Дисертації з теми "Capillarity equation"
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Rivetti, Sabrina. "Bounded variation solutions of capillarity-type equations." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10161.
Повний текст джерелаWe investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
XXV Ciclo
1985
Alvarellos, Jose. "Fundamental Studies of Capillary Forces in Porous Media." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5314.
Повний текст джерелаKamat, Madhusudan Sunil. "Soil moisture change due to variable water table." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54922.
Повний текст джерелаDE, LUCA ALESSANDRA. "On some nonlocal issues: unique continuation from the boundary and capillarity problems for anisotropic kernels." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/378950.
Повний текст джерелаThe aim of the present thesis is to discuss the results obtained during my PhD studies, mainly devoted to nonlocal issues. We first deal with strong unique continuation principles and local asymptotic expansions at certain boundary points for solutions of two different classes of elliptic equations. We start the investigation by a class of fractional elliptic equations in a bounded domain under some outer homogeneous Dirichlet boundary condition. To do this, we exploit the Caffarelli-Silvestre extension procedure, which allows us to get an equivalent formulation of the nonlocal problem as a local problem in one dimension more, consisting in a mixed Dirichlet-Neumann boundary value problem. Then, we use a classical idea by Garofalo and Lin to obtain a doubling-type condition via a monotonicity formula for a suitable Almgren-type frequency function. To overcome the difficulties related to the lack of regularity at the Dirichlet-Neumann junction, we introduce a new technique based on an approximation argument, which leads us to derive a so-called Pohozaev-type identity needed to estimate the derivative of the Almgren function. Thus we gain a strong unique continuation result in the local context, which is in turn combined with blow-up arguments to deduce local asymptotics and, consequently, a strong unique continuation result in the nonlocal setting as well. We also provide a strong unique continuation result from the edge of a crack for the solutions to a specific class of second order elliptic equations in an open bounded domain with a fracture, on which a homogeneous Dirichlet boundary condition is prescribed, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or some suitable integrability properties. This local problem is related to a particular case of the setting described above, by virtue of a strong connection between this type of problems and the mixed Dirichlet-Neumann boundary value problems. We also treat a capillarity theory of nonlocal type. In our setting, we consider more general interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invariance is modeled via two different fractional exponents in order to take into account the possibility that the container and the environment present different features with respect to particle interactions. We determine a nonlocal Young's law for the contact angle between the droplet and the surface of the container and discuss the unique solvability of the corresponding equation in terms of the interaction kernels and of the relative adhesion coefficient.
Deng, Shengfu. "A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28254.
Повний текст джерелаPh. D.
MacLaurin, James Normand. "The buckling of capillaries in tumours." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:ba252220-3c06-4d49-8696-655f6fefcd31.
Повний текст джерелаBurtea, Cosmin. "Méthodes d'analyse de Fourier en hydrodynamique : des mascarets aux fluides avec capillarité." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1047/document.
Повний текст джерелаThe first part of the present thesis deals with the so -called abcd systems which were derived by J.L. Bona, M. Chen and J.-C. Saut back in 2002. These systems are approximation models for the waterwaves problem in the Boussinesq regime, that is, waves of small amplitude and long wavelength. In the first two chapters we address the long time existence problem which consists in constructing solutions for the Cauchy problem associated to the abcd systems and prove that the maximal time of existence is bounded from below by some physically relevant quantity. First, we consider the case of initial data belonging to some Sobolev spaces imbedded in the space of continuous functions which vanish at infinity. Physically, this corresponds to spatially localized waves. The key ingredient is to construct a nonlinear energy functional which controls appropriate Sobolev norms on the desired time scales. This is accomplished by working with spectrally localized equations. The two important features of our method is that we require lower regularity levels in order to develop a long time existence theory and we may treat in an uni ed manner most of the cases corresponding to the di erent values of the parameters. In the second chapter, we prove the long time existence results for the case of data thatdoes not necessarily vanish at in nity. This is especially useful if one has in mind bore propagation. One of the key ideas of the proof is to consider a well-adapted high-low frequency decomposition of the initial data. In the third chapter, we propose infinite volume schemes in order to construct numerical solutions. We use these schemes in order to study traveling waves interaction.The second part of this manuscript, is devoted to the study of optimal regularity issues for the incompressible inhomogeneous Navier-Stokes system and the Navier-Stokes-Korteweg system used in order to take in account capillarity effects. More precisely, we prove that these systems are well-posed in their truly critical spaces i.e. the spaces that have the same scale invariance as the system itself. Inorder to achieve this we derive new estimates for a Stoke-like problem with time independent variable coefficients
Colinet, Pierre. "Amplitude equations and nonlinear dynamics of surface-tension and buoyancy-driven convective instabilities." Doctoral thesis, Universite Libre de Bruxelles, 1997. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212204.
