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Showing 1 to 19 of 19 for “"nonlinear diffusion"”.
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Dynamics of Nonlinear Diffusion Processes
<p>The purpose of this thesis is to analyze nonlinear diffusion processes. In particular, some of the results arrived at by Newman and Sagan in their 1981 paper "Galactic Civilizations: Population Dynamics and Interstellar Diffusion," will be reproduced by different means. First, a thorough …
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Travelling Wave Analysis of a Nonlinear Diffusion Equation
… continuum model, which can be formulated as a nonlinear diffusion free boundary (nonlinear Stefan) problem, indicate a travelling wave behaviour that is subsequently investigated using a travelling wave analysis. Considering first a simplified linear problem, we perform a travelling wave …
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A nonlinear diffusion theory model for xenon-induced flux oscillations
A nonlinear model is developed for the xenon induced flux oscillation problem that occurs in nuclear power plants. The model is based on Galerkins' method of weighted residuals applied to multigroup diffusion theory. A similar linear model is developed by the same methods in order to consider the …
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Monte Carlo and thermal hydraulic coupling using low-order nonlinear diffusion acceleration
… as a benchmark tool for other transport and diffusion methods. In this work, we identify and resolve a few of the issues associated with using MC as a reactor design tool. It is widely thought that MC tallies converge at an ideal rate proportional to the inverse of the square root of the …
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Online higher-order error correction of nonlinear diffusion generalized perturbation theory using neural networks
… theory (GPT) approximation of the neutron diffusion fundamental-mode eigenvalues (1/ k[Subscript eff)] The primary application of this work is nuclear fuel loading optimization. The k[Subscript eff] approximation is generated which estimates perturbed conditions as a function of fuel …
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Chaotic diffusion in nonlinear Hamiltonian systems
This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional …
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Quantitative studies and Hydrodynamical limits for interacting particle systems
… We give bounds on the spectral gap for weak nonlinearities of the chain, i.e. perturbations around linear homogeneous chains and also a complete answer for the linear, homogeneous and disordered, chain of oscillators as well as $d$-dimensional grids of oscillators. The methods range from …
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On some nonlinear partial differential equations for classical and quantum many body systems
… deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that …
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ΕΠΙΛΥΣΗ ΤΟΥ ΜΗ ΓΡΑΜΜΙΚΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΤΩΝ ΠΟΛΛΩΝ ΡΕΥΜΑΤΟΦΟΡΩΝ ΑΓΩΓΩΝ ΜΕ ΤΗ ΜΕΘΟΔΟ ΠΕΠΕΡΑΣΜΕΝΩΝ ΣΤΟΙΧΕΙΩΝ
… THE SECOND PART IS A COMPLEX ANALYSIS OF THE NONLINEAR DIFFUSION PROBLEM IN FERROMAGNETIC MATERIALAS UNDER STEADY-STATE EXCITATION, THE PROBLEM IS SOLVED BY CONSIDERING AN EQUIVALENT FICTITIOUS MATERIAL WHERE THE RELATIVE PERMEABILITY IS ASSUMED TO BE CONSTANT IN TIME BUT DIFFERENT FROM POINT …
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Design and Fabrication of Electrostatically Actuated Serpentine-Hinged Nickel-Phosphorous Micromirror Devices
… which the deposition was intended to occur, and nonlinear diffusion of dissolved oxygen in the solution.</p>
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Mathematical modeling of lithium-ion intercalation particles and their electrochemical dynamics
… of the efficient numerical algorithm for solving nonlinear diffusion equations, we numerically investigate the thermodynamics and electrokinetics of the 1D spherical CHR model with different possible material properties in detail. We also extend the CHR model to 2D and briefly study the effects of …
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Physical and chemical analysis of pig carcass decomposition in a fine sand
… presence of a decomposition site. Furthermore, a nonlinear diffusion model was developed to predict the development of the cadaver decomposition island (CDI) in soil over time. The simulation of the model indicated that the diffusion model has the potential to generate PMI estimations for early …
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
… equation; Laplace's equation; and a class of nonlinear diffusion equations. Our method uses the inspectional symmetries of each of these differential equations to determine the equation's remaining symmetries. In these cases the method is so effective that the simplified determining systems …
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Transient method of characteristics via the Adiabatic, Theta, and Multigrid Amplitude Function methods
… for both problems. A relaxation factor on the nonlinear diffusion coefficient was required to maintain stability for both problems with optimum values between 0.4-0.7. A sensitivity study was conducted on the C5G7 and LRA transient problems to understand the effects of time step and spatial …
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Modelling surface evolution coupled with tectonics
… structured surface mesh. Both SECs involve diffusion as approach for hillslope processes and the stream power law to reflect riverbed incision. The 1D SEC settles sediment that was produced by fluvial incision in the appropriate minimum, while the supply-limited 2D SEC DANSER uses a fast …
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Strongly Stable and Accurate Numerical Integration Schemes for Nonlinear Systems in Atmospheric Models
Nonlinearity accompanied with stiffness in atmospheric boundary layer physical parameterizations is a well-known concern in numerical weather prediction (NWP) models. Nonlinear diffusion equations, furthermore, are a class of equations which are extensively applicable in different fields of science …
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Structural Conditions for Global Existence in Some Chemotaxis Systems with Different Logistics
… system dynamics. By analyzing linear and nonlinear production laws, sensitivity functions, and threshold values of parameters, the thesis demonstrates how repulsive signaling can counteract destabilizing aggregation effects. Special attention is given to nonlinear diffusion and chemotactic …
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Modelling the spreading and draining of viscous films
… The model is systematically reduced to a nonlinear diffusion PDE. The subsequent analysis is applicable to a broad family of PDEs, hence the analysis is presented in some generality. Solutions to the PDEs under consideration exhibit an interesting behaviour in which the front of a …
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Efficient Multiphysics Coupling for Fast Burst Reactors in Slab Geometry
… a tightly coupled multiphysics algorithm of diffusion neutronics and linear. An implicit-explicit (IMEX) algorithm was used to follow the dynamical time-scale of the problem. However, as noted by him and his co-authors, the diffusion model does not adequately represent the neutronics of the …