Turing patterns formation on surfaces under deformation: A total lagrangian method approach

En este artículo se desarrollan varios ejemplos numéricos sobre ecuaciones de reacción-difusión con dominio creciente. Para este fin se utiliza el modelo de reacción de Schnakenberg, con parámetros en el espacio de Turing. Por tanto se realizan ensayos numéricos sobre la aparición de los patrones de Turing en superficies que tienen alta tasa de deformación. Para la solución de las ecuaciones de reacción difusión se presenta un método de solución en superficies en 3 dimensiones mediante el método de los elementos finitos bajo el uso de la formulación lagrangiana total. Los resultados muestran que la formación de los patrones de Turing depende de las funciones de deformación de la superficie y la tasa a la cual se presenta el cambio de posición de cada punto del dominio donde se lleva a cabo la solución numérica. Estos resultados pueden esclarecer algunos fenómenos de cambio de patrón en la superficie de la piel de aquellos animales que exhiben manchas características.In this work we have developed several numerical examples of reaction-diffusion equations with growing domain. For this purpose we have used the Schnakenberg reaction model with parameters in space Turing. Therefore numerical tests are performed on the appearance of Turing patterns on surfaces that have high deformation rate. For the solution of reaction diffusion equations is presented a solution method on surfaces in three dimensions using the finite element method under the use of the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the features of surface deformation and the rate at which change in position of each point of the domain. These results can explain some phenomena of change of pattern on the surface of the skin of animals that exhibit characteristic spots.Peer Reviewe

A GIS-based fire spread simulator integrating a simplified physical wildland fire model and a wind field model

[EN]This article discusses the integration of two models, namely, the Physical Forest Fire Spread (PhFFS) and the High Definition Wind Model (HDWM), into a Geographical Information System-based interface. The resulting tool automates data acquisition, preprocesses spatial data, launches the aforementioned models and displays the corresponding results in a unique environment. Our implementation uses the Python language and Esri’s ArcPy library to extend the functionality of ArcMap 10.4. The PhFFS is a simplified 2D physical wildland fire spread model based on conservation equations, with convection and radiation as heat transfer mechanisms. It also includes some 3D effects. The HDWM arises from an asymptotic approximation of the Navier–Stokes equations, and provides a 3D wind velocity field in an air layer above the terrain surface. Both models can be run in standalone or coupled mode. Finally, the simulation of a real fire in Galicia (Spain) confirms that the tool developed is efficient and fully operational.Junta de Castilla y León; Fundación General de la Universidad de Salamanc

Some results on a set of data driven stochastic wildfire models

Across the globe, the frequency and size of wildfire events are increasing. Research focused on minimizing wildfire is critically needed to mitigate impending humanitarian and environmental crises. Real-time wildfire response is dependent on timely and accurate prediction of dynamic wildfire fronts. Current models used to inform decisions made by the U.S. Forest Service, such as Farsite, FlamMap and Behave do not incorporate modern remotely sensed wildfire records and are typically deterministic, making uncertainty calculations difficult. In this research, we tested two methods that combine artificial intelligence with remote sensing data. First, a stochastic cellular automata that learns algebraic expressions was fit to the spread of synthetic wildfire through symbolic regression. The validity of the genetic program was tested against synthetic spreading behavior driven by a balanced logistic model. We also tested a deep learning approach to wildfire fire perimeter prediction. Trained on a time-series of geolocated fire perimeters, atmospheric conditions, and satellite images, a deep convolutional neural network forecasts the evolution of the fire front in 24-hour intervals. The approach yielded several relevant high-level abstractions of input data such as NDVI vegetation indexes and produced promising initial results. These novel data-driven methods leveraged abundant and accessible remote sensing data, which are largely unused in industry level wildfire modeling. This work represents a step forward in wildfire modeling through a curated aggregation of satellite image spectral layers, historic wildfire perimeter maps, LiDAR, atmospheric conditions, and two novel simulation models. The results can be used to train and validate future wildfire models, and offer viable alternatives to current benchmark physics-based models used in industry

Estudio comparativo entre los métodos espectrales y la formulación Petrov-Galerkin para la solución numérica de problemas con convección dominante

El presente trabajo analiza y compara los problemas numéricos derivados al modelar problemas altamente convectivos empleando diversos métodos espectrales y el método Streamline Petrov-Galerkin de elementos finitos (SUPG). El análisis comparativo de las gráficas de convergencia para diferentes números de Peclet, mostraron la superioridad de los métodos espectrales sobre las técnicas convencionales usadas para tratar problemas de advección dominante: elementos finitos SUPG y diferencias finitas en contracorriente. Por otro lado se observó que a diferencia de los elementos finitos convencionales (no jerárquicos), los métodos espectrales aumentan su rata de convergencia a medida que aumenta el número de grados de libertad. La implementación y solución de múltiples problemas tipo permitieron concluir sobre las diferencias generadas por el uso de incógnitas con sentido físico, como las empleadas en los métodos de colocación, y las incógnitas trabajadas en los métodos espectrales propiamente dichos. Dichas diferencias marcan complejidades importantes cuando se imponen condiciones de borde o cuando se trabajan problemas no lineales. No obstante las ventajas de convergencia encontradas en los métodos espectrales, se pueden citar grandes limitantes en la aplicación de estas técnicas en problemas multidimensionales, en cuyos casos muchas veces son necesarios complejos mapeos para poder transformar el dominio del problema en una geometría regular. / Abstract. The present work analizes and compares the numerical problems derivates when highly convective problems are modelled using several spectral methods and Streamline Petrov-Galernkin method of ?nite elements (SUPG). The comparative analisis of the convergence graphs to di?erent Peclet numbers showed the superiority of the spectral methods over conventional techniques used to treat advection dominant problems: Finite elements SUPG and upwind ?nite di?erences. On the other hand it was observed unlike the conventional ?nite element (nonhierarchical), spectral methods increase its rate of convergence as the number of degrees of freedom. The implementation and solution of example problems allow make conclusions about the di?erences generated by the use of unknows with phisycal sense, as those used in the colocation methods, and the unknows worked in the spectral methods themselves.These di?erences mark important complexities when boundary conditions are imposed or when nonlineal problems are considered. Despite of the advantages of convergency found in the spectral methods, big limitations may be mentioned in applying these techniques to multidimensional problems, These cases are often complex mappings required to transform the problem domain into a regular geometry.Maestrí

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described