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 $t$, 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 $x$ and/or $t$) invariant under a group $G$ 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 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

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

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

The mummy of Ferdinando Orsini, 5th Duke of Gravina (†1549): a paleopathological study

In the monumental Sacristy of the Abbey of Saint Domenico Maggiore, Naples, 37 wooden sarcophagi contain the well preserved bodies of ten Aragonese kings, princes and other Neapolitan nobles who died between the 15th and 16th centuries. One of the arks revealed the natural mummy of Ferdinando Orsini, 5th Duke of Gravina, identified by an epigraph with his name and date of death (1549), in good condition, with the exception of the face, completely skeletonized. The skull suffers from an extensive destructive lesion that afflicted the medial wall of the orbit right, the root of the nose and, partly, the ethmoid without osteitic reaction. The histological examination performed on the bone showed wide lacunae with, inside, epithelial-like cells, partially necrotic, positive for the immunohistochemical stain for PanCK. The border between the bone and the surrounding neoplasia were clear; the brownish fleshy appearance mass had darker margins (like a palisade) and was separated from the bone by clefting artifacts. In our opinion, the pathology that affected Orsini 500 years ago was the basal cell carcinoma in an advanced stage, in fact it is the most frequent form of skin cancer and occurs predominantly on the sun-exposed skin of adults. Microscopically the tumour tends to infiltrate the subcutaneous tissue with a peripherical palisade surrounded by loose of stroma and cleft-like retraction spaces of artifactual nature. It grows in a slow and indolent fashion, but can ulcerate and may invade skull, nares, orbit or temporal bone with wide osteolithic lesion, enough to deserve the Latin name of ‘ulcus rodens’, i.e. erosive ulcer. Immunohistochemically, the cells are positive for keratin and distant metastases are very rare. This case is very important because it represents one of the only four cases of malignant soft tissue tumor diagnosed in paleopathology