subject:(schrodinger)

University of Illinois – Urbana-Champaign

1. Demirbas, Seckin. A study on certain periodic Schrödinger equations.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

In the first part of this thesis we consider the cubic Schrödinger equation iu_t+Delta u =+/-|u|^2u, x in T_theta², t∈ [-T,T], u(x,0)=u₀(x) in H^s(T_theta²). T is the time of existence of the solutions and T_theta² is the irrational torus given by R²/theta₁ Z * θ₂ Z for theta₁, theta₂ > 0 and theta₁/theta₂ irrational. Our main result is an improvement of the Strichartz estimates on irrational tori using a counting argument by Huxley [43], which estimates the number of lattice points on ellipsoids. With this Strichartz estimate, we obtain a local well-posedness result in H^s for s>131/416. We also use energy type estimates to control the H^s norm of the solution and obtain improved growth bounds for higher order Sobolev norms. In the second and the third parts of this thesis, we study the Cauchy problem for the 1d periodic fractional Schrödinger equation: iu_t+(-Delta)^alpha u =+/- |u|^2u, x in T, t in R, u(x,0)=u₀(x) in H^s(T), where alpha in (1/2,1). First, we prove a Strichartz type estimate for this equation. Using the arguments from Chapter 3, this estimate implies local well-posedness in H^s for s>(1-alpha)/2. However, we prove local well-posedness using direct X^(s,b) estimates. In addition, we show the existence of global-in-time infinite energy solutions. We also show that the nonlinear evolution of the equation is smoother than the initial data. As an important consequence of this smoothing estimate, we prove that there is global well-posedness in H^s for s>(10*alpha+1)/(12). Finally, for the fractional Schrödinger equation, we define an invariant probability measure mu on H^s for s<alpha-1/2, called a Gibbs measure. We define mu so that for any epsilon>0 there is a set Omega, a subset of H^s, such that mu(Omega^c)<epsilon and the equation is globally well-posed for initial data in Omega. We achieve this by showing that for the initial data in Omega, the H^s norms of the solutions stay finite for all times. This fills the gap between the local well-posedness and the global well-posedness range in almost sure sense for (1-alpha)/2<alpha-1/2, i.e. alpha>2/3. Advisors/Committee Members: Tzirakis, Nikolaos (advisor), Erdogan, Burak (advisor), Junge, Marius (Committee Chair), Bronski, Jared C. (committee member).

Subjects/Keywords: Periodic Schrodinger equation; Fractional Schrodinger equation

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APA (6^th Edition):

Demirbas, S. (2015). A study on certain periodic Schrödinger equations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/87978

Chicago Manual of Style (16^th Edition):

Demirbas, Seckin. “A study on certain periodic Schrödinger equations.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 26, 2021. http://hdl.handle.net/2142/87978.

MLA Handbook (7^th Edition):

Demirbas, Seckin. “A study on certain periodic Schrödinger equations.” 2015. Web. 26 Jan 2021.

Vancouver:

Demirbas S. A study on certain periodic Schrödinger equations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2142/87978.

Council of Science Editors:

Demirbas S. A study on certain periodic Schrödinger equations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/87978

2. Godet, Nicolas. Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations.

Degree: Docteur es, Mathématiques - EM2C, 2012, Cergy-Pontoise

URL: http://www.theses.fr/2012CERG0619

►

Cette thèse porte sur l'étude des phénomènes d'explosion pour certaines équations aux dérivées partielles dispersives et plus particulièrement pour l'équation de Schrodinger non linéaire. Ces… (more)

Subjects/Keywords: Edp; Équation de Schrodinger; Explosion; Pde; Schrodinger equation; Blow up

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APA (6^th Edition):

Godet, N. (2012). Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations. (Doctoral Dissertation). Cergy-Pontoise. Retrieved from http://www.theses.fr/2012CERG0619

Chicago Manual of Style (16^th Edition):

Godet, Nicolas. “Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations.” 2012. Doctoral Dissertation, Cergy-Pontoise. Accessed January 26, 2021. http://www.theses.fr/2012CERG0619.

MLA Handbook (7^th Edition):

Godet, Nicolas. “Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations.” 2012. Web. 26 Jan 2021.

Vancouver:

Godet N. Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations. [Internet] [Doctoral dissertation]. Cergy-Pontoise; 2012. [cited 2021 Jan 26]. Available from: http://www.theses.fr/2012CERG0619.

Council of Science Editors:

Godet N. Explosion pour certaines équations Hamiltoniennes : Blow up for some Hamiltonian equations. [Doctoral Dissertation]. Cergy-Pontoise; 2012. Available from: http://www.theses.fr/2012CERG0619

University of Oklahoma

3. Adekoya, Oreoluwa. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/319611

► We study the existence, uniqueness and stability of solutions to the initial-value problem for the periodic dispersion-managed nonlinear Schrödinger (DMNLS) equation, an equation that models… (more)

Subjects/Keywords: Dispersion-managed; Dispersion; Nonlinear; Schrodinger; Periodic dispersion managed nonlinear schrodinger equation

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APA (6^th Edition):

Adekoya, O. (2019). PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/319611

Chicago Manual of Style (16^th Edition):

Adekoya, Oreoluwa. “PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed January 26, 2021. http://hdl.handle.net/11244/319611.

MLA Handbook (7^th Edition):

Adekoya, Oreoluwa. “PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION.” 2019. Web. 26 Jan 2021.

Vancouver:

Adekoya O. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/11244/319611.

Council of Science Editors:

Adekoya O. PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/319611

Texas A&M University

4. Rupam, Rishika. Meromorphic Inner Functions and their Applications.

Degree: PhD, Mathematics, 2015, Texas A&M University

URL: http://hdl.handle.net/1969.1/155377

► In this dissertation we study an important class of functions in complex analysis, known as Meromorphic Inner Functions (MIF) and we exploit their properties to… (more)

Subjects/Keywords: Inner functions; Hardy spaces; Inverse spectral; Schrodinger

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APA (6^th Edition):

Rupam, R. (2015). Meromorphic Inner Functions and their Applications. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/155377

Chicago Manual of Style (16^th Edition):

Rupam, Rishika. “Meromorphic Inner Functions and their Applications.” 2015. Doctoral Dissertation, Texas A&M University. Accessed January 26, 2021. http://hdl.handle.net/1969.1/155377.

MLA Handbook (7^th Edition):

Rupam, Rishika. “Meromorphic Inner Functions and their Applications.” 2015. Web. 26 Jan 2021.

Vancouver:

Rupam R. Meromorphic Inner Functions and their Applications. [Internet] [Doctoral dissertation]. Texas A&M University; 2015. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1969.1/155377.

