Departament de Matemàtiques
http://hdl.handle.net/2117/3917
Mon, 16 Jan 2017 22:01:06 GMT2017-01-16T22:01:06ZNon-regularised inverse finite element analysis for 3D traction force microscopy
http://hdl.handle.net/2117/99311
Non-regularised inverse finite element analysis for 3D traction force microscopy
Muñoz Romero, José
The tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.
Mon, 16 Jan 2017 12:38:07 GMThttp://hdl.handle.net/2117/993112017-01-16T12:38:07ZMuñoz Romero, JoséThe tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.Non-commutative integrable systems on b-symplectic manifolds
http://hdl.handle.net/2117/99219
Non-commutative integrable systems on b-symplectic manifolds
Miranda Galcerán, Eva; Kiesenhoferb, Anna
In this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.
Fri, 13 Jan 2017 12:25:40 GMThttp://hdl.handle.net/2117/992192017-01-13T12:25:40ZMiranda Galcerán, EvaKiesenhoferb, AnnaIn this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.On the set of periods of the 2-periodic Lyness' equation
http://hdl.handle.net/2117/99190
On the set of periods of the 2-periodic Lyness' equation
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
We study the periodic solutions of the non-autonomous periodic Lyness’ recurrence un+2=(an+un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a,b)¿(1,1), then there exists a value p0(a,b) such that for any p>p0(a,b) there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when (a,b)¿(0,8)2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a¿b, then it does not appear any odd period, except 1.
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-52927-0_22
Fri, 13 Jan 2017 09:24:26 GMThttp://hdl.handle.net/2117/991902017-01-13T09:24:26ZBastien, GuyMañosa Fernández, VíctorRogalski, MarcWe study the periodic solutions of the non-autonomous periodic Lyness’ recurrence un+2=(an+un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a,b)¿(1,1), then there exists a value p0(a,b) such that for any p>p0(a,b) there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when (a,b)¿(0,8)2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a¿b, then it does not appear any odd period, except 1.Novel results on decentralized H-infinity controller design for structural vibration control of large buildings
http://hdl.handle.net/2117/98974
Novel results on decentralized H-infinity controller design for structural vibration control of large buildings
Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
In this paper, we present a novel control design methodology for structural vibration control of large buildings. The main idea consists in decomposing the overall building system into decoupled single-story subsystems and modeling the subsystem interactions as external disturbances. Then, a complete set of local decentralized controllers can be efficiently computed using the existing LMI solvers. In the proposed approach, two different levels of decentralization can be distinguished: decentralized design and decentralized implementation, which are both of critical importance in large-scale control problems. From the design point of view, the local controllers are independently synthesized using only the low-dimensional subsystem models. The implementation phase is through the overall decentralized controller defined by the set of local controllers, which can drive the actuation devices using only local state-feedback information. To illustrate the proposed methodology, decentralized H8 controllers are designed for the seismic protection of a five-story building and a twenty-story building. A proper set of numerical simulations is carried out to demonstrate the effectiveness of the proposed decentralized controllers and the computation times are considered to assess the computational effectiveness of the decentralized design methodology.
Tue, 10 Jan 2017 15:52:43 GMThttp://hdl.handle.net/2117/989742017-01-10T15:52:43ZPalacios Quiñonero, FranciscoRubió Massegú, JosepRossell Garriga, Josep MariaKarimi, Hamid RezaIn this paper, we present a novel control design methodology for structural vibration control of large buildings. The main idea consists in decomposing the overall building system into decoupled single-story subsystems and modeling the subsystem interactions as external disturbances. Then, a complete set of local decentralized controllers can be efficiently computed using the existing LMI solvers. In the proposed approach, two different levels of decentralization can be distinguished: decentralized design and decentralized implementation, which are both of critical importance in large-scale control problems. From the design point of view, the local controllers are independently synthesized using only the low-dimensional subsystem models. The implementation phase is through the overall decentralized controller defined by the set of local controllers, which can drive the actuation devices using only local state-feedback information. To illustrate the proposed methodology, decentralized H8 controllers are designed for the seismic protection of a five-story building and a twenty-story building. A proper set of numerical simulations is carried out to demonstrate the effectiveness of the proposed decentralized controllers and the computation times are considered to assess the computational effectiveness of the decentralized design methodology.New offset-free method for model predictive control of open channels
http://hdl.handle.net/2117/98804
New offset-free method for model predictive control of open channels
Horváth, Klaudia; Galvis, Eduard; Gómez Valentín, Manuel; Rodellar Benedé, José
Irrigation or drainage canals can be controlled by model predictive control (MPC). Applying MPC with an internal model in the presence of unknown disturbances in some cases can lead to steady state offset. Therefore an additional component should be implemented along with the MPC. A new method eliminating the offset has been developed in this paper for MPC. It is based on combining two basic approaches of MPC. It has been implemented to control water levels in the three-pool UPC laboratory canal and further numerically tested using a test case benchmark proposed by the American Society of Civil Engineers (ASCE). It has been found that the developed offset-free method is able to eliminate the steady-state offset, while taking into account known and unknown disturbances.