Повний текст джерелаThis work is a theoretical contribution to the study of thermo-hydrodynamic instabilities in fluids submitted to surface-tension (Marangoni) and buoyancy (Rayleigh) effects in layered (Benard) configurations. The driving constraint consists in a thermal (or a concentrational) gradient orthogonal to the plane of the layer(s).
Linear, weakly nonlinear as well as strongly nonlinear analyses are carried out, with emphasis on high Prandtl (or Schmidt) number fluids, although some results are also given for low-Prandtl number liquid metals. Attention is mostly devoted to the mechanisms responsible for the onset of complex spatio-temporal behaviours in these systems, as well as to the theoretical explanation of some existing experimental results.
As far as linear stability analyses (of the diffusive reference state) are concerned, a number of different effects are studied, such as Benard convection in two layers coupled at an interface (for which a general classification of instability modes is proposed), surface deformation effects and phase-change effects (non-equilibrium evaporation). Moreover, a number of different monotonous and oscillatory instability modes (leading respectively to patterns and waves in the nonlinear regime) are identified. In the case of oscillatory modes in a liquid layer with deformable interface heated from above, our analysis generalises and clarifies earlier works on the subject. A new Rayleigh-Marangoni oscillatory mode is also described for a liquid layer with an undeformable interface heated from above (coupling between internal and surface waves).
Weakly nonlinear analyses are then presented, first for monotonous modes in a 3D system. Emphasis is placed on the derivation of amplitude (Ginzburg-Landau) equations, with universal structure determined by the general symmetry properties of the physical system considered. These equations are thus valid outside the context of hydrodynamic instabilities, although they generally depend on a certain number of numerical coefficients which are calculated for the specific convective systems studied. The nonlinear competitions of patterns such as convective rolls, hexagons and squares is studied, showing the preference for hexagons with upflow at the centre in the surface-tension-driven case (and moderate Prandtl number), and of rolls in the buoyancy-induced case.
A transition to square patterns recently observed in experiments is also explained by amplitude equation analysis. The role of several fluid properties and of heat transfer conditions at the free interface is examined, for one-layer and two-layer systems. We also analyse modulation effects (spatial variation of the envelope of the patterns) in hexagonal patterns, leading to the description of secondary instabilities of supercritical hexagons (Busse balloon) in terms of phase diffusion equations, and of pentagon-heptagon defects in the hexagonal structures. In the frame of a general non-variational system of amplitude equations, we show that the pentagon-heptagon defects are generally not motionless, and may even lead to complex spatio-temporal dynamics (via a process of multiplication of defects in hexagonal structures).
The onset of waves is also studied in weakly nonlinear 2D situations. The competition between travelling and standing waves is first analysed in a two-layer Rayleigh-Benard system (competition between thermal and mechanical coupling of the layers), in the vicinity of special values of the parameters for which a multiple (Takens-Bogdanov) bifurcation occurs. The behaviours in the vicinity of this point are numerically explored. Then, the interaction between waves and steady patterns with different wavenumbers is analysed. Spatially quasiperiodic (mixed) states are found to be stable in some range when the interaction between waves and patterns is non-resonant, while several transitions to chaotic dynamics (among which an infinite sequence of homoclinic bifurcations) occur when it is resonant. Some of these results have quite general validity, because they are shown to be entirely determined by quadratic interactions in amplitude equations.
