1,026 research outputs found
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
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 ,
where is a parameter related to the equilibrium distance between bases
in a Watson-Crick pair. Here we analyze the Yakushevich model without . The model still supports soliton solutions indexed by two winding
numbers ; 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 -prolongations of vector
fields, and hence of -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 , and we speak of -prolongations of vector fields
and -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
Heterogeneous effects of spinoff foundations on the means of technology transfer: the role of past academic-industry collaborations
Focusing on the Italian population of academic entrepreneurs, we analyze the effect of establishing a spinoff firm on researchers' attitudes towards carrying out other activities in collaboration with firms, namely, co-publishing and co-patenting. We investigate the heterogeneity in this effect in terms of existing collaborations with firms in the pre-spinoff period. Using a counterfactual analysis on subgroups, we verify that academic entrepreneurs with previous publications with firms diminish their co-publishing and increase their co-patenting after founding a spinoff. Conversely, academic entrepreneurs who had no previous publications with firms increase their co-publishing and decrease their co-patenting. We maintain that such results are related to academics' learning processes connected with their previous technology transfer activities. The policy implications are related to technology transfer aims and contradict the idea that promoting spinoffs is an appropriate "one-size-fits-all" initiative
Poincare' normal forms and simple compact Lie groups
We classify the possible behaviour of Poincar\'e-Dulac normal forms for
dynamical systems in 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
Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device
We observe competition between the modulation instability (MI) and stimulated
Brillouin scattering (SBS) in a 9.2-GHz broadband SBS slow light device, in
which a standard 20-km-long single-mode LEAF fibre is used as the SBS medium.
We find that MI is dominant and depletes most of the pump power when we use an
intense pump beam at ~1.55 {\mu}m, where the LEAF fibre is anomalously
dispersive. The dominance of the MI in the LEAF-fibre-based system suppresses
the SBS gain, degrading the SBS slow light delay and limiting the SBS
gain-bandwidth to 126 dB \cdot GHz. In a dispersion-shifted highly nonlinear
fibre, the SBS slow light delay is improved due to the suppression of the MI,
resulting in a gain-bandwidth product of 344 dB \cdot GHz, limited by our
available pump power of 0.82 W
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