Council of Science Editors:

Rupam R. Meromorphic Inner Functions and their Applications. [Doctoral Dissertation]. Texas A&M University; 2015. Available from: http://hdl.handle.net/1969.1/155377

Universidad de Chile

5. Zárate Devia, Yair Daniel. Phase shielding solitons.

Degree: 2013, Universidad de Chile

URL: http://repositorio.uchile.cl/handle/2250/115388

► Los solitones son el fen omeno universal m as profundamente estudiado, debido a los innumerables sistemas físicos en los cuales se observa. Estas soluciones corresponden… (more)

▼ Los solitones son el fen omeno universal m as profundamente estudiado, debido a los innumerables sistemas físicos en los cuales se observa. Estas soluciones corresponden a estados localizados y coherentes que surgen naturalmente en sistemas extendidos, siendo una de sus propiedades m as fascinantes el hecho de que pueden ser tratados como partículas macroscópicas a pesar de estar formados por numerosos componentes microscópicos. Desde su primera descripci on, realizada por J. S. Russell en 1884, el estudio de solitones se centró en sistemas conservativos por más de cien años. Sin embargo, los pioneros trabajos de Alan Turing e Ilya Prigogine demostraron que los sistemas fuera del equilibrio se auto{ organizan por medio de la generación de estructuras disipativas. Hoy en día, sabemos que es justamente este mecanismo el que permite la formación de solitones disipativos en sistemas con inyección y disipación de energía. Nuestro principal interés ha sido caracterizar de forma analítica y numérica a los solitones que emergen en sistemas forzados paramétricamente{sistemas forzados por medio de un parámetro efectivo que var a en el espacio y/o tiempo. Los sistemas forzados param etricamente pueden experimentar una resonancia paramétrica, la cual se caracteriza por una respuesta subarm onica (subm ultiplos de la frecuencia natural del sistema). Dada la complejidad que presentan los sistemas paramétricos, focalizamos nuestro estudio en la ecuación de Schrödinger no lineal disipativa forzada paramétricamente (PDNLS). Este modelo caracteriza bien la din amica de sistemas forzados param etricamente, en torno al punto de aparición de la resonancia paramétrica, en el límite de baja disipación e inyección de energía. Los solitones disipativos, presentes en PDNLS, típicamente muestran una estructura de fase uniforme. Dichas estructuras han sido ampliamente utilizadas para describir a los solitones hidrodinámicos que aparecen en el experimento de Faraday, estados localizados de la magnetización en un hilo magnético, o los clásicos solitones presentes en una cadena de péndulos con soporte verticalmente vibrado, entre otros. Por medio de simulaciones numéricas interactivas de solitones disipativos en la ecuaciónPDNLS, hemos logrado observar una interesante din amica de frentes de fase hasta ahora desconocida. Estos frentes de fase se propagan hasta alcanzar un punto de equilibrio estacionarioarbitrario. A este tipo de solitones los hemos llamado solitones escudados por la fase (phase shielding solitons), dado que la estructura nal de fase pareciera proteger al módulodel solit on. Hemos logrado caracterizar anal ticamente estas soluciones localizadas, determinando ocho posibles con guraciones. Los solitones estudiados poseen una talla característica dada por el tamaño de la estructura de fase estacionaria. Adem ás, extendimos nuestro estudio al caso bidimensional, mostrando los resultados, dos tipos de phase shilding solitons bidimensionales; axialmente simétricos y asimétricos. Los primeros pueden ser entendidos como una rotación…

Subjects/Keywords: Solitones; Ecuaciones de Schrodinger; Estructuras localizadas; PDNLS

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APA (6^th Edition):

Zárate Devia, Y. D. (2013). Phase shielding solitons. (Thesis). Universidad de Chile. Retrieved from http://repositorio.uchile.cl/handle/2250/115388

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zárate Devia, Yair Daniel. “Phase shielding solitons.” 2013. Thesis, Universidad de Chile. Accessed January 26, 2021. http://repositorio.uchile.cl/handle/2250/115388.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zárate Devia, Yair Daniel. “Phase shielding solitons.” 2013. Web. 26 Jan 2021.

Vancouver:

Zárate Devia YD. Phase shielding solitons. [Internet] [Thesis]. Universidad de Chile; 2013. [cited 2021 Jan 26]. Available from: http://repositorio.uchile.cl/handle/2250/115388.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zárate Devia YD. Phase shielding solitons. [Thesis]. Universidad de Chile; 2013. Available from: http://repositorio.uchile.cl/handle/2250/115388

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Ontario Institute of Technology

6. Metherall, Brady. A new method of modelling tuneable lasers with functional composition.

Degree: 2019, University of Ontario Institute of Technology

URL: http://hdl.handle.net/10155/1073

► A new nonlinear model is proposed for tuneable lasers. Using the generalized nonlinear Schrodinger equation as a starting point, expressions for the transformations undergone by… (more)

Subjects/Keywords: Tuneable lasers; Nonlinear Schrodinger equation; Laser cavity

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APA (6^th Edition):

Metherall, B. (2019). A new method of modelling tuneable lasers with functional composition. (Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/1073

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Metherall, Brady. “A new method of modelling tuneable lasers with functional composition.” 2019. Thesis, University of Ontario Institute of Technology. Accessed January 26, 2021. http://hdl.handle.net/10155/1073.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Metherall, Brady. “A new method of modelling tuneable lasers with functional composition.” 2019. Web. 26 Jan 2021.

Vancouver:

Metherall B. A new method of modelling tuneable lasers with functional composition. [Internet] [Thesis]. University of Ontario Institute of Technology; 2019. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10155/1073.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Metherall B. A new method of modelling tuneable lasers with functional composition. [Thesis]. University of Ontario Institute of Technology; 2019. Available from: http://hdl.handle.net/10155/1073

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

7. Luciana Maria Mendonça Bragança. O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem.

Degree: Instituto de Matemática, Estatística e Computação Científica, 2007, Universidade Estadual de Campinas

URL: http://libdigi.unicamp.br/document/?code=vtls000417496

►

In this work we study the Cauchy problem associated to a system of coupled third-order nonlinear Schrodinger equation. We establish local well-posedness results for the… (more)

Subjects/Keywords: Cauchy; Schrodinger; Nonlinear differential equtions; Equações diferenciais não-lineares; Cauchy problem; Problemas de; Equações de; Schrodinger equation

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APA (6^th Edition):

Bragança, L. M. M. (2007). O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem. (Thesis). Universidade Estadual de Campinas. Retrieved from http://libdigi.unicamp.br/document/?code=vtls000417496

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bragança, Luciana Maria Mendonça. “O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem.” 2007. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://libdigi.unicamp.br/document/?code=vtls000417496.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bragança, Luciana Maria Mendonça. “O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem.” 2007. Web. 26 Jan 2021.

Vancouver:

Bragança LMM. O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem. [Internet] [Thesis]. Universidade Estadual de Campinas; 2007. [cited 2021 Jan 26]. Available from: http://libdigi.unicamp.br/document/?code=vtls000417496.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bragança LMM. O problema de Cauchy para um sistema de equações do tipo Schrodinger não linear de terceira ordem. [Thesis]. Universidade Estadual de Campinas; 2007. Available from: http://libdigi.unicamp.br/document/?code=vtls000417496

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

NSYSU

8. Lee, Yuanhan. Block elimination algorithms for bordered linear systems and its applications.

Degree: Master, Applied Mathematics, 2013, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720113-145623

► Many applications need to solve a number of large bordered linear systems such as the prediction and correction processes in continuation method.If the original linear… (more)

Subjects/Keywords: Block elimination algorithm; bordered linear system; nonlinear Schrodinger equation

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APA (6^th Edition):

Lee, Y. (2013). Block elimination algorithms for bordered linear systems and its applications. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720113-145623

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lee, Yuanhan. “Block elimination algorithms for bordered linear systems and its applications.” 2013. Thesis, NSYSU. Accessed January 26, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720113-145623.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lee, Yuanhan. “Block elimination algorithms for bordered linear systems and its applications.” 2013. Web. 26 Jan 2021.

Vancouver:

Lee Y. Block elimination algorithms for bordered linear systems and its applications. [Internet] [Thesis]. NSYSU; 2013. [cited 2021 Jan 26]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720113-145623.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lee Y. Block elimination algorithms for bordered linear systems and its applications. [Thesis]. NSYSU; 2013. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720113-145623

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

9. Pachouri, Dipti. Equation of state and microscopic optical potential; -.

Degree: Physics, 2012, Aligarh Muslim University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/55629

Abstract not available newline newline

-

Advisors/Committee Members: Haider, Wasi.

Subjects/Keywords: Scattering; Feshbach; Repulsive; Schrodinger; Monotonic

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APA (6^th Edition):

Pachouri, D. (2012). Equation of state and microscopic optical potential; -. (Thesis). Aligarh Muslim University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/55629

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pachouri, Dipti. “Equation of state and microscopic optical potential; -.” 2012. Thesis, Aligarh Muslim University. Accessed January 26, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/55629.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pachouri, Dipti. “Equation of state and microscopic optical potential; -.” 2012. Web. 26 Jan 2021.

Vancouver:

Pachouri D. Equation of state and microscopic optical potential; -. [Internet] [Thesis]. Aligarh Muslim University; 2012. [cited 2021 Jan 26]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/55629.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pachouri D. Equation of state and microscopic optical potential; -. [Thesis]. Aligarh Muslim University; 2012. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/55629

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

10. Irismar Goncalves da Paz. Ondas de matéria e propagação paraxial da luz.

Degree: 2006, Universidade Federal de Minas Gerais

URL: http://hdl.handle.net/1843/ESCZ-6XXHBP

► Características quânticas intrínsecas podem ser observadas em experimentos simples, como por exemplo, na difração de pacotes gaussianos. A evolução livre desses estados contém um tempo… (more)

Subjects/Keywords: Ondas eletromagnéticas; Ótica quântica; Luz Propagação; Equação de Schrodinger

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APA (6^th Edition):

Paz, I. G. d. (2006). Ondas de matéria e propagação paraxial da luz. (Thesis). Universidade Federal de Minas Gerais. Retrieved from http://hdl.handle.net/1843/ESCZ-6XXHBP

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Paz, Irismar Goncalves da. “Ondas de matéria e propagação paraxial da luz.” 2006. Thesis, Universidade Federal de Minas Gerais. Accessed January 26, 2021. http://hdl.handle.net/1843/ESCZ-6XXHBP.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Paz, Irismar Goncalves da. “Ondas de matéria e propagação paraxial da luz.” 2006. Web. 26 Jan 2021.

Vancouver:

Paz IGd. Ondas de matéria e propagação paraxial da luz. [Internet] [Thesis]. Universidade Federal de Minas Gerais; 2006. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1843/ESCZ-6XXHBP.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Paz IGd. Ondas de matéria e propagação paraxial da luz. [Thesis]. Universidade Federal de Minas Gerais; 2006. Available from: http://hdl.handle.net/1843/ESCZ-6XXHBP

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – San Diego

11. Pizzo, Nicholas Edward. Properties of nonlinear and breaking deep-water surface waves.

Degree: Oceanography, 2015, University of California – San Diego

URL: http://www.escholarship.org/uc/item/0g45s3j6

► In this thesis we study nonlinear and breaking deep-water surface waves. First, we consider the vorticity generated by an individual breaking wave, drawing on classical… (more)

▼ In this thesis we study nonlinear and breaking deep-water surface waves. First, we consider the vorticity generated by an individual breaking wave, drawing on classical literature on vortex generation by impulsive forcing. We employ this theory to develop a scaling argument for the relationship between the generated circulation and the variables characterizing the breaking wave. This model is then compared to limited laboratory experiments, and good agreement is found. We next pursue a related problem, namely the partitioning of energy in the breaking induced currents, between the turbulent and mean flow. This is the inverse problem to the vortex generation model, as we work backwards from the structure of the induced flow, using existing results on vortex dynamics to find the energy necessary to generate the (half) vortex ring induced by breaking. This yields a theoretical model for the ratio of the energy in the mean flow currents to the total energy lost from the wave field, in terms of the characteristic variables of the breaking wave. This relationship is then examined numerically, using a direct numerical simulation of the two-phase air-water Navier-Stokes equations, and agreement between the model, the numerical experiments, and limited available laboratory data is found. One approach to breaking is through the focusing of wave packets. Here, we theoretically and numerically examine weakly nonlinear narrow-banded wave packets. By employing moment evolution equations of the modified nonlinear Schrodinger equation (MNLSE), we derive new predictions for the geometry, kinematics, and dynamics of focusing wave packets. In particular, we predict that as the wave group focuses: the group velocity increases; the packet leans forward; and the energy equipartition (between kinetic and potential) breaks down. These results are then corroborated by numerical integration of both the MNLSE and the fully nonlinear evolution equations for irrotational inviscid deep-water surface gravity waves. Finally we present several ongoing projects related to nonlinear and breaking surface waves. First, we present a Lagrangian for deep-water surface gravity waves and discuss its numerical implementation. Next, a virial theorem for surface gravity waves is derived. Finally, we derive the criterion for the Benjamin-Feir instability based on a variance identity for the nonlinear Schrodinger equation.

Subjects/Keywords: Physical oceanography; Applied mathematics; Nonlinear Schrodinger Equation; Physical Oceanography; Wave breaking

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APA (6^th Edition):

Pizzo, N. E. (2015). Properties of nonlinear and breaking deep-water surface waves. (Thesis). University of California – San Diego. Retrieved from http://www.escholarship.org/uc/item/0g45s3j6

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pizzo, Nicholas Edward. “Properties of nonlinear and breaking deep-water surface waves.” 2015. Thesis, University of California – San Diego. Accessed January 26, 2021. http://www.escholarship.org/uc/item/0g45s3j6.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pizzo, Nicholas Edward. “Properties of nonlinear and breaking deep-water surface waves.” 2015. Web. 26 Jan 2021.

Vancouver:

Pizzo NE. Properties of nonlinear and breaking deep-water surface waves. [Internet] [Thesis]. University of California – San Diego; 2015. [cited 2021 Jan 26]. Available from: http://www.escholarship.org/uc/item/0g45s3j6.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pizzo NE. Properties of nonlinear and breaking deep-water surface waves. [Thesis]. University of California – San Diego; 2015. Available from: http://www.escholarship.org/uc/item/0g45s3j6

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Alberta

12. Dosser, Hayley V. Propagation and breaking of nonlinear internal gravity waves.

Degree: MS, Department of Physics, 2010, University of Alberta

URL: https://era.library.ualberta.ca/files/hh63sx19v

► Internal gravity waves grow in amplitude as they propagate upwards in a non-Boussinesq fluid and weakly nonlinear effects develop due to interactions with an induced… (more)

Subjects/Keywords: internal gravity wave; anelastic; modulational; atmosphere; nonlinear; Schrodinger; non-Boussinesq

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APA (6^th Edition):

Dosser, H. V. (2010). Propagation and breaking of nonlinear internal gravity waves. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/hh63sx19v

Chicago Manual of Style (16^th Edition):

Dosser, Hayley V. “Propagation and breaking of nonlinear internal gravity waves.” 2010. Masters Thesis, University of Alberta. Accessed January 26, 2021. https://era.library.ualberta.ca/files/hh63sx19v.

MLA Handbook (7^th Edition):

Dosser, Hayley V. “Propagation and breaking of nonlinear internal gravity waves.” 2010. Web. 26 Jan 2021.

Vancouver:

Dosser HV. Propagation and breaking of nonlinear internal gravity waves. [Internet] [Masters thesis]. University of Alberta; 2010. [cited 2021 Jan 26]. Available from: https://era.library.ualberta.ca/files/hh63sx19v.

Council of Science Editors:

Dosser HV. Propagation and breaking of nonlinear internal gravity waves. [Masters Thesis]. University of Alberta; 2010. Available from: https://era.library.ualberta.ca/files/hh63sx19v

13. Sohani, Vijay Kumar. Nonlinear schrodinger equation and the twisted laplacian; -.

Degree: Mathematical Sciences, 2013, INFLIBNET

URL: http://shodhganga.inflibnet.ac.in/handle/10603/37405

None

Bibliograpgy p.103 - 106

Advisors/Committee Members: Ratankumar, P K.

Subjects/Keywords: equation; Nonlinear; schrodinger; twisted laplacian

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APA (6^th Edition):

Sohani, V. K. (2013). Nonlinear schrodinger equation and the twisted laplacian; -. (Thesis). INFLIBNET. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/37405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sohani, Vijay Kumar. “Nonlinear schrodinger equation and the twisted laplacian; -.” 2013. Thesis, INFLIBNET. Accessed January 26, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/37405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sohani, Vijay Kumar. “Nonlinear schrodinger equation and the twisted laplacian; -.” 2013. Web. 26 Jan 2021.

Vancouver:

Sohani VK. Nonlinear schrodinger equation and the twisted laplacian; -. [Internet] [Thesis]. INFLIBNET; 2013. [cited 2021 Jan 26]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/37405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sohani VK. Nonlinear schrodinger equation and the twisted laplacian; -. [Thesis]. INFLIBNET; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/37405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Stellenbosch University

14. Wessels, Gert Jermia Cornelus. A numerical and analytical investigation into non-Hermitian Hamiltonians.

Degree: Mathematical Sciences, 2009, Stellenbosch University

URL: http://hdl.handle.net/10019.1/2894

►

Thesis (MSc (Physical and Mathematical Analysis)) – University of Stellenbosch, 2009.

In this thesis we aim to show that the Schr odinger equation, which is a… (more)

Subjects/Keywords: Mathematics; Schrodinger equation; Perturbation (Mathematics)

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APA (6^th Edition):

Wessels, G. J. C. (2009). A numerical and analytical investigation into non-Hermitian Hamiltonians. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/2894

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wessels, Gert Jermia Cornelus. “A numerical and analytical investigation into non-Hermitian Hamiltonians.” 2009. Thesis, Stellenbosch University. Accessed January 26, 2021. http://hdl.handle.net/10019.1/2894.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wessels, Gert Jermia Cornelus. “A numerical and analytical investigation into non-Hermitian Hamiltonians.” 2009. Web. 26 Jan 2021.

Vancouver:

Wessels GJC. A numerical and analytical investigation into non-Hermitian Hamiltonians. [Internet] [Thesis]. Stellenbosch University; 2009. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10019.1/2894.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wessels GJC. A numerical and analytical investigation into non-Hermitian Hamiltonians. [Thesis]. Stellenbosch University; 2009. Available from: http://hdl.handle.net/10019.1/2894

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

McMaster University

15. miladinovic, nick k. Adiabatic Transfer of Light in a Double Cavity.

Degree: MS, 2011, McMaster University

URL: http://hdl.handle.net/11375/9154

►

The goal of this thesis is to perform a simple theoretical analysis of the problem of two optical cavities coupled by a common mirror… (more)

Subjects/Keywords: Adiabatic; Maxwell; Schrodinger; Cavity; Landau-Zener; Light; Optics; Optics

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APA (6^th Edition):

miladinovic, n. k. (2011). Adiabatic Transfer of Light in a Double Cavity. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/9154

Chicago Manual of Style (16^th Edition):

miladinovic, nick k. “Adiabatic Transfer of Light in a Double Cavity.” 2011. Masters Thesis, McMaster University. Accessed January 26, 2021. http://hdl.handle.net/11375/9154.

MLA Handbook (7^th Edition):

miladinovic, nick k. “Adiabatic Transfer of Light in a Double Cavity.” 2011. Web. 26 Jan 2021.

Vancouver:

miladinovic nk. Adiabatic Transfer of Light in a Double Cavity. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/11375/9154.

Council of Science Editors:

miladinovic nk. Adiabatic Transfer of Light in a Double Cavity. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/9154

University of Toronto

16. Rifkind, Benjamin Amichai. Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator.

Degree: PhD, 2014, University of Toronto

URL: http://hdl.handle.net/1807/68309

► In this thesis we focus on two distinct random processes constructed using a sequence of independent identically distributed random variables along with a product structure… (more)

▼ In this thesis we focus on two distinct random processes constructed using a sequence of independent identically distributed random variables along with a product structure on the underlying space. The first, a collection of random variables attached to vertices of the rooted binary tree, uses the multiplicative structure of paths along the tree while the second, a collection of two by two random matrices, uses the usual multiplication of matrices.In the first chapter we construct a continuous time version of the multiplicative cascade. The multiplicative cascade can be thought of as a randomization of an initial measure on the boundary of a tree, constructed from an independent, identically distributed collection of random variables attached to the tree vertices. The new random measure is constructed from the old by weighting the measure of any vertex in the the tree by the product of the random variables along the path from the root to the vertex. Given an initial measure with certain regularity properties, we construct a continuous time, measure-valued process whose value at each time is a cascade of the initial one. We do this by replacing the random variables on the vertices with independent increment processes satisfying certain moment assumptions. This process has a Markov property: at any given time it is a cascade of the process at any earlier time by random variables that are independent of the past. It is also a martingale and, under certain extra conditions, it is also continuous. For Gaussian independent increments processes we develop the infinite-dimensional stochastic calculus that describes the evolution of the measure process, and use it to compute the optimal Holder exponent in the Wasserstein distance on measures.In the second chapter, we focus on the eigenvectors of the one-dimensional discrete random Schrodinger operator. This is the Hamiltonian operator on the lattice of integers given by the discrete Laplacian plus an independent, identically distributed delta potential at each point. We restrict this operator to a finite box, pick an eigenvector uniformly at random and characterize the scaling limit as we take the size of the box to infinity. We show that the envelope of this random eigenvector converges weakly to an exponential Brownian martingale. Our analysis uses the well known transfer matrix formulation of the spectral problem; the spectral information is encapsulated in a process of products of independent, identically distributed two by two random matrices. The limiting diffusion for this product process was developed in (Kritchevski, Valko, Virag - 2011) to study the local eigenvalue point process. Our work makes heavy use of that framework. Advisors/Committee Members: Balint, Virag, Mathematics.

Subjects/Keywords: Point Processes; Probability; Random Measures; Random Schrodinger Operators; Stochastic Process; 0405

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APA (6^th Edition):

Rifkind, B. A. (2014). Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/68309

Chicago Manual of Style (16^th Edition):

Rifkind, Benjamin Amichai. “Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator.” 2014. Doctoral Dissertation, University of Toronto. Accessed January 26, 2021. http://hdl.handle.net/1807/68309.

MLA Handbook (7^th Edition):

Rifkind, Benjamin Amichai. “Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator.” 2014. Web. 26 Jan 2021.

Vancouver:

Rifkind BA. Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator. [Internet] [Doctoral dissertation]. University of Toronto; 2014. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1807/68309.

Council of Science Editors:

Rifkind BA. Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator. [Doctoral Dissertation]. University of Toronto; 2014. Available from: http://hdl.handle.net/1807/68309

Texas Tech University

17. Walker, John David. An investigation into the possibility of an integral solution to the radical Schrodinger equation.

Degree: Physics, 1964, Texas Tech University

URL: http://hdl.handle.net/2346/13431

Subjects/Keywords: Schrodinger equation; Scattering (Physics)

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APA (6^th Edition):

Walker, J. D. (1964). An investigation into the possibility of an integral solution to the radical Schrodinger equation. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/13431

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Walker, John David. “An investigation into the possibility of an integral solution to the radical Schrodinger equation.” 1964. Thesis, Texas Tech University. Accessed January 26, 2021. http://hdl.handle.net/2346/13431.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Walker, John David. “An investigation into the possibility of an integral solution to the radical Schrodinger equation.” 1964. Web. 26 Jan 2021.

