Departament de Matemàtiques
http://hdl.handle.net/2117/3917
Mon, 02 May 2016 19:42:15 GMT
20160502T19:42:15Z

Oscillatory motions for the restricted planar circular three body problem
http://hdl.handle.net/2117/86502
Oscillatory motions for the restricted planar circular three body problem
Guàrdia Munarriz, Marcel; Martín, Pau; MartínezSeara Alonso, M. Teresa
© 2015, SpringerVerlag Berlin Heidelberg. The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Simó [Math Ann 248(2):153–184, 1980] proved the existence of oscillatory motions for this system. That is, orbits which leave every bounded region but which return infinitely often to some fixed bounded region. To prove their existence they had to assume the ratio between the masses of the primaries to be small enough. In this paper we prove the existence of such motions for any value of the mass ratio(Formula presented.) closing the problem of existence of oscillatory motions in the RPC3BP. To obtain such motions, we restrict ourselves to the level sets of the Jacobi constant. We show that, for any value of the mass ratio and for large values of the Jacobi constant, there exist transversal intersections between the stable and unstable manifolds of infinity in these level sets. These transversal intersections guarantee the existence of a symbolic dynamics that creates the oscillatory orbits. The main achievement is to prove the existence of these orbits without assuming the mass ratio (Formula presented.) small. When (Formula presented.) is not small, this transversality can not be checked by means of classical perturbation theory. Since our method is valid for all values of v, we are able to detect a curve in the parameter space, formed by (Formula presented.) and the Jacobi constant, where cubic homoclinic tangencies between the invariant manifolds of infinity appear.
Mon, 02 May 2016 17:44:48 GMT
http://hdl.handle.net/2117/86502
20160502T17:44:48Z
Guàrdia Munarriz, Marcel
Martín, Pau
MartínezSeara Alonso, M. Teresa
© 2015, SpringerVerlag Berlin Heidelberg. The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Simó [Math Ann 248(2):153–184, 1980] proved the existence of oscillatory motions for this system. That is, orbits which leave every bounded region but which return infinitely often to some fixed bounded region. To prove their existence they had to assume the ratio between the masses of the primaries to be small enough. In this paper we prove the existence of such motions for any value of the mass ratio(Formula presented.) closing the problem of existence of oscillatory motions in the RPC3BP. To obtain such motions, we restrict ourselves to the level sets of the Jacobi constant. We show that, for any value of the mass ratio and for large values of the Jacobi constant, there exist transversal intersections between the stable and unstable manifolds of infinity in these level sets. These transversal intersections guarantee the existence of a symbolic dynamics that creates the oscillatory orbits. The main achievement is to prove the existence of these orbits without assuming the mass ratio (Formula presented.) small. When (Formula presented.) is not small, this transversality can not be checked by means of classical perturbation theory. Since our method is valid for all values of v, we are able to detect a curve in the parameter space, formed by (Formula presented.) and the Jacobi constant, where cubic homoclinic tangencies between the invariant manifolds of infinity appear.

