Cosmological tests of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher-dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories.The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ∼ kpc (galaxy scales) to ∼ Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages — we summarize these tests and discuss the interesting prospects for new tests in the coming decade.     

Synthesis and functionalization of meso-aryl-substituted corroles.

The Rothemund condensation reaction of pyrrole and aldehydes is an extensively used route to meso-tetraarylporphyrins, but simple modifications of the reaction conditions allow the formation of different macrocycles other than the expected porphyrin. In the presence of an excess of pyrrole, this modified Rothemund approach leads to the synthesis of meso-triary-substituted corroles. This methodology allows the preparation of a wide range of substituted corroles starting from commercially available products. Higher yields have been obtained in the case of benzaldehydes bearing electron-withdrawing substituents, while the reaction fails in the presence of 2,6-disubstituted benzaldehydes. Although if not isolated, some experimental evidences indicate that the linear 5,10,15-triphenylbilane 4 is the precursor of the final corrole ring. Reaction of 5,10,15-triphenylcorrole 2 with an excess of NBS leads to the complete bromination of the macrocycle. Spectroscopic characterization seems to indicate the formation of the porphodimethene-like structure 5, where the macrocyclic aromatic conjugation is interrupted at the 10 position. Metalation of this compound with cobalt acetate and PPh3 affords the corresponding complex. The X-ray crystal structure of triphenylphosphine [2,3,7,8,12,13,17,18-octabromo-5,10,15-tris(4-nitrophenyl)corrolato]- cobalt(III) 8 confirms the ability of corrole ring to retain an almost planar conformation when fully substituted at the peripheral position.     

The Tabular Mode: Not Just Another Way to Represent a Function

Understanding mathematical functions as systematic processes involving the covariation of related variables is foundational in learning mathematics. In this article, findings are reported from two investigations examining students' thinking processes with functions. The first study focused on seven middle school students' explorations with a dynamic physical model. Students were videotaped during the 20‐ to 45‐minute sessions occurring two or three times per week over a period of 2 months, and students' written work was collected. The second investigation included 19 preservice elementary and middle school teachers enrolled in a course focusing on a combination of mathematical content and pedagogy. Participants' written problem‐solving work and reflective writing were collected, and participants were individually interviewed in 50‐minute videotaped sessions. Results from both investigations indicated that students often relied on a table, or some variation of a table, as a cognitive link advancing the development of their reasoning about underlying function relationships.     

Enforced helicity: efficient access to self-organized helical molecular strands by the imine route

The condensation of the two oligoheterocyclic aldehydes 8 and 16 with the bis-hydrazine 17 gives the bis-hydrazones 1 and 2. These molecular strands are shown to adopt helical conformations of 1.5 and 2.5 turns, respectively. The helical shape of 1 has been confirmed and structurally characterized by X-ray crystallography. The results indicate that the pyrimidine-hydrazone unit is a satisfatory helicity codon, so that the facile hydrazone formation provides an efficient procedure for generating helical structures. This greatly widens the scope of the methodology based on designed heterocyclic sequences for enforcing helicity in molecular strands, and opens interesting routes towards a variety of derived structures.     

Helical molecular programming: supramolecular double helices by dimerization of helical oligopyridine-dicarboxamide strands

Helically preorganized oligopyridine-dicarboxamide strands are found to undergo dimerization into double helical supramolecular architectures. Dimerization of single helical strands with five or seven pyridine rings has been characterized by NMR and mass spectrometry in various solvent/ temperature conditions. Solution studies and stochastic dynamic simulations consistently show an increasing duplex stability with increasing strand length. The double helical structures of three different dimers was characterized in the solid phase by X-ray diffraction analysis. Both aromatic stacking and hydrogen bonding contribute the double helical arrangement of the oligopyridinedicarboxamide strand. Inter-strand interactions involve extensive face-to-face overlap between aromatic rings, which is not possible in the single helical monomers. Most hydrogen bonds occur within each strand of the duplex and stabilize its helical shape. Some inter-strand hydrogen bonds are found in the crystal structures. Dynamic studies by NMR as well as by molecular modeling computations yield structural and kinetic information on the double helices and on monomer-dimer interconversion. In addition, they reveal the presence of a spring-like extension/compression as well as rotational displacement motions.     

Characterization of aromatic polymers (benzenoid and heterocyclic) by cross-polarization,magic-angle 13C-NMR spectroscopy

The cross-polarization, magic-angle ¹³C-NMR spectra of solid samples of poly(p-phenylene), its nitro derivative, polymerized biphenyl, poly(p-phenylene sulfide), poly(1-methyl-2,5-pyrrolylene), poly(1-phenyl-2,5-pyrrolylene), poly(2,5-thienylene), and poly(2,5-selenienylene) and the high-resolution ¹³C-NMR spectrum of poly(m-phenylene) in solution are presented and assigned. In all cases the chemical shifts are similar to those of model compounds in solution. In most instances the resonances of the nonprotonated carbon atoms in the solid polymers are more intense than those of the protonated carbons and appear to depend on the charge distribution in the molecular orbitals.     

Assessment of the plasma desorption time-of-flight mass spectrometry technique for pesticide adsorption and degradation on 'as-received' treated soil samples

The assessment of the plasma desorption time-of-flight mass spectrometry (PD-TOFMS) technique as a tool for direct characterization of pesticides adsorbed on agricultural soil is made for the first time in this study. Pellets of soils impregnated by solutions of three pesticides, namely norflurazon, malathion and oxyfluorfen, as well as deposits of these solutions onto aluminum surfaces, were investigated to this end. The yield values of the most characteristic peaks of the negative ion mass spectra were used to determine both the lowest concentrations detected on soils and limits of detection from thin films. The lowest values on soils are for malathion (1000 ppm range), and the largest for norflurazon (20,000 ppm), which is close to the limit of detection (LOD) found for the pesticide on the aluminum substrate (approximately 0.2 microg . cm(-2)). Different behaviors were observed as a function of time of storage in the ambient atmosphere or under vacuum; norflurazon adsorbed on soil exhibited high stability for a long period of time, and a rapid degradation of malathion with the elapsed time was clearly observed. The behavior of oxyfluorfen was also investigated but segregation processes seem to occur after several days. Although by far less sensitive than conventional methods based on extraction processes and used for real-world analytical applications, this technique is well suited to the study of the transformations occurring at the sample surface. A discussion is presented of the future prospects of such experiments in degradation studies.     

Simulating turbulent Dean flow in Cartesian coordinates

A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier–Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher‐order terms are neglected. The curvature terms are implemented in a conventional Navier–Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier–Stokes model. It is particularly rewarding that also distinct pairs of counter‐rotating streamwise‐oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd.     

Sensