Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere

Optimal FPE for non-linear 1d-SDE. I: Additive Gaussian colored noise

Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear and non-markovian, so a Fokker Planck equation (FPE), for the probability density function (PDF), is generally not obtainable. However, a FPE is desirable because it is the main tool to obtain relevant analytical statistical information such as stationary PDF and First Passage Time. This problem has been addressed by many authors in the past, but due to an incorrect use of the interaction picture (the standard tool to obtain a reduced FPE) previous theoretical results were incorrect, as confirmed by direct numerical simulation of the SDE. We will show, in general, how to address the problem and we will derived the correct best FPE from a perturbation approach. The method followed and the results obtained have a general validity beyond the simple case of exponentially correlated Gaussian driving used here as an example; they can be applied even to non Gaussian drivings with a generic time correlation.Comment: 23 pages, 13 figure

Linear or Nonlinear Modeling for ENSO Dynamics?

The observed ENSO statistics exhibits a non-Gaussian behavior, which is indicative of the presence of nonlinear processes. In this paper, we use the Recharge Oscillator Model (ROM), a largely used Low-Order Model (LOM) of ENSO, as well as methodologies borrowed from the field of statistical mechanics to identify which aspects of the system may give rise to nonlinearities that are consistent with the observed ENSO statistics. In particular, we are interested in understanding whether the nonlinearities reside in the system dynamics or in the fast atmospheric forcing. Our results indicate that one important dynamical nonlinearity often introduced in the ROM cannot justify a non-Gaussian system behavior, while the nonlinearity in the atmospheric forcing can instead produce a statistics similar to the observed. The implications of the non-Gaussian character of ENSO statistics for the frequency of extreme El Nino events is then examined

NEW REMAINS OF CASATIA THERMOPHILA (CETACEA, MONODONTIDAE) FROM THE LOWER PLIOCENE MARINE VERTEBRATE-BEARING LOCALITY OF ARCILLE (TUSCANY, ITALY)

An incomplete cranium, three cervicals (including the axis) and two likely lumbars of a monodontid cetacean are here described from lower Pliocene (ca. 5.1–4.5 Ma) marine sandstones cropping out at Arcille (Grosseto Province, Tuscany, Italy). This fossil find comes from the same locality as the holotype of Casatia thermophila, which it resembles in terms of overall size and cranial morphology, and especially, by displaying a similarly depressed portion of the dorsal surface of the premaxillae anterior to the premaxillary sac fossae and medial to the anteromedial sulci. Our new find is thus assigned to C. thermophila, and significant anatomical parts that are missing in the holotype are described in order to improve the diagnosis of this monodontid species. Some dentigerous fragments of the maxillae hint at a homodont and polydont dentition, which in turn suggests a ram prey capture method that differs from the highly derived suction method that is proper of extant monodontids. This second find of C. thermophila from the warm-water Arcille palaeoenvironment lends further support to the hypothesis that monodontids once thrived in tropical and subtropical habitats

Recovery of a medieval Brucella melitensis genome using shotgun metagenomics

Shotgun metagenomics provides a powerful assumption-free approach to the recovery of pathogen genomes from contemporary and historical material. We sequenced the metagenome of a calcified nodule from the skeleton of a 14th-century middle-aged male excavated from the medieval Sardinian settlement of Geridu. We obtained 6.5-fold coverage of a Brucella melitensis genome. Sequence reads from this genome showed signatures typical of ancient or aged DNA. Despite the relatively low coverage, we were able to use information from single-nucleotide polymorphisms to place the medieval pathogen genome within a clade of B. melitensis strains that included the well-studied Ether strain and two other recent Italian isolates. We confirmed this placement using information from deletions and IS711 insertions. We conclude that metagenomics stands ready to document past and present infections, shedding light on the emergence, evolution, and spread of microbial pathogens

Comparative analysis of digital models from 3D photogrammetry and structured light scanning for the study of tetrapod tracks

The present work aims at analyzing the acquisition capacity of different digital reconstruction techniques for three-dimensional models, in the frame of the study of the remarkable Middle Triassic (Ladinic) tetrapod ichnoassemblage from the Quarziti del Monte Serra Formation (Monti Pisani, Tuscany, central Italy). Tracks stored in different Italian museum collections were processed and analyzed through two different digital acquisition methodologies, namely, digital photogrammetry and structured light scanning (with the EinScan Pro HD scanner model, capable of a maximum resolution of 0.2 mm) to evaluate which of these techniques is most suitable for the study of small- to medium-sized tetrapod tracks. Two models were created for each sample, one for each acquisition methodology. These models were processed using the software Meshmixer, Meshlab and CloudCompare, to locate any possible error in the mesh, correct them and compare the models with each other in terms of quality and graphical rendering, respectively. The RStudio software was also used to verify and control, by using statistical tests, the normal distribution of the data, as well as to further process them. We noticed that the average number of triangles is higher for the meshes obtained via photogrammetry; likewise, the values of the metric “Per Face Quality according to triangle shape and aspect ratio – Mean ratio of triangle”, available on Meshlab and used here to evaluate the quality of a mesh, is higher. Photogrammetry is thus preferable in the study of centimetric tracks as it allows for very high levels of mesh detail. That said, more experience and a deeper understanding of the acquisition process by the operator are needed for fruitfully exploiting the full potentialities of photogrammetr

Chaos and thermal conductivity

Article discussing research on chaos and thermal conductivity

A revision of Stenopterygius (Ichthyosauria: Thunnosauria) in Italian museum collections

Natural history museum collections are invaluable resources for scientific research, providing material for many fields, and notably for palaeontology. Over the last two centuries, many relevant vertebrate fossils have been discovered, gathered, and traded all over Europe, sometimes without being subsequently published or described. This is also the case for ichthyosaur fossils of the genus Stenopterygius, a high number of which were found in near Holzmaden (SW Germany), in lower Toarcian rocks of the Posidonia Shale Formation. From the mid-19th century onwards, these fossils made their way into palaeontological collections all over the world, including Italian museums. Stenopterygius is one of the most studied ichthyosaur taxa in literature. Research on Stenopterygius ranges from its trophic niche to ontogenesis, biological responses to environmental stress and soft tissue histology (from cells structures to skin pigmentation). Even though the role of Stenopterygius as a model organism for marine vertebrate palaeontology is well established, difficulties nonetheless exist regarding the taxonomy and systematics of this genus, with four valid species being currently differentiated using a linear morphometric approach. Here, we provide new data on 19 Stenopterygius specimens from five Italian museum collections: Pisa, Milano, Napoli, Padova and Bologna. Out of these specimens, four belong to S. triscissus (a relatively rare species), and ten are juveniles (an underrepresented ontogenetic group). Additionally, CT scans were performed on two historical Stenopterygius specimens stored at the Museo di Storia Naturale dell’Università di Pisa, providing images of skeletal parts that are still embedded in rock, which may prove crucial for the species-level identification, as well as for detecting the presence of associated macrofaun