Well-posedness for a class of fourth order diffusions for image processing

A number of image denoising models based on higher order parabolic partial differential equations (PDEs) have been proposed in an effort to overcome some of the problems attendant to second order methods such as the famous Perona–Malik model. However, there is little analysis of these equations to be found in the literature. In this paper, methods of maximal regularity are used to prove the existence of unique local solutions to a class of fourth order PDEs for noise removal. The proof is laid out explicitly for two newly proposed fourth order models, and an outline is given for how to apply the techniques to other proposed models.     

Quaternion algebras, Heegner points and the arithmetic of Hida families

Given a newform f, we extend Howard??s results on the variation of Heegner points in the Hida family of f to a general quaternionic setting. More precisely, we build big Heegner points and big Heegner classes in terms of compatible families of Heegner points on towers of Shimura curves. The novelty of our approach, which systematically exploits the theory of optimal embeddings, consists in treating both the case of definite quaternion algebras and the case of indefinite quaternion algebras in a uniform way. We prove results on the size of Neková???s extended Selmer groups attached to suitable big Galois representations and we formulate two-variable Iwasawa main conjectures both in the definite case and in the indefinite case. Moreover, in the definite case we propose refined conjectures à la Greenberg on the vanishing at the critical points of (twists of) the L-functions of the modular forms in the Hida family of f living on the same branch as f.     

Activity and stereoselectivity of Ru-based catalyst bearing a fluorinated imidazolinium ligand

Grubbs II generation catalyst (3), bearing a fluorinated imidazolinium ligand, was investigated in cross metathesis (CM), ring closing metathesis (RCM) and ring opening polymerization metathesis (ROMP) for a variety of substrates. Kinetic studies showed reduced stability of the catalyst in methylene chloride following the first 15 minutes of reaction preventing a higher efficiency despite the very high activity. Beneficial solvent effects on the catalyst stability were observed by performing RCM in C₆F₆.      

Experimental measurement of thermophysical properties of oxide-water nano-fluids down to ice-point

This paper presents the measurement of the thermal conductivity and the dynamic viscosity of Al₂O₃-water (1-4% particle volume fraction) and TiO₂-water (1-6% particle volume fraction) nano-fluids carried out at atmospheric pressure in the temperature range from 1 to 40 °C, which is particularly interesting for the application of nano-fluids as thermal medium in refrigeration and air-conditioning.The thermal conductivity measurement was performed by using a Transient Hot Disk TPS 2500S apparatus instrumented with a 7577 probe (2.001 mm in radius) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading. The dynamic viscosity measurement and the rheological analysis were carried out by a rotating disc type rheometer Haake Mars II instrumented with a single cone probe (60 mm in diameter and 1° angle) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading.The thermal conductivity measurements of the tested nano-fluids show a great sensitivity to particle volume fraction and temperature and a weak sensitivity to cluster average size: TiO₂-water and Al₂O₃-water nano-fluids show a thermal conductivity enhancement (with reference to pure water) from −2 to 16% and from −2 to 23% respectively.TiO₂-water and Al₂O₃-water nano-fluids exhibit a Newtonian behaviour in all the investigated ranges of temperature and nano-particle volume fraction. The relative viscosity shows a great sensitivity to particle volume fraction and cluster average size and no sensitivity to temperature: TiO₂-water and Al₂O₃-water nano-fluids show a dynamic viscosity increase with respect to pure water from 17 to 210% and from 15 to 150% respectively.Al₂O₃-water nano-fluid seems to be more promising as thermal medium than TiO₂-water nano-fluid, particularly at low thermal level (between ambient temperature and ice point) where TiO₂-water is not suitable showing worse performance than pure water.Present experimental measurements were compared both with available measurements carried out by different researchers and computational models for thermophysical properties of suspensions.     

Crystallization study of SrSnO3:Fe

Alkaline earth stannates have recently become important materials in ceramic technology due to its application as humidity sensor. In this work, alkaline earth stannates doped with Fe³⁺ were synthesized by the polymeric precursor method, with calcination at 300 °C/7 h and between 400 and 1100 °C/4 h. The powder precursors were characterized by TG/DTA after partial elimination of carbon. Characterization after the second calcination step was done by X-ray diffraction, infrared spectroscopy, and UV?Cvis spectroscopy. Results confirmed the formation of the SrSnO₃:Fe with orthorhombic perovskite structure, besides SrCO₃ as secondary phase. Crystallization occurred at 600 °C, being much lower than the crystallization temperature of perovskites synthesized by solid state reaction. The analysis of TG curves indicated that the phase crystallization was preceded by two thermal decomposition steps. Carbonate elimination occurred at two different temperatures, around 800 °C and above 1000 °C.     

