Dissertations / Theses: 'FREE-FREE BOUNDARY'

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Morgan, J. D. "Codimension-two free boundary problems." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359484.

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O'Brien, Stephen Brian Gerard. "Free boundary problems from industry." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314860.

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Gillow, Keith A. "Codimension-two free boundary problems." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298393.

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Over the past 30 years the study of free boundary problems has stimulated much work. However, there exists a widely occurring, but little studied subclass of free boundary problems in which the free boundary has dimension two fewer than that of the underlying space rather than the more commonly studied case of one less. These problems are called `codimension-two' free boundary problems. In Chapter 1 the typical geometries required for such problems, the main mathematical techniques and the methodology used are discussed. Then, in Chapter 2, the techniques required to solve them are demonstrated using the particular example of the water entry problem. Further results for the water entry problem are then derived including an analysis of the relatively poorly understood water exit problem. In Chapter 3 a review is given of some classical contact and crack problems in solid mechanics. The inclusion of a cohesive zone in a dynamic type-III crack problem is considered. The Muskhelishvili potential method is presented and used to solve both a contact and crack problem. This enables the solution of a type-I crack problem relating to an ink delivery system to be found. In Chapter 4 a problem posed by car windscreen forming is addressed. A local solution near a corner is analysed to explain when and how point forces occur at the corners of the frame on which the simply supported windscreen rests. Then the full problem is solved numerically for different types of boundary condition. Chapters 5 and 6 deal with several sintering problems in viscous flow highlighting the value of the methodology introduced in Chapter 1. It will be shown how the Muskhelishvili potential method also carries over to Stokes flow problems. The difficulties of matching to an inner as opposed to an outer region are investigated. Last two interface problems between immiscible liquids are considered which show how the solution procedure is adapted when the field equation in the thin region is non-trivial. In the final chapter results are summarised, open problems listed and conclusions drawn.

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Minne, Andreas. "Non-linear Free Boundary Problems." Doctoral thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-178110.

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This thesis consists of an introduction and four research papers related to free boundary problems and systems of fully non-linear elliptic equations. Paper A and Paper B prove optimal regularity of solutions to general elliptic and parabolic free boundary problems, where the operators are fully non-linear and convex. Furthermore, it is proven that the free boundary is continuously differentiable around so called "thick" points, and that the free boundary touches the fixed boundary tangentially in two dimensions. Paper C analyzes singular points of solutions to perturbations of the unstable obstacle problem, in three dimensions. Blow-up limits are characterized and shown to be unique. The free boundary is proven to lie close to the zero-level set of the corresponding blow-up limit. Finally, the structure of the singular set is analyzed. Paper D discusses an idea on how existence and uniqueness theorems concerning quasi-monotone fully non-linear elliptic systems can be extended to systems that are not quasi-monotone.

QC 20151210

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Hylamia, Abdullah. "Towards Battery-free Radio Tomographic Imaging : Battery-free Boundary Crossing Detection." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-234819.

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Radio tomographic imaging (RTI) is a novel device-free localization technique which utilizes the changes in radio signals caused by obstruction to enable various sensing applications. However, the deployment of these applications is hindered by the energy-expensive radio sensing techniques employed in these systems. In this thesis, we tackle this issue by introducing a novel way to realize a battery-free RTI sensor. We go through the design process and produce and evaluate a working prototype that operates on minuscule amounts of energy. Our design reduces power consumption by orders of magnitude compared to traditional RTI sensors by eliminating the energy-expensive components used in current RTI systems, enabling battery-free operation of RTI sensors. We demonstrate the efficiency and accuracy of our system in a boundary crossing scenario. We Discuss its limitations and tackle some of the security threats correlated with the deployment of such a system.
Radiotomografisk avbildning (RTA) är en ny, anordningsfri lokaliseringstekniksom utnyttjar förändringarna i radiosignaler orsakat av obstruktioner för att möjliggöraolika avkänningsapplikationer. Utvecklingen av dessa applikationer hindrasemellertid av de energiineffektiva radioavkännande tekniker som användsi dessa system. I denna avhandling behandlar vi problemet genom att introduceraen ny metod för att skapa en batterifri RTA-sensor. Vi går igenom konstruktionsprocessenoch producerar och utvärderar en arbetsprototyp som kräver minusklermängder energi. Vår design minskar energiförbrukningen signifikantjämfört med traditionella RTA-sensorer, genom att eliminera de energiineffektivakomponenterna som används i dagens RTA-system, vilket möjliggör batterifridrift av RTA-sensorer. Vi demonstrerar effektiviteten och noggrannheten hos vårtsystem i ett gränsöverskridande scenario. Vi diskuterar begränsningarna och taritu med några av de säkerhetshot som är korrelerade med utplaceringen av ettsådant system.

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Petrosyan, Arsak. "Convex configurations in free boundary problems." Doctoral thesis, KTH, Mathematics, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-2966.

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Petrosyan, Arshak. "Convex configurations in free boundary problems." Doctoral thesis, KTH, Matematik, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-2966.

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8

Cummings, Linda Jane. "Free boundary models in viscous flow." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339364.

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Mason, C. J. "Numerical methods for free boundary problems." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37775.

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Aleksanyan, Gohar. "Regularity results in free boundary problems." Doctoral thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-195178.

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This thesis consists of three scientific papers, devoted to the regu-larity theory of free boundary problems. We use iteration arguments to derive the optimal regularity in the optimal switching problem, and to analyse the regularity of the free boundary in the biharmonic obstacle problem and in the double obstacle problem.In Paper A, we study the interior regularity of the solution to the optimal switching problem. We derive the optimal C1,1-regularity of the minimal solution under the assumption that the zero loop set is the closure of its interior.In Paper B, assuming that the solution to the biharmonic obstacle problem with a zero obstacle is suÿciently close-to the one-dimensional solution (xn)3+, we derive the C1,-regularity of the free boundary, under an additional assumption that the noncoincidence set is an NTA-domain.In Paper C we study the two-dimensional double obstacle problem with polynomial obstacles p1 p2, and observe that there is a new type of blow-ups that we call double-cone solutions. We investigate the existence of double-cone solutions depending on the coeÿcients of p1, p2, and show that if the solution to the double obstacle problem with obstacles p1 = −|x|2 and p2 = |x|2 is close to a double-cone solution, then the free boundary is a union of four C1,-graphs, pairwise crossing at the origin.

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Smith, Carlo. "Free boundary problems in thin fluid films." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.422704.

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Chakrabarti, Roma. "Numerical solution of some free boundary problems." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/46994.

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Alzwayi, Ali Saad. "Transition of free convection boundary layer flow." Thesis, University of Glasgow, 2013. http://theses.gla.ac.uk/4803/.

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Transition of natural convection flow on a heated flat plate and inside a heated channel is studied numerically. Three different RANS based turbulent k-ε models namely standard, RNG and Realizable with an enhanced wall function are employed in the simulations. Additionally, a Large Eddy Simulation (LES) technique is also applied to particularly investigate the flow field and transition in a heated plate facing upward. Numerous published papers presented the typical characteristic behaviour of natural convection flow inside a channel, however, none of these provided information about the transition behaviour of flow inside a channel, and importantly, how the transition is affected by the merging of two growing boundary layers which occur inside a channel. Therefore, taking the above important things into consideration, the aim of the study is to carry out in-depth investigations of the transition of the free convection flow inside a channel with an effect of its width, angular orientation and several important thermal and boundary conditions. Moreover, the transition phenomena of the free convection flow developing in a heated channel facing both downward and upward are thoroughly investigated in the thesis. Numerically predicted results are compared with available experimental data in the published literatures. Fluid properties are assumed to be constant except for the density which changes with temperature and gives rise to the buoyancy forces and is treated by using the Boussinesq approach. Air with a Prandtl number of 0.7 is used as a test fluid in all the simulations. In the RANS based models, the results show that the Realizable model with an enhanced wall function predicts numerical results well compared to the experiment than those obtained by the other two models (standard and RNG), therefore this model was selected to perform all the other RANS based numerical simulations in this work. The results particularly indicate that the inclination of the channel has major effects on the transition stage. As the inclination angle is increased, the transition stage moves further downstream of the channel. However, the predicted local heat flux, reached its minimum further upstream of the channel, does not agree with that of the velocity and turbulent kinetic energy in a small channel width. Natural convection from an isothermal plate is conducted by using a Large Eddy Simulation method. The results show that with an increase in the angle the peak of the thermal and velocity boundary layers move from the near outlet of the plate for the vertical case to the middle of the plate when θ = -70°. So the thermal and boundary layers become fatter which causes an early transition.

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Fulton, Joseph M. "LQG/LTR optimal attitude control of small flexible spacecraft using free-free boundary conditions." Diss., Connect to online resource, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3219032.

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15

Forcillo, Nicolò. "Free Boundary Regularity of Some Non-Homogeneous Problems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16392/.

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In this work, we deal with the study of some free boundary problems governed by non-homogeneous equations. In particular, we are interested in the regularity of the free boundaries for solutions of one-phase problems associated with non-divergence elliptic operators with variable coefficients.

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Edquist, Anders. "Monotonicity formulas and applications in free boundary problems." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12405.

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This thesis consists of three papers devoted to the study of monotonicity formulas and their applications in elliptic and parabolic free boundary problems. The first paper concerns an inhomogeneous parabolic problem. We obtain global and local almost monotonicity formulas and apply one of them to show a regularity result of a problem that arises in connection with continuation of heat potentials.In the second paper, we consider an elliptic two-phase problem with coefficients bellow the Lipschitz threshold. Optimal $C^{1,1}$ regularity of the solution and a regularity result of the free boundary are established.The third and last paper deals with a parabolic free boundary problem with Hölder continuous coefficients. Optimal $C^{1,1}\cap C^{0,1}$ regularity of the solution is proven.
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17

Lindgren, Erik. "Regularity properties of two-phase free boundary problems." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10336.

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This thesis consists of four papers which are all related to the regularity properties of free boundary problems. The problems considered have in common that they have some sort of two-phase behaviour.In papers I-III we study the interior regularity of different two-phase free boundary problems. Paper I is mainly concerned with the regularity properties of the free boundary, while in papers II and III we devote our study to the regularity of the function, but as a by-product we obtain some partial regularity of the free boundary.The problem considered in paper IV has a somewhat different nature. Here we are interested in certain approximations of the obstacle problem. Two major differences are that we study regularity properties close to the fixed boundary and that the problem converges to a one-phase free boundary problem.
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18

Stamicar, Robert. "A free boundary problem modelling zoning in rocks." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0004/NQ42881.pdf.

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Stamic̆ar, Robert Nikola. "A free boundary problem modelling zoning in rocks /." *McMaster only, 1998.

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Shahinfar, Shahab. "Transitional boundary layers caused by free-stream turbulence." Licentiate thesis, KTH, Mekanik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34150.

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The present measurement campaign on the free-stream turbulence (FST) induced boundary layer transition scenario has provided a unique set of experimental data, with potential to enhance the understanding of the eect of the free-stream turbulence characteristic length scales on the transition location and not only the turbulence intensity, which has been the focus in most previous studies. Recent investigations where the turbulence intensity has been kept essentially constant, while the integral length scale has been changed, show that the transition location is advanced for increasing length scale. However, the present data show that the integral and Taylor length scales of the FST have a relatively small inuence on the transition location as compared to the turbulence intensity and data analyses are now directed towards enhanced understanding of how the dierent parts of the incoming energy spectrum aects the energy growth inside the boundary layer.
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Kawai, S. "Boundary conformal field theory in free-field representation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249280.

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22

Shola, Peter Bamidele. "Numerical solution of a free-boundary viscous flow." Thesis, University of Essex, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.256393.

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Paul, Manosh C. "The stability of free convective boundary layer flows." Thesis, University of Bath, 2002. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760799.

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Khalid, A. H. "Free boundary problems in a Hele-Shaw cell." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1463159/.

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The motion of a free boundary separating two immiscible fluids in an unbounded Hele-Shaw cell is considered. In the one-phase problem, a viscous fluid is separated from an inviscid fluid by a simple closed boundary. Preliminaries for a complex variable technique are presented by which the one-phase problem can be solved explicitly via conformal mappings. The Schwarz function of the boundary plays a major role giving rise to the so called Schwarz function equation which governs the evolution of exact solutions. The Schwarz function approach is used to study the stability of a translating elliptical bubble due to a uniform background flow, and the stability of a blob (or bubble) subject to an external electric field. The one-phase problem of a translating free boundary and of a free boundary subject to an external field are studied numerically. A boundary integral method is formulated in the complex plane by considering the Cauchy integral formula and the complex velocity of a fluid particle on the free boundary. In the case of a free boundary subject to an external electric field due to a point charge, it is demonstrated that a stable steady state is achieved for appropriate charge strength. The method is also employed to study breakup of a single translating bubble in which the Schwarz function singularities (shown to be stationary) of the initial boundary play an important role. The two-phase problem is also considered, where the free boundary now separates two viscous fluids, and the construction of exact solutions is studied. The one-phase numerical model is enhanced, where a boundary integral method is formulated to accommodate the variable pressure in both viscous phases. Some numerical experiments are presented with a comparison to analytical results, in particular for the case where the free boundary is driven by a uniform background flow.

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Peskir, Goran. "Principles of optimal stopping and free-boundary problems /." Aarhus, Denmark : Univ. of Aarhus, 2001. http://www.gbv.de/dms/goettingen/344144879.pdf.

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Kent, Stuart Thomas. "Multi-Scale Conformal Maps and Free Boundary Problems." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/301534.

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In this dissertation, we study free boundary problems that describe equilibrium configurations of electromechanical systems consisting of a conducting elastic sheet deflected by an external charge distribution. Such systems are non-local in nature - the electrostatic pressure experienced by any individual point on the sheet depends on the entire deflection profile (as a result of the requirement that the deflected sheet must remain an equipotential). The magnitude of the electrostatic pressure varies quadratically with the magnitude of the local electric field. Similar non-local free boundary problems arise in two-layer fluid systems forced by withdrawal flows, but the normal viscous stress experienced by the fluid-fluid interface instead varies linearly with the local velocity gradients. The analysis presented focuses on two configurations in particular: the electromechanical system described above, forced by a point charge, and an artificially modified version of the same electromechanical system in which the induced electrostatic pressure varies linearly with the local electric field and the forcing is provided by an electric dipole. This second model is constructed as a crude approximation of the two-layer fluid flow forced by a point sink, and is primarily used to explore the influence of the forcing exponent on the bifurcation structure and solution types of the associated system. Our main contribution is the development of new techniques for the analysis and efficient numerical computation of large-deflection profiles for the true electromechanical system. The induced charge on such profiles accumulates near the interface tip, so that the geometry there is primarily determined by a balance between elastic and electrostatic forces. Away from the tip, the electrostatic pressure is low and the interface relaxes under the influences of gravity and elasticity only. Such interfaces exhibit features on widely disparate length scales. We exploit this separation of the interface into two regions dominated by different force balances to create a separate representation of each region (in appropriately rescaled coordinates), and then match the two representations together while ensuring that the relationship between local induced stress and global interface geometry is respected. This is achieved by combining tools and results from complex analysis and the method of matched asymptotic expansions.

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Lee, Yoon-Mee. "Hopf Bifurcation in a Parabolic Free Boundary Problem." DigitalCommons@USU, 1992. https://digitalcommons.usu.edu/etd/7138.

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We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion. The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence results can be applied. We then show that as the bifurcation parameter r decreases and passes through a critical value rc, the stationary solution loses stability and a stable periodic solution appears. Several figures have been included, which illustrate this transistion. The pascal source program used in the numerical simulation is included in an appendix.

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28

Chick, Eric. "Problems in forced and free convection." Thesis, Keele University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241449.

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COHEN, JACOB. "INSTABILITIES IN TURBULENT FREE SHEAR FLOWS." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/188143.

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The evolution of the large scale structures and the mean field were investigated in axisymmetric and plane mixing layers. Some aspects of the linear instability of an axisymmetric jet have been demonstrated. The axisymmetric geometry admits two additional length scales with relation to the two-dimensional shear layer: the radius of the jet column and the azimuthal wavelength. The importance of these two length scales in governing the instability of an axisymmetric jet was explored. The special case of a thin axisymmetric shear layer was analyzed and the results stressing the evolution of different azimuthal modes were compared with some phase-locked data which was produced by subjecting the jet to axisymmetric and helical excitation. The importance of the initial spectral distribution in a natural jet was demonstrated when it is used as an input to the amplification curve obtained from linear stability theory to predict a measured spectral distribution at a further downstream location. The inclusion of the nonlinear terms in the stability analysis reveals two main interactions: mean flow-wave interaction and wave-wave interaction. The modification of the mean flow of an axisymmetric jet was examined by exciting two azimuthal modes simultaneously. The interaction resulted in an azimuthal modulation of the mean velocity profile having a cosine shape. Effectively, the geometry of the jet was modified without changing the geometry of the nozzle. The coupling between an excited periodic disturbance and the mean flow was analyzed and the spatial evolution of both were compared with experimental results obtained in a plane mixing layer. The behavior of the concommittant Reynolds stresses is discussed in detail. The conditions under which one disturbance will transfer energy to another were derived and demonstrated in an axisymmetric jet. The interaction between a large amplitude plane wave with a weak subharmonic component was shown to enhance the amplification rate of the subharmonic. It was further shown that the nonlinear interaction between two azimuthal modes can produce a third azimuthal mode which was not initially present in the flow. The coupling between a fundamental wave and its subharmonic in a parallel plane mixing layer was demonstrated numerically.

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Matevosyan, Norayr. "Tangential Touch Between Free And Fixed Boundaries." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3559.

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Banu, Nurzahan. "Free convection in fluid-saturated porous media." Thesis, University of Bath, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311254.

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Bozorgnia, Farid. "Numerical Algorithms for Free Boundary Problems of Obstacle Types." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10930.

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Arnarson, Teitur. "PDE methods for free boundary problems in financial mathematics." Doctoral thesis, KTH, Matematik (Inst.), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4777.

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We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation. The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.
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Volkmann, Alexander [Verfasser]. "Free boundary problems governed by mean curvature / Alexander Volkmann." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1067442340/34.

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35

Buckland, John A. (John Anthony) 1978. "Mean curvature flow with free boundary on smooth hypersurfaces." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/5809.

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Andersson, John. "Free boundary problems and global solutions in half spaces /." Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-195.

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Parham, Jonathan Brent. "Physically consistent boundary conditions for free-molecular satellite aerodynamics." Thesis, Boston University, 2014. https://hdl.handle.net/2144/21230.

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Thesis (M.Sc.Eng.)
To determine satellite trajectories in low earth orbit, engineers need to adequately estimate aerodynamic forces. But to this day, such a task su↵ers from inexact values of drag forces acting on complicated shapes that form modern spacecraft. While some of the complications arise from the uncertainty in the upper atmosphere, this work focuses on the problems in modeling the flow interaction with the satellite geometry. The only numerical approach that accurately captures e↵ects in this flow regime—like self-shadowing and multiple molecular reflections—is known as Test Particle Monte Carlo. This method executes a ray-tracing algorithm to follow particles that pass through a control volume containing the spacecraft and accumulates the momentum transfer to the body surfaces. Statistical fluctuations inherent in the approach demand particle numbers on the order of millions, often making this scheme too costly to be practical. This work presents a parallel Test Particle Monte Carlo method that takes advantage of both graphics processing units and multi-core central processing units. The speed at which this model can run with millions of particles enabled the exploration of regimes where a flaw was revealed in the model’s initial particle seeding. A new model introduces an analytical fix to this flaw—consisting of initial position distributions at the boundary of a spherical control volume and an integral for the correct number flux—which is used to seed the calculation. This thesis includes validation of the proposed model using analytical solutions for several simple geometries and demonstrates uses of the method for the aero-stabilization of the Phobos-Grunt Martian probe and pose-estimation for the ICESat mission.
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38

Doria, Celso Malchiades. "On the existence of minimal surfaces with free boundary." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/108041/.

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39

Alkhateeb, Osama. "Singularity-Free Boundary Methods for Electrostatics and Wave Scattering." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1334816052.

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40

Green, Christopher. "Mathematical techniques for free boundary problems with multiple boundaries." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/11598.

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In this thesis, we study six different free boundary problems arising in the field of fluid mechanics, and the mathematical methods used to solve them. The free boundary problems are all characterised by having more than one boundary and the solution of these problems requires special mathematical treatment. The challenge in each of these problems is to determine the shape of the multiple fluid interfaces making up the particular system under consideration. In each of the free boundary problems we employ aspects of complex function theory, conformal mapping between multiply connected domains, and specialist techniques devised in recent years by Crowdy and collaborators. At the heart of these techniques lies a special transcendental function known as the Schottky-Klein prime function. This thesis makes use of this function in a variety of novel contexts. We first examine a single row of so-called hollow vortices in free space. This problem has been solved before but we present a new methodology which is convenient in being extendible to the case of a double row, or von Karman vortex street, of hollow vortices. We find a concise formula for the conformal mapping describing the shapes of the free boundaries of two hollow vortices in a typical period window in the vortex street and thereby solve the free boundary problem. We next focus on the problem of a pair of hollow vortices in an infinite channel. This free boundary problem exhibits similar mathematical features to the vortex street problem but now involves the new ingredient of solid impenetrable walls. Again we solve the free boundary problem by finding a concise formula for the conformal mapping governing the hollow vortex shapes. We then extend this analysis to a single row of hollow vortices occupying the channel. The problem of a pair of hollow vortices of equal and opposite circulation positioned behind a circular cylinder, superposed with a uniform flow, is then considered. This system is a desingularisation of the so-called Foppl point vortex equilibrium. For this free boundary problem, we employ a hybrid analytical-numerical scheme and we are able to offer a Fourier-Laurent series expansion for the conformal mapping determining the shape of the hollow vortex boundaries. Finally, we investigate an asymmetric assembly of steadily translating bubbles in a Hele- Shaw channel. This free boundary problem can be formulated as a special Riemann-Hilbert problem solvable in terms of the Schottky-Klein prime function. Our method of solution can be used to determine the shapes of any finite number of bubbles in a given assembly.

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Artola, Such Francisco Javier. "Free-boundary simulations of MHD plasma instabilities in tokamaks." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0441/document.

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Un des dispositifs les plus prometteurs pour réaliser la fusion contrôlée est le réacteur de type tokamak. Dans ces réacteurs, un plasma chaud ionisé est confiné à l'aide d'un champ magnétique intense. Ce travail de thèse porte sur l'étude d'une classe particulière d'instabilités au sein d'un tokamak. Cette étude est menée par des simulations numériques magnétohydro-dynamiques (MHD). Le code JOREK-STARWALL est adapté et appliqué pour étudier les instabilités dites à frontière libre. Ce type d'instabilités nécessitent un traitement spécial concernant les conditions de bord du plasma, où l'interaction du plasma avec le vide et les structures conductrices environnantes doit être prise en compte. JOREK-STARWALL permet d'étudier la physique de deux instabilités particulières à frontière libre: les modes localisés au bord ("Edge Localized Modes", ELMs) déclenchés par des oscillations de la position verticale du plasma et les évènements de déplacement vertical (Vertical Displacement Events, VDEs). Deux résultats majeurs sont obtenus: 1. Le déclenchement des ELMs par des oscillations de la position verticale est pour la première fois reproduit avec des simulations auto-cohérentes. Celles-ci permettent d'étudier le mécanisme physique sous-jacent à ce phénomène. Les simulations révèlent que pour le projet international ITER, ces ELMs déclenchés sont principalement dus à une augmentation du courant au bord du plasma due au mouvement vertical. 2. Pour les VDEs, plusieurs comparaisons effectuées avec d'autres codes MHD existants montrent un bon accord avec JOREK-STARWALL et permettant ainsi de réaliser des simulations pour estimer la quantité attendue de courants de halo dans ITER
One of the most promising concepts for future fusion reactors is the tokamak. In these devices, a hot ionized plasma is confined with the use of large magnetic fields. The subject of this thesis is the study of a particular type of tokamak instabilities with MagnetoHydroDynamic (MHD) simulations. The code JOREK-STARWALL is adapted and applied to the simulation of the so-called free-boundary instabilities. The investigation of this type of instabilities requires a special treatment for the plasma boundary conditions, where the interaction of the plasma with the vacuum and the surrounding conducting structures needs to be taken into account. In this work, the modelling of the electromagnetic plasma-wall-vacuum interaction is reviewed and generalized for the so-called halo currents. The adapted JOREK-STARWALL code is applied in order to study the physics of two particular free-boundary instabilities: Edge Localized Modes (ELMs) triggered by vertical position oscillations and Vertical Displacement Events (VDEs). Two major results are obtained: 1. The triggering of ELMs during vertical position oscillations is for the first time reproduced with self-consistent simulations. These allow for the investigation of the physical mechanism underlying this phenomenon. The simulations reveal that for the international ITER project, a large-scale tokamak, these triggered ELMs are mainly due to an increase in the plasma edge current due to the vertical plasma motion. 2. For VDEs, several benchmarks are performed with other existing MHD codes showing a good agreement and therefore allowing the performance of ITER simulations to estimate the expected amount of halo currents in ITER

