2,316 research outputs found
Symmetry and integrability for stochastic differential equations
No full textWe discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A43 (2010) & 44 (2011)]. Together with integrability, we also consider the relations between symmetries and reducibility of a system of SDEs to a lower dimensional one. We consider both “deterministic” symmetries and “random” ones, in the sense introduced recently by Gaeta and Spadaro [J. Math. Phys.58 (2017)]
Molecular recognition of organic dyes in aqueous environments using prismarene hosts
No full textIn 2020, Prof. Gaeta introduced a new class of macrocyclic hosts named prism[n]arenes [1],
consisting of 1,5-methylene-bridged naphthalene units characterized by a deep π-electron
rich cavity. Water-soluble carboxylate-primaries [2] (PrS[n]COO), exhibit special recognition
properties in water, such that in the medium the formation of endo-cavity complexes is driven
by C−H···π interactions and by the hydrophobic effect. These prismarenes have already
attracted much interest in the scientific community, moreover, research groups are exploiting
the structural and supramolecular properties of prismarenes for very interesting applications
[3,4]. Prismarenes exhibit an S0-S1 transition peaking at ca. 350 nm in UV-Vis spectra and
emit blue-violet light at 390 nm with a moderate quantum yield of Φ = 0.10. Prismarene
macrocycles exhibit a significant cavity, which is modulated based on the macrocycle size, i.e.
the number (n) of arene units used, which is usually indicated in the name of prisma[n]arenes.
Furthermore, prismarenes exhibit planar chirality and are dynamically racemic [1,2] through
rapid interconversion of enantiomers by rotation of aromatic units. Prismarene macrocycles
exhibit very specific structural and supramolecular properties, which make them promising
candidates for host-guest complexation of organic dyes such as Rhodamine B or Methylene
Blue in aqueous buffer solution. The results of UV-Vis titrations indicate the formation of
prismarene[6]sulfate and dye complex (Figure1), and the association constant has been
calculated by using the inferred equation. Also, the possible mechanism of molecular
interaction will be discussed in the meantim
La voie littorale Sperlonga-Gaeta-Formia
No full textXavier Lafon, La voie littorale «Sperlonga, Gaeta, Formia», p. 399-429.
La voie littorale Sperlonga-Gaeta appelée communément Via Flacca est connue depuis longtemps en raison des restes importants encore conservés. Cette étude a donc pour but d'essayer de comprendre quand et pourquoi cette route a été construite, en étudiant les structures encore visibles, son tracé dans le cadre à la fois géographique et historique de cette zone du Latium méridional, et de confronter ces données à celles fournies par les textes, en particulier Tite-Live.
Ainsi se trouve précisé le cadre dans lequel ont pu commencer à se développer à partir du IIe siècle av. J.-C. les nombreuses villae qui jalonnent son parcours.Lafon Xavier. La voie littorale Sperlonga-Gaeta-Formia. In: Mélanges de l'École française de Rome. Antiquité, tome 91, n°1. 1979. pp. 399-429
Strontian fluoro-magnesiohastingsite in Alban Hills lavas (Central Italy): constraints on crystallization conditions
No full textA magmatic calcic amphibole (Ca-M4 greater than or equal to1.50) characterized by large Sr and F contents (SrO >1 wt.%, F >2.5 wt.%) is described. According to the crystal-chemical formula, the amphibole can be classified as a strontian fluoro-magnesiohastingsite and the presence of Sr cations in the A sites is suggested. The amphibole occurs in the groundmass of ultrapotassic lavas from the Alban Hills Volcanic District (Central Italy). This peculiar chemical composition is due to the lavas' groundmass compositional trend occurring under low silica-activity conditions. We suggest that the occurrence of F amphiboles allows us to consider the Alban Hills Volcanic District magmas to be as rich in F as other ultrapotassic magmas
A discrete linearizability test based on multiscale analysis
No full textIn this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation
Prism[n]arenes macrocycles for chiral recognition in supramolecular sensing
No full textChiral sensing has gained great interest in the recent years, due to its application in several
fields, such as medicinal chemistry, environmental control, and natural products. Among the
most promising molecular structures for chiral sensing and recognition are the so-called
stereodynamic chiroptical probes.[1] To this family belong polyaromatic host macrocycles
having planar chirality, able provide host-guest complexes with chiral guests in which the host
exhibits a preferred chiral conformation that correlates with the absolute configuration (AC) of
the guest. In 2020 a novel class of macrocyclic hosts named prism[n]arenes have been
reported by Gaeta and coworkers.[2] Prismarenes are constituted by 1,5-methylene bridged
2,6-dialkoxynaphthalene units and exhibit a deep π-electron rich aromatic cavity, thus being
able to form endo-cavity complexes with ammonium guests stabilized by secondary
interactions such as cation⋯π, C–H⋯π, van der Waals, and hydrophobic effect. For these
macrocycles, the changes in the chiral conformations of the probe can be easily detected and
interpreted by means of Electronic Circular Dichroism (ECD) spectroscopy due to its ability to
discriminate between enantiomers (Figure 1).[3] Additionally, Vibrational CD (VCD), provides
useful insight on local interaction and conformational stability of the Host-Guest system.[4] In
this work, we report the study of the chiral induction and host/guest interactions among different
chiral guests and Prism[n]arenes hosts supported by ECD and VCD measurements and their
DFT simulation
1D Numerical modelling of crustal heat transfer in the Antarctic glaciers of Northern Victoria Land
No full textThe Antarctic glacial system is both highly sensitive to, and driver of global climate changes being as well sensitive to other external events, such as endogenous factors, that may affect glaciers energy balance. In this framework, thermal regime and heat flow evolution within the continental crust below the ice sheet must be considered. The present work focused on preliminary result of 1D numerical modelling of pure conductive heat transfer model pointing out the role of several factor in crustal heat transfer and its effects of thermal regime of east Antarctic glacial system. Here we present a case study on northern Victoria Land (Antarctica) glacial system ,a key site for investigating the amplitude of past ice volume variations in the East Antarctic Ice Sheet (EIAS, Baroni et al.[1]), comprising a relevant sector of the Transantarctic Mountains and the Mt. Melbourne Volcanic Province (MVP). With the support of thermo-barometric data obtained by the study of spinel-peridotites xenoliths, Armienti and Perinelli [2] inferred a change of mantle’s geothermal gradients from 0.5 °C/km to 3 °C/km, as response to lithospheric thinning caused by Ross Sea Rifting. On the basis of such petrologic and geo-thermometric data, combined, in a first analysis, with bibliographic thermal properties of rock materials, a simulation of the heat flow propagation from the upper mantle across the continental crust has been performed. These data provided the input for a multi-parametric analysis that has assumed a stationary and conductive heat flow and was performed through a sensitivity approach by varying thermal parameters and stratigraphic profiles, i.e. considering different thickness for the different proportions of the continental crust. A local heat source in the upper crust has been also considered and no surficial thermal perturbation due to volcanic systems were modelled. The numerical model so defined, took into account a crustal heat flux of 120 mW/m2 (Della Vedova et al. [3]), typical value of Victoria Land Basin, and temperature values at Moho ranging between 750 and 1450 °C. In addition we considered a sensitivity analysis to the ice thickness of the glacial system up to 800 m, according to Pleistocene EAIS variations and ice fluctuations amplitudes reconstructed in NVL (Strasky et al.[4]). At lateral boundary of 1D model a thermal isolation has been also assumed. The 1D thermal model, has been validated matching experimental data obtained from a nearby deep borehole (Morin et al. [5]), assumed as reference point, representative of the geodynamic and volcanic conditions of the study area, in which a temperature of about 75 °C at depth of 1000 m b.s.l. has been reached. The modelling provides encouraging results, highlighting a main contribution of regional heat source and ice sheet thickness on the thermal regime of the upper crust respect to geometrical and thermal parameters. Our results lead to a deep origin in thermal perturbations of glacial system, which seems to be less sensitive to thermal anomalies in the upper crust. Notably, the high pressure accumulation (i.e. upper mantle/lower crust) of hot parental magmas in the Ross Island and MVP, that has been proposed on the basis of experimental (Iacovino et al. [6]) and cumulate rocks (Perinelli and Gaeta [7]) studies, proves the regional, deep thermal perturbations beneath the studied area. The 1D thermal model represent the basis for further analysis focused on the evaluation of thermo-mechanical interactions between bedrock and ice masses with particular interest on stress-strain effects on the kinematic of the glaciers.
References:
[1] Baroni et al. (2005)Bulletin of the Geological Society of America 117: 212-228
[2] Armienti and Perinelli C. (2010)Tectonophysics 486: 28–35.
[3] Della Vedova et al. (1992) In: Proceedings of the 6th ISAES: Saitama, Japan, 627–637.
[4] Strasky et al. (2009) Antarctic Science21: 59–69.
[5] Morin et al. (2010) Geosphere 6: 370–378.
[6] Iacovino et al. (2016) Journal of Petrology doi: 10.1093/petrology/egv083.
[7] Perinelli and Gaeta (submitted) Periodico di Mineralogi
Non-quadratic additional conserved quantities in Birkhoff normal forms
No full textFor resonant Hamiltonian systems in Poincaré–Birkhoff normal form, the quadratic part of the Hamiltonian is a constant of motion. In the resonant case, the normal form is not unique; this corresponds to free parameters in the solution to homological equations. The “standard” prescription in this case is to set these parameters to zero; however, it was remarked already by Dulac that a different prescription could actually produce a simpler normal form. One such prescription was provided in previous work by the present author; here we discuss how—and under which conditions—this can be used to obtain normal forms which admit, besides the quadratic part, (one or a set of) additional constants of motion of higher degree in nested small neighborhoods of the origin. A concrete example with a cubic natural Hamiltonian in 3 DOF is considered
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