Prediction system for the anticipation of Space Weather events affecting ionosphere and GNSS satellite systems
http://hdl.handle.net/2117/86493
Prediction system for the anticipation of Space Weather events affecting ionosphere and GNSS satellite systems
García Rigo, Alberto; Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W; Jiggens, Piers; Pérez, Gustau; Hernández Pajares, Manuel; Hilgers, Alain
The solar activity can be considered one of the main sources of hazards not only affecting launch operations but also the reliability of Global Navigation Satellite Systems (GNSS), such as Galileo, and Satellite Based Augmentation Systems (SBAS), such as EGNOS. Thus, it could impact critically on GNSSbased services, among other impacts on society. In particular, Solar Energetic Particle (SEP) events pose a serious health risk to humans in space and can result in increased radiation doses for highlatitude aircraft flights and can constitute a serious concern for the microelectronics and other hardware elements of satellites, aircraft and launchers. In addition, severe malfunctioning of GNSS and SBAS systems have been reported as well. In this way, nowadays, it shall become a priority to provide GNSS users with predictions and/or warning alerts on potential disturbances associated to increased solar activity. For instance, such predictions or early warnings could allow significant mitigation of the risk of radiation damage by preventive actions and improve of the reliability of GNSS systems.
In this context, the webbased SEPsFLAREs prototype system has been recently deployed to serve as a provider of early warnings and predictions of solar flares and Solar Energetic Particle (SEP) events. The system covers the preflare, postflare/preSEP, and intraSEP scenarios by means of: (1) prediction of solar flares occurrence from 48 to 6hour ahead based on Automated Solar Activity Prediction (ASAP), (2) prediction of the SEP onset and occurrence based on UMASEP predictor and the socalled Warning Tool, and, finally, (3) prediction of the SEP peak and duration once there is evidence of a SEP occurrence.
Regarding the performance of the flare predictor, it has been evaluated considering a dataset from January, 2014 to May, 2014 (with a training period of 32 years). It has been found that the 24hour forecast horizon provides the best performance, with a Probability of Detection (POD), a False Alarm Ratio (FAR) and True Skill Statistics (TSS) estimations of 63.8%, 99.0% and 0.5 respectively for predicting Xclass flares; and of 88.7%, 87.0% and 0.59 respectively, for predicting Mclass flares. Regarding the SEP occurrence and onset prediction, it has been validated taking into account all 129 SEP events from January, 1994 to June, 2014. Then, a POD of 86.82%, a FAR of 25.83%, and an Average Warning Time (AWT) of 3.93 h have been obtained. Regarding the evaluation of the Warning Tool, the best performance has led to a POD of 58.3%, a FAR of 90.1%, and an AWT of 23.1 h. Regarding the SEP flux intensity and duration prediction, taking into account the same input dataset, a Mean Absolute Error (MAE) of SEP peak time predictions of 11.3 h has been obtained, a MAE of peak intensity predictions of 0.53 in log10 units of pfu, and a MAE of SEP end time predictions of 28.8 h.
In addition, SEPsFLAREs system provides as well, from ESA’s MONITOR server, two realtime products on solar flares nowcasting based on ionospheric monitorization by Global Navigation Satellite Systems (GNSS) and a worldwide network of GNSS receivers from the International GNSS Service (IGS): (1) the GNSS Solar Flare Detector (GSFLAD) and (2) the Sunlit Ionosphere Sudden TEC Enhancement Detector (SISTED), both developed by authors of this work.
Mon, 02 May 2016 15:24:38 GMT
http://hdl.handle.net/2117/86493
20160502T15:24:38Z
García Rigo, Alberto
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W
Jiggens, Piers
Pérez, Gustau
Hernández Pajares, Manuel
Hilgers, Alain
The solar activity can be considered one of the main sources of hazards not only affecting launch operations but also the reliability of Global Navigation Satellite Systems (GNSS), such as Galileo, and Satellite Based Augmentation Systems (SBAS), such as EGNOS. Thus, it could impact critically on GNSSbased services, among other impacts on society. In particular, Solar Energetic Particle (SEP) events pose a serious health risk to humans in space and can result in increased radiation doses for highlatitude aircraft flights and can constitute a serious concern for the microelectronics and other hardware elements of satellites, aircraft and launchers. In addition, severe malfunctioning of GNSS and SBAS systems have been reported as well. In this way, nowadays, it shall become a priority to provide GNSS users with predictions and/or warning alerts on potential disturbances associated to increased solar activity. For instance, such predictions or early warnings could allow significant mitigation of the risk of radiation damage by preventive actions and improve of the reliability of GNSS systems.
In this context, the webbased SEPsFLAREs prototype system has been recently deployed to serve as a provider of early warnings and predictions of solar flares and Solar Energetic Particle (SEP) events. The system covers the preflare, postflare/preSEP, and intraSEP scenarios by means of: (1) prediction of solar flares occurrence from 48 to 6hour ahead based on Automated Solar Activity Prediction (ASAP), (2) prediction of the SEP onset and occurrence based on UMASEP predictor and the socalled Warning Tool, and, finally, (3) prediction of the SEP peak and duration once there is evidence of a SEP occurrence.
Regarding the performance of the flare predictor, it has been evaluated considering a dataset from January, 2014 to May, 2014 (with a training period of 32 years). It has been found that the 24hour forecast horizon provides the best performance, with a Probability of Detection (POD), a False Alarm Ratio (FAR) and True Skill Statistics (TSS) estimations of 63.8%, 99.0% and 0.5 respectively for predicting Xclass flares; and of 88.7%, 87.0% and 0.59 respectively, for predicting Mclass flares. Regarding the SEP occurrence and onset prediction, it has been validated taking into account all 129 SEP events from January, 1994 to June, 2014. Then, a POD of 86.82%, a FAR of 25.83%, and an Average Warning Time (AWT) of 3.93 h have been obtained. Regarding the evaluation of the Warning Tool, the best performance has led to a POD of 58.3%, a FAR of 90.1%, and an AWT of 23.1 h. Regarding the SEP flux intensity and duration prediction, taking into account the same input dataset, a Mean Absolute Error (MAE) of SEP peak time predictions of 11.3 h has been obtained, a MAE of peak intensity predictions of 0.53 in log10 units of pfu, and a MAE of SEP end time predictions of 28.8 h.
In addition, SEPsFLAREs system provides as well, from ESA’s MONITOR server, two realtime products on solar flares nowcasting based on ionospheric monitorization by Global Navigation Satellite Systems (GNSS) and a worldwide network of GNSS receivers from the International GNSS Service (IGS): (1) the GNSS Solar Flare Detector (GSFLAD) and (2) the Sunlit Ionosphere Sudden TEC Enhancement Detector (SISTED), both developed by authors of this work.

Looking for efficient and accurate ways of computing the global ionospheric electron density distribution from huge amounts of GNSS observations
http://hdl.handle.net/2117/86453
Looking for efficient and accurate ways of computing the global ionospheric electron density distribution from huge amounts of GNSS observations
Hernández Pajares, Manuel; Juan Zornoza, José Miguel; Sanz Subirana, Jaume; Monte Moreno, Enrique; Aragón Ángel, María Ángeles
In this work the authors will explore different potential ways of estimating efficiently and accurately the global
number density of ionospheric free electrons from the most part of nowadays available GNSS measurements, taken from ground based GPS receivers (IGS network) and LEO onboard GPS receivers (such as FORMOSAT3/COSMIC constellation).
It is basically designed as a bootstrapping approach, from a first determination of VTEC global maps based on
the ground data, to a final electron density extrapolation process aided by simple firstprinciple conditions, and
passing by an optimal error decorrelation treatment in the VTEC interpolation and corresponding application to
improve the inversion of the GPS occultation measurements.
The performances against external reference data, including dual frequency altimeters and ionosonde measurements, will be also shown to support the conclusions in different Solar Cycle conditions.
Mon, 02 May 2016 08:39:12 GMT
http://hdl.handle.net/2117/86453
20160502T08:39:12Z
Hernández Pajares, Manuel
Juan Zornoza, José Miguel
Sanz Subirana, Jaume
Monte Moreno, Enrique
Aragón Ángel, María Ángeles
In this work the authors will explore different potential ways of estimating efficiently and accurately the global
number density of ionospheric free electrons from the most part of nowadays available GNSS measurements, taken from ground based GPS receivers (IGS network) and LEO onboard GPS receivers (such as FORMOSAT3/COSMIC constellation).
It is basically designed as a bootstrapping approach, from a first determination of VTEC global maps based on
the ground data, to a final electron density extrapolation process aided by simple firstprinciple conditions, and
passing by an optimal error decorrelation treatment in the VTEC interpolation and corresponding application to
improve the inversion of the GPS occultation measurements.
The performances against external reference data, including dual frequency altimeters and ionosonde measurements, will be also shown to support the conclusions in different Solar Cycle conditions.