On the hydrogen bond networks in the water-methanol mixtures: topology, percolation and small-world

Statistical mechanics based topological analysis and island (or cluster) statistics were used to study the hydrogen bond (H-bond) networks in the water-methanol mixtures with the following methanol mole fractions (x(m)): 0.00, 0.10, 0.20, 0.25, 0.28, 0.30, 0.32, 0.36, 0.38, 0.42, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00. NPT-Monte Carlo simulations were performed at room conditions using the TIP5P model potential for water and united-atoms (OPLS) for methanol to generate the H-bond networks. We have found evidence for non-ideal behavior of mixtures with x(m) ≈ 0.3. Several structural and topological properties present strong dependence with the mixture composition. Island statistics indicate a change from the percolated to non-percolate regime at x(m) ≈ 0.5. Statistical analysis of the islands' nature (homo-clusters: same type of molecules × hetero-clusters: two types of molecules) yields a preferential formation of homo-clusters that quantifies the local composition and preferential solvation ("microimmiscibility"). The topology of the hydrogen bond networks was characterized by local (clustering coefficients, average degrees), semi-global (path lengths) and global (spectral densities) properties. Small-world patterns (highly clustered and small path lengths) appear for x(m) in the range 0.40-0.70, and the momenta in the spectral densities correlate quite well with previous analysis based on rings, chains and branched chains topologies. It also seems that small quantities of methanol in water cause disruption of the continuous fully connected H-bond networks formed by water molecules.     

Hydrogen bond networks in water and methanol with varying interaction strengths

Metropolis Monte Carlo simulations of hydrogen-bonded liquids (water and methanol) were performed with the well tested effective pair potentials TIP5P and OPLS. The Coulomb contribution for the interaction potential was damped by a factor η varied from 1 to 0.49 for water and 1 to 0.15 for methanol. As a result, the networks formed by the hydrogen-bonded molecules presented interesting properties as a function of η, including small-world patterns and percolation transitions. These complex networks were analyzed by local (clustering coefficients, average degrees), semi-global (path lengths) and global (spectral densities) properties, and islands statistics. From these properties, small-world behavior was found for η in the range 0.60-0.75 for both liquids, interestingly independent of the molecular structure of the liquid. Phase transition behavior was observed for the average degrees and the clustering coefficient curves with critical values at 0.55 for water and 0.34 for methanol. Macroscopic properties such as mass density and vaporization enthalpy were also parametrically dependent on η and they presented phase transition behavior that coincides with the critical values obtained from the topological analysis. This is probably the first time that such phase transitions are observed for these quantities and shows a direct relation between macroscopic properties and topological features of hydrogen bond networks.     

Self-rewetting carbon nanofluid as working fluid for space and terrestrial heat pipes

Thermal management is very important in modern electronic systems. Recent researches have been dedicated to the study of the heat transfer performances of binary heat transfer fluids with peculiar surface tension properties and in particular to that of “self-rewetting fluids”, i.e., liquids with a surface tension increasing with temperature and concentration. Since in the course of liquid/vapor-phase change, self-rewetting fluids behavior induces a rather strong liquid inflow (caused by both temperature and concentration gradients) from the cold region (where liquid condensates) to the hot evaporator region, this fluids have been proposed and investigated as new heat transfer fluids for advanced heat transfer devices, e.g., heat pipes or heat spreaders for terrestrial and space applications (Savino et al. in Space Technol 25(1):59–61, 2009). The present work is dedicated to the study of the thermophysical properties of a new class of heat transfer fluids based on water/alcohol solutions with suspended carbon nanostructures, in particular single-wall carbon nanohorns (SWNH), synthesized by a homemade apparatus with an AC arc discharge in open air (Mirabile Gattia et al. in Nanotechnology 18:255604, 2007). SWNHs are cone-shaped nanoparticles with diameters between 1 and 5 nm and lengths in the range of 20–100 nm. SWNHs could be found in the form of quite-spherical aggregates with diameters ranging from 20 to 100 nm. The paper also discusses the results of these investigations and laboratory characterization tests of different heat pipes, including reference ordinary heat pipes and innovative pipes filled with self-rewetting fluids and self-rewetting nanofluids. The potential interest of the proposed studies stems from the large number of possible industrial applications, including space technologies and terrestrial applications, such as cooling of electronic components.     

Study of Structural and Photoluminescent Properties of Ca8Eu2(PO4)6O2

In this work it is presented for the first time the nanostructured hydroxyapatites doped with 0.5, 1.0 and 2.0 wt% of Eu³⁺ prepared at room temperature by the mechanical alloying technique. X-ray diffraction powder (XRD), infrared (IR) and Raman scattering spectroscopy, scanning electron microscopy (SEM), microhardness measurements as well as luminescent data of Eu³⁺ were used to investigate the structural and optical properties of these nanomaterials. The electrical and dielectrical analyses were used with the intention of having a better comprehension about the electromagnetic fields in pure and doped hydroxyapatites.