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

Solitons in a double pendulums chain model, and DNA roto-torsional dynamics

It was first suggested by Englander et al to model the nonlinear dynamics of DNA relevant to the transcription process in terms of a chain of coupled pendulums. In a related paper [q-bio.BM/0604014] we argued for the advantages of an extension of this approach based on considering a chain of double pendulums with certain characteristics. Here we study a simplified model of this kind, focusing on its general features and nonlinear travelling wave excitations; in particular, we show that some of the degrees of freedom are actually slaved to others, allowing for an effective reduction of the relevant equations

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

Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation $\ell_0 \to 0$, where $\ell_0$ is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without $\ell_0 \to 0$. The model still supports soliton solutions indexed by two winding numbers $(n,m)$; we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively

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

A new generation of bio-composite thermoplastic filaments for a more sustainable design of parts manufactured by FDM

The most recent developments of Fused Deposition Modelling (FDM) techniques are moving the application of Additive Manufacturing (AM) technologies toward new areas of investigation such as the biomedical, aerospace, and marine engineering in addition to the more consolidated industrial and civil fields. Some specific characteristics are required for the components designed for peculiar applications, such as complex geometries, lightweight, and high strength as well as breathability and aesthetic appearance specifically in the biomedical field. All these design specifications could be potentially satisfied by manufacturing with 3D printing techniques. Moreover, the development of purpose-dedicated filaments can be considered a key factor to successfully meet all the requirements. In this paper, fabrication and applications of five new thermoplastic materials with fillers are described and analyzed. They are organic bio-plastic compounds made of polylactic acid (PLA) and organic by-products. The growing interest in these new composite materials reinforced with organic by-products is due to the reduction of production management costs and their low environmental impact. In this study, the production workflow has been set up and described in detail. The main properties of these new thermoplastic materials have been analyzed with a major emphasis on strength, lightweight, and surface finish. The analysis showed that these materials can be particularly suitable for biomedical applications. Therefore, two different biomedical devices were selected and relative prototypes were manufactured with one of the analyzed thermoplastic materials. The feasibility, benefits, and performance of the thermoplastic material considered for these applications were successfully assessed

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

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

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