Fri, 23 Dec 2016 15:41:12 GMThttp://hdl.handle.net/2117/988042016-12-23T15:41:12ZHorváth, KlaudiaGalvis, EduardGómez Valentín, ManuelRodellar Benedé, JoséIrrigation or drainage canals can be controlled by model predictive control (MPC). Applying MPC with an internal model in the presence of unknown disturbances in some cases can lead to steady state offset. Therefore an additional component should be implemented along with the MPC. A new method eliminating the offset has been developed in this paper for MPC. It is based on combining two basic approaches of MPC. It has been implemented to control water levels in the three-pool UPC laboratory canal and further numerically tested using a test case benchmark proposed by the American Society of Civil Engineers (ASCE). It has been found that the developed offset-free method is able to eliminate the steady-state offset, while taking into account known and unknown disturbances.Decisiveness indices are semiindices: addendum
http://hdl.handle.net/2117/98770
Decisiveness indices are semiindices: addendum
Freixas Bosch, Josep; Pons Vallès, Montserrat
In the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.
Thu, 22 Dec 2016 15:36:17 GMThttp://hdl.handle.net/2117/987702016-12-22T15:36:17ZFreixas Bosch, JosepPons Vallès, MontserratIn the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.Stochastic stability for a model representing the intake manifold pressure of an automotive engine
http://hdl.handle.net/2117/98758
Stochastic stability for a model representing the intake manifold pressure of an automotive engine
Vargas do Nascimiento, Alessandro; Acho Zuppa, Leonardo; Bonifacio, Edison; Arens, Walter; B. R. do Va, Joao
The paper presents conditions to assure stochastic stability for a nonlinear model. The proposed model is used to represent the input-output dynamics of the angle of aperture of the throttle valve (input) and the manifold absolute pressure (output) in an automotive spark-ignition engine. The automotive model is second moment stable, as stated by the theoretical result—data collected from real-time experiments supports this finding.
Thu, 22 Dec 2016 12:19:53 GMThttp://hdl.handle.net/2117/987582016-12-22T12:19:53ZVargas do Nascimiento, AlessandroAcho Zuppa, LeonardoBonifacio, EdisonArens, WalterB. R. do Va, JoaoThe paper presents conditions to assure stochastic stability for a nonlinear model. The proposed model is used to represent the input-output dynamics of the angle of aperture of the throttle valve (input) and the manifold absolute pressure (output) in an automotive spark-ignition engine. The automotive model is second moment stable, as stated by the theoretical result—data collected from real-time experiments supports this finding.On (non-)exponential decay in generalized thermoelasticity with two temperatures
http://hdl.handle.net/2117/98756
On (non-)exponential decay in generalized thermoelasticity with two temperatures
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón; Racke, Reinhard
We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential
stability for the Lord-Shulman model
Konstanzer Schriften in Mathematik ; 355
Thu, 22 Dec 2016 11:55:43 GMThttp://hdl.handle.net/2117/987562016-12-22T11:55:43ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónRacke, ReinhardWe study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential
stability for the Lord-Shulman modelOrder regularity for Birkhoff interpolation with lacunary polynomials
http://hdl.handle.net/2117/98736
Order regularity for Birkhoff interpolation with lacunary polynomials
Palacios Quiñonero, Francisco; Rubio Díaz, Pedro; Díaz Barrero, José Luis; Rossell Garriga, Josep Maria
In this short paper we present sufficient conditions for the order
regularity problem in Birkhoff interpolation with lacunary polynomials.
These conditions are a generalization of the Atkinson-Sharma theorem.
Wed, 21 Dec 2016 18:49:37 GMThttp://hdl.handle.net/2117/987362016-12-21T18:49:37ZPalacios Quiñonero, FranciscoRubio Díaz, PedroDíaz Barrero, José LuisRossell Garriga, Josep MariaIn this short paper we present sufficient conditions for the order
regularity problem in Birkhoff interpolation with lacunary polynomials.
These conditions are a generalization of the Atkinson-Sharma theorem.Sequence mixed graphs
http://hdl.handle.net/2117/98676
Sequence mixed graphs
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López, Nacho
A mixed graph can be seen as a type of digraph containing some edges (or two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and literated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the degree/diameter problem. Thus, our generalized approach gives rise to graphs that have also good ratio order/diameter. Moreover, we propose a general method for obtaining a sequence mixed diagraph by identifying some vertices of certain iterated line digraph. As a consequence, some results about distance-related parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.
Wed, 21 Dec 2016 08:37:00 GMThttp://hdl.handle.net/2117/986762016-12-21T08:37:00ZDalfó Simó, CristinaFiol Mora, Miquel ÀngelLópez, NachoA mixed graph can be seen as a type of digraph containing some edges (or two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and literated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the degree/diameter problem. Thus, our generalized approach gives rise to graphs that have also good ratio order/diameter. Moreover, we propose a general method for obtaining a sequence mixed diagraph by identifying some vertices of certain iterated line digraph. As a consequence, some results about distance-related parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.