Mikrostruktur und Magnetisierungsdynamik feinmodulierter Co/Pt-Heterostrukturen

Gegenstand dieser Arbeit ist die Untersuchung der strukturellen und magnetischen Eigenschaften von (111)-texturierten epitaktischen dünnen Co/Pt-Vielfachschichten und Pt/Co/Pt-Heterostrukturen. Mit Hilfe von Röntgen-Diffraktions-Experimenten wurde der Einfluß der Oberflächenqualität des MgO (111) Substratmaterials auf die Zwischenlagenstruktur und die kristalline Ordnung in den Filmen analysiert. Es konnte nachgewiesen werden, daß die Unordnung an der Co/Pt-Grenzfläche unterhalb einer Längenskala von 6 nm allein durch die Wachstums- und Interdiffusionsprozesse zwischen der Co- und der Pt-Lage bestimmt ist, unabhängig von der Qualität der Substratoberfläche. Demgegenüber zeigte sich, daß durch eine besondere Substratbehandlung eine langreichweitige kristalline Kohärenz der Schichten und eine Unterdrückung der Verzwillingung aus abc- und acb-Wachstumsdomänen des fcc-Platin erzielt werden können. Anhand integraler Messungen des magneto-optischen Kerr-Effektes wurde ein direkter Zusammenhang zwischen der Substrat-induzierten Defektdichte der Filme und der Nukleation magnetischer Domänen während der Ummagnetisierung nachgewiesen. Pt/Co/Pt-Dreifachlagen mit Kobalt-Dicken bis zu 1 nm besitzen eine senkrechte magnetische Anisotropie und zeigen magnetische Domänen mit Größen von bis zu einigen hundert Mikrometern, die mit Hilfe optischer Kerr-Mikroskopie visualisiert wurden. In Pt/Co/Pt-Dreifachschichten mit weniger als drei Monolagen Kobalt, welche auf vicinalen MgO (111)-Substraten aufgebracht wurden, treten während der Ummagnetisierung aufgrund anisotroper Domänenwandbewegung charakteristische dreieckige Domänenformen auf. Es wurde ein mikroskopischer Mechanismus vorgeschlagen, welcher dieses anisotrope Pinning von magnetischen Domänenwänden an mesoskopischen Stufen-Strukturen der Substratoberfläche beschreibt. Zur quantitativen Beschreibung der anisotropen Domänenwandbewegung wurden zweidimensionale numerische Simulationen durchgeführt, basierend auf einem modifizierten Random-Field-Ising-Modell mit einem Ginzburg-Landau-artigen Hamiltonian, in dem der Einfluß der Stufenkanten auf den Ordnungsparamter durch ein neu eingeführtes effektives anisotropes Feld G(r) repräsentiert ist. Unter Annahme einer lateralen Anordnung der Stufenkanten in Form eines Fischgrätenmusters konnten im Rahmen dieses Modells die experimentell beobachteten charakteristischen anisotropen Domänenformen sowie die Skaleneigenschaften der Domänenwände in exzellenter Weise numerisch reproduziert werden.

Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Accelerating CFD via local POD plus Galerkin projections

Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Dissipative Raman solitons

A new type of dissipative solitons - dissipative Raman solitons - are revealed on the basis of numerical study of the generalized complex nonlinear Ginzburg-Landau equation. The stimulated Raman scattering significantly affects the energy scalability of the dissipative solitons, causing splitting to multiple pulses. We show, that an appropriate increase of the group-delay dispersion can suppress the multipulsing instability due to formation of the dissipative Raman soliton, which is chirped, has a Stokes-shifted spectrum, and chaotic modulation on its trailing edge. The strong perturbation of a soliton envelope caused by the stimulated Raman scattering confines the energy scalability, preventing the so-called dissipative soliton resonance. We show that in practical implementations, a spectral filter can extend the stability regions of high-energy pulses.

Fast and slowly evolving vector solitons in mode-locked fibre lasers

We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by elliptically polarized pump field. Interplay of aforementioned factors changes coherent coupling of two polarization modes at a long time scale and so results in a new family of vector solitons (VSs) with fast and slowly evolving states of polarization. The observed VSs can be of interest in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetization in data storage devices and many other areas.

Stabilization of standing waves through time-delay feedback

Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform oscillations with respect to spatially periodic perturbations. The solution of the standing wave pattern is given analytically and studied through simulations. © 2013 American Physical Society.

Dissipative vector solitons with fast evolving states of polarization

We report on a new vector model of an erbium doped fiber laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. It results in a new family of vector solitons with fast evolving states of polarization experimentally observed in our previous papers.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Énergétique des vortex et comportement magnétique de la supraconductivité SO(5)

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Dissipative parametric modulation instability and pattern formation in nonlinear optical systems

We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.

Self-pulsating nonlinear systems via dissipative parametric instability

The recently discovered dissipative parametric instability is presented in the framework of the universal complex Ginzburg-Landau equation. The pattern formation associated with the instability is discussed in connection to the relevant applications in nonlinear photonics especially as a new tool for pulsed lasers design.

Énergétique des vortex et comportement magnétique de la supraconductivité SO(5)

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.