A Modelling Study on Tsunami Propagation in the Caspian Sea

A numerical model that simulates the propagation of tsunamis produced by submarine earthquakes was applied to the Caspian Sea. The model was first applied to the June 1990 (Rudbar) earthquake and our results proved to be coherent with previous simulations. It was also applied to the Krasnovodsk earthquake (1895), which had not been simulated before, and it was found that the coastal area was flooded by a tsunami, as reported in literature. Nevertheless, it was a rather local effect since the tsunami was generated in very shallow waters. Some worst-case hypothetical earthquakes were simulated in the most seismically active regions of the Caspian. In general, both the east and west coasts of the central Caspian Sea would be the most affected by these earth quake-induced tsunamis, with potential significant effects in some cases in cities such as Baku

Euclidean position in Euclidean 2-orbifolds

Intuitively, a set of sites on a surface is in Euclidean position if points are so close to each other that planar algorithms can be easily adapted in order to solve most of the classical problems in Computational Geometry. In this work we formalize a definition of the term “Euclidean position” for a relevant class of metric spaces, the Euclidean 2-orbifolds, and present methods to compute whether a set of sites has this property. We also show the relation between the convex hull of a point set in Euclidean position on a Euclidean 2-orbifold and the planar convex hull of the inverse image (via the quotient map) of the set

Quadrangulations and 2-Colorations

Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of the set, such that edges of the quadrangulation can only join points with different colors. In this work we focus in 2-colorations and study whether they admit a quadrangulation or not, and whether, given two quadrangulations of the same 2-coloration, it is possible to carry one into the other using some local operations, called diagonal slides and diagonal rotation. Although the answer is negative in general, we can show a very wide family of 2-colorations, called onions 2-coloration, that are quadrangulable and which graph of quadrangulations is always connected

Diagonal flips in outer-triangulations on closed surfaces

We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonal flips, up to isotopy, if they have a sufficiently large and equal number of vertices

Transforming triangulations on non planar-surfaces

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinde

K-Factores en nubes bicromáticas

Consideramos una colección de puntos bicromática y nos preguntamos cuántos puntos adicionales son necesarios considerar para asegurar la existencia de un k {factor. Dos tipos de puntos adicionales serán tratados: puntos de Steiner y puntos blancos (con posición prefijada pero no así su color

Transforming Triangulations on Nonplanar Surfaces

We consider whether any two triangulations of a polygon or a point set on a nonplanar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder

Reporting Bichromatic Segment Intersections from Point Sets

In this paper, we introduce a natural variation of the problem of computing all bichromatic intersections between two sets of segments. Given two sets R and B of n points in the plane defining two sets of segments, say red and blue, we present an O(n2) time and space algorithm for solving the problem of reporting the set of segments of each color intersected by segments of the other color. We also prove that this problem is 3-Sum hard and provide some illustrative examples of several point configurations

Compact Grid Representation of Graphs

A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some graph families