1,705 research outputs found
Asymptotic scaling in a model class of anomalous reaction-diffusion equations
We analyze asymptotic scaling properties of a model class of anomalous
reaction-diffusion (ARD) equations. Numerical experiments show that solutions
to these have, for large , well defined scaling properties. We suggest a
general framework to analyze asymptotic symmetry properties; this provides an
analytical explanation of the observed asymptotic scaling properties for the
considered ARD equations.Comment: To appear in J. Nonlin. Math. Phy
Asymptotic scaling symmetries for nonlinear PDEs
In some cases, solutions to nonlinear PDEs happen to be asymptotically (for
large and/or ) invariant under a group which is not a symmetry of
the equation. After recalling the geometrical meaning of symmetries of
differential equations -- and solution-preserving maps -- we provide a precise
definition of asymptotic symmetries of PDEs; we deal in particular, for ease of
discussion and physical relevance, with scaling and translation symmetries of
scalar equations. We apply the general discussion to a class of
``Richardson-like'' anomalous diffusion and reaction-diffusion equations, whose
solution are known by numerical experiments to be asymptotically scale
invariant; we obtain an analytical explanation of the numerically observed
asymptotic scaling properties. We also apply our method to a different class of
anomalous diffusion equations, relevant in optical lattices. The methods
developed here can be applied to more general equations, as clear by their
geometrical construction
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
Asymptotic symmetries of difference equations on a lattice
It is known that many equations of interest in Mathematical Physics display
solutions which are only asymptotically invariant under transformations (e.g.
scaling and/or translations) which are not symmetries of the considered
equation. In this note we extend the approach to asymptotic symmetries for the
analysis of PDEs, to the case of difference equations
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
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
Paleopathological and metagenomic study of a XIIth cetury Perucian mummy: an ancient case of Chagas disease
Among the results obtained from this study there is the only known complete paleopathological study of Chagas’ disease (American Trypanosomiasis), comprising macroscopic, microscopic and ultrastructural data, as well as information on atherosclerosis, anthracosis, emphysema and pneumonia. We characterized the gut microbiome of two pre-Columbian Andean mummies dating to the 10–15th centuries using 16S rRNA gene high-throughput sequencing and metagenomics, and compared them to a previously characterized gut microbiome of an 11th century AD pre-Columbian Andean mummy. Our previous study showed that the Clostridiales represented the majority of the bacterial communities in the mummified gut remains, but that other microbial communities were also preserved during the process of natural mummification, as shown with the metagenomics analyses. Metagenome analyses showed the presence of other microbial groups that were positively or negatively correlated with specific metabolic profiles. The presence of sequences similar to both Trypanosoma cruzi and Leishmania donovani could suggest that these pathogens were prevalent in pre-Columbian individuals
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
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