1,715 research outputs found
Dimension increase and splitting for Poincare'-Dulac normal forms
Integration of nonlinear dynamical systems is usually seen as associated to a
symmetry reduction, e.g. via momentum map. In Lax integrable systems, as
pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero
system, one proceeds in the opposite way, enlarging the nonlinear system to a
system of greater dimension. We discuss how this approach is also fruitful in
studying non integrable systems, focusing on systems in normal form.Comment: 16 page
Side conditions for ordinary differential equations
We specialize Olver's and Rosenau's side condition heuristics for the
determination of particular invariant sets of ordinary differential equations.
It turns out that side conditions of so-called LaSalle type are of special
interest. Moreover we put side condition properties of symmetric and partially
symmetric equations in a wider context. In the final section we present an
application to parameter-dependent systems, in particular to quasi-steady state
for chemical reactions.Comment: To appear in J. of Lie Theor
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
Variational principles for involutive systems of vector fields
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector
field can be characterized by means of a variational principle based on a
one-form. We discuss how a vector field on a manifold can also be characterized
in a similar way by means of an higher order variational principle, and how
this extends to involutive systems of vector fields.Comment: 31 pages. To appear in International Journal of Geometric Methods in
Modern Physics (IJGMMP
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
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
High-Performance Silicon-Based Multiple Wavelength Source
We demonstrate a stable CMOS-compatible on-chip multiple-wavelength source by
filtering and modulating individual lines from a frequency comb generated by a
microring resonator optical parametric oscillator.. We show comb operation in a
low-noise state that is stable and usable for many hours. Bit-error rate
measurements demonstrate negligible power penalty from six independent
frequencies when compared to a tunable diode laser baseline. Open eye diagrams
confirm the fidelity of the 10 Gb/s data transmitted at the comb frequencies
and the suitability of this device for use as a fully integrated silicon-based
WDM source.Comment: 3 pages, 3 figure
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