El impacto de las políticas de evaluación del profesorado en la posición en los ránquines universitarios: el caso de la Universidad Politécnica de Cataluña
http://hdl.handle.net/2117/86427
El impacto de las políticas de evaluación del profesorado en la posición en los ránquines universitarios: el caso de la Universidad Politécnica de Cataluña
GarcíaBerro Montilla, Enrique; Roca Martín, Santiago; Navallas Ramos, Francisco Javier; Soriano Ibáñez, Miguel; Ras Sabido, Antoni
La universidad española ha afrontado con éxito el tránsito entre una universidad clásica, eminentemente docente, y una universidad moderna, en la que la investigación juega un papel esencial. Gran parte de este éxito reside en la instauración de sistemas de evaluación. No obstante, a pesar de los indiscutibles logros, aún queda un camino importante por recorrer para situarla en los lugares que le corresponden en las clasificaciones internacionales por el lugar que ocupamos dentro de los países de nuestro entorno. La Universidad Politécnica de Cataluña dispone de un modelo de evaluación docente, así como de información sobre la actividad investigadora del profesorado. Ello ha permitido implementar un modelo de evaluación global, que presentamos en este artículo. Asimismo, usando una muestra de 4.996 evaluaciones individuales de unos 1.700 profesores, analizamos la evolución temporal de las evaluaciones de los años 2011, 2012 y 2013, estudiamos si existen diferencias entre los ámbitos de conocimiento y examinamos si existe una relación entre la productividad académica así evaluada y la posición de la universidad en los ránquines universitarios. Los datos de este estudio corroboran que el modelo ha tenido éxito, al haber permitido que la universidad progresara en el ranquin Quacquarelli Symonds del puesto 350 al 337.
Spanish universities have moved from a classical model, a teaching university, to a modern one, in which research is essential. Part of this success is due to the implementation of quality assessment policies. Nonetheless, and in spite of this, there is still a long way to place it at the level of similar countries in university rankings. The Universidad Politécnica de Cataluña has an evaluation model of the teaching performance of its staff, and also abundant information of their research. This has allowed implementing a global evaluation model. Here we present the evaluation model. Also, using 4,996 individual evaluations corresponding to about 1,700 academic staff members we analyze the evolution of the results of the evaluations of years 2011, 2012 and 2013, we study if there are differences among the various academic fields, and we examine if there exists a correlation between the evolution of the academic productivity measured using this model and the position of the university in the university rankings. We show that this model has allowed the university to improve its classification in the Quacquarelli Symonds Top University Ranking, from position 350 to 337.
Fri, 29 Apr 2016 12:32:32 GMT
http://hdl.handle.net/2117/86427
20160429T12:32:32Z
GarcíaBerro Montilla, Enrique
Roca Martín, Santiago
Navallas Ramos, Francisco Javier
Soriano Ibáñez, Miguel
Ras Sabido, Antoni
La universidad española ha afrontado con éxito el tránsito entre una universidad clásica, eminentemente docente, y una universidad moderna, en la que la investigación juega un papel esencial. Gran parte de este éxito reside en la instauración de sistemas de evaluación. No obstante, a pesar de los indiscutibles logros, aún queda un camino importante por recorrer para situarla en los lugares que le corresponden en las clasificaciones internacionales por el lugar que ocupamos dentro de los países de nuestro entorno. La Universidad Politécnica de Cataluña dispone de un modelo de evaluación docente, así como de información sobre la actividad investigadora del profesorado. Ello ha permitido implementar un modelo de evaluación global, que presentamos en este artículo. Asimismo, usando una muestra de 4.996 evaluaciones individuales de unos 1.700 profesores, analizamos la evolución temporal de las evaluaciones de los años 2011, 2012 y 2013, estudiamos si existen diferencias entre los ámbitos de conocimiento y examinamos si existe una relación entre la productividad académica así evaluada y la posición de la universidad en los ránquines universitarios. Los datos de este estudio corroboran que el modelo ha tenido éxito, al haber permitido que la universidad progresara en el ranquin Quacquarelli Symonds del puesto 350 al 337.
Spanish universities have moved from a classical model, a teaching university, to a modern one, in which research is essential. Part of this success is due to the implementation of quality assessment policies. Nonetheless, and in spite of this, there is still a long way to place it at the level of similar countries in university rankings. The Universidad Politécnica de Cataluña has an evaluation model of the teaching performance of its staff, and also abundant information of their research. This has allowed implementing a global evaluation model. Here we present the evaluation model. Also, using 4,996 individual evaluations corresponding to about 1,700 academic staff members we analyze the evolution of the results of the evaluations of years 2011, 2012 and 2013, we study if there are differences among the various academic fields, and we examine if there exists a correlation between the evolution of the academic productivity measured using this model and the position of the university in the university rankings. We show that this model has allowed the university to improve its classification in the Quacquarelli Symonds Top University Ranking, from position 350 to 337.