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42

Forcillo, Nicolò <1994&gt. "Regularity in degenerate elliptic and parabolic free boundary problems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amsdottorato.unibo.it/10001/1/tesi%20di%20dottorato_Nicol%C3%B2%20Forcillo.pdf.

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In this thesis, the main topic is the study of some free boundary problems, more precisely the investigation of regularity issues in degenerate elliptic and parabolic ones. Specifically, three different problems are treated. The first one is the one-phase Stefan problem, for which the regularity of flat free boundaries is dealt with by relying on perturbation arguments leading to a linearization of the problem. This approach is inspired by the elliptic counterpart. The second problem concerns the question of the existence of an Alt-Caffarelli-Friedman monotonicity formula in the Heisenberg group. Following the ideas exploited in the Euclidean setting, a necessary condition about the existence of such tool in that noncommutative setting is found. The last problem faced is related to almost minimizers of the p-Laplacian. In particular, the optimal Lipschitz continuity of almost minimizers, for p greater or equal than 2, is proved as well as the regularity of the free boundary is studied.

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43

Teixeira, Miguel Angelo Cortez. "Interaction of turbulence with a free surface." Thesis, University of Reading, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340045.

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44

Muthedath, Premkumar. "Numerical study of nonlinear free-surface flows." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-07212009-040300/.

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45

Grine, K. "Free convection problems from a semi-infinite horizontal plate." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383889.

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46

Hipp, Hans Christoph 1959. "Numerical investigation of mode interaction in free shear layers." Thesis, The University of Arizona, 1988. http://hdl.handle.net/10150/276871.

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Numerical simulations of incompressible, two-dimensional, monochromatically and bichromatically forced laminar free shear layers are performed on the basis of a vorticity-velocity formulation of the complete Navier-Stokes equations employing central finite differences. Spatially periodic shear layers developing in time (temporal model) are compared with shear layers developing in the stream-wise direction (spatial model). The regimes of linear growth and saturation of the fundamental are quantitatively scrutinized, the saturation of the subharmonic and vortex merging are investigated, and the effects of a forcing phase-shift between fundamental and subharmonic. For the spatial model the appearance of an unforced subharmonic was also examined. It was found that contrary to temporal shear layers a significant control of vortex merging by means of a forcing phase-shift and vortex shredding are not possible in spatial shear layers due to strong dispersion.

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47

Arakelyan, Avetik. "The Finite Difference Methods for Multi-phase Free Boundary Problems." Doctoral thesis, KTH, Matematik (Avd.), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-33543.

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This thesis consist of an introduction and four research papers concerning numerical analysis for a certain class of free boundary problems. Paper I is devoted to the numerical analysis of the so-called two-phase membrane problem. Projected Gauss-Seidel method is constructed. We prove general convergence of the algorithm as well as obtain the error estimate for the finite difference scheme. In Paper II we have improved known results on the error estimates for a Classical Obstacle (One-Phase) Problem with a finite difference scheme. Paper III deals with the parabolic version of the two-phase obstacle-like problem. We introduce a certain variational form, which allows us to definea notion of viscosity solution. The uniqueness of viscosity solution is proved, and numerical nonlinear Gauss-Seidel method is constructed. In the last paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support. The proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions.
QC 20110510

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48

Uda, Tomoki. "On shape derivative and free-boundary problems in vortex dynamics." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225378.

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Han, F. S. "Non-linear free surface problems using the boundary element method." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378300.

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50

Wynne, M. C. "Effect of boundary imperfections on free convection in fluid layers." Thesis, University of Bristol, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379535.

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