http://hdl.handle.net/2117/127 2013-05-21T16:21:35Z http://hdl.handle.net/2117/19298 Title: A phase-field fracture model of ferroelectric materials under electro-mechanical loading Authors: Abdollahi Hosnijeh, Amir; Arias Vicente, Irene Abstract: A phase-field model is proposed for the coupled simulation of microstructure and fracture evolution in ferroelectric materials. The model is based on energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The variational nature of these approaches makes their coupling very natural. However the main challenge is to encode the electro-mechanical conditions of the sharp crack faces into the phase-field framework since the crack in this model is smeared and represented by an internal layer. We develope the model for different crack face boundary conditions. Simulations show the microstructure induced by the presence of the crack. Interactions between the microstructure and the crack are investigated under different electro-mechanical loadings. 2013-05-16T12:58:07Z http://hdl.handle.net/2117/19287 Title: The Manhattan product of digraphs Authors: Comellas Padró, Francesc de Paula; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel Abstract: We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants. 2013-05-16T11:26:48Z http://hdl.handle.net/2117/19246 Title: Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator Authors: Soto, De A R; Recasens Ferrés, Jorge Abstract: This work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up. 2013-05-15T11:39:15Z http://hdl.handle.net/2117/19242 Title: A reformulation of entropy in the presence of indistinguishability operators Authors: Recasens Ferrés, Jorge; Hernández, E Abstract: This paper deals with the measurement of entropy when an indistinguishability relation on the set of events has been defined. Our approach states that entropy could be measured in terms of the observed distinguishability of the set of events. In this sense, the “observer paradigm” is introduced, and definitions for joint and conditional entropy under this paradigm are given. We also present some interesting properties and relationships with Shannon's entropy measure. 2013-05-15T10:58:59Z http://hdl.handle.net/2117/19241 Title: On a geometric combinatorial problem Authors: Recasens Ferrés, Jorge Abstract: The study of the betweenness relations defined by metrics leads to a geometric problem that yields an upper bound to Turán's number T(n,5,3). 2013-05-15T10:49:35Z http://hdl.handle.net/2117/19240 Title: Finite-valued indistinguishability operators Authors: Mayor, Gaspar; Recasens Ferrés, Jorge Abstract: Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this assignment cannot be done in such a precise way and the use of indistinguishability operators valued on a finite set of linguistic labels such as small, very much, etc. would be advisable. Recent advances in the study of finite-valued t-norms allow us to combine this kind of linguistic labels and makes the development of a theory of finite-valued indistinguishability operators and their application to real problems possible. 2013-05-15T10:41:27Z http://hdl.handle.net/2117/19237 Title: Fixed points and generators of fuzzy relations Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: The fixed points of a T-indistinguishability operator are characterized as its generators in the sense of the Representation Theorem of Valverde. The geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it. 2013-05-15T10:27:44Z http://hdl.handle.net/2117/19235 Title: E-T-lipschitzian and E-T-kernel aggregation operators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: Lipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T. 2013-05-15T10:10:56Z http://hdl.handle.net/2117/19234 Title: Aggregation of T-transitive Relations Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: This article studies the aggregation of transitive fuzzy relations. We first find operators that preserve transitivity and then extend the results to aggregating operators. As special cases, means and some kind of suitable ordered weighted averaging (OWAs) are used to aggregate transitive fuzzy relations with respect to an Archimedean t-norm. Three families of transitive relations that allow us to modify the entries of a given relation R continuously towards the smallest and the greatest ones in our universe are given. Aggregation of nonfinite families of transitive relations also is studied and applied to calculate the degree of inclusion or similarity of fuzzy quantities (fuzzy subsets of an interval of the real line). © 2003 Wiley Periodicals, Inc. 2013-05-15T10:05:21Z http://hdl.handle.net/2117/19228 Title: The group of isometries of an indistinguishability operator Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: This paper studies some geometric aspects of indistinguishability operators (also called similarities and fuzzy equivalences). Concretely, it will be focused on the (geometric) group associated to a T-indistinguishability operator E on X (i.e., the group of all bijective maps View the MathML source such that E(x,y)=E(h(x),h(y))∀x,y∈X). The cases for E being one dimensional and invariant under translations on the real line will be completely studied. This last property will be generalized to any group and there will be stated a bijection between indistinguishability operators invariant under translations on a group and its normal fuzzy subgroups. 2013-05-15T08:28:50Z http://hdl.handle.net/2117/19227 Title: One dimensional indistinguishability operators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: The main result of the paper is an algorithm that allows us to decide when a given fuzzy relation is a one-dimensional T-indistinguishability operator for some archimedean t-norm T (in the sense of the Representation Theorem of Valverde (Fuzzy Sets and Systems 17 (1985) 313–328)). The algorithm also finds all t-norms with this property. 2013-05-15T08:20:17Z http://hdl.handle.net/2117/19226 Title: Fuzzy t-transitive relations: eigenvectors and generators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: After some preliminaries, the set of generators of a generalized equality relation (T-indistinguishability operator) is studied. This set is identified with the set of the eigenvectors of the relation. The relation between the fuzzy and “metric” topologies derived from these equalities is stablished. The concept of basis is introduced and the construction of a procedure in order to calculate explicitly a basis of a T-indistinguishability operator, for T archimedean, is proposed. 2013-05-15T08:08:39Z http://hdl.handle.net/2117/19223 Title: How to make T-transitive a proximity relation Authors: Garmendia, L; Recasens Ferrés, Jorge Abstract: Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R macr of R with a (maximal) T-transitive relation B contained in R . The second one computes the closest homotecy of R macr or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper. 2013-05-15T07:39:50Z http://hdl.handle.net/2117/19212 Title: Statistical properties of subgroups of free groups Authors: Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal Abstract: The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k -tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. 2013-05-14T13:22:38Z http://hdl.handle.net/2117/19209 Title: ICT based estimation of time-dependent origin-destination matrices Authors: Barceló Bugeda, Jaime; Montero Mercadé, Lídia; Marqués, Laura; Carmona, Carlos Abstract: Time-Dependent Origin-Destination (OD) matrices are a key input to Dynamic Traffic Models, microscopic and mesoscopic traffic simulators are relevant examples of such models, traditionally used to assist in the design and evaluation of Traffic Management and Information Systems (ATMS/ATIS). Dynamic traffic models are also starting to be used to support real-time traffic management decisions. The typical approaches to the time-dependent OD estimation have been based either on ad hoc heuristics using mathematical programming approaches, or on Kalman-Filtering. The advent of the new Information and Communication Technologies (ICT), as for example Automatic Vehicle Location, License Plate Recognition, detection of mobile devices, Vehicle to Infrastructure (V2I) and so on, makes available new types of traffic data of higher quality and accuracy allowing for new modeling hypothesis leading to more computationally efficient algorithms. This paper extends the previous research on Kalman Filtering approaches for Freeway OD estimation using these data, to more complex topologies of urban networks were alternative path choices between origins and destinations are available. Ad hoc procedures based on Kalman Filtering have been designed and implemented successfully and the numerical results of the computational experiments are presented and discussed. 2013-05-14T12:53:43Z