Latin American cities are challenged by the effects of population growth and insufficient infrastructure. As a consequent, Informal Car Share (ICS) is increasingly filling the gap as a transportation choice for underserved populations. ICS is the use of private vehicles to provide transportation for a fare that is neither taxed nor regulated by any type of government. Although this practice contributes significantly to development and economic growth, it is often stigmatized as unreliable and inconsistent, and little is known about it. This research expands existing definitions of ICS, using cases from Quito, Ecuador, a mountain city located in the Andes region in South America. It does so by analyzing Quito's ICS perceived effectiveness and performance from its users and drivers, the disruptions this system faces in the communities in which it operates, and its resiliency to bounce back from those disruptions. Findings suggested that despite its informality, ICS works with fixed stops, schedules, routes and fares. This is similar to formal systems operated by the government. Users and drivers described ICS as reliable and consistent, and they all reported a positive experience with the service. Findings also suggested that Quito's ICS is disrupted by six natural and political disruptions that delay the ICS service for 10 to 40 minutes. However, ICS proved to be adaptable and able to circumvent disruptions to ensure passengers connectivity to the city. Lastly, findings suggested that ICS users and drivers developed eight adaptation strategies to circumvent disruptions. Those strategies have created a system that aligns with features of resilient urban systems from UN-Habitat. Expanding the current understanding of how ICS operates, as well as its resilience capacity, is the first step to understanding better the value these self-organized systems provide to cities. / Doctor of Philosophy / The population in Latin America's cities is increasing and cities have been unable to keep up with the infrastructure demands that growth has created. As a consequent, Informal Car Share (ICS) are self-organized systems that arose as a solution to fill the gap in the peripheral areas that government provided transportation have not addressed. ICS is the use of private vehicles to provide transportation for a fare that is neither taxed nor regulated by any type of government. Although this practice contributes significantly to development and economic growth, it is often stigmatized as unreliable, inconsistent, and little is known about it. This research explores existing definitions of ICS, using cases from Quito, Ecuador, a mountain city located in the Andes region in South America It does so by analyzing Quito's ICS perceived effectiveness and performance from its users and drivers, the disruptions this system faces in the communities it operates, and its ability to adapt to those disruptions. Findings suggested that despite its informality, users and drivers described ICS as reliable and consistent, and they all reported a positive experience with the service. Findings also suggested that Quito's ICS is disrupted by six natural and political disruptions that delay the ICS service for 10 to 40 minutes. However, ICS proved to be adaptable and able to overcome disruptions to ensure passenger connectivity to the city. Findings suggest that ICS developed eight adaptation strategies that align well with UN-Habitat (2018) characteristics of resilient urban systems. Expanding the understanding of how ICS operates is the first step to understanding the value ICS provide to cities and their urban resilience.

