Articles de revista
http://hdl.handle.net/2117/79765
20220517T21:29:01Z

An inextensible model for the robotic manipulation of textiles
http://hdl.handle.net/2117/366342
An inextensible model for the robotic manipulation of textiles
Coltraro Ianniello, Franco; Amorós Torrent, Jaume; Alberich Carramiñana, Maria; Torras, Carme
We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces that are inextensible, admitting only isometric motions. Inextensibility is derived in a continuous setting, prior to any discretization, which gives consistency with respect to remeshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the difference between the simulated and the real position of each point in the garment is lower than 1cm in average even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, when compared to the recorded dynamics of real textiles, description of cloth motion incorporating aerodynamic effects by using only two parameters.
20220426T12:35:38Z
Coltraro Ianniello, Franco
Amorós Torrent, Jaume
Alberich Carramiñana, Maria
Torras, Carme
We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces that are inextensible, admitting only isometric motions. Inextensibility is derived in a continuous setting, prior to any discretization, which gives consistency with respect to remeshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the difference between the simulated and the real position of each point in the garment is lower than 1cm in average even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, when compared to the recorded dynamics of real textiles, description of cloth motion incorporating aerodynamic effects by using only two parameters.

An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator
http://hdl.handle.net/2117/366197
An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator
Casanellas Rius, Marta; Fernández Sánchez, Jesús; Roca Lacostena, Jordi
A Markov matrix is embeddable if it can represent a homogeneous continuoustime Markov process. It is well known that if a Markov matrix has real and pairwisedifferent eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices that are close enough to the identity matrix. In this paper we exhibit open sets of Markov matrices that are embeddable and whose principal logarithm is not a rate matrix, thus proving that the principal logarithm test above does not suffice generically.
20220422T06:45:29Z
Casanellas Rius, Marta
Fernández Sánchez, Jesús
Roca Lacostena, Jordi
A Markov matrix is embeddable if it can represent a homogeneous continuoustime Markov process. It is well known that if a Markov matrix has real and pairwisedifferent eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices that are close enough to the identity matrix. In this paper we exhibit open sets of Markov matrices that are embeddable and whose principal logarithm is not a rate matrix, thus proving that the principal logarithm test above does not suffice generically.

The groupoid of finite sets is biinitial in the 2category of rig categories
http://hdl.handle.net/2117/366041
The groupoid of finite sets is biinitial in the 2category of rig categories
Elgueta Montó, Josep
The groupoid of finite sets has a “canonical” structure of a symmetric 2rig with the sum and product respectively given by the coproduct and product of sets. This 2rig ^ FSet is just one of the many nonequivalent categorifications of the commutative rig N of natural numbers, together with the rig N itself viewed as a discrete rig category, the whole category of finite sets, the category of finite dimensional vector spaces over a field k, etc. In this paper it is shown that ^ FSet is the right categorification of N in the sense that it is biinitial in the 2category of rig categories, in the same way as N is initial in the category of rigs. As a byproduct, an explicit description of the homomorphisms of rig categories from a suitable version of ^ FSet into any (semistrict) rig category S is obtained in terms of a sequence of automorphisms of the objects 1+ n)· · · +1 in S for each n = 0.
20220419T10:43:39Z
Elgueta Montó, Josep
The groupoid of finite sets has a “canonical” structure of a symmetric 2rig with the sum and product respectively given by the coproduct and product of sets. This 2rig ^ FSet is just one of the many nonequivalent categorifications of the commutative rig N of natural numbers, together with the rig N itself viewed as a discrete rig category, the whole category of finite sets, the category of finite dimensional vector spaces over a field k, etc. In this paper it is shown that ^ FSet is the right categorification of N in the sense that it is biinitial in the 2category of rig categories, in the same way as N is initial in the category of rigs. As a byproduct, an explicit description of the homomorphisms of rig categories from a suitable version of ^ FSet into any (semistrict) rig category S is obtained in terms of a sequence of automorphisms of the objects 1+ n)· · · +1 in S for each n = 0.

