Coordinated missions with platoons of autonomous agents are rapidly becoming popular because of technological advances in computing, networking, miniaturization and combination of electromechanical systems. These multi-agents networks coordinate their actions to perform challenging spatially-distributed tasks such as search, survey, exploration, and mapping. Environmental monitoring and locational optimization are among the main applications of the emerging technology of wireless sensor networks where the optimality refers to the assignment of sub-regions to each agent, in such a way that a suitable coverage metric is maximized. Usually the coverage metric encodes a distribution of risk defined on the area, and a measure of the performance of individual robots with respect to points inside the region of interest. The risk density can be used to quantify spatial distributions of risk in the domain. The solution of the optimal control problem in which the risk measure is not time varying is well known in the literature, with the optimal con figuration of the robots given by the centroids of the Voronoi regions forming a centroidal Voronoi tessellation of the area. In other words, when the set of mobile robots converge to the corresponding centroids of the Voronoi tessellation dictated by the coverage metric, the coverage itself is maximized. In this work, it is considered a time-varying risk density evolving according to a diffusion equation with varying boundary conditions that quantify a time-varying risk on the border of the workspace. Boundary conditions model a time varying flux of external threats coming into the area, averaged over the boundary length, so that rather than considering individual kinematics of incoming threats it is considered an averaged, distributed effect. This approach is similar to the one commonly adopted in continuum physics, in which kinematic descriptors are averaged over spatial domain and suitable continuum fields are introduced to describe their evolution. By adopting a first gradient constitutive relation between the flux and the density, a simple diffusion equation is obtained. Asymptotic convergence and optimality of the non-autonomous system are studied by means of Barbalat's lemma and connections with varying boundary conditions are established. Some criteria on time-varying boundary conditions and evolution are established to guarantee the stabilities of agents' trajectories. A set of numerical simulations illustrate theoretical results.

Magíster en Ciencias, mención Física / En esta tesis se diseñó e implementó una metodología experimental a escala microfluídica, enfocada al estudio de la difusión en redes cuasi-bidimensionales aleatorias de microcanales. Para ello, se adaptó la técnica de la recuperación de la fluorescencia después del fotoblanqueo (FRAP) con el objetivo de determinar el coeficiente de difusión efectivo adimensional $D/D_0$ de la fluoresceína en una solución acuosa dentro de estas redes; donde $D_0$ es el coeficiente de difusión molecular de esta especie. Se estudió el comportamiento de $D/D_0$ en función de dos parámetros adimensionales que describen las cualidades geométricas de estas redes: la homogeneidad $\gamma=R/\langle L \rangle$ y el aspecto reticular $\eta=\langle L \rangle/w$, donde $\langle L \rangle$ y $w$ son la longitud media y el ancho de los canales, y $R$ es el radio de la zona en que la difusión es medida. El parámetro $\gamma$ describe los efectos de los detalles geométricos sobre la difusión y $\eta$ cuantifica el volumen accesible al fluido. Adicionalmente, en estas geometrías estudiamos la respuesta de $D/D_0$ frente la acción de un flujo periódico de amplitud $x$ y promedio nulo. Determinamos un parámetro crítico $\gamma_c\sim2.7$ a partir del cual la red puede ser descrita como un medio efectivo. En esta escala, encontramos que $D/D_0\sim 0.7$ para un valor fijo de $\eta=3.64$. Además, medimos el efecto del aspecto reticular $\eta$ sobre la difusión; en este caso $D/D_0$ disminuye cuando $\eta$ aumenta, llegando rápidamente a un nivel de saturación $D/D_0\sim0.4-0.5$ para $\eta>2.5$. Por otro lado, para $\gamma=0.6$, lo que llamamos la micro-escala, se encontró que existe una dependencia del número de conexiones existentes en un nodo de la red sobre $D/D_0$. En el caso de la acción del flujo externo, observamos un importante incremento de $D/D^*$ en términos de la amplitud adimensional de oscilación de este flujo $x/\langle L \rangle$, siendo $D^*$ el coeficiente efectivo de difusión en ausencia de flujo. En la primera parte de esta tesis establecemos la base teórica correspondiente del proceso de difusión, incluyendo una descripción para medios no homogéneos. También discutimos los aspectos relevantes del FRAP, que es la metodología experimental que usamos en este trabajo. Más adelante, describimos los métodos experimentales desarrollados, donde reseñamos, entre otros detalles, la forma de obtener geometrías reticulares desordenadas mediante los mosaicos de Voronoi y el procedimiento de construcción de los microcanales que reproducen estas geometrías. Luego, mostramos en detalle los resultados experimentales, entre ellos, los ya mencionados. Finalmente incluimos las conclusiones del presente trabajo, presentando además las sugerencias para futuras investigaciones en este tema.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-66). Also available in print.

Commonly held opinion is that particle trajectory descriptions are incompatible with quantum mechanics. Louis de Broglie (1926) first proposed a way to include trajectories in quantum mechanics, but the idea was abandoned until David Bohm (1952) re-invented and improved the theory. Bohm interprets the particle trajectories as physically real; for example, an electron actually is a particle moving on a well defined trajectory with a position and momentum at all times. By design, Bohm's trajectories never make predictions that differ from standard quantum mechanics, and their existence cannot be experimentally verified. Three new methods to obtain Bohm's particle trajectories are presented. The methods are non-dynamical, and utilize none of Bohm's equations of motion; in fact, two of the methods have no equations for a particle's trajectory. Instead, all three methods use only the evolving probability density ρ=ψ*ψ to extract the trajectories. The first two methods rest upon probability conservation and density sampling, while the third method employs the informational or geometrical construction of centroidal Voronoi tessellations. In one-dimension all three methods are proved to be equivalent to Bohm's particle trajectories. For higher dimensional configuration spaces, the first two methods can be used in limited situations, but the last method can be applied in all cases. Typically, the resulting higher dimensional non-dynamical trajectories are also identical to Bohm. Together the three methods point to a new interpretation of Bohm's particle trajectories, namely, the Bohm trajectories are simply a kinematic portrayal of the evolution of the probability density. In addition, the new methods can be used to measure Schrödinger's wave function and Planck's constant. / text

In these theses are pepresented the Voronoi diagram and Network Voronoi diagram. The shortest path Dijkstra’s algorithm was modified in this way that calculates shortest paths from several Voronoi generators at the same time. The first result - partition of the nodes of the network. The seond result - arcs of the network are attributed to the generators, considering especially their direction and asymmetric costs. Applications allow compare Network Voronoi diagrams to Voronoi diagrams. For this puspose we modified Fortune algorithm. We made particular product for Taxi depot. The user can make his own implementation.

Diplomarbeit - Technische Universität Berlin / Title from title screen (viewed on June 17, 2008). Abstract in German and English. Title from document title page. Includes bibliographical references. Available in PDF format via the World Wide Web.

As the demand for a low-carbon and environmentally friendly future increases, so does the importance of mineral and metal commodities. The production of solar panels, wind turbines, energy storage systems and other green technologies require large quantities of minerals and rare earth metals. Natural Resources Canada noted that in 2019, Canada was a global leading producer in minerals required for green technology including graphite, nickel, cobalt, and others [1]. While mineral production continues to rise year over year, the ore grade, i.e., the concentration of a desired material, of multiple common minerals continues to decline. To liberate valuable minerals from low ore grade deposits size reduction processes such as crushing and grinding are required; however, these processes account for over half of all energy consumption on the average mine. As mines are typically remote, fossil fuels are normally used as the main energy source, producing large amounts greenhouse gases, necessitating the need for more efficient size reduction processes. This could be accomplished by predicting how a particular orebody would break. With the surge in image sensing and computing technologies at mining sites many researchers are exploring ore texture and processability characteristics of the ore body. If distinct processability characteristics change based on ore textural feature from a 2D image, then general trends for optimal size reduction of orebodies of similar texture can developed. This work builds on previous work by simulating ore breakage through the superimposition of a predetermined fragmentation pattern, called a mask, onto multiple ore textures. Synthetic, periodic black and white 2D ore textures were created to find a link between simple textural features such as different mineral grain shape, size, and orientation and processability characteristics. A Monte Carlo simulation was performed to generate a large quantity of realistic product particles using the Voronoi tessellations masking technique. To assess the processability of different textures, the percentage area distribution of valuable minerals of each ore texture was compared across the complete range of particle sizes. The valuable mineral percentage area distributions were analyzed for rate and shape of the distribution as particle size decreases, with noticeable differences between textures. The distributions were also parameterized using a two-beta mixture distribution model, expanding on the traditional one beta model developed by King [2,3,4]. These distributions can eventually help the mining industry make informed decisions on how much grinding and crushing will be required to liberate desired minerals from waste rock.

No description available.

published_or_final_version / Computer Science / Master / Master of Philosophy

Zugl.: Karlsruhe, Universiẗat, Diss., 2007.