SEPsFLAREs: Executive Summary
http://hdl.handle.net/2117/86424
SEPsFLAREs: Executive Summary
Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W; García Rigo, Alberto; Hernández Pajares, Manuel
Fri, 29 Apr 2016 11:08:39 GMT
http://hdl.handle.net/2117/86424
20160429T11:08:39Z
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W
García Rigo, Alberto
Hernández Pajares, Manuel

Polygons as sections of higherdimensional polytopes
http://hdl.handle.net/2117/86389
Polygons as sections of higherdimensional polytopes
Padrol Sureda, Arnau; Pfeifle, Julián
We show that every heptagon is a section of a 3polytope with 6 vertices. This implies that every ngon with n >= 7 can be obtained as a section of a (2 + [n/7])dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).
Thu, 28 Apr 2016 14:55:10 GMT
http://hdl.handle.net/2117/86389
20160428T14:55:10Z
Padrol Sureda, Arnau
Pfeifle, Julián
We show that every heptagon is a section of a 3polytope with 6 vertices. This implies that every ngon with n >= 7 can be obtained as a section of a (2 + [n/7])dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).

Automorphisms and reduction of Heegner points on Shimura curves at CerednikDrinfeld primes
http://hdl.handle.net/2117/86360
Automorphisms and reduction of Heegner points on Shimura curves at CerednikDrinfeld primes
Molina Blanco, Santiago; Rotger Cerdà, Víctor
The aim of this short note is to show how the interplay of the action of the automorphism
group of a Shimura curve on the special fiber of its CerednikDrinfeld’s integral model at a prime of bad reduction
and its sets of Heegner points, can be exploited to prove some instances of a conjecture that predicts that any
automorphism must be an AtkinLehner involution.
Thu, 28 Apr 2016 11:11:59 GMT
http://hdl.handle.net/2117/86360
20160428T11:11:59Z
Molina Blanco, Santiago
Rotger Cerdà, Víctor
The aim of this short note is to show how the interplay of the action of the automorphism
group of a Shimura curve on the special fiber of its CerednikDrinfeld’s integral model at a prime of bad reduction
and its sets of Heegner points, can be exploited to prove some instances of a conjecture that predicts that any
automorphism must be an AtkinLehner involution.

The kernel of Ribet’s isogeny for genus three Shimura curves
http://hdl.handle.net/2117/86355
The kernel of Ribet’s isogeny for genus three Shimura curves
Molina Blanco, Santiago; González Rovira, Josep
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.
Thu, 28 Apr 2016 10:52:55 GMT
http://hdl.handle.net/2117/86355
20160428T10:52:55Z
Molina Blanco, Santiago
González Rovira, Josep
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.

Minimal representations for majority games
http://hdl.handle.net/2117/86215
Minimal representations for majority games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.
Wed, 27 Apr 2016 07:22:54 GMT
http://hdl.handle.net/2117/86215
20160427T07:22:54Z
Freixas Bosch, Josep
Molinero Albareda, Xavier
Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.

Cellcentred model for the simulation of curved cellular monolayers
http://hdl.handle.net/2117/86189
Cellcentred model for the simulation of curved cellular monolayers
Mosafa, Payman; Asadipour, Nina; Millán, Raúl Daniel; Rodríguez Ferran, Antonio; Muñoz Romero, José
This paper presents a cellcentred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active nonlinear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cellcell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cellcell interaction model may induce a global nonlinear response due to the reorganisation of the cell connectivity. This plasticlike behaviour is combined with a nonlinear rheological law where the resting length depends on the elastic strain, mimicking the global viscoelastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.
Tue, 26 Apr 2016 10:28:30 GMT
http://hdl.handle.net/2117/86189
20160426T10:28:30Z
Mosafa, Payman
Asadipour, Nina
Millán, Raúl Daniel
Rodríguez Ferran, Antonio
Muñoz Romero, José
This paper presents a cellcentred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active nonlinear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cellcell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cellcell interaction model may induce a global nonlinear response due to the reorganisation of the cell connectivity. This plasticlike behaviour is combined with a nonlinear rheological law where the resting length depends on the elastic strain, mimicking the global viscoelastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.