Vancouver:

Walker JD. An investigation into the possibility of an integral solution to the radical Schrodinger equation. [Internet] [Thesis]. Texas Tech University; 1964. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2346/13431.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Walker JD. An investigation into the possibility of an integral solution to the radical Schrodinger equation. [Thesis]. Texas Tech University; 1964. Available from: http://hdl.handle.net/2346/13431

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Clemson University

18. Gao, Zhe. Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices.

Degree: MS, Mechanical Engineering, 2012, Clemson University

URL: https://tigerprints.clemson.edu/all_theses/1417

► As the dimensions of commonly used semiconductor devices have shrunk into nanometer regime, it is recognized that the influence of quantum effects on their… (more)

▼ As the dimensions of commonly used semiconductor devices have shrunk into nanometer regime, it is recognized that the influence of quantum effects on their electrostatic and transport properties cannot be ignored. In the past few decades, various computational models and approaches have been developed to analyze these properties in nanostructures and devices. Among these computational models, the Schršdinger-Poisson model has been widely adopted for quantum mechanical electrostatic and transport analysis of nanostructures and devices such as quantum wires, metal-oxide-semiconductor field effect transistors (MOSFETs) and nanoelectromechanical systems (NEMS). The numerical results allow for evaluations of the electrical properties such as charge concentration and potential profile in these structures. The emergence of MOSFETs with multiple gates, such as Trigates, FinFETs and Pi-gates, offers a superior electrostatic control of devices by the gates, which can be therefore used to reduce the short channel effects within those devices. Full 2-D electrostatic and transport analysis enables a better understanding of the scalability of devices, geometric effects on the potential and charge distribution, and transport characteristics of the transistors. The Schršdinger-Poisson model is attractive due to its simplicity and straightforward implementation by using standard numerical methods. However, as it is required to solve a generalized eigenvalue problem generated from the discretization of the Schršdinger equation, the computational cost of the analysis increases quickly when the system's degrees of freedom (DOFs) increase. For this reason, techniques that enable an efficient solution of discretized Schršdinger equation in multidimensional domains are desirable. In this work, we seek to accelerate the numerical solution of the Schršdinger equation by using a component mode synthesis (CMS) approach. In the CMS approach, a nanostructure is divided into a set of substructures or components and the eigenvalues (energy levels) and eigenvectors (wave functions) are computed first for all the substructures. The computed wave functions are then combined with constraint or attachment modes to construct a transformation matrix. By using the transformation matrix, a reduced-order system of the Schršdinger equation is obtained for the entire nanostructure. The global energy levels and wave functions can be obtained with the reduced-order system. Through an iteration procedure between the Schršdinger and Poisson equations, a self-consistent solution for charge concentration and potential profile can be obtained. In this work, the CMS approach is applied to compute the electrostatic and transport properties of a set of semiconductor devices including a quantum wire and several multiple-gate MOSFETs. It is demonstrated that the CMS approach greatly reduces the computational cost while giving accurate results. Advisors/Committee Members: Li, Gang, Xuan, Xiangchun, Zhao, Huijuan.

Subjects/Keywords: Boundary; CMS; Poisson; Quantum; Schrodinger; Transmitting; Nanoscience and Nanotechnology

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APA (6^th Edition):

Gao, Z. (2012). Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices. (Masters Thesis). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_theses/1417

Chicago Manual of Style (16^th Edition):

Gao, Zhe. “Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices.” 2012. Masters Thesis, Clemson University. Accessed January 26, 2021. https://tigerprints.clemson.edu/all_theses/1417.

MLA Handbook (7^th Edition):

Gao, Zhe. “Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices.” 2012. Web. 26 Jan 2021.

Vancouver:

Gao Z. Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices. [Internet] [Masters thesis]. Clemson University; 2012. [cited 2021 Jan 26]. Available from: https://tigerprints.clemson.edu/all_theses/1417.

Council of Science Editors:

Gao Z. Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices. [Masters Thesis]. Clemson University; 2012. Available from: https://tigerprints.clemson.edu/all_theses/1417

University of Kansas

19. Claassen, Kyle Matthew. Stability of Periodic Waves in Nonlocal Dispersive Equations.

Degree: PhD, Mathematics, 2018, University of Kansas

URL: http://hdl.handle.net/1808/27876

► In this work consisting of joint projects with my advisor, Dr. Mathew Johnson, we study the existence and stability of periodic waves in equations that… (more)

Subjects/Keywords: Mathematics; Bidirectional Whitham models; Dispersive Equations; Fractional Nonlinear Schrodinger Equation

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APA (6^th Edition):

Claassen, K. M. (2018). Stability of Periodic Waves in Nonlocal Dispersive Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27876

Chicago Manual of Style (16^th Edition):

Claassen, Kyle Matthew. “Stability of Periodic Waves in Nonlocal Dispersive Equations.” 2018. Doctoral Dissertation, University of Kansas. Accessed January 26, 2021. http://hdl.handle.net/1808/27876.

MLA Handbook (7^th Edition):

Claassen, Kyle Matthew. “Stability of Periodic Waves in Nonlocal Dispersive Equations.” 2018. Web. 26 Jan 2021.

Vancouver:

Claassen KM. Stability of Periodic Waves in Nonlocal Dispersive Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1808/27876.

Council of Science Editors:

Claassen KM. Stability of Periodic Waves in Nonlocal Dispersive Equations. [Doctoral Dissertation]. University of Kansas; 2018. Available from: http://hdl.handle.net/1808/27876

University of Kentucky

20. Music, Michael. Inverse Scattering For The Zero-Energy Novikov-Veselov Equation.

Degree: 2016, University of Kentucky

URL: https://uknowledge.uky.edu/math_etds/40

► For certain initial data, we solve the Novikov-Veselov equation by the inverse scat- tering method. This is a (2+1)-dimensional completely integrable system that gen- eralizes… (more)

Subjects/Keywords: inverse scattering; Novikov-Veselov equation; Schrodinger equation; Analysis

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APA (6^th Edition):

Music, M. (2016). Inverse Scattering For The Zero-Energy Novikov-Veselov Equation. (Doctoral Dissertation). University of Kentucky. Retrieved from https://uknowledge.uky.edu/math_etds/40

Chicago Manual of Style (16^th Edition):

Music, Michael. “Inverse Scattering For The Zero-Energy Novikov-Veselov Equation.” 2016. Doctoral Dissertation, University of Kentucky. Accessed January 26, 2021. https://uknowledge.uky.edu/math_etds/40.

MLA Handbook (7^th Edition):

Music, Michael. “Inverse Scattering For The Zero-Energy Novikov-Veselov Equation.” 2016. Web. 26 Jan 2021.

Vancouver:

Music M. Inverse Scattering For The Zero-Energy Novikov-Veselov Equation. [Internet] [Doctoral dissertation]. University of Kentucky; 2016. [cited 2021 Jan 26]. Available from: https://uknowledge.uky.edu/math_etds/40.

