Solitons in Yakushevich-like models of DNA dynamics with improved intrapair potential

The Yakushevich (Y) model provides a very simple pictures of DNA torsion dynamics, yet yields remarkably correct predictions on certain physical characteristics of the dynamics. In the standard Y model, the interaction between bases of a pair is modelled by a harmonic potential, which becomes anharmonic when described in terms of the rotation angles; here we substitute to this different types of improved potentials, providing a more physical description of the H-bond mediated interactions between the bases. We focus in particular on soliton solutions; the Y model predicts the correct size of the nonlinear excitations supposed to model the ``transcription bubbles'', and this is essentially unchanged with the improved potential. Other features of soliton dynamics, in particular curvature of soliton field configurations and the Peierls-Nabarro barrier, are instead significantly changed

Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain

We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure

On the geometry of lambda-symmetries, and PDEs reduction

We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions

Assessing the volcanic hazard for Rome. 40Ar/39Ar and In-SAR constraints on the most recent eruptive activity and present-day uplift at Colli Albani Volcanic District

We present new 40Ar/39Ar data which allow us to refine the recurrence time for the most recent eruptive activity occurred at Colli Albani Volcanic District (CAVD) and constrain its geographic area. Time elapsed since the last eruption (36 kyr) overruns the recurrence time (31 kyr) in the last 100 kyr. New interferometric synthetic aperture radar data, covering the years 1993–2010, reveal ongoing inflation with maximum uplift rates (>2 mm/yr) in the area hosting the most recent (<200 ka) vents, suggesting that the observed uplift might be caused by magma injection within the youngest plumbing system. Finally, we frame the present deformation within the structural pattern of the area of Rome, characterized by 50 m of regional uplift since 200 ka and by geologic evidence for a recent (<2000 years) switch of the local stress-field, highlighting that the precursors of a new phase of volcanic activity are likely occurring at the CAVD

Implementation of In-Situ Impedance Techniques on a Full Scale Aero-Engine System

Determination of acoustic liner impedance for jet engine applications remains a challenge for the designer. Although suitable models have been developed that take account of source amplitude and the local flow environment experienced by the liner, experimental validation of these models has been difficult. This is primarily due to the inability of researchers to faithfully mimic the environment in jet engine nacelles in the laboratory. An in-situ measurement technique, one that can be implemented in an actual engine, is desirable so an accurate impedance can be determined for future modeling and quality control. This paper documents the implementation of such a local acoustic impedance measurement technique that is used under controlled laboratory conditions as well as on full scale turbine engine liner test article. The objective for these series of in-situ measurements is to substantiate treatment design, provide understanding of flow effects on installed liner performance, and provide modeling input for fan noise propagation computations. A series of acoustic liner evaluation tests are performed that includes normal incidence tube, grazing incidence tube, and finally testing on a full scale engine on a static test stand. Lab tests were intended to provide insight and guidance for accurately measuring the impedance of the liner housed in the inlet of a Honeywell Tech7000 turbofan. Results have shown that one can acquire very reasonable liner impedance data for a full scale engine under realistic test conditions. Furthermore, higher fidelity results can be obtained by using a three-microphone coherence technique that can enhance signal-to-noise ratio at high engine power settings. This research has also confirmed the limitations of this particular type of in-situ measurement. This is most evident in the installation of instrumentation and its effect on what is being measured

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.

Maximum likelihood estimators applied to the non gaussian source separation

A combination of signais emitted by several sources is received on an array ofsensors. In this situation frequently realized in application, we want to separate the sources in obtaining a transformation of the observed signais giving components related for each of them uniquely to a specific source . This separation cannot be successfull using the spectral matrix and then people use a priori information . We show here that this separation can be donc using Higher Order Statistics of the observed signais and we give the maximum likelihood estimator of the source models that defines the separation .Une combinaison de signaux émis par plusieurs sources est reçue sur un réseau de capteurs . Dans cette situation qui se rencontre dans de nombreux domaines d'application, on cherche à séparer les sources en construisant une transformation des signaux reçus dont chaque composante est liée de manière exclusive à chacune des sources . Cette séparation des sources ne peut être réalisée sans hypothèse supplémentaire en se limitant à l'utilisation de la matrice spectrale . Nous montrons ici que cette séparation peut être menée à bien en utilisant les statistiques d'ordre supérieur et nous établissons la forme de l'estimateur du maximum de vraisemblance du modèle de sources conduisant à la séparation

Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae