Translating the dynamics of the Hénon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold... more Translating the dynamics of the Hénon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold, we obtain a local and synthetic geometric indicator of chaos (GIC), which represents a link between local quantities and asymptotic behavior of orbits and gives a strikingly evident, oneto-one, correspondence between geometry and instability. Going beyond the results attained using the customary dynamical approach and improving also on the global criteria established within the Riemannian framework, the GIC is able to discriminate between regular and stochastic orbits on a given energy surface, simply on the basis of the value it assumes along a relatively small piece of the trajectory, without long integrations of the dynamics and without any reference to a perturbation. [S0031-9007(98)07882-X]
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002
Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to dete... more Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN's) or Poincaré Surface of Section. Moreover, at variance with other fast indicators proposed in the Literature, it gives informations about the asymptotic behaviour of trajectories, though being local in phase-space. Furthermore, it detects the chaotic or regular nature of geodesics without any reference to a given perturbation and it allows also to discriminate between different regimes (and possibly sources) of chaos in distinct regions of phase-space.
We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmologic... more We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmological models, giving a gauge-invariant and unapproximated description of the full continuous dynamics, achieved through a geometrical descrip- tion of the equations of motion in the framework of the theory of Finsler Spaces. The numerical integrations of the geodesics and geodesic deviation equations show clearly the absence of any "traditional" signature of Chaos, while suggesting a chaotic scattering dynamics scenario. 02.40.-k ; 04.20.-q ; 05.45.+b The characterization of Chaos in the framework of General Relativity is still an open question, receiving re- cently an increasing attention (1). The issue is related to the well known ambiguities hidden in any gauge theory, and in particular to the freedom in the choice of the co- ordinate system. A gauge invariant description of Chaos must be invariant under any such choice, in particular with respect to rescaling of the "time...
The Dynamics of Small Bodies in the Solar System, 1999
Recently, [6, 7, 3, 8], we proposed a generalization to non Riemannian manifolds of the so-called... more Recently, [6, 7, 3, 8], we proposed a generalization to non Riemannian manifolds of the so-called Geometro-Dynamical Approach (GDA) to Chaos, [11, 2], able to widen the applicability of the method to a considerably larger class of dynamical systems (DS’s). Here, we carry on our efforts on a pathway directed towards a synthetic and a priori characterization of the qualitative properties of generic DS’s. Although being aware that this goal is very ambitious, and that, up to now, many of the trials have been discouraging, we shouldn’t forget the theoretical as well practical relevance held by a possible successful attempt. Indeed, if only it would be concevaible to single out a synthetic indicator of (in)stability, we will be able to avoid all the consuming computations needed to empirically discover the nature of a particular orbit, perhaps noticeably different with respect to another one very nearby. Besides this, going beyond the semi-phenomenological mere recognition of the occurrence of dynamical instability, this approach could give deeper hints on its sources, even in those situations where the boundary between Order and Chaos tends to become more and more nuanced, and different tools seem to give conflicting answers. Lately, a renewed interest towards a concise description of dynamical instability1 has grown, together with the feeling of the need to look deeply at the intermingled structures underlving the transition from quasi-integrable to stochastic motions.
Multilayered nanovectors made up from a controlled binary lipid mixture (POPC and DMPS) and trime... more Multilayered nanovectors made up from a controlled binary lipid mixture (POPC and DMPS) and trimethyl chitosan (TMC) have been prepared and characterized by light-and small angle neutron scattering. The morphology and the multilayer structure of the particle outer shell has been described in detail. By varying the amount of TMC in the starting solution it is possible to tune the overall surface particle charge as well as its multilamellarity. In this way the drug loading/release properties of the particles can be controlled. Therefore the use of controlled POPC/DMPS mixtures can be a valid alternative to commercial lecithin to obtain nanovectors with specific release properties.
... Maria Di Bari Corresponding Author Contact Information , E-mail The Corresponding Author , a ... more ... Maria Di Bari Corresponding Author Contact Information , E-mail The Corresponding Author , a , Antonio Deriu a and Marco Sampoli b. ... In: Kluwer, Dordrecht (1991). 3. D. Di Cola, A. Deriu, M. Sampoli and A. Torcini. J. Chem. Phys. 104 (1996), p. 4223. ...
