Constraining extended theories of gravity using Solar System tests

Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and geodesic precession. Assuming that each reasonable theory of gravitation should satisfy Solar System tests, we use these limits on the estimated value of the cosmological constant to constrain extended theories of Gravity, which are nowadays studied as possible theories for cosmological models and provide viable solutions to the cosmological constant problem and the explanation of the present acceleration of the Universe. We obtain that the estimated values, from Solar System tests, for the parameters appearing in the extended theories of Gravity are orders of magnitude bigger than the values obtained in the framework of cosmologically relevant theories.     

Modeling the phase diagram of carbon

We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respectively. The graphite-diamond transition line that we computed is in good agreement with experimental data, confirming the accuracy of the employed empirical potential. On the basis of the computed slope of the graphite melting line, we rule out the hotly debated liquid-liquid phase transition of carbon. Our simulations allow us to give accurate estimates of the location of the diamond melting curve and of the graphite-diamond-liquid triple point.     

Multiple periodic solutions of scalar second order differential equations

We prove multiplicity of periodic solutions for a scalar second order differential equation with an asymmetric nonlinearity, thus generalizing previous results by Lazer and McKenna (1987) [1] and Del Pino, Manasevich and Murua (1992) [2]. The main improvement lies in the fact that we do not require any differentiability condition on the nonlinearity. The proof is based on the use of the Poincaré-Birkhoff Fixed Point Theorem.     

Water absorption kinetics in different wettability conditions studied at pore and sample scales in porous media by NMR with portable single-sided and laboratory imaging devices

NMR relaxation time distributions of water (1)H obtained by a portable single-sided surface device have been compared with MRI internal images obtained with a laboratory imaging apparatus on the same biocalcarenite (Lecce Stone) samples during capillary water uptake. The aim of this work was to check the ability of NMR methods to quantitatively follow the absorption phenomenon under different wettability conditions of the internal pore surfaces. Stone wettability changes were obtained by capillary absorption of a chloroform solution of Paraloid PB72, a hydrophobic acrylic resin frequently used to protect monuments and buildings, through one face of each sample. Both relaxation and imaging data have been found in good quantitative agreement each other and with masses of water determined by weighing the samples. In particular the Washburn model of water capillary rise applied to the imaging data allowed us to quantify the sorptivity in both treated and untreated samples. Combining relaxation and imaging data, a synergetic improvement of our understanding of the water absorption kinetics at both pore and sample scales is obtained. Since relaxation data have been taken over the course of time without interrupting the absorption process, simply by keeping the portable device on the surface opposite to the absorption, the results show that the single-sided NMR technique is a powerful tool for in situ evaluation of water-repellent treatments frequently used for consolidation and/or protection of stone artifacts.     

A unified theory for brittle and ductile shear mode fracture

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids, the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocation-free zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture.     

Electronic Transitions in Different Redox States of Trinuclear 5,6,11,12,17,18-Hexaazatrinaphthylene-Bridged Titanium Complexes: Spectroelectrochemistry and Quantum Chemistry

Multinuclear transition metal complexes bridged by ligands with extended π-electronic systems show a variety of complex electronic transitions and electron transfer reactions. While a systematic understanding of the photochemistry and electrochemistry has been attained for binuclear complexes, much less is known about trinuclear complexes such as hexaphenyl-5,6,11,12,17,18-hexaazatrinaphthylene-tristitanocene [(Cp₂Ti)₃HATN(Ph)₆]. The voltammogram of [(Cp₂Ti)₃HATN(Ph)₆] shows six oxidation and three reduction waves. Solution spectra of [(Cp₂Ti)₃HATN(Ph)₆] and of the electrochemically formed oxidation products show electronic transitions in the UV, visible and the NIR ranges. Density functional theory (DFT) and linear response time-dependent DFT show that the three formally titanium(II) centers transfer an electron to the HATN ligand in the ground state. The optically excited transitions occur exclusively between ligand-centered orbitals. The charged titanium centers only provide an electrostatic frame to the extended π-electronic system. Complete active self-consistent field (CASSCF) calculation on a structurally simplified model compound, which considers the multi-reference character imposed by the three titanium centers, can provide an interpretation of the experimentally observed temperature-dependent magnetic behavior of the different redox states of the title compound in full consistency with the interpretation of the electronic spectra.     

estimates for overdetermined Radon transforms

We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning bounds for convolution with all rotations of arc length measure on a fixed convex curve in . Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth -dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.

     

Short interval asymptotics for a class of arithmetic functions

Summary We provide a general asymptotic formula which permits applications to sums like <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation> \sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x< n\le x+y}r(n^3), $$ where $d(n)$ and $r(n)$ are the usual arithmetic functions (number of divisors, sums of two squares), and $y$ is small compared to~$x$.     

Application of high-resolution magic-angle spinning NMR spectroscopy to define the cell uptake of MRI contrast agents

A new method, based on proton high-resolution magic-angle spinning ((1)H HR-MAS) NMR spectroscopy, has been employed to study the cell uptake of magnetic resonance imaging contrast agents (MRI-CAs). The method was tested on human red blood cells (HRBC) and white blood cells (HWBC) by using three gadolinium complexes, widely used in diagnostics, Gd-BOPTA, Gd-DTPA, and Gd-DOTA, and the analogous complexes obtained by replacing Gd(III) with Dy(III), Nd(III), and Tb(III) (i.e., complexes isostructural to the ones of gadolinium but acting as shift agents). The method is based on the evaluation of the magnetic effects, line broadening, or induced lanthanide shift (LIS) caused by these complexes on NMR signals of intra- and extracellular water. Since magnetic effects are directly linked to permeability, this method is direct. In all the tests, these magnetic effects were detected for the extracellular water signal only, providing a direct proof that these complexes are not able to cross the cell membrane. Line broadening effects (i.e., the use of gadolinium complexes) only allow qualitative evaluations. On the contrary, LIS effects can be measured with high precision and they can be related to the concentration of the paramagnetic species in the cellular compartments. This is possible because the HR-MAS technique provides the complete elimination of bulk magnetic susceptibility (BMS) shift and the differentiation of extra- and intracellular water signals. Thus with this method, the rapid quantification of the MRI-CA amount inside and outside the cells is actually feasible.