Les solitons de cavité sont des pics stationnaires d'intensité qui apparaissent dans le plan transverse d'un résonateur optique non linéaire injecté par un champ électromagnétique cohérent (faisceau de maintien). Ils peuvent être allumés et éteints individuellement par une perturbation locale sous la forme d'un pulse de lumière (faisceau d'écriture). La possibilité de contrôler leur position et leur mouvement par l'introduction d'un gradient de phase ou d'amplitude dans le faisceau de maintien permet leur application comme pixels mobiles de lumière dans un processeur d'information tout optique. D'un point de vue fondamental, les solitons de cavité sont des Structures Localisées à un seul pic en tous points analogues à celles observées dans les milieux granulaire, dans la décharge électrique dans un gaz, dans les instabilités chimique et dans l'hydrodynamique. Ces structures apparaissent en présence d'une instabilité modulationelle de la solution homogène qui se produit de façon sous critique, où il y a donc cœxistence de solutions différentes pour les mêmes valeurs de paramètres. Les solitons de cavité ont donc une nature très différente par rapport aux solitons spatiaux qui sont basés sur un mécanisme de compensation entre diffraction et non linéarité qui se produit lors de la propagation.<br /><br />Dans cette thèse je résumerai les principaux résultats de ma recherche sur les solitons de cavité dans les Lasers à Semi-conducteurs à Cavité Verticale. J'introduirai le concept de Soliton de cavité dans le cadre de la morphogènes en optique et je mettrai en évidence la similitude avec les structures localisées observées dans d'autres systèmes optiques. Je montrerai expérimentalement leur existence et j'analyserai leurs propriétés dans l'espace de paramètres. Je montrerai qu'il est possible de les positionner en forme de matrices qui peuvent être reconfigurées optiquement. Je mettrai en évidence expérimentalement la possibilité d'utiliser les solitons de cavité pour la réalisation d'une ligne de retard tout optique basée sur leur coulissement en présence d'un gradient de phase dans le faisceau de maintien.

Nous présentons ici, l'analyse détaillée et l'étude de la stabilité de nouvelles solutions de type vortex dans le secteur bosonique de la théorie électrofaible. Les nouvelles solutions généralisent le plongement des solutions d'Abrikosov-Nielsen-Olesen dans la théorie électrofaible et reproduisent les résultats précédemment connus. Les vortex, génériquement porteurs d'un courant électrique, sont constitués d'un coeur massif de bosons chargés W entouré d'une superposition non-linéaire de champs Z et Higgs. Au loin la solution est purement électromagnétique avec un potentiel de Biot et Savart. Les solutions sont génériques de la théorie et existent en particulier pour les valeurs expérimentales des constantes de couplage. Il est en particulier démontré que le courant dont l'échelle typique est le milliard d'Ampères peut être arbitrairement grand. Dans un second temps la stabilité linéaire des vortex supraconducteurs vis-à-vis des perturbations génériques est considérée. Le spectre de l'opérateur de fluctuations est étudié qualitativement. Lorsque des modes instables sont détectés, ils sont explicitement construits ainsi que leurs relations de disperion. La plupart des modes instables sont supprimés par une périodisation du vortex. Il subsiste cependant un unique mode instable homogène. On peut espérer qu'un tel mode puisse être supprimé par des effets de courbure si une portion de vortex est refermée afin de former une boucle stabilisée par le courant électrique.

Proteins in nature fold to one dominant native structure. Despite being a heavily studied field, predicting the native structure from the amino acid sequence and modeling the folding process can still be considered unsolved problems. In this thesis I present a new approach to this problem with methods borrowed from theoretical physics. In the first part I show how it is possible to use a discrete Frenet frame to define the discrete curvature and torsion of the main chain of the protein. This method is then extended to the side chains as well. In particular I show how to use the discrete Frenet frame to produce a statistical distribution of angles that works in similar fashion as the commonly used Ramachandran plot and side chain rotamers. The discrete Frenet frame displays a gauge symmetry, in the choice of basis vectors on the normal plane, that is reminiscent of features of Abelian-Higgs theory. In the second part of the thesis I show how this similarity with Abelian-Higgs theory can be translated into an effective energy for a protein. The loops of the proteins are shown to correspond to solitons so that the whole protein can be constructed by gluing together any number of solitons. I present results of simulating proteins by minimizing the energy, starting from a real line or straight helix, where the correct native fold is attained. Finally the model is shown to display the same phase structure as real proteins.

Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed temporal and spatial features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is formed with the wave crest perpendicular to the wall; this stem wave is not in the form of a Korteweg-de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression wave. Evolution of stem-wave amplification is in good agreement with the Kadomtsev-Petviashvili (KP) theory. The asymptotic characteristics and behaviors are also in agreement with the theory of Miles (1977b) except those in the neighborhood of the transition between the Mach reflection and the regular reflection. The maximum fourfold amplification of the stem wave at the transition predicted by Miles is not realized in the laboratory environment: the maximum amplification measured in the laboratory is 2.92, which is however in excellent agreement with the numerical results of Tanaka (1993). The present laboratory study is the first to sensibly analyze validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking along the wall results in the substantial increase in wave height and slope away from the wall. Extending the foregoing study on the reflection of a single solitary wave at a vertical wall, laboratory and numerical experiments are performed on two co-propagating obliquely incident solitary waves with different amplitudes that are reflected at the wall. The larger wave catches up with the smaller wave; hence the two waves collide with the strong interaction. The resulting wave pattern near the wall is complex due to the interaction among the two incident solitons and the two reflected solitons. The numerical predictions of the KP theory are in good agreement with the experimental results. Another comparison of the KP theory with laboratory experiments is demonstrated for one of the exact soliton solutions of the KP equation by Chakravarty and Kodama (2009). This solution is called the T-type solution by Kodama. The theoretically predicted formation of the 'box'-shape wave pattern in the vicinity of two-soliton intersection is realized in the laboratory tank. The agreement between the laboratory observation and the KP theory is found better for the cases with the larger wave amplitude a and smaller oblique angle ψ (i.e. tan ψ/(√3a cos ψ) < 0.6). Subtle and unavoidable differences among the analytical KP solution, the setup of numerical calculation, and the laboratory condition are discussed. / Graduation date: 2013