In der vorliegenden Arbeit werden Musterbildungsphänomene auf Submikrometerskalen in reaktiven Adsorbaten auf einkristallinen Katalysatoroberflächen theoretisch untersucht. Da auf solch kleinen Skalen Fluktuationen nicht mehr vernachlässigt werden können, wird eine mesoskopische Theorie entwickelt, die zwischen mikroskopischen Gittermodellen und Reaktions-Diffusions-Systemen vermittelt. Sie beschreibt die Dynamik lokal gemittelter Adsorbatbedeckungen im Rahmen eines Kontinuumsmodells unter Berücksichtigung interner Fluktuationen. Dieser Ansatz wird auf verschiedene Systeme angewendet, in denen sich Muster auf Längenskalen ausbilden, die kleiner als die charakterist ische Diffusionslänge sind, die typischerweise im Mikrometerbereich liegt. Wie beispielsweise in kürzlich durchgefh hrten Experimenten mit einem vergleichsweise schnellen Rastertunnelmikroskop beobachtet wurde, können attraktive Adsorbat-Adsorbat-Wech sel wirkungen zu verschiedenen Mustern auf Nanometerskalen führen. Hier wird zunächst eine einzelne Adsorbatspezies betrachtet. In Abwesenheit von Nichtgleichgewichtsreaktionen können hinreichend starke attraktive laterale Adsorbatwechselwirkungen einen Phasenh bergang erster Ordnung in der Adsorbatbedeckung induzieren. Die mesoskopische Entwicklungsgleichung wird auf die Modellierung der Kinetik dieses Phasenh bergangs angewendet. Berücksichtigt man zusätzlich eine Nichtgleichgewichtsreakti on, so können sich stationäre räumlich periodische Mikrostrukturen aufgrund der Konkurrenz zwischen dem Phasenh bergang und der Reaktion ausbilden. Die Vorraussetzungen für deren Auftreten und ihre charakteristischen Eigenschaften werden hier detailliert analysiert. Unter anderem werden alternierende Wechselwirkungen diskutiert und der Einfluß globaler Kopplung durch die Gasphase auf die Musterbildung wird betrachtet. Außerdem wird gezeigt, da8 die Mikrostrukturen auch durch vergleichsweise starke interne Fluktuationen nicht zerstört werden. Im nächsten Schritt wird ein hypothetisches Modell für zwei verschiedene Adsorbatspezies untersucht, in dem ein ähnlicher Mechanismus zur Bildung von laufenden und stehenden Wellenmustern auf der Nanoskala führt. Werden vergleichsweise starke interne Fluktuationen berücksichtigt, so brechen diese Wellenmuster auf und man beobachtet eine komplexe Dynamik miteinander wechselwirkender Wellenfragmente. Im letzten Beispiel wird anhand der Analyse eines einfachen Modells gezeigt, da8 sich auf Skalen unterhalb der Diffusionslänge selbstorganisierte Mikroreaktoren in einer einzelnen reaktiven Adsorbatspezies ausbilden können, ohne daß die Teilchen miteinander wechselwirken. Sie entsprechen lokalisierten Strukturen, die aufgrund des Zusammenspiels einer Nichtgleichgewichtsreaktion, der Diffusion und eines adsorbatinduzierten strukturellen Phasenh bergangs in der Substratoberfläche entstehen. / Nanoscale pattern formation in reactive adsorbates on single crystal surfaces is investigated theoretically. Because on such small scales fluctuations become important, a mesoscopic theory for the adsorbate coverage is developed, which aims at providing a link between microscopic lattice models and reaction-diffusion equations. It describes the dynamics for the locally averaged adsorbate coverages in a continuum model taking into account internal fluctuations. This approach is applied to several systems, where patterns on scales smaller than the characteristic diffusion length, which typically lies in the micrometer range, can be formed. As has been observed e.g. in recent experiments with fast scanning tunneling microscopy, a variety of nanoscale patterns can result from the presence of attractive adsorbate-adsorbate interactions. Here, at first a single species of such an adsorbate is considered. In the absence of nonequilibrium reactions, strong enough attractive lateral interactions can induce a first-order phase transition in the adsorbate coverage. The mesoscopic evolution equation is applied to model the kinetics of this phase transition. If additionally a nonequilibrium reaction is present, stationary spatially periodic microstructures may arise as a result of the competition of the attractive lateral interactions and the reactions. The conditions for their appearance and their properties are investigated in detail, e.g. alternating lateral interactions are discussed and the influence of global coupling through the gas phase is analyzed. Furthermore, it is shown that they are not destroyed by relatively strong internal fluctuations. In the next step, a hypothetical model for two different reactive adsorbate species is investigated, where a similar mechanism leads to the formation of nanoscale traveling and standing waves. In the presence of relatively strong internal fluctuations these waves break up and a complex dynamics of interacting wave fragments is observed. In the last example, it is shown in the analysis of a simple model that self-organized nonequilibrium microreactors with submicrometer sizes may spontaneously develop in a single reactive adsorbate species without attractive lateral interactions. They represent localized structures resulting from the interplay between reaction, diffusion and an adsorbate-induced structural transformation of the surface.

In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzburg-Landau equations. These equations predict that the model exhibits bistability between travelling waves and Turing patterns. We present a study of interfaces separating wave and Turing patterns arising from the codimension-2 instability. We study theoretically and numerically the dynamics of such interfaces in the framework of the amplitude equations and compare these results with numerical simulations of the model near and far away from the codimension-2 instability. Near the instability, the dynamics of interfaces separating small amplitude Turing patterns and travelling waves is well described by the amplitude equations, while, far from the codimension-2 instability, we observe a locking of the interface velocities. This locking mechanism is imposed by the absence of defects near the interfaces and is responsible for the formation of drifting pattern domains, i.e. moving localised patches of travelling waves embedded in a Turing pattern background and vice versa.

In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzburg-Landau equations. These equations predict that the model exhibits bistability between travelling waves and Turing patterns. We present a study of interfaces separating wave and Turing patterns arising from the codimension-2 instability. We study theoretically and numerically the dynamics of such interfaces in the framework of the amplitude equations and compare these results with numerical simulations of the model near and far away from the codimension-2 instability. Near the instability, the dynamics of interfaces separating small amplitude Turing patterns and travelling waves is well described by the amplitude equations, while, far from the codimension-2 instability, we observe a locking of the interface velocities. This locking mechanism is imposed by the absence of defects near the interfaces and is responsible for the formation of drifting pattern domains, i.e. moving localised patches of travelling waves embedded in a Turing pattern background and vice versa.