A Kcontact Lagrangian formulation for nonconservative field theories
http://hdl.handle.net/2117/365729
A Kcontact Lagrangian formulation for nonconservative field theories
Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso
Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper where we introduced the notion of kcontact structure, and obtained a modified version of the De Donder–Weyl equations of covariant Hamiltonian field theory. In this paper we continue this study by presenting a kcontact Lagrangian formulation for nonconservative field theories. The Lagrangian density is defined on the product of the space of kvelocities times a kdimensional Euclidean space with coordinates sa, which are responsible for the dissipation. We analyze the regularity of such Lagrangians; only in the regular case we obtain a kcontact Hamiltonian system. We study several types of symmetries for kcontact Lagrangian systems, and relate them with dissipation laws, which are analogous to conservation laws of conservative systems. Several examples are discussed: we find contact Lagrangians for some kinds of secondorder linear partial differential equations, with the damped membrane as a particular example, and we also study a vibrating string with a magneticlike term.
20220412T09:23:38Z
Gaset Rifà, Jordi
Gràcia Sabaté, Francesc Xavier
Muñoz Lecanda, Miguel Carlos
Rivas Guijarro, Xavier
Román Roy, Narciso
Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper where we introduced the notion of kcontact structure, and obtained a modified version of the De Donder–Weyl equations of covariant Hamiltonian field theory. In this paper we continue this study by presenting a kcontact Lagrangian formulation for nonconservative field theories. The Lagrangian density is defined on the product of the space of kvelocities times a kdimensional Euclidean space with coordinates sa, which are responsible for the dissipation. We analyze the regularity of such Lagrangians; only in the regular case we obtain a kcontact Hamiltonian system. We study several types of symmetries for kcontact Lagrangian systems, and relate them with dissipation laws, which are analogous to conservation laws of conservative systems. Several examples are discussed: we find contact Lagrangians for some kinds of secondorder linear partial differential equations, with the damped membrane as a particular example, and we also study a vibrating string with a magneticlike term.

Skinner–Rusk formalism for kcontact systems
http://hdl.handle.net/2117/365716
Skinner–Rusk formalism for kcontact systems
Gràcia Sabaté, Francesc Xavier; Rivas Guijarro, Xavier; Román Roy, Narciso
In previous papers, a geometric framework has been developed to describe nonconservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of kcontact Hamiltonian systems, which is based on the ksymplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner–Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the secondorder condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher’s equations, and Maxwell’s equations with dissipation terms.
© 2022 Elsevier. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20220412T08:00:05Z
Gràcia Sabaté, Francesc Xavier
Rivas Guijarro, Xavier
Román Roy, Narciso
In previous papers, a geometric framework has been developed to describe nonconservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of kcontact Hamiltonian systems, which is based on the ksymplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner–Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the secondorder condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher’s equations, and Maxwell’s equations with dissipation terms.

Regular local rings of dimension four and Gorenstein syzygetic prime ideals
http://hdl.handle.net/2117/365507
Regular local rings of dimension four and Gorenstein syzygetic prime ideals
Planas Vilanova, Francesc d'Assís
Let R be a Noetherian local ring. We prove that R is regular of dimension at most 4 if, and only if, every prime ideal, defining a Gorenstein quotient ring, is syzygetic. We deduce a characterization of these rings in terms of the AndréQuillen homology.
20220407T14:18:03Z
Planas Vilanova, Francesc d'Assís
Let R be a Noetherian local ring. We prove that R is regular of dimension at most 4 if, and only if, every prime ideal, defining a Gorenstein quotient ring, is syzygetic. We deduce a characterization of these rings in terms of the AndréQuillen homology.

Slope inequalities for fibrations of nonmaximal Albanese dimension
http://hdl.handle.net/2117/365493
Slope inequalities for fibrations of nonmaximal Albanese dimension
Barja Yáñez, Miguel Ángel
We study and obtain Slope inequalities for fibred irregular varieties of nonmaximal Albanese dimension. We give a comparison theorem between Clifford–Severi and Slope inequalities for this type of fibrations. We also obtain a set of Slope inequalities considering the geometry of the Albanese map and the associated eventual maps.
The version of record is available online at: http://dx.doi.org/10.1007/s40574021002945
20220407T11:49:29Z
Barja Yáñez, Miguel Ángel
We study and obtain Slope inequalities for fibred irregular varieties of nonmaximal Albanese dimension. We give a comparison theorem between Clifford–Severi and Slope inequalities for this type of fibrations. We also obtain a set of Slope inequalities considering the geometry of the Albanese map and the associated eventual maps.

