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Showing 1 to 20 of 48 for “"Nonlinear Evolution"”.
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Nonlinear evolution of Vlasov equilibria
In this work, we investigate numerically the evolution of perturbed Vlasov equilibria. according to the full nonlinear system with particular emphasis on analyzing the asymptotic states towards which the system evolves. The simulations are carried out with the numerical code that we have …
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The nonlinear evolution of secondary instabilities in boundary layers
Following the concepts of stability analysis, a study is made of the pre-breakdown stage of transition to turbulence in boundary layers. The first step consists of a ’decoupling’ of the primary and secondary instabilities. A perturbation method is used to solve for the primary wave, in the absence …
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Asymptotic analysis of the parametrically driven damped nonlinear evolution equation
… for the parametrically driven damped linear and nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear oscillator, we apply the Lindstedt-Poincare method and the …
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Nonlinear evolution of annular layers and liquid threads in electric fields
The nonlinear dynamics of viscous perfectly conducting liquid jets or threads under the action of a radial electric field are studied theoretically and numerically here. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. A …
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Theory of Instability and Nonlinear Evolution of Self -Sustained Detonation Waves
Linear stability properties and nonlinear dynamics of self-sustained detonations is investigated by means of asymptotic analysis and numerical simulations. The normal-mode linear stability analysis is carried out for gaseous detonations propagating in cylindrical tubes. By comparison of the …
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Nonlinear Evolution of Mirror Instability in the Earth's Magnetosheath in PIC Simulations
… anisotropy left to significantly impact the evolution of the mirror instability.</p> <p>Observational studies have shown that the shape of mirror structures is related to local plasma parameters and distance to the mirror instability threshold. Mirror structures in the form of magnetic holes …
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Spatially coherent solutions of damped-driven nonlinear evolution equations and reaction-diffusion system
Bibliography: leaves 128-134.
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Stability of a liquid thread and stability and nonlinear evolution of multi-layer fluid flow
This thesis is concerned with stability and existence of waves in interfacial and free surface problems. Considered is the curtain coating problem, with specific emphasis on trilayer and bilayer flows, and the breakup of a viscous thread with a solid core. Experiments on curtain coating and sheet …
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The effect of polymer additives on the hydrodynamic stability and nonlinear evolution of thin liquid films
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1996.
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Nonlinear hydrodynamic instability and turbulence in eccentric astrophysical discs
The nonlinear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at mean-motion resonances, …
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Instabilities and transport in magnetized plasmas
… fluid theory is inapplicable. We determine its nonlinear evolution in an ab initio kinetic calculation (for parallel gradients only). We use a particular physical asymptotic ordering to derive a closed nonlinear equation for the firehose turbulence, which we solve. We find secular (∝ t) growth …
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Analysis of a Partial Differential Equation Model of Surface Electromigration
… modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function <em>h</em>(<em>x</em>,<em>t</em>) of the film in the horizontal electric field, followed by the results of the linear …
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Instability of electrified viscous films
… the leading order. Our target is to analyse the nonlinear stability of the flow. We attain this by deriving and numerically solving a set of nonlinear evolution equations for the local film thickness and for symmetrical interfacial perturbations. We find that the electric field forces enhance the …
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Asymptotic Stability of the Ground States of the Nonlinear Schrodinger Equation
"We consider a class of nonlinear Schrodinger equations in N = 3, 4, 5 space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2( RN )) nonlinearities. We study the asymptotic stability of …
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
… norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to the nonlinear evolution. In our work, we …
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Mathematical problems arising in interfacial electrohydrodynamics
In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, …
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Stability analysis of a bilayer contained within a cylindrical tube
… the formation of the liquid bridge. A system of nonlinear coupled equations for the deflections of the interfaces and the surfactant concentration is derived by using an extended lubrication theory analysis. A linear stability study using normal modes is conducted by linearizing the nonlinear …
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Analytical and Numerical Studies of the Generation and Propagation of Nonlinear Water Waves by a Wavemaker
The ability to predict the nonlinear effects of extreme wave events is paramount for the preparation of modern experimental tests in large wave basins. Currently, linear theory is routinely used, hence nonlinear wave-wave interactions between propagating waves are often ignored. In addition, the …
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Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models
… thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and …
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mKdV Loop Travelling Waves and Interactions of Loop Solitons
… Vries (mKdV) equation is an integrable nonlinear evolution equation which has applications in modeling various physical phenomena. It also describes the curvature of curve which undergoes a certain non-stretching geometrical evolution in the Euclidean plane. This curve motion finds …
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