Finally, models of strongly nonlinear surface-tension-driven convection are derived and analysed, which are thought to be representative of the transitions to thermal turbulence occurring at very high driving gradient. The role of the fastest growing modes (intrinsic length scale) is discussed, as well as scalings of steady regimes and their secondary instabilities (due to instability of the thermal boundary layer), leading to chaotic spatio-temporal dynamics whose preliminary analysis (energy spectrum) reveals features characteristic of hydrodynamic turbulence. Some of the (2D and 3D) results presented are in qualitative agreement with experiments (interfacial turbulence).
Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished
Cancès, Clément. "Écoulements diphasiques en milieux poreux hétérogènes : modélisation et analyse des effets liés aux discontinuités de la pression capillaire." Phd thesis, Université de Provence - Aix-Marseille I, 2008. http://tel.archives-ouvertes.fr/tel-00335506.
Повний текст джерелаDans un premier temps, on suppose que l'on peut connecter les pressions au niveau des interfaces. Cela nécessite des hypothèses sur les profils de pression capillaire, afin que les raccords soient possibles. On démontre l'existence d'une solution faible du problème parabolique dégénéré obtenu par convergence d'une famille de solutions approchées obtenues à l'aide d'un schéma Volumes Finis. L'unicité est garantie, sous hypothèse sur les dégénérescence, par une méthode de dédoublement de variable aboutissant à un principe de contraction $L^1$.
La modélisation ne garantit pas forcément que le raccord des pressions capillaires aux interfaces soit possible. Dans le chapitre 3, on donne une condition de raccord graphique des pressions capillaires aux interfaces qui permet de traiter des cas beaucoup plus généraux. On montre que de le problème avec raccords graphiques admet une solution. Un résultat d'unicité et de contraction $L^1$ est donné dans le cas unidimensionnel.
Dans le chapitre 4, on montre la convergence d'une approximation Volumes Finis vers l'unique solution du problème unidimensionnel. Ce résultat utilise une borne uniforme sur les flux discrets, analogie discrète de la preuve dans le cas continue faite au chapitre précédent.
On étudie dans les chapitres 5 et 6 la limite des solutions lorsque la dépendance de la pression capillaire par rapport à l'inconnue saturation devient très faible, et que la pression capillaire ne dépend plus que du sous milieux poreux homogène. Il apparaît alors des phénomènes différents selon l'orientation des forces de gravité et de capillarité. Soit la solution su problème est la solution entropique d'une équation hyperbolique à flux discontinus, soit une solution faible, entropique à l'intérieur des sous-domaines homogènes, et laissant apparaître un choc non classique à l'interface.
Annavarapu, Rama Kishore. "Elastocapillary Behavior and Wettability Control in Nanoporous Microstructures." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1544705326035201.
Повний текст джерелаCosper, Lane. "Existence of a Unique Solution to a System of Equations Modeling Compressible Fluid Flow with Capillary Stress Effects." Thesis, Texas A&M University - Corpus Christi, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10790012.
Повний текст джерелаThe purpose of this thesis is to prove the existence of a unique solution to a system of partial differential equations which models the flow of a compressible barotropic fluid under periodic boundary conditions. The equations come from modifying the compressible Navier-Stokes equations. The proof utilizes the method of successive approximations. We will define an iteration scheme based on solving a linearized version of the equations. Then convergence of the sequence of approximate solutions to a unique solution of the nonlinear system will be proven. The main new result of this thesis is that the density data is at a given point in the spatial domain over a time interval instead of an initial density over the entire spatial domain. Further applications of the mathematical model are fluid flow problems where the data such as concentration of a solute or temperature of the fluid is known at a given point. Future research could use boundary conditions which are not periodic.
Fu, An. "Investigation of Fluid Wicking Behavior in Micro-Channels and Porous Media by Direct Numerical Simulation." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563272437544414.
Повний текст джерелаBrenner, Konstantin. "Méthodes de volumes finis sur maillages quelconques pour des systèmes d'évolution non linéaires." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00647336.