Council of Science Editors:

Music M. Inverse Scattering For The Zero-Energy Novikov-Veselov Equation. [Doctoral Dissertation]. University of Kentucky; 2016. Available from: https://uknowledge.uky.edu/math_etds/40

Virginia Tech

21. Ran, Yu. Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations.

Degree: PhD, Mathematics, 2014, Virginia Tech

URL: http://hdl.handle.net/10919/47930

► The dissertation focuses on the initial boundary value problems (IBVPs) of a class of nonlinear Schrodinger equations posed on a half plane R x R+… (more)

▼ The dissertation focuses on the initial boundary value problems (IBVPs) of a class of nonlinear Schrodinger equations posed on a half plane R x R+ and on a strip domain R x [0,L] with Dirichlet nonhomogeneous boundary data in a two-dimensional plane. Compared with pure initial value problems (IVPs), IBVPs over part of entire space with boundaries are more applicable to the reality and can provide more accurate data to physical experiments or practical problems. Although there is less research that has been made for IBVPs than that for IVPs, more attention has been paid for IBVPs recently. In particular, this thesis studies the local well-posedness of the equation for the appropriate initial and boundary data in Sobolev spaces H^s with non-negative s and investigates the global well-posedness in the H^1-space. The main strategy, especially for the local well-posedness, is to derive an equivalent integral equation (whose solution is called mild solution) from the original equation by semi-group theory and then perform the Banach fixed-point argument. However, along the process, it is essential to select proper auxiliary function spaces and prepare all the corresponding norm estimates to complete the argument. In fact, the IBVP posed on R x R+ and the one posed on R x [0,L] are two independent problems because the techniques adopted are different. The first problem is more related to the initial value problem (IVP) posed on the whole plane R² and the major ingredients are Strichartz's estimate and its generalized theory. On the other hand, the second problem can be studied as an IVP over a half-line and periodic domain, which is established on the analysis for series inspired by Bourgain's work. Moreover, the corresponding smoothing properties and regularity conditions of the solution are also considered. Advisors/Committee Members: Sun, Shu-Ming (committeechair), Kim, Jong U. (committee member), Yue, Pengtao (committee member), Renardy, Michael J. (committee member), Russell, David L. (committee member).

Subjects/Keywords: Nonlinear Schrodinger Equations; Nonhomogeneous Boundary Value Problem; Harmonic Analysis

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APA (6^th Edition):

Ran, Y. (2014). Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/47930

Chicago Manual of Style (16^th Edition):

Ran, Yu. “Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations.” 2014. Doctoral Dissertation, Virginia Tech. Accessed January 26, 2021. http://hdl.handle.net/10919/47930.

MLA Handbook (7^th Edition):

Ran, Yu. “Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations.” 2014. Web. 26 Jan 2021.

Vancouver:

Ran Y. Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations. [Internet] [Doctoral dissertation]. Virginia Tech; 2014. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10919/47930.

Council of Science Editors:

Ran Y. Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations. [Doctoral Dissertation]. Virginia Tech; 2014. Available from: http://hdl.handle.net/10919/47930

University of Illinois – Urbana-Champaign

22. Toprak, Ebru. Global dynamics of Schrodinger and Dirac equations.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101665

► In this document, we study the linear Schrödinger operator and linear massive Dirac operator in the L¹ → L^∞ settings. In Chapter~I, we focus on the… (more)

Subjects/Keywords: Schrodinger equation; Dirac equation; dispersive estimate; threshold-energy obstruction

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APA (6^th Edition):

Toprak, E. (2018). Global dynamics of Schrodinger and Dirac equations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101665

Chicago Manual of Style (16^th Edition):

Toprak, Ebru. “Global dynamics of Schrodinger and Dirac equations.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 26, 2021. http://hdl.handle.net/2142/101665.

MLA Handbook (7^th Edition):

Toprak, Ebru. “Global dynamics of Schrodinger and Dirac equations.” 2018. Web. 26 Jan 2021.

Vancouver:

Toprak E. Global dynamics of Schrodinger and Dirac equations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2142/101665.

Council of Science Editors:

Toprak E. Global dynamics of Schrodinger and Dirac equations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101665

23. Pliakis, Dimitris. Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points.

Degree: 2000, University of Crete (UOC); Πανεπιστήμιο Κρήτης

URL: http://hdl.handle.net/10442/hedi/30218

► Στη διατριβή αυτή αντιμετωπίζονται προβλήματα ιδιομορφιών που συναντώνται στις εξισώσεις Schrodinger και Euler-Lagrange, παρέχονται δε ασυμπτωτικά αναπτύγματα συναρτήσεων που έχουν ενδιαφέρον στη Φυσική. Συγκεκριμένα στο… (more)

▼ Στη διατριβή αυτή αντιμετωπίζονται προβλήματα ιδιομορφιών που συναντώνται στις εξισώσεις Schrodinger και Euler-Lagrange, παρέχονται δε ασυμπτωτικά αναπτύγματα συναρτήσεων που έχουν ενδιαφέρον στη Φυσική. Συγκεκριμένα στο πρώτο μέρος μελετάται το ασυμπτωτικό ανάπτυγμα μικρού χρόνου του ίχνους του τελεστή της θερμότητας που ορίζεται μέσω του γενικού τυπικού τελεστή Schrodinger με ομαλές ιδιομορφίες. Αυτό το ασυμπτωτικό ανάπτυγμα μας επιτρέπει να εξετάσουμε τις προϋποθέσεις για το φασματικό προσδιορισμό του δυναμικού που εμφανίζεται σε έναν τέτοιο τελεστή. Η απάντηση είναι καταφατική εφόσον το δυναμικό είναι αναλυτική συνάρτηση σε κάποιο διάστημα (0,R) με συγκλίνον ανάπτυγμα σε δυνάμεις και λογαρίθμους καθώς χ Υ 0+. Στη συνέχεια αποδεικνύεται μία γενίκευση της ανισότητας Hardy προς την ακόλουθη κατεύθυνση: έστω P ένα γενικό τυπικό πολυώνυμο, ομογενές βαθμού m σε n-μεταβλητές με ρίζες επί του αλγεβρικού συνόλου V(P), τότε υπάρχει C>0 ώστε για κάθε f Ξ C0 ₯ (Rn V(P)) ισχύει ς Rn P-2/m f 2 dx £ C ς Rn (grad f)2 dx. Η ανισότητα αυτή, όπως και κάποιες συγγενείς απαιτεί τη χρήση τεχνικών της αλγεβρικής γεωμετρίας προκειμένου να εξεταστούν αλγεβρικά σύνολα με ιδιομορφίες, αποτελεί δε το θεμέλιο λίθο για τη μελέτη αντίστροφων προβλημάτων σε υψηλότερη διάσταση. Στο δεύτερο μέρος μελετώνται ιδιόμορφα προβλήματα του λογισμού μεταβολών. Με αφετηρία την κίνηση ενός σωματιδίου με μικρή μάζα εντός ενός ισχυρού πεδίου Yang-Mills, κατά την οποία η Λαγκρανζιανή συνάρτηση είναι γραμμική ως προς τις ταχύτητες, μελετάται η γενική τυπική Λαγκρανζιανή συνάρτηση που οδηγεί σε ιδιόμορφο μετασχηματισμό Legendre και κατ΄ επέκταση σε ιδιόμορφες εξισώσεις Euler-Lagrange. Η μελέτη εστιάζεται στην αναζήτηση των προϋποθέσεων κάτω από τις οποίες οι ιδιομορφίες των εξισώσεων αναιρούνται, οπότε έχουμε την εισαγωγή μίας κατάλληλης άλγεβρας λείων συναρτήσεων δυναμικού. Η μελέτη μας προσδιορίζει τη μορφή αυτών των συναρτήσεων κοντά στον τόπο ιδιομορφιών των εξισώσεων Euler-Lagrange. Η μελέτη απαιτεί τη λήψη διαφόρων θεωρημάτων διαίρεσης στην κατηγορία των λείων συναρτήσεων.

Subjects/Keywords: Εξίσωση schrodinger; Εξίσωση Euler-Lagrange

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APA (6^th Edition):

Pliakis, D. (2000). Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points. (Thesis). University of Crete (UOC); Πανεπιστήμιο Κρήτης. Retrieved from http://hdl.handle.net/10442/hedi/30218

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pliakis, Dimitris. “Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points.” 2000. Thesis, University of Crete (UOC); Πανεπιστήμιο Κρήτης. Accessed January 26, 2021. http://hdl.handle.net/10442/hedi/30218.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pliakis, Dimitris. “Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points.” 2000. Web. 26 Jan 2021.