Thesis (Ph. D.)--University of Washington, 2001. / Includes bibliographical references (leaves 156-168).

Thesis (M.S. in Physical Oceanography)--Naval Postgraduate School, June 2003. / Thesis advisor(s): Timothy P. Stanton, Edward B. Thornton. Includes bibliographical references (p. 77-79). Also available online.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

The magnetosphere of pulsars is thought to consist of an electron-positron plasma rotating in the pulsar magnetic field (Beskin, Gurevich & Istomin 1983; Lominadze, Melikidze & Pataraya 1984; Gurevich & Istomin 1985). A finite, and indeed large, longitudinal electric field exists outside the star, and may accelerate particles, stripped from the surface, to high energies (Goldreich & Julian 1969; Beskin 1993). These particles may leave the magnetosphere via open magnetic field lines at the poles of the pulsar. This depletion of particles causes a vacuum gap to arise, a double layer of substantial potential difference. The primary particles, extracted from the star's surface, are accelerated in the double layer, along the pulsar magnetic field lines, and so produce curvature radiation. The curvature photons, having travelled the distance of the double layer may produce electron-positron pairs above the vacuum gap. These first-generation secondary particles, although no longer accelerating, may synchroradiate, generating photons which may then produce further electron-positron pairs. These synchrophoton produced pairs will be at energies lower than curvature photon produced pairs, since synchrophoton energies are approximately an order of magnitude less than that of the parent curvature photon. An attempt to model the electron-positron pulsar magnetosphere is made. A four component fluid electron-positron plasma is considered, consisting of a hot electron and positron species, at temperature Th , and a cool electron and positron species at temperature Tc . The hot components represent the parent first-generation curvature-born pairs, and the cooler components represent the second-generation pairs, born of synchrophotons. The hot components are assumed to be highly mobile, and are thus described by a Boltzmann density distribution. The cool components are more sluggish and are thus described as adiabatic fluids. The model is symmetric in accordance with pair production mechanisms, so that both species of hot(cool) electrons and positrons have the same temperature Th(Tc, and number density Nh(Nc ) . In the interests of completeness, linear electrostatic waves in five different types of electron-positron plasmas are considered. The dispersion relations for electrostatic waves arising in these unmagnetized plasmas are derived. Single species electron-positron plasmas are investigated, considering the constituents to be: both Boltzmann distributed; both adiabatic fluids; and finally, one species of each type. Linear electrostatic acoustic waves in multi-component electron-positron plasmas are then considered, under the four component model and a three component model (Srinivas, Popel & Shukla 1996). Small amplitude nonlinear electron-positron acoustic waves are investigated, under the four component electron-positron plasma model. Reductive perturbation techniques (Washimi & Taniuti 1966) and a derivation of the Korteweg-de Vries equation result in a zero nonlinear coefficient, and a purely dispersive governing wave equation. Higher order nonlinearity is included, leading to a modified Korteweg-de Vries equation (Watanabe 1984; Verheest 1988), which yields stationary soliton solutions with a sech dependence rather than the more familiar sech2. Arbitrary amplitude solitons are then considered via both numerical and analytical (Chatterjee & Roychoudhury 1995) analysis of the Sagdeev potential. The symmetric nature of the model leads to the existence of purely symmetrical compressive and rarefactive soliton solutions. Small and arbitrary amplitude soliton solutions are compared, and show good correlation. Under the assumption of Boltzmann distributed hot particles, severe restrictions are imposed on the existence domains of arbitrary amplitude soliton solutions. The Boltzmann assumption places a stringent upper limit on the cool species number density, in order for the solutions to be physical. An investigation is made of results obtained for an asymmetric electronpositron plasma (Pillay & Bharuthram 1992), consisting of cold electrons and positrons, and hot Boltzmann electrons and positrons at different temperatures Teh and Tph , and number density Neh and Nph . It is found that the assumption of Boltzmann particles again places restrictions on the acoustic soliton existence space, and that the results obtained may be physically invalid. Valid solutions are obtained numerically, within the boundaries of allowed cool species density values. / Thesis (M.Sc.)-University of Natal, Durban, 1998.

Nonlinear Dirac equations exhibiting soliton phenomena are studied. Conditions are derived for the existence of solitons and an analysis of their stability is presented. New results are obtained for models previously considered in the literature. A particular model is studied for which all stationary states are localized in a finite domain and have positive energy but indefinite charge. The electromagnetic field is introduced by minimal coupling and it is shown that the discrete nature of the electric charge, and of the angular momentum, follow from a many-body stability principle. This principle also implies the de Broglie frequency relation, and furnishes an expression for the fine structure constant. The resulting charged soliton is tentatively identified with the electron.