MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura
http://hdl.handle.net/2117/3558
2017-01-22T16:32:09ZA new approach to the vakonomic mechanics
http://hdl.handle.net/2117/24993
A new approach to the vakonomic mechanics
Llibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia Guennadievna
The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider the generalization of the Hamiltonian principle for nonholonomic systems with non-zero transpositional relations. We apply this variational principle, which takes into the account transpositional relations different from the classical ones, and we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with the d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular, the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems, the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian mechanics. We illustrate our results with examples.
2014-12-11T08:01:15ZLlibre Saló, JaumeRamírez Ros, RafaelSadovskaia Nurimanova, Natalia GuennadievnaThe aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider the generalization of the Hamiltonian principle for nonholonomic systems with non-zero transpositional relations. We apply this variational principle, which takes into the account transpositional relations different from the classical ones, and we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with the d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular, the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems, the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian mechanics. We illustrate our results with examples.Emotional inertia: a key to understanding psychotherapy process and outcome
http://hdl.handle.net/2117/24368
Emotional inertia: a key to understanding psychotherapy process and outcome
Bornas Agustí, F. Xavier; Noguera Batlle, Miquel; Pincus, David; Buela Casal, Gualberto
The processes underlying psychotherapeutic change have increasingly been emphasized in both research and clinical practice. Nonlinear dynamical systems theory (NDS) offers a transdisciplinary scientific approach to the study of these processes. This paper introduces the NDS concept of
2014-10-14T17:39:56ZBornas Agustí, F. XavierNoguera Batlle, MiquelPincus, DavidBuela Casal, GualbertoThe processes underlying psychotherapeutic change have increasingly been emphasized in both research and clinical practice. Nonlinear dynamical systems theory (NDS) offers a transdisciplinary scientific approach to the study of these processes. This paper introduces the NDS concept ofAn improvement of Ostrowski root-finding method
http://hdl.handle.net/2117/18913
An improvement of Ostrowski root-finding method
Grau Sánchez, Miguel; Díaz Barrero, José Luis
An improvement to the iterative method based on the Ostrowski one to compute nonlinear equation solutions, which increases the local order of convergence is suggested. The adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system with a floating point system representing 200 decimal digits support this theory.
"Applied Mathematics and Computation Top Cited Article 2005-2010"
2013-04-22T10:46:22ZGrau Sánchez, MiguelDíaz Barrero, José LuisAn improvement to the iterative method based on the Ostrowski one to compute nonlinear equation solutions, which increases the local order of convergence is suggested. The adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system with a floating point system representing 200 decimal digits support this theory.Theoretical dark matter halo kinematics and triaxial shape
http://hdl.handle.net/2117/17510
Theoretical dark matter halo kinematics and triaxial shape
Salvador-Solé, Eduard; Serra, Sinué; Manrique, Alberto; González Casado, Guillermo
In a recent paper, Salvador-Solé et al. have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power spectrum of density perturbations characterizing the hierarchical cosmology under consideration. In this paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power spectrum of density perturbations through the typical shape of peaks. The trends of the
predicted typical halo shape, pseudo-phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo-phase-space density profile for virialized haloes.
2013-01-24T13:19:32ZSalvador-Solé, EduardSerra, SinuéManrique, AlbertoGonzález Casado, GuillermoIn a recent paper, Salvador-Solé et al. have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power spectrum of density perturbations characterizing the hierarchical cosmology under consideration. In this paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power spectrum of density perturbations through the typical shape of peaks. The trends of the
predicted typical halo shape, pseudo-phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo-phase-space density profile for virialized haloes.Dynamical behavior of asteroids near resonance: the 4:1 gap and the 7:2 group
http://hdl.handle.net/2117/14731
Dynamical behavior of asteroids near resonance: the 4:1 gap and the 7:2 group
Grau Sánchez, Miguel; González Casado, Guillermo
A comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1
and 7:2 resonances is performed by means of two techniques that proceed differently from the
Hamiltonian corresponding to the planar restricted elliptic three-body problem. One technique is
based on the classical Schubart averaging while the other is based on a mapping method in which
the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to
a weight function that depends on the powers of eccentricities and the coefficients of the terms. For
the mapping method the effect of Saturn on the asteroidal evolution is introduced and the degree of
chaos is estimated by means of the Lyapunov time. Both methods are shown to lead to similar results
and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gap
and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.