Vancouver:

Pliakis D. Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points. [Internet] [Thesis]. University of Crete (UOC); Πανεπιστήμιο Κρήτης; 2000. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10442/hedi/30218.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pliakis D. Asymptotic behaniour of Schrodinger and Euler Lagrange equations near singular points. [Thesis]. University of Crete (UOC); Πανεπιστήμιο Κρήτης; 2000. Available from: http://hdl.handle.net/10442/hedi/30218

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Sydney

24. Marting, Zechariah Lanka. Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents .

Degree: 2015, University of Sydney

URL: http://hdl.handle.net/2123/14162

► There are two main types of ErbB-RTK subfamily inhibitors, viz, a) the mAbs and b) the RTKIs, which act at different domains of the receptors.… (more)

Subjects/Keywords: Anti-EGFR anti-oligomer; oligomerization region; human cancer; Schrodinger Software

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APA (6^th Edition):

Marting, Z. L. (2015). Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/14162

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Marting, Zechariah Lanka. “Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents .” 2015. Thesis, University of Sydney. Accessed January 26, 2021. http://hdl.handle.net/2123/14162.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Marting, Zechariah Lanka. “Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents .” 2015. Web. 26 Jan 2021.

Vancouver:

Marting ZL. Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents . [Internet] [Thesis]. University of Sydney; 2015. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2123/14162.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Marting ZL. Targeting the ‘Oligomerization Region’ of the Epidermal Growth Factor Receptor using Small Molecule Inhibitors as Novel Anticancer Agents . [Thesis]. University of Sydney; 2015. Available from: http://hdl.handle.net/2123/14162

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of New South Wales

25. Sun, Yang. Soliton dynamics in frequency-modulated lattices.

Degree: Physical, Environmental & Mathematical Sciences, 2014, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/53902 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12612/SOURCE02?view=true

► Currently, experimental and theoretical studies of solitons have been conducted in the context of several areas of science, from applied mathematics and physics to chemistry… (more)

Subjects/Keywords: nonlinear Schrodinger equation; soliton; periodic potential; parametric resonance

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APA (6^th Edition):

Sun, Y. (2014). Soliton dynamics in frequency-modulated lattices. (Masters Thesis). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/53902 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12612/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Sun, Yang. “Soliton dynamics in frequency-modulated lattices.” 2014. Masters Thesis, University of New South Wales. Accessed January 26, 2021. http://handle.unsw.edu.au/1959.4/53902 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12612/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Sun, Yang. “Soliton dynamics in frequency-modulated lattices.” 2014. Web. 26 Jan 2021.

Vancouver:

Sun Y. Soliton dynamics in frequency-modulated lattices. [Internet] [Masters thesis]. University of New South Wales; 2014. [cited 2021 Jan 26]. Available from: http://handle.unsw.edu.au/1959.4/53902 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12612/SOURCE02?view=true.

Council of Science Editors:

Sun Y. Soliton dynamics in frequency-modulated lattices. [Masters Thesis]. University of New South Wales; 2014. Available from: http://handle.unsw.edu.au/1959.4/53902 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12612/SOURCE02?view=true

The Ohio State University

26. Lee, Jong-eao John. The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation.

Degree: PhD, Graduate School, 1986, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429

Subjects/Keywords: Mathematics; Schrodinger equation; Wave mechanics

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APA (6^th Edition):

Lee, J. J. (1986). The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429

Chicago Manual of Style (16^th Edition):

Lee, Jong-eao John. “The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation.” 1986. Doctoral Dissertation, The Ohio State University. Accessed January 26, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429.

MLA Handbook (7^th Edition):

Lee, Jong-eao John. “The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation.” 1986. Web. 26 Jan 2021.

Vancouver:

Lee JJ. The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation. [Internet] [Doctoral dissertation]. The Ohio State University; 1986. [cited 2021 Jan 26]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429.

Council of Science Editors:

Lee JJ. The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation. [Doctoral Dissertation]. The Ohio State University; 1986. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429

University of Cincinnati

27. Hill, Thomas. Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension.

Degree: PhD, Arts and Sciences: Mathematical Sciences, 2020, University of Cincinnati

URL: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1595850253465442

► This dissertation will discuss one-dimensional dispersive estimates of the Schrodinger equation and a fourth-order Schrodinger-like equation.We prove dispersive estimates for the Schrodinger equation with Hamiltonians… (more)

Subjects/Keywords: Mathematics; Schrodinger equation; dispersive estimates; fourth-order; Wiener algebra; one-dimensional

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APA (6^th Edition):

Hill, T. (2020). Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension. (Doctoral Dissertation). University of Cincinnati. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ucin1595850253465442

Chicago Manual of Style (16^th Edition):

Hill, Thomas. “Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension.” 2020. Doctoral Dissertation, University of Cincinnati. Accessed January 26, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1595850253465442.

MLA Handbook (7^th Edition):

Hill, Thomas. “Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension.” 2020. Web. 26 Jan 2021.

Vancouver:

Hill T. Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension. [Internet] [Doctoral dissertation]. University of Cincinnati; 2020. [cited 2021 Jan 26]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1595850253465442.

Council of Science Editors:

Hill T. Dispersive Estimates of Schrodinger and Schrodinger-Like Equations in One Dimension. [Doctoral Dissertation]. University of Cincinnati; 2020. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1595850253465442

University of South Carolina

28. DeCosta, Richard Henry. Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates.

Degree: PhD, Physics, 2020, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/6003

► In an attempt to merge the two prominent areas of physics: The Standard Model and General Relativity, there have been many theories for the… (more)

▼ In an attempt to merge the two prominent areas of physics: The Standard Model and General Relativity, there have been many theories for the underlying physics that may lead to Lorentz- and CPT-symmetry violations. At the present moment, technology allows numerous types of Planck-sensitive tests of these symmetries in a range of physical systems. We address a curiosity in isotropic CPT- and Lorentz-violating electrodynamics where there is a kinematic allowance for Cerenkov radiation of a charged particle in a vacuum moving with uniform motion. This however, should not be the case as it is known that constant motion in a vacuum should not cause the particle to lose any energy. Taking Fourier transforms of the modified magnetic field confirms the cancellation of the apparent radiation. The Fourier transform can be used to show that modes for short and long wavelengths cancel. In the second area of research we focus on solutions of the Schrödinger equation which may be found by separation of variables in more than one coordinate system. This class of potentials includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. There are multiple separable Hamiltonians that exhibit a number of interesting features, including “accidental” degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schrödinger equation is separable in both cylindrical and parabolic coordinates: a z-independent V ∝ 1/p² = 1/ (x² + y²) in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at ρ = 0. When separated in parabolic coordinates, the Schrödinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential—one equation with an attractive potential, the other with an equally strong repulsive potential. Advisors/Committee Members: Brett Altschul.

Subjects/Keywords: Physics; Cerenkov; Chern-Simons; CPT; Lorentz; Parabolic; Schrodinger

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APA (6^th Edition):

DeCosta, R. H. (2020). Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/6003

Chicago Manual of Style (16^th Edition):

DeCosta, Richard Henry. “Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates.” 2020. Doctoral Dissertation, University of South Carolina. Accessed January 26, 2021. https://scholarcommons.sc.edu/etd/6003.

MLA Handbook (7^th Edition):

DeCosta, Richard Henry. “Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates.” 2020. Web. 26 Jan 2021.

Vancouver:

DeCosta RH. Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates. [Internet] [Doctoral dissertation]. University of South Carolina; 2020. [cited 2021 Jan 26]. Available from: https://scholarcommons.sc.edu/etd/6003.

