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Showing 1 to 20 of 26 for “"Klein-Gordon equation."”.
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A Numerical Method for Computing Radially Symmetric Solutions of a Dissipative Nonlinear Modified Klein-Gordon Equation
… solutions of a dissipative nonlinear modified Klein-Gordon equation in an open sphere around the origin, with constant internal and external damping coefficients and nonlinear term of the form G' (w) = w ^p, with p an odd number greater than 1. We prove that our scheme is consistent of …
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ERROR ESTIMATES OF NUMERICAL METHODS FOR THE LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN-GORDON EQUATION
… for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter.The analytical results indicate that the life-span of a smooth solution to this NKGE is at least …
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Mode stabilities and instabilities for scalar fields on Kerr exterior spacetimes
In this thesis we study wave and Klein-Gordon equations on Kerr exterior spacetimes. For the wave equation, we give a quantitative refinement and simple proofs of mode stability type statements on Kerr backgrounds in the full sub-extremal range ([absolute value of]a < M). As an application, we are …
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Decay for quasilinear wave equations on cosmological black hole backgrounds
… and stability of linear and quasilinear wave equations of Schwarzschild--de~Sitter $(M,\Lambda)$ and Kerr de Sitter $(a,M,\Lambda)$ black hole backgrounds, where $a,M,\Lambda$ are respectively the rotation parameter of the black hole, the mass of the black hole and the cosmological constant. …
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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… approximation for two nonlinear Schrödinger equations. Chapter 1 focuses on the non-relativistic limit of the one-dimensional cubic nonlinear Klein-Gordon equation, which is known (formally) to converge to the cubic nonlinear Schrödinger equation as c → ∞. More precisely, it is known that …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… nonlinear Schrodinger/Gross Pitaevskii (NLS/GP) equation with a linear double-well potential and study justifications of the rotating wave approximations in lattice systems. First, we study the long-time dynamics near a symmetry breaking bifurcation point of the cubic-quintic NLS/GP with …
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Scattering at threshold in massive wave propagation and ionization
… infinity for two PDEs, the Schrödinger–Helmholtz equation with an attractive long range potential and the Klein–Gordon equation. In the former case, the transition occurs as the spectral parameter 𝐸 → 0⁺, and thus describes the ionization of Hydrogenic atoms, and in the latter case the transition …
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Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… dispersive PDEs, including the nonlinear Klein-Gordon equation in the nonrelativistic regime and the Zakharov system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification purposes. …
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Instabilities in asymptotically AdS spacetimes
… as solutions to the Einstein vacuum equations \begin{align*} \mathrm{Ric}(g)=\frac{2}{n-2}\Lambda\, g \end{align*} with negative cosmological constant $\Lambda$. This has been motivated mainly by the conjectured instability of these solutions. The author of this thesis joins these …
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ELASTIC SCATTERING AT RELATIVISTIC ENERGIES OF ALPHA PARTICLES AND PIONS BY NUCLEI USING AN OPTICAL POTENTIAL
… elastic scattering cross sections using the Klein-Gordon equation. The reason for writing this code is because existing codes do not include relativistic kinematics and therefore are only valid for lower energies. This code was used to analyze alpha particle and pion scattering at …
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The Search for a Reduced Order Controller: Comparison of Balanced Reduction Techniques
… Following, there will be mention of the linear Klein-Gordon equation and the development of the one-dimensional finite element approximation of the PDE. Finally, simulations and numerical experiments are used to discuss the differences between the two balanced reduction methods.
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On the parallels between the Maxwell and Dirac equations
… the similarity between the Maxwell and Dirac equations. We reformulate the Dirac equation in an \emph{exact} form of the Maxwell equations, which we refer to as the ``electronic Maxwell equations.'' In this formulation, the standard free Maxwell equations emerge as a special case corresponding …
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I. A pressure Poisson method for the incompressible Navier-Stokes equations : II. Long time behavior of the Klein-Gordon equations
… two problems involving partial differential equations. In the first problem, we reformulate the incompressible Navier-Stokes equations into an equivalent pressure Poisson system. The new system allows for the recovery of the pressure in terms of the fluid velocity, and consequently is ideal …
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Numerical Reconstruction and Applications of Acoustic and Electromagnetic Ultra-Wideband Localized Pulses Generated by Dynamic Aperture Antennas
… connection with LW solutions to the scalar wave equation, especially with respect to their handling of acausal components incorporated in the aperture excitation fields. In addition, a study is presented of the characteristic properties of LWs propagating through dispersive media modeled by the …
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Topological solitons of the nonlinear Dirac equation in 2+1 dimensional space time
… (2 + 0) dimensional reduction the complex sine-Gordon. This is a tachyonic nonlinear Dirac equation whose linear part can be reduced to the imaginary mass Klein-Gordon equation. Although this model is tachyonic it can be restored into a real and non-hypothetical version by considering it in …
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Nonlinear dispersive equations with random initial data
… thesis we consider the defocusing nonlinear wave equation of power-type on R3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of initial data of supercritical regularity which lead to global …
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Quantum Fields on BTZ Black Holes
… linear real scalar field which satisfies the Klein-Gordon equation and also, in the 1+2 dimensional case, for a general QFT satisfying the axioms of Algebraic Quantum Field Theory in Curved Spacetime. We also study how these states map to states on the conformal boundary of AdS spacetime. In …
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Three-dimensional effects on flag flapping dynamics ; [and], Study and modeling of incompressible highly variable density turbulence in the bubbly wake of a transom stern
… direct numerical simulation of the Navier-Stokes equations on a moving body-fitted computational grid for thin membrane structure undergoing arbitrarily (large) displacement. We perform direct numerical simulations, initialized using normal modes we derive, up to Reynolds number 1000 based on L. …
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LONG TIME BEHAVIOR OF LINEAR AND NONLINEAR WAVES:LARGE LARGE AMPLITUDE TRAVELING QUASI-PERIODIC SOLUTIONS IN FLUID MECHANICS AND DYNAMICS OF LINEAR WAVE EQUATIONS
… and a stability result for the linear Klein-Gordon Equation with a small quasi-periodic perturbation. In the first part of the thesis, where we consider two different models on $\mathbb{T}^2$: the non-resistive Magnetohydrodynamics (MHD) system and the 2D-Euler equation for rotating …
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