Повний текст джерелаEnchéry, Guillaume. "Modèles et schémas numériques pour la simulation de genèse de bassins sédimentaires." Phd thesis, Université de Marne la Vallée, 2004. http://tel.archives-ouvertes.fr/tel-00007371.
Повний текст джерелаet à la simulation de genèse de bassins sédimentaires.
Nous présentons tout d'abord les modèles mathématiques et
les schémas numériques mis en oeuvre à l'Institut Français
du Pétrole dans le cadre du projet Temis. Cette première partie
est illustrée à l'aide de tests numériques portant sur des bassins 1D/2D.
Nous étudions ensuite le schéma amont des pétroliers utilisé pour la résolution des équations de Darcy et nous établissons des résultats mathématiques nouveaux
dans le cas d'un écoulement de type Dead-Oil.
Nous montrons également comment construire un schéma à nombre
de Péclet variable en présence de pression capillaire.
Là encore, nous effectuons une étude mathématique
détaillée et nous montrons la convergence du schéma
dans un cas simplifié. Des tests numériques réalisés
sur un problème modèle montrent que l'utilisation d'un nombre
de Péclet variable améliore la précision des calculs.
Enfin nous considérons dans une dernière partie
un modèle d'écoulement où les changements de lithologie et
les changements de courbes de pression capillaire sont liés.
Nous précisons la condition physique que doivent vérifier
les solutions en saturation aux interfaces de changement de roche et
nous en déduisons une formulation faible originale.
L'existence d'une solution à ce problème est obtenue
par convergence d'un schéma volumes finis.
Des exemples numériques montrent l'influence de la condition
d'interface sur le passage ou la retenue des hydrocarbures.
Alshammari, Abdullah A. A. M. F. "Mathematical modelling of oxygen transport in skeletal and cardiac muscles." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:65a34cb0-ef00-44c9-a04d-4147844c76ac.
Повний текст джерелаMoodley, Shawn. "Gas separation of steam and hydrogen mixtures using an α-alumina-Alumina supported NaA membrane / by S. Moodley". Thesis, North-West University, 2007. http://hdl.handle.net/10394/1890.
Повний текст джерелаAshari, Alireza. "Dual-Scale Modeling of Two-Phase Fluid Transport in Fibrous Porous Media." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2326.
Повний текст джерелаTrinh, Philippe H. "Exponential asymptotics and free-surface flows." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:e87b1f22-2569-4c0f-86a2-5bde76f34953.
Повний текст джерелаAlastal, Khalil. "Ecoulements oscillatoires et effets capillaires en milieux poreux partiellement saturés et non saturés : applications en hydrodynamique côtière." Thesis, Toulouse, INPT, 2012. http://www.theses.fr/2012INPT0039/document.
Повний текст джерелаIn this thesis, we study hydrodynamic oscillations in porous bodies (unsaturated or partially saturated), due to tidal oscillations of water levels in adjacent open water bodies. The focus is on beach hydrodynamics, but potential applications concern, more generally, time varying and oscillating water levels in coupled systems involving subsurface / open water interactions (natural and artificial beaches, harbor dykes, earth dams, river banks, estuaries). The tidal forcing of groundwater is represented and modeled (both experimentally and numerically) by quasi-static oscillations of water levels in an open water reservoir connected to the porous medium. Specifically, we focus on vertical water movements forced by an oscillating pressure imposed at the bottom of a soil column. Experimentally, a rotating tide machine is used to achieve this forcing. Overall, we use three types of methods (experimental, numerical, analytical) to study the vertical motion of the groundwater table and the unsaturated flow above it, taking into account the vertical head drop in the saturated zone as well as capillary pressure gradients in the unsaturated zone. Laboratory experiments are conducted on vertical sand columns, with a tide machine to force water table oscillations, and with porous cup tensiometers to measure both positive pressures and suctions along the column (among other measurement methods). Numerical simulations of oscillatory water flow are implemented with the