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Showing 1 to 19 of 19 for “"biharmonic"”.
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Biharmonic maps
… of the gradient flow for the (intrinsic) biharmonic energy under suitable curvature or initial energy assumptions. Moreover we use the biharmonic energy to regularize the Dirichlet energy for maps from a Riemannian surface into a round sphere. Finally we prove the so called energy identity …
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Mixed Problems and Layer Potentials for Harmonic and Biharmonic Functions
<p>The mixed problem is to find a harmonic or biharmonic function having prescribed Dirichlet data on one part of the boundary and prescribed Neumann data on the remainder. One must make a choice as to the required boundary regularity of solutions. When only weak regularity conditions are imposed, …
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A Comparison of Two Boundary Methods For Biharmonic Boundary Value Problems
<p>The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped …
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A Comparison of Two Different Methods for Solving Biharmonic Boundary Valve Problems
… the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a …
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Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips
We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.
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The 1-dimensional [lambda]-self shrinkers in R² and the nodal sets of biharmonic Steklov problems
… of the asymptotic behavior of the nodal set of biharmonic Steklov problems. Chapter 1 gives the background of mean curvature flow and the importance of self-shrinkers as solitons of the flow equation. We also introduce the background of the [lambda]-hypersurface and explain how this is related …
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Analytic Solutions to the Laplace, Poisson, and Biharmonic Equations with Internal Boundaries: Theory and Application to Microfluidic Dynamics
… elliptic PDE problems: Laplace, Poisson, biharmonic, and Stokes flow. First we introduce our main analytic result known as the Parity Split Method (PSM) developed in the context of the Laplace and the Poisson equation. The method is then applied to the problem of a thermally driven …
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A C<sup>0</sup> Interior Penalty Method for the von Kármán Equations
… C<sup>0</sup> interior penalty method for the biharmonic problem. Motivated by these results, we propose a C<sup>0</sup> interior penalty method for the linearized von Kármán equations in Chapter 5 and show the well-posedness and stability of this method. We then introduce the new C<sup>0</sup> …
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Evolution of atmospheric baroclinic waves
… Ekman layer, a Newtonian cooling and an interior biharmonic friction as the dissipation and (iii) an initial state consisting of a weak but general wave field superimposed on a jet-like zonal mean flow. The whole evolution of the baroclinic waves can be divided into three periods; namely, the …
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Ratchet dynamics in nonlinear Klein-Gordon systems
… nonlinear extended systems in the presence of a biharmonic force and dissipation. We have shown that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the …
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On the rolling motion of viscous fluid on a rigid surface
… rolls on a super-hydrophobic surface. The biharmonic boundary element method (BBEM) is used to implement numerical simulations of rolling motion. The numerical results agree well with the experimental results and theoretical prediction. Numerical evidence is also found that the stress …
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Large Scale Simulation of Spinodal Decomposition
… partial differential equation involving a biharmonic form and a noise forcing term. When the potential term is a polynomial, the CHC equation is split into a lower order PDE system of two harmonic equations. T he space is discretized by the standard finite element method. The evolution of …
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Finite elements for higher-order problems in isogeometric analysis and statistical inference
… are numerically observed for the Poisson and biharmonic problems in one and two dimensions. The statistical finite element method coherently sythesises data and finite element models using Bayesian inference. However, the Gaussian process inference using covariance matrices is computationally …
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Multiple equilibria and low-frequency variability of wind-driven ocean models
… pitchfork bifurcations as the model's biharmonic viscosity is reduced. Succesive pairs of mirror image equilibria have an additional half meander in the jet. The distinct energy levels of the steady state solutiOris can be understood in part by there different inter-gyre fluxes of …
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Application of an inverse model in the community modeling effort results
… but also (part of) the temporal variation and biharmonic terms which are not explicitly included in the inverse model. Given the essentially red spectrum of the ocean, it makes sense to look for smooth solutions. Aliasing due to subsampling on a coarse grid and the effects of spatial smoothing …
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Topological Chaos and Mixing in Lid-Driven Cavities and Rectangular Channels
… stream function satisfies the two-dimensional biharmonic equation. When the flow occurs in a lid-driven cavity with solid side walls, this equation can be solved using a method that is similar to the traditional Fourier expansion but uses an asymptotic approximation for the sum of high order …
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Infinite soluzioni deboli per un problema non-lineare con condizioni al contorno di tipo Navier coinvolgente l'operatore p-biarmonico.
In questo articolo stabiliamo alcuni risultati di esistenza di infinite soluzioni deboli per un problema di tipo ellittico, con condizioni al contorno di tipo Navier, coinvolgente l'operatore p-biarmonico e l'operatore p-laplaciano. La natura dell'approccio è variazionale e lo strumento …
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Dynamics of the Antarctic circumpolar current : evidence for topographic effects from altimeter data and numerical model output
… momentum transfer is dominated by horizontal biharmonic friction. In the upper ocean, horizontal friction, mean momentum flux divergence, transient momentum flux divergence, and mean vertical flux divergence all contribute significantly to the momentum balance. Although the relative importance …
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Spectral approach for improving the Ill-conditioning of the method of fundamental solutions
O método das soluções fundamentais, em inglês, method of fundamental solutions (MFS), é um método para solução de problemas de valor de fronteira de equações diferenciais com derivadas parciais. O método pertence à classe dos métodos que não necessitam de discretização do domínio, evitando, dessa …