Council of Science Editors:

DeCosta RH. Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates. [Doctoral Dissertation]. University of South Carolina; 2020. Available from: https://scholarcommons.sc.edu/etd/6003

Universidade do Estado do Rio de Janeiro

29. Bruno Fernando Inchausp Teixeira. Dualidade na teoria de Landau-Ginzburg da supercondutividade.

Degree: Master, 2010, Universidade do Estado do Rio de Janeiro

URL: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=2828 ;

►

Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e… (more)

▼

Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e descrever a transição de fase que sofrem alguns metais de uma fase normal para uma fase supercondutora. Durante uma transição de fase em supercondutores do tipo II é característico o surgimento de linhas de fluxo magnético em determinadas regiões de tamanho finito chamadas comumente de vórtices. A dinâmica destas estruturas topológicas é de grande interesse na comunidade científica atual e impulsiona incontáveis núcleos de pesquisa na área da supercondutividade. Baseado nisto estudamos como essas estruturas topológicas influenciam em uma transição de fase em um modelo bidimensional conhecido como modelo XY. No modelo XY vemos que os principais responsáveis pela transição de fase são os vórtices (na verdade pares de vórtice-antivórtice). Villain, observando este fato, percebeu que poderia tornar explícita a contribuição desses defeitos topológicos na função de partição do modelo XY realizando uma transformação de dualidade. Este modelo serve como inspiração para a proposta deste trabalho. Apresentamos aqui um modelo baseado em considerações físicas sobre sistemas de matéria condensada e ao mesmo tempo utilizamos um formalismo desenvolvido recentemente na referência [29] que possibilita tornar explícita a contribuição dos defeitos topológicos na ação original proposta em nossa teoria. Após isso analisamos alguns limites clássicos e finalmente realizamos as flutuações quânticas visando obter a expressão completa da função correlação dos vórtices o que pode ser muito útil em teorias de vórtices interagentes (dinâmica de vórtices).

In this work we introduced the Ginzburg-Landau theory of superconductivity (GL theory). We have shown your foundations, features and more important results. The fundamental idea of this theory is to describe the phase transition that some metals undergoes from a normal to a superconductor phase. During a phase transition in superconductors of type II is common the appearance of magnetic flux lines in given regions of finite size called of vortices. The knowledge of the dynamics of these vortices is of great importance in the current cientific community and drives many research centers to study the superconductivity. In view of this we study how these vortices changes a phase transition in a bidimensional model known as XY model.In XY model one can show that the main responsible for the phase transition are the vortices (or still, vortice-antivortice pairs). Villain, noting this fact, realized that could to turn explicit the contribution of theses topological defects in the partition function of XY model making a duality transformation. This model inspired us to study the subject of this master thesis. We presented here a model based in physical considerations about systems of condensed matter. At the same time we used a formalism developed in reference [29] that permits to turn explicit the…

Advisors/Committee Members: Cesar Augusto Linhares da Fonseca Junior, Marco Moriconi, Daniel Gustavo Barci.

Subjects/Keywords: FISICA DA MATERIA CONDENSADA; Teoria GL; Transições de fase; Dinâmica de vórtices; Dualidade; Modelo de Schrodinger-Ginzburg-Landau; GL theory; Phase Transitions; Vortex Dynamics; Duality; Schrodinger-Ginzburg-Landau Model

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APA (6^th Edition):

Teixeira, B. F. I. (2010). Dualidade na teoria de Landau-Ginzburg da supercondutividade. (Masters Thesis). Universidade do Estado do Rio de Janeiro. Retrieved from http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=2828 ;

Chicago Manual of Style (16^th Edition):

Teixeira, Bruno Fernando Inchausp. “Dualidade na teoria de Landau-Ginzburg da supercondutividade.” 2010. Masters Thesis, Universidade do Estado do Rio de Janeiro. Accessed January 26, 2021. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=2828 ;.

MLA Handbook (7^th Edition):

Teixeira, Bruno Fernando Inchausp. “Dualidade na teoria de Landau-Ginzburg da supercondutividade.” 2010. Web. 26 Jan 2021.

Vancouver:

Teixeira BFI. Dualidade na teoria de Landau-Ginzburg da supercondutividade. [Internet] [Masters thesis]. Universidade do Estado do Rio de Janeiro; 2010. [cited 2021 Jan 26]. Available from: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=2828 ;.

Council of Science Editors:

Teixeira BFI. Dualidade na teoria de Landau-Ginzburg da supercondutividade. [Masters Thesis]. Universidade do Estado do Rio de Janeiro; 2010. Available from: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=2828 ;

Texas A&M University

30. Weyand, Tracy Kathleen. Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator.

Degree: PhD, Mathematics, 2014, Texas A&M University

URL: http://hdl.handle.net/1969.1/153392

► In this dissertation, we analyze characteristics of eigenfunctions of the Schrödinger operator on graphs. In particular, we are interested in the zeros of the eigenfunctions… (more)

▼ In this dissertation, we analyze characteristics of eigenfunctions of the Schrödinger operator on graphs. In particular, we are interested in the zeros of the eigenfunctions and their relation to the spectrum of the magnetic Schrödinger operator. We begin by studying the nodal count on finite quantum graphs, analyzing both the number and location of the zeros of eigenfunctions. This question was completely solved by Sturm in one dimension. In higher dimensions (including domains and graphs), we only know bounds for the nodal count. We discover more information about the nodal count on quantum graphs while analyzing eigenvalues of the magnetic Schrödinger operator. In particular, we show a relation between the stability of eigenvalues of the magnetic Schrödinger operator with respect to magnetic flux and the number of zeros of the corresponding eigenfunctions. We also study the location of the zeros of eigenfunctions while analyzing partitions. Specifically, we show that the critical points of the energy functional are the nodal partitions corresponding to zeros of an eigenfunction and that the stability of these critical points is related to the nodal count. Then using Floquet-Bloch theory, we study the spectrum of the Schrödinger operator on infinite periodic graphs by analyzing the eigenvalues of the magnetic Schrödinger operator on a fundamental domain. Here we consider both discrete and quantum graphs. We find a characterization of critical points of the dispersion relation that occur inside the Brillouin zone under certain conditions on the graph. In particular, we show that if the fundamental domain is a tree, then the eigenfunction corresponding to an interior critical point must be zero on a vertex. Finally, we use the results from infinite periodic graphs to study the magnetic Schrödinger operator on a finite quantum d-mandarin graph. We find that extremal points of the dispersion surface occur inside the Brillouin zone where two surfaces touch and the corresponding eigenfunction is zero on a vertex. Advisors/Committee Members: Berkolaiko, Gregory (advisor), Kuchment, Peter (advisor), Ross, Jr., Joseph H. (committee member), Walton, Jay R. (committee member).

Subjects/Keywords: Quantum graphs; Schrodinger operator on graphs; nodal count; zeros of eigenfunctions; magnetic Schrodinger operator; magnetic-nodal connection; dispersion relation; spectral band edges; infinite periodic graphs; Wronskian on graphs

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

APA (6^th Edition):

Weyand, T. K. (2014). Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/153392

Chicago Manual of Style (16^th Edition):

Weyand, Tracy Kathleen. “Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator.” 2014. Doctoral Dissertation, Texas A&M University. Accessed January 26, 2021. http://hdl.handle.net/1969.1/153392.

MLA Handbook (7^th Edition):

Weyand, Tracy Kathleen. “Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator.” 2014. Web. 26 Jan 2021.

Vancouver:

Weyand TK. Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator. [Internet] [Doctoral dissertation]. Texas A&M University; 2014. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1969.1/153392.

Council of Science Editors:

Weyand TK. Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator. [Doctoral Dissertation]. Texas A&M University; 2014. Available from: http://hdl.handle.net/1969.1/153392

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Open Access Theses and Dissertations