BIGFLOW 3D code (implicit finite volumes, with conjugate gradients for the matrix solver and modified Picard iterations for the nonlinear problem). In addition, an automatic calibration based on a genetic optimization algorithm is implemented for a given tidal frequency, to obtain the hydrodynamic parameters of the experimental soil. Calibrated simulations are then compared to experimental results for other non calibrated frequencies. Finally, a family of quasi-analytical multi-front solutions is developed for the tidal oscillation problem, as an extension of the Green-Ampt piston flow approximation, leading to nonlinear, non-autonomous systems of Ordinary Differential Equations with initial conditions (dynamical systems). The multi-front solutions are tested by comparing them with a refined finite volume solution of the Richards equation. Multi-front solutions are at least 100 times faster, and the match is quite good even for a loamy soil with strong capillary effects (the number of fronts required is small, no more than N≈ to 20 at most). A large set of multi-front simulations is then produced in order to analyze water table and flux fluctuations for a broad range of forcing frequencies. The results, analyzed in terms of means and amplitudes of hydrodynamic variables, indicate the existence, for each soil, of a characteristic frequency separating low frequency / high frequency flow regimes in the porous system
Aoki, Yasunori. "Study of Singular Capillary Surfaces and Development of the Cluster Newton Method." Thesis, 2012. http://hdl.handle.net/10012/6908.
Повний текст джерелаAkers, Benjamin Fearing. "Model equations for gravity-capillary waves." 2008. http://www.library.wisc.edu/databases/connect/dissertations.html.
Повний текст джерела"On the existence and nonexistence of capillary surfaces." 1998. http://library.cuhk.edu.hk/record=b5889539.
Повний текст джерелаThesis submitted in: July 1997.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.
Includes bibliographical references (leaves 89-92).
Chapter 1 --- Introduction --- p.5
Chapter 1.1 --- The Euler-Lagrange Equation for Capillary Surfaces --- p.6
Chapter 1.2 --- The Capillary Tube --- p.12
Chapter 2 --- Comparison Principles --- p.16
Chapter 2.1 --- The General Comparison Principle --- p.16
Chapter 2.2 --- Applications --- p.24
Chapter 3 --- Existence Criteria --- p.30
Chapter 3.1 --- Necessary Conditions --- p.31
Chapter 3.2 --- Sufficient Conditions --- p.35
Chapter 4 --- Uniqueness --- p.53
Chapter 4.1 --- General Bounded Domains Case --- p.53
Chapter 4.2 --- Infinite Strip Case --- p.56
Chapter 5 --- Gradient Estimate of Surfaces of Constant Mean Curvature --- p.66
Chapter 5.1 --- The Gradient Estimate --- p.67
Chapter 5.2 --- Behavior as R→ 1 --- p.70
Chapter 5.3 --- Existence of the Comparison Surfaces --- p.76
Chapter 5.4 --- Ro is Best Possible --- p.82
Appendix Mean Curvature --- p.85
Fang, Ning. "Principles and applications of affinity capillary electrophoresis based on mass transfer equation." Thesis, 2006. http://hdl.handle.net/2429/18468.
Повний текст джерелаScience, Faculty of
Chemistry, Department of
Graduate
Tsai, Chung-Hsien. "Contributions to a fifth order model equation for steady capillary-gravity waves over a bump." 1999. http://catalog.hathitrust.org/api/volumes/oclc/43794213.html.
Повний текст джерелаTsai, Bing-Kun, and 蔡秉昆. "On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domainwith Capillary Boundary Condition." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/42474911736552288301.
Повний текст джерела國立臺灣大學
數學研究所
96
We consider the minimal surface equation in an infinite sector domain with given capillary boundary conditions.First, we give a necessary and sufficient conditions for the existence of the linear solution. Second, we study the behavior of the solutions of the minimal surface equation at the origin and at the infinite by using the blow up and the sip in process. Finally, we claim that the solution is linear on the boundary and conclude that it is a plane.
Tsai, Bing-Kun. "On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domain with Capillary Boundary Condition." 2008. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2407200811150700.
Повний текст джерела