Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for subject:(Self similar solution). Showing records 1 – 3 of 3 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


Georgia Southern University

1. Chan, Fun Choi. One-Dimensional Fractal Wave Equations.

Degree: MSin Mathematics (M.S.), Department of Mathematical Sciences, 2011, Georgia Southern University

We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated function systems with overlaps, such as the well-known infinite Bernoulli convolution associated with golden ratio and the 3-fold convolution of the Cantor measure. The iterated function systems defining these measures do not satisfy the open set condition or the post-critically finite condition, and therefore the existing theory, introduced by Kigami and developed by many other mathematicians, cannot be appled. First, by using a weak formulation of the problem, we prove the existence, uniqueness and regularity of weak solutions of these wave equations. Second, we study numerical computations of the solutions. By using the second-order self-similar identities introduced by Strichartz et al., we discretize the equation and use the finite element method and central difference method to obtain numerical solutions. Last, we also prove that the numerical solutions converge to the weak solution, and obtain estimates for the convergence of this approximation scheme. Advisors/Committee Members: Scott Kersey, Frederic Mynard, Shijun Zheng.

Subjects/Keywords: ETD; Fractal; Wave equation; Iterated function system; Second-order self-similar identities; Weak solution; Finite element method; Jack N. Averitt College of Graduate Studies, Electronic Theses & Dissertations, ETDs, Student Research

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chan, F. C. (2011). One-Dimensional Fractal Wave Equations. (Masters Thesis). Georgia Southern University. Retrieved from https://digitalcommons.georgiasouthern.edu/etd/657

Chicago Manual of Style (16th Edition):

Chan, Fun Choi. “One-Dimensional Fractal Wave Equations.” 2011. Masters Thesis, Georgia Southern University. Accessed November 28, 2020. https://digitalcommons.georgiasouthern.edu/etd/657.

MLA Handbook (7th Edition):

Chan, Fun Choi. “One-Dimensional Fractal Wave Equations.” 2011. Web. 28 Nov 2020.

Vancouver:

Chan FC. One-Dimensional Fractal Wave Equations. [Internet] [Masters thesis]. Georgia Southern University; 2011. [cited 2020 Nov 28]. Available from: https://digitalcommons.georgiasouthern.edu/etd/657.

Council of Science Editors:

Chan FC. One-Dimensional Fractal Wave Equations. [Masters Thesis]. Georgia Southern University; 2011. Available from: https://digitalcommons.georgiasouthern.edu/etd/657

2. Vallet, Alexandra. Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel.

Degree: Docteur es, Astrophysique, plasmas, nucléaire, 2014, Bordeaux

Le schéma d'allumage par choc pour la fusion par confinement inertiel utilise une impulsion laser intense à la fin d'une phase d'assemblage de combustible. Les paramètres clefs de ce schéma sont la génération d'une haute pression d'ablation, l'amplification de la pression du choc généré par un facteur supérieur à cent et le couplage du choc avec le point chaud de la cible. Dans cette thèse, de nouveaux modèles semi-analytiques sont développés afin de décrire le choc d'allumage depuis sa génération jusqu'à l'allumage du combustible. Tout d'abord, un choc sphérique convergent dans le coeur pré-chauffé de la cible est décrit. Le modèle est obtenu par perturbation de la solution auto-semblable de Guderley en tenant compte du nombre de Mach du choc élevé mais fini. La correction d'ordre un tient compte de l'effet de la force du choc. Un critère d'allumage analytique est exprimé en fonction de la densité surfacique du point chaud et de la pression du choc d'allumage. Le seuil d'allumage est plus élevé pour un nombre de Mach faible. Il est montré que la pression minimale du choc, lorsqu'il entre dans le coeur de la cible, est de 20Gbar. La dynamique du choc dans la coquille en implosion est ensuite analysée. Le choc se propage dans un milieu non inertiel avec un fort gradient de pression et une augmentation temporelle générale de la pression. La pression du choc est amplifiée plus encore durant la collision avec une onde de choc divergente provenant de la phase d'assemblage. Les modèles analytiques développés permettent une description de la pression et de la force du choc dans une simulation typique de l'allumage par choc. Il est démontré que, dans le cas d'une cible HiPER, une pression initiale du choc de l'ordre de 300 Mbar dans la zone d'ablation est nécessaire. Il est proposé une analyse des expériences sur la génération de chocs forts avec l'installation laser OMEGA. Il est montré qu'une pression du choc proche de 300Mbar est atteinte près de la zone d'ablation avec une intensité laser absorbée de l'ordre de 2 X 10(15) W.cm-2 et une longueur d'onde de 351 nm. Cette valeur de la pression est deux fois plus importante que la valeur attendue en considérant une absorption collisionnelle de l'énergie laser. Cette importante différence est expliquée par la contribution d'électrons supra-thermiques générés durant l'interaction laser/plasma dans la couronne. Les modèles analytiques proposés permettent une optimisation de l'allumage par choc lorsque les paramètres de la phase d'assemblage, sont pris en compte. Les diverses approches analytiques, numériques et expérimentales sont cohérentes entre-elles.