2012-01-23T10:59:32ZGrau Sánchez, MiguelGonzález Casado, GuillermoA comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1
and 7:2 resonances is performed by means of two techniques that proceed differently from the
Hamiltonian corresponding to the planar restricted elliptic three-body problem. One technique is
based on the classical Schubart averaging while the other is based on a mapping method in which
the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to
a weight function that depends on the powers of eccentricities and the coefficients of the terms. For
the mapping method the effect of Saturn on the asteroidal evolution is introduced and the degree of
chaos is estimated by means of the Lyapunov time. Both methods are shown to lead to similar results
and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gap
and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.Origin and modelling of cold dark matter halo properties: IV. Triaxial ellipticity
http://hdl.handle.net/2117/14392
Origin and modelling of cold dark matter halo properties: IV. Triaxial ellipticity
Salvador-Solé, Eduard; Serra, Sinué; Manrique, Alberto; González Casado, Guillermo
In the three preceding papers in the series, we presented a model dealing with the
global and small-scale structure and kinematics of hierarchically assembled, virialised,
collisionless systems, which correctly accounted for the typical properties of simulated
cold darkmatter (CDM) haloes. This model relied, however, on the spherical symmetry
assumption. Here we show that the foundations of the model hold equally well for
triaxial systems and extend it in a fully accurate way to objects that satisfy the latter
more general symmetry. The master equations in the new version take the same form
as in the version for spherically symmetric objects, but the profiles of all the physical
quantities are replaced by their respective spherical averages. All the consequences
of the model drawn under the spherical symmetry assumption continue to hold. In
addition, the new version allows one to infer the axial ratios of virialised ellipsoids from
those of the corresponding protoobjects. The present results generalise and validate
those obtained in Papers I, II and III for CDM haloes. In particular, they confirm that
all halo properties are the natural consequence of haloes evolving through accretion
and major mergers from triaxial peaks (secondary maxima) in the primordial density
field.
2012-01-02T12:38:30ZSalvador-Solé, EduardSerra, SinuéManrique, AlbertoGonzález Casado, GuillermoIn the three preceding papers in the series, we presented a model dealing with the
global and small-scale structure and kinematics of hierarchically assembled, virialised,
collisionless systems, which correctly accounted for the typical properties of simulated
cold darkmatter (CDM) haloes. This model relied, however, on the spherical symmetry
assumption. Here we show that the foundations of the model hold equally well for
triaxial systems and extend it in a fully accurate way to objects that satisfy the latter
more general symmetry. The master equations in the new version take the same form
as in the version for spherically symmetric objects, but the profiles of all the physical
quantities are replaced by their respective spherical averages. All the consequences
of the model drawn under the spherical symmetry assumption continue to hold. In
addition, the new version allows one to infer the axial ratios of virialised ellipsoids from
those of the corresponding protoobjects. The present results generalise and validate
those obtained in Papers I, II and III for CDM haloes. In particular, they confirm that
all halo properties are the natural consequence of haloes evolving through accretion
and major mergers from triaxial peaks (secondary maxima) in the primordial density
field.A technique to composite a modified Newton's method for solving nonlinear equations
http://hdl.handle.net/2117/12477
A technique to composite a modified Newton's method for solving nonlinear equations
Grau Sánchez, Miguel; Díaz Barrero, José Luis
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is
improved is presented. The key idea in deriving this procedure is to compose a
given iterative method with a modified Newton’s method that introduces just one
evaluation of the function. To carry out this procedure some classical methods with
different orders of convergence are used to obtain root-finders with higher efficiency
index.
Nova tècnica que permet construir mètodes iteratius d'ordre alt.
2011-05-05T11:44:52ZGrau Sánchez, MiguelDíaz Barrero, José LuisA zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is
improved is presented. The key idea in deriving this procedure is to compose a
given iterative method with a modified Newton’s method that introduces just one
evaluation of the function. To carry out this procedure some classical methods with
different orders of convergence are used to obtain root-finders with higher efficiency
index.On computational order of convergence of some multi-precision solvers of nonlinear systems of equations
http://hdl.handle.net/2117/12475
On computational order of convergence of some multi-precision solvers of nonlinear systems of equations
Grau Sánchez, Miguel; Grau Gotés, Mª Ángela; Díaz Barrero, José Luis
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown. Most important, an adaptive multi-precision arithmetics is used hereof, where in each step the length of the mantissa is defined independently of the knowledge of the root.
Furthermore, generalizations of the one dimensional case to m-dimensions of three approximations of computational order of convergence are defined. Examples illustrating the previous results are given.
Report d'un treball de recerca on es presenten noves tècniques de càlcul de l'ordre de convergència amb una aritmètica adaptativa.
2011-05-05T11:25:05ZGrau Sánchez, MiguelGrau Gotés, Mª ÁngelaDíaz Barrero, José LuisIn this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown. Most important, an adaptive multi-precision arithmetics is used hereof, where in each step the length of the mantissa is defined independently of the knowledge of the root.
Furthermore, generalizations of the one dimensional case to m-dimensions of three approximations of computational order of convergence are defined. Examples illustrating the previous results are given.Uso de sismogramas antiguos para el estudio de paràmetros focales de terremotos ibèricos.
http://hdl.handle.net/2117/12274
Uso de sismogramas antiguos para el estudio de paràmetros focales de terremotos ibèricos.
Batlló Ortiz, Josep; Teves-Costa, Paula; Stich, Daniel; Macià Jové, Ramon; Morales Soto, Jose
2011-04-06T09:42:21ZBatlló Ortiz, JosepTeves-Costa, PaulaStich, DanielMacià Jové, RamonMorales Soto, JoseOn the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
http://hdl.handle.net/2117/12028
On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N.
2011-03-23T10:34:46ZLlibre Saló, JaumeRamírez Inostroza, Rafael OrlandoSadovskaia Nurimanova, Natalia GuennadievnaWe give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N.