Monophase thorium–zirconium hydrides (ThZr2Hx) have been fabricated starting from a metallic allo... more Monophase thorium–zirconium hydrides (ThZr2Hx) have been fabricated starting from a metallic alloy and the hydrogen stoichiometry determined by X-ray diffraction. Incoherent Quasielastic Neutron Scattering (IQNS) on the hydrides was conducted over the temperature range 650–750K at the Backscattering Silicon Spectrometer (BASIS) at the Spallation Neutron Source (SNS) at ORNL. The isotropic Chudley–Elliott model was utilized to analyze the quasielastic linewidth
In this paper we discuss some general aspects of the so-called geometrodynamical approach (GDA) t... more In this paper we discuss some general aspects of the so-called geometrodynamical approach (GDA) to Chaos and present some results obtained within this framework. We firstly derive a naïve and yet general geometrization procedure, and then specialize the discussion to the descriptions of motion within the frameworks of two among the most representative implementations of the approach, namely the Jacobi and the Finsler geometrodynamics. In order to support the claim that the GDA isn't simply a mere re-transcription of the usual dynamics, but instead can give various hints on the understanding of the qualitative behaviour of dynamical systems (DS's), we then compare, from a formal point of view, the tools used within the usual framework of Hamiltonian dynamics to detect the presence of Chaos with the corresponding ones used within the GDA, i.e., the tangent dynamics and the geodesic deviation equations, respectively, pointing out their general inequivalence. Moreover, to go ahead the mathematical analysis and to highlight both the peculiarities of the methods and the analogies between them, we work out two concrete applications to the study of very different, yet typical in distinct contexts, dynamical systems. The first is the well-known Hénon-Heiles Hamiltonian, which allows to exploit how the Finsler GDA is well suited not only for testing the dynamical behaviour of systems with few degrees of freedom, but even to get deeper insights on the sources of instability. We show the effectiveness of the GDA, both in recovering fully satisfactory agreement with the most well established outcomes and also in helping the understanding of the sources of Chaos. Then, in order to point out the general applicability of the method, we present the results obtained from the geometrical description of a General Relativistic DS, whose peculiarity is well known, as its very nature has been debated since long time, namely the Bianchi IX (BIX) cosmological model. Using the Finsler GDA, we obtain results with a built-in invariance, which give evidence to the non chaotic behaviour of this system, excluding any global exponential instability in the evolution of the geodesic deviation.
Translating the dynamics of the Hénon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold... more Translating the dynamics of the Hénon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold, we obtain a local and synthetic geometric indicator of chaos (GIC), which represents a link between local quantities and asymptotic behavior of orbits and gives a strikingly evident, oneto-one, correspondence between geometry and instability. Going beyond the results attained using the customary dynamical approach and improving also on the global criteria established within the Riemannian framework, the GIC is able to discriminate between regular and stochastic orbits on a given energy surface, simply on the basis of the value it assumes along a relatively small piece of the trajectory, without long integrations of the dynamics and without any reference to a perturbation. [S0031-9007(98)07882-X]
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002
Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to dete... more Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN's) or Poincaré Surface of Section. Moreover, at variance with other fast indicators proposed in the Literature, it gives informations about the asymptotic behaviour of trajectories, though being local in phase-space. Furthermore, it detects the chaotic or regular nature of geodesics without any reference to a given perturbation and it allows also to discriminate between different regimes (and possibly sources) of chaos in distinct regions of phase-space.
We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmologic... more We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmological models, giving a gauge-invariant and unapproximated description of the full continuous dynamics, achieved through a geometrical descrip- tion of the equations of motion in the framework of the theory of Finsler Spaces. The numerical integrations of the geodesics and geodesic deviation equations show clearly the absence of any "traditional" signature of Chaos, while suggesting a chaotic scattering dynamics scenario. 02.40.-k ; 04.20.-q ; 05.45.+b The characterization of Chaos in the framework of General Relativity is still an open question, receiving re- cently an increasing attention (1). The issue is related to the well known ambiguities hidden in any gauge theory, and in particular to the freedom in the choice of the co- ordinate system. A gauge invariant description of Chaos must be invariant under any such choice, in particular with respect to rescaling of the "time...