The shock ignition concept in inertial confinement fusion uses an intense power spike at the end of an assembly laser pulse. the key feature of shock ignition are the generation of a high ablation pressure, the shock pressure amplification by at least a factor of a hundred in the cold fuel shell and the shock coupling to the hot-spot. in this theses, new semi-analytical hydrodynamic models are developed to describe the…

Advisors/Committee Members: Tikhonchuk, Vladimir (thesis director), Ribeyre, Xavier (thesis director).

Subjects/Keywords: Allumage par choc; Fusion par confinement inertiel; Choc sphérique; Solution auto-semblable,; Dynamique du choc; Pression d'ablation; Eléctrons chauds; Shock ignition; Inertial confinement fusion; Spherical shock wave; Self-similar solution; Perturbative approach; Shock dynamics; Ablation pressure; Hot-electrons

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Vallet, A. (2014). Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2014BORD0214

Chicago Manual of Style (16th Edition):

Vallet, Alexandra. “Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel.” 2014. Doctoral Dissertation, Bordeaux. Accessed November 28, 2020. http://www.theses.fr/2014BORD0214.

MLA Handbook (7th Edition):

Vallet, Alexandra. “Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel.” 2014. Web. 28 Nov 2020.

Vancouver:

Vallet A. Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel. [Internet] [Doctoral dissertation]. Bordeaux; 2014. [cited 2020 Nov 28]. Available from: http://www.theses.fr/2014BORD0214.

Council of Science Editors:

Vallet A. Hydrodynamic modelling of the shock ignition scheme for inertial confinement fusion : Modélisation hydrodynamique du schéma d'allumage par choc pour la fusion par confinement inertiel. [Doctoral Dissertation]. Bordeaux; 2014. Available from: http://www.theses.fr/2014BORD0214


Louisiana State University

3. Zhang, Jin. Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films.

Degree: PhD, Mechanical Engineering, 2006, Louisiana State University

A liquid film of thickness h < 100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory for uniform films gives Pi = Pi(h). It becomes unbounded as h -> 0. We present a theory of curvature-dependent disjoining pressure. The new Pi depends on the curvature hxx, slope hx, and h. When this theory is implemented for Lennard-Jones liquid films, the new Pi is bounded as h -> 0. We show that this Pi captures three regimes of drop behavior (complete wetting, partial wetting, and pseudo partial wetting) without altering the signs of the long and short-range interactions. We also find that a drop with a uniform film is linearly stable, whereas a drop without a uniform film is unstable. Evaporating thin films is important in solvent coating and thin-film heat transfer. In some experiments, satellite liquid drops were observed when an evaporating film retracts. We model the evolution of a two-dimensional evaporating thin film on a heated substrate. The results show that the film thins and the film edge retracts. The thinning film forms a ridge at the edge followed by a thin neck before it returns to the uniform thickness. This profile is maintained till dry-out. The ridge breaks away to form a droplet and the remaining film keeps evolve. In this way, a series of droplets is formed with decreasing volumes. We find that the drop volume depends on the evaporation parameters and the drops have similar profiles. We explore the reasons for the similar profiles of satellite droplets. We study self-similar retraction of a step liquid film pinned at the contact line. We find a self-similar solution in which the x-coordinate is scaled with time t. We also simulate the evolution of a pinned step film and find that the film profile always approaches the self-similar solution as t -> infinity. We study the linear stability of the self-similar solution and find that the self-similar solution is stable.

Subjects/Keywords: evaporating film; evolution equation; thin film; self-similar solution; pseudo partial wetting; dewetting; disjoining pressure; intermolecular forces; augmented Young-Laplace equation; wetting

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zhang, J. (2006). Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07132006-023633 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3428

Chicago Manual of Style (16th Edition):

Zhang, Jin. “Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films.” 2006. Doctoral Dissertation, Louisiana State University. Accessed November 28, 2020. etd-07132006-023633 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3428.

MLA Handbook (7th Edition):

Zhang, Jin. “Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films.” 2006. Web. 28 Nov 2020.

Vancouver:

Zhang J. Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films. [Internet] [Doctoral dissertation]. Louisiana State University; 2006. [cited 2020 Nov 28]. Available from: etd-07132006-023633 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3428.

Council of Science Editors:

Zhang J. Theory of Curvature-Dependent Disjoining Pressure and Its Application to Liquid Films. [Doctoral Dissertation]. Louisiana State University; 2006. Available from: etd-07132006-023633 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3428

.