed to show extremal" constitutive behavior. More precisely
48
Stelzig, Philipp Emanuel. "On problems in homogenization and two-scale convergence." Doctoral thesis, University of Trento, 2012. http://eprints-phd.biblio.unitn.it/780/1/Stelzig2012_Diss.pdf.
Full textAbstract:
This thesis addresses two problems from the theory of periodic homogenization and the related notion of two-scale convergence. Its main focus rests on the derivation of equivalent transmission conditions for the interaction of two adjacent bodies which are connected by a thin layer of interface material being perforated by identically shaped voids. Herein, the voids recur periodically in interface direction and shall in size be of the same order as the interface thickness. Moreover, the constitutive properties of the material occupying the bodies adjacent to the interface are assumed to be described by some convex energy densities of quadratic growth. In contrast, the interface material is supposed to show "extremal" constitutive behavior. More precisely, it is assumed that the constitutive relations of the interface material are once more characterized by a convex energy density of quadratic growth which, however, scales with the inverse thickness of the interface layer. In accordance to recent works on homogeneous interfaces in an analogous constitutive setting, it is found that in the limit of vanishing interface thickness and void size the interaction of the bodies adjacent to the interface can asymptotically be described by equivalent transmission conditions on the flattened interface. These transmission conditions are such that they penalize in-plane gradients in the interface. Cell formulas defining the homogenized transmission conditions on the flattened interface are derived, using a combination of Gamma-convergence methods and suitable adaptions of the periodic unfolding method in rescaled (perforated) thin domains. Depending on whether the voids touch the periodicity cells' faces, different periodic unfolding operators can be applied. The thesis' final chapter contains the results of a recent collaboration with Stefan Neukamm on the effects on two-scale convergence caused by a translation of the coordinate frame. It is observed that given a vanishing sequence of microscale parameters, a once two-scale convergent sequence is in general no longer two-scale convergent when described in a translated coordinate frame, even though it remains two-scale convergent along suitable subsequences. Yet, all two-scale cluster points of the translated sequence are indeed revealed as translates of the original two-scale limit. In fact, these two-scale cluster points are not only translated in the macroscopic variable, but also in the microscopic variable by microtranslations which belong to a set that is determined solely by the translation of the coordinate frame and the vanishing sequence of microscale parameters. This result is then applied to a novel homogenization problem that involves two different coordinate frames and yields a limiting behavior governed by emerging microscopic translations. Finally, in addition to these results the thesis also indicates a possible extension of the periodic unfolding method to so-called non-translatory periodic microstructures.
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Vernier, Patricia. "Homogenization of composite materials with fractional viscoelastic constituents." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS552.
Full textAbstract:
Cette thèse porte sur la prédiction des propriétés mécaniques effectives de matériaux hétérogènes composés de constituants viscoélastiques fractional, au moyen d'une approche incrémentale variationnelle. Nous appliquons la méthode Effective Internal Variable (EIV) développée par Lahellec and Suquet (2007), particulièrement attrayante pour le traitement de comportements viscoélastiques (Tressou et al., 2016). Contrairement aux méthodes d'homogénéisation communément utilisées qui reposent sur le principe de correspondance et pour lesquelles les fluctuations des champs ne sont pas accessibles, cette approche incrémentale permet de calculer les propriétés effectives dans le domaine direct au moyen des méthodes variationalles de Ponte Castañeda (1991 et 2002) qui prennent en compte les seconds-moments des champs mécaniques. La méthode EIV s'inscrit dans le cadre des Matériaux Standards Généralisés (MSG), dans lequel le comportement des matériaux dissipatifs est décrit par deux potentiels thermodynamiques convexes. Nous considérons des constituants viscoélastiques fractionnaires, dont la loi constitutive est décrite par des équations différentielles linéaires avec des dérivées fractionnaires. En accord avec des observations expérimentales, ce formalisme prend en compte des effets de mémoire longue à travers la superposition de plusieurs temps caractéristiques (Caputo et Mainardi, 1971). La distribution de ces derniers est donnée explicitement par l'expression du spectre en loi puissance. Les potentiels thermodynamiques des matériaux viscoélastiques fractionnaires sont définis en cohérence avec le cadre des MSG. Cette cohérence s'appuie sur l'interprétation rhéologique de l'élément fractionnaire comme un Maxwell généralisé (Lion, 1997). Ainsi, nous tirons parti de l'extension de la méthode EIV à plusieurs variables internes développée par Tressou et al. (2023) afin d'homogénéiser des matériaux composites contenant des constituants viscoélastiques fractionnaires. De plus, les temps caractéristiques sont adéquatement choisis à partir de la discrétisation du spectre. Cette discrétisation est réalisée avec la procédure de Papoulia et al. (2010), basée sur une méthode des trapèzes améliorée. Plus précisément, nous appliquons cette méthode à la fonction de Mittag-Leffler impliquée dans la définition des spectres de relaxation. Nous abordons deux problèmes hétérogènes différents au moyen de la méthode EIV. Nous considérons d'abord un composite de type matrice-inclusions sous chargement harmonique, pour lequel nous rencontrons des difficultés numériques. Nous évaluons ensuite la méthode EIV sur un polycristal de glace soumis à un essai de fluageThis PhD thesis deals with the prediction of the mechanical effective properties of composite materials with linear fractional viscoelastic constituents by means of an incremental variational approach. We make use of the Effective Internal Variable (EIV) method developed by Lahellec and Suquet (2007), which is particularly attractive for viscoelasticity (Tressou et al., 2016). Contrary to the common homogenization methods that rely on the correspondence principle and where the fluctuations are not accessible, this incremental method evaluates the effective properties into the direct domain through the variational methods of Ponte Castañeda (1991 and 2002) that take into account the second-moments of the fields. The EIV method is based on the Generalized Standard Materials framework, in which the dissipative materials are described by means of two convex thermodynamic potentials. We consider local fractional viscoelastic constituents, of which the constitutive behaviours follow linear differential equations with fractional derivative operators. In accordance with experimental observations, this formalism takes into account long-memory effects through the superposition of several characteristic times (Caputo and Mainardi, 1971). Their distribution is provided by the explicit expression of the spectrum as a power law. The potentials of fractional viscoelastic constituents are consistently defined in the GSM framework through the rheological interpretation of the fractional damping element as a generalized Maxwell model (Lion, 1997). Therefore, we take advantage of the extension of the EIV method to several internal variables, developed by Tressou et al. (2023) for the homogenization of composites with local fractional viscoelastic behaviours. Besides, the characteristic times are appropriately chosen by discretizing the spectrum. This is done using the midpoint-based procedure developed by Papoulia et al. (2010). More specifically, we apply their method to the Mittag-Leffler function involved in the definition of the relaxation spectrum. We use the EIV method to tackle two different heterogeneous problems. We consider a matrix-inclusion composite under harmonic loading, for which we come accros numerical issues. We then evaluate the EIV method for a polycrystal subject to a monotonous creep loading
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Machovičová, Tatiana. "Banachovy algebry." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445456.
Full textAbstract:
By Banach algebra we mean Banach space enriched with a multiplication operation. It is a mathematical structure that is used in the non-periodic homogenization of composite materials. The theory of classical homogenization studies materials assuming the periodicity of the structure. For real materials, the assumption of a periodicity is not enough and is replaced by the so-called an abstract hypothesis based on a concept composed mainly of the spectrum of Banach algebra and Sigma convergence. This theory was introduced in 2004.