The secondorder problem for kpresymplectic Lagrangian field theories: application to the Einstein–Palatini model
http://hdl.handle.net/2117/365264
The secondorder problem for kpresymplectic Lagrangian field theories: application to the Einstein–Palatini model
Adame Carrillo, David; Gaset Rifà, Jordi; Román Roy, Narciso
In general, the system of 2ndorder partial differential equations made of the Euler–Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the socalled secondorder problem. The first aim of this work is to develop a fully geometric constraint algorithm which allows us to find a submanifold where the Euler–Lagrange equations have solution, and split the constraints into two kinds depending on their origin. We do so using ksymplectic geometry, which is the simplest intrinsic description of classical field theories. As a second aim, the Einstein–Palatini model of General Relativity is studied using this algorithm.
The version of record of this article, first published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, is available online at Publisher’s website: http://dx.doi.org/10.1007/s1339802101136x
20220405T07:48:35Z
Adame Carrillo, David
Gaset Rifà, Jordi
Román Roy, Narciso
In general, the system of 2ndorder partial differential equations made of the Euler–Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the socalled secondorder problem. The first aim of this work is to develop a fully geometric constraint algorithm which allows us to find a submanifold where the Euler–Lagrange equations have solution, and split the constraints into two kinds depending on their origin. We do so using ksymplectic geometry, which is the simplest intrinsic description of classical field theories. As a second aim, the Einstein–Palatini model of General Relativity is studied using this algorithm.

Turing universality of the incompressible Euler equations and a conjecture of Moore
http://hdl.handle.net/2117/365194
Turing universality of the incompressible Euler equations and a conjecture of Moore
Cardona Aguilar, Robert; Miranda Galcerán, Eva; PeraltaSalas, Daniel
In this article, we construct a compact Riemannian manifold of high dimension on which the timedependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain global solution of the Euler equations entering a certain open set in the space of divergencefree vector fields. In particular, this implies the undecidability of whether a solution to the Euler equations with an initial datum will reach a certain open set or not in the space of divergencefree fields. This result goes one step further in Tao’s programme to study the blowup problem for the Euler and Navier–Stokes equations using fluid computers. As a remarkable spinoff, our method of proof allows us to give a counterexample to a conjecture of Moore dating back to 1998 on the nonexistence of analytic maps on compact manifolds that are Turing complete.
20220401T11:23:17Z
Cardona Aguilar, Robert
Miranda Galcerán, Eva
PeraltaSalas, Daniel
In this article, we construct a compact Riemannian manifold of high dimension on which the timedependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain global solution of the Euler equations entering a certain open set in the space of divergencefree vector fields. In particular, this implies the undecidability of whether a solution to the Euler equations with an initial datum will reach a certain open set or not in the space of divergencefree fields. This result goes one step further in Tao’s programme to study the blowup problem for the Euler and Navier–Stokes equations using fluid computers. As a remarkable spinoff, our method of proof allows us to give a counterexample to a conjecture of Moore dating back to 1998 on the nonexistence of analytic maps on compact manifolds that are Turing complete.

Integrable systems on singular symplectic manifolds: from local to global
http://hdl.handle.net/2117/364971
Integrable systems on singular symplectic manifolds: from local to global
Cardona Aguilar, Robert; Miranda Galcerán, Eva
In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a bsymplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of actionangle coordinates for these structures initiated in [34] and [35] by proving an actionangle theorem for folded symplectic integrable systems. Contrary to expectations, the actionangle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and bsymplectic forms in [34]. Global constructions of integrable systems are provided and obstructions for the global existence of actionangle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set Z of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on Z¿.
20220329T14:11:26Z
Cardona Aguilar, Robert
Miranda Galcerán, Eva
In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a bsymplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of actionangle coordinates for these structures initiated in [34] and [35] by proving an actionangle theorem for folded symplectic integrable systems. Contrary to expectations, the actionangle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and bsymplectic forms in [34]. Global constructions of integrable systems are provided and obstructions for the global existence of actionangle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set Z of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on Z¿.