The Dynamics of Small Bodies in the Solar System, 1999
Recently, [6, 7, 3, 8], we proposed a generalization to non Riemannian manifolds of the so-called... more Recently, [6, 7, 3, 8], we proposed a generalization to non Riemannian manifolds of the so-called Geometro-Dynamical Approach (GDA) to Chaos, [11, 2], able to widen the applicability of the method to a considerably larger class of dynamical systems (DS’s). Here, we carry on our efforts on a pathway directed towards a synthetic and a priori characterization of the qualitative properties of generic DS’s. Although being aware that this goal is very ambitious, and that, up to now, many of the trials have been discouraging, we shouldn’t forget the theoretical as well practical relevance held by a possible successful attempt. Indeed, if only it would be concevaible to single out a synthetic indicator of (in)stability, we will be able to avoid all the consuming computations needed to empirically discover the nature of a particular orbit, perhaps noticeably different with respect to another one very nearby. Besides this, going beyond the semi-phenomenological mere recognition of the occurrence of dynamical instability, this approach could give deeper hints on its sources, even in those situations where the boundary between Order and Chaos tends to become more and more nuanced, and different tools seem to give conflicting answers. Lately, a renewed interest towards a concise description of dynamical instability1 has grown, together with the feeling of the need to look deeply at the intermingled structures underlving the transition from quasi-integrable to stochastic motions.
Multilayered nanovectors made up from a controlled binary lipid mixture (POPC and DMPS) and trime... more Multilayered nanovectors made up from a controlled binary lipid mixture (POPC and DMPS) and trimethyl chitosan (TMC) have been prepared and characterized by light-and small angle neutron scattering. The morphology and the multilayer structure of the particle outer shell has been described in detail. By varying the amount of TMC in the starting solution it is possible to tune the overall surface particle charge as well as its multilamellarity. In this way the drug loading/release properties of the particles can be controlled. Therefore the use of controlled POPC/DMPS mixtures can be a valid alternative to commercial lecithin to obtain nanovectors with specific release properties.
... Maria Di Bari Corresponding Author Contact Information , E-mail The Corresponding Author , a ... more ... Maria Di Bari Corresponding Author Contact Information , E-mail The Corresponding Author , a , Antonio Deriu a and Marco Sampoli b. ... In: Kluwer, Dordrecht (1991). 3. D. Di Cola, A. Deriu, M. Sampoli and A. Torcini. J. Chem. Phys. 104 (1996), p. 4223. ...
Monophase thorium–zirconium hydrides (ThZr2Hx) have been fabricated starting from a metallic allo... more Monophase thorium–zirconium hydrides (ThZr2Hx) have been fabricated starting from a metallic alloy and the hydrogen stoichiometry determined by X-ray diffraction. Incoherent Quasielastic Neutron Scattering (IQNS) on the hydrides was conducted over the temperature range 650–750K at the Backscattering Silicon Spectrometer (BASIS) at the Spallation Neutron Source (SNS) at ORNL. The isotropic Chudley–Elliott model was utilized to analyze the quasielastic linewidth
In this paper we discuss some general aspects of the so-called geometrodynamical approach (GDA) t... more In this paper we discuss some general aspects of the so-called geometrodynamical approach (GDA) to Chaos and present some results obtained within this framework. We firstly derive a naïve and yet general geometrization procedure, and then specialize the discussion to the descriptions of motion within the frameworks of two among the most representative implementations of the approach, namely the Jacobi and the Finsler geometrodynamics. In order to support the claim that the GDA isn't simply a mere re-transcription of the usual dynamics, but instead can give various hints on the understanding of the qualitative behaviour of dynamical systems (DS's), we then compare, from a formal point of view, the tools used within the usual framework of Hamiltonian dynamics to detect the presence of Chaos with the corresponding ones used within the GDA, i.e., the tangent dynamics and the geodesic deviation equations, respectively, pointing out their general inequivalence. Moreover, to go ahead the mathematical analysis and to highlight both the peculiarities of the methods and the analogies between them, we work out two concrete applications to the study of very different, yet typical in distinct contexts, dynamical systems. The first is the well-known Hénon-Heiles Hamiltonian, which allows to exploit how the Finsler GDA is well suited not only for testing the dynamical behaviour of systems with few degrees of freedom, but even to get deeper insights on the sources of instability. We show the effectiveness of the GDA, both in recovering fully satisfactory agreement with the most well established outcomes and also in helping the understanding of the sources of Chaos. Then, in order to point out the general applicability of the method, we present the results obtained from the geometrical description of a General Relativistic DS, whose peculiarity is well known, as its very nature has been debated since long time, namely the Bianchi IX (BIX) cosmological model. Using the Finsler GDA, we obtain results with a built-in invariance, which give evidence to the non chaotic behaviour of this system, excluding any global exponential instability in the evolution of the geodesic deviation.
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