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Showing 1 to 19 of 19 for “"stationary solutions"”.
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Stationary solutions of abstract kinetic equations
The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a …
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Stochastic hypodissipative hydrodynamic equations: well-posedness, stationary solutions and ergodicity
… case, we obtain the existence of martingale solutions and pathwise uniqueness of the solutions, which imply the existence of the probabilistically strong solution to this system by the Yamada–Watanabe Theorem.<br /> 2. We also study stationary solutions and ergodicity of both anisotropic …
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On the stationary solutions of Van Der Pol's equation with a forcing term
Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Mathematics, 1946.
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Stability of flat galaxies
… we investigate the existence and properties of stationary solutions of the flat Vlasov-Poisson system. This system of partial differential equations can be used as a model of extremely flat astronomical objects and is a combination between the two-dimensional motion of particles and the …
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Theory of optical rectification in a travelling wave structure
… is elucidated. It is shown that continuous wave solutions of the conservative system are modulationally unstable in a large range of relevant system parameters. The possibility of formation of solitary waves due to the mutual interaction of optical wave and microwave is considered in the context …
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Existence and stability of stellardynamic models
We examine existence and stability of stationary solutions to the Vlasov-Poisson system. This system is used in stellardynmaics to describe the evolution of galaxies where collissions are neglected and the evolution is determined by the self-consistent gravitational field which is created by the …
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Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space
… the first convergence guarantees to first-order stationary solutions when π is only log-smooth. Additionally, in the setting where the potential admits a representation as the average of many smooth component functionals, we develop and analyze a variance-reduced extension to (Stochastic) FB–GVI …
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Modelling of microgravity ignition phenomena
… the heat loss mechanism necessary for stable solutions is the radiation from burnt gas. If heat loss is less than quenching value, there are two stationary solutions, but the small branch solution is always unstable to the one dimensional disturbances regardless of Lewis number when Le $\leq$ …
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Distributed Training with Heterogeneous Data: Bridging Median- and Mean-Based Algorithms
… signSGD, and further enjoy global convergence to stationary solutions. Our perturbation technique can be of independent interest when one wishes to estimate mean through a median estimator.
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Response of nonlinear structures to deterministic and random excitations
… compared with those obtained by using the exact stationary solutions of the Fokker-Planck-Kolmogorov equation. It is found that the presence of the nonlinearities bend the frequency-response curves and this causes multi-valued regions for the mean-square responses. The multi-valuedness is …
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Generalized Navier-Stokes equations for active turbulence
… tractable in planar and curved geometry. Exact stationary bulk solutions include Abrikosovtype vortex lattices in 2D and chiral Beltrami fields in 3D. Numerical simulations for a plane Couette shear geometry predict a low viscosity phase mediated by stress defects, in qualitative agreement with …
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Floquet theory of electronic stopping processes of projectiles in solids
… systems. Floquet theory allows to find the solutions of time-periodic Hamiltonians through the same techniques used in time-independent problems: this provides the new framework with an intrinsic advantage over the the real time first principles calculations that are currently employed for …
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The effect of shear flow on the Isotropic-Nematic transition in liquid crystals
… equations, respectively. We examine the stable stationary solutions to these equations to determine the nature of the nonequilibrium phases, and discuss the analogies and differences between this system and equilibrium systems. From homogeneous solutions we obtain a state diagram analogous to …
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Analyses and Applications of the Peaceman--Rachford and Douglas--Rachford Splitting Schemes
… are ideal choices for studying convergence to stationary solutions, a property related to their favorable local error structure. In this thesis we consider the Peaceman--Rachford and Douglas--Rachford schemes, which were the first ADI methods to be constructed and to this day are the most …
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Deterministic numerical simulation of the Boltzmann and kinetic model equations for classical and quantum dilute gases
… results with the exact Bobylev-Krook-Wu solutions of the space-homogeneous Boltzmann equation for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the …
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Stationary Anti-de Sitter Black Hole Solutions in and out of Equilibrium
Stationary solutions are perhaps the most fundamental objects in any physical theory. In this thesis we numerically obtain a number of stationary black hole solutions to the Einstein-Maxwell equations with a negative cosmological constant. The AdS/CFT correspondence has caused an upsurge in …
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Asymptotics, exact results, and analogies in p-adic random matrix theory
… to ∞, we show that this process converges to a stationary limit, with density explicitly expressed in terms of certain intricate exponential sums. The proof uses new Macdonald process computations, which feature a symmetric function incarnation of the explicit solution to the inverse moment …
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Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field
… 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 consider vector-valued solitary …
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Well balanced Arbitrary-Lagrangian-Eulerian Finite Volume schemes on moving nonconforming meshes for non-conservative Hyperbolic systems
… precision. Perturbations around such equilibrium solutions are resolved with high accuracy and minimal dissipation on moving contact discontinuities even for very long computational times. The core of our ALE scheme is the use of a space-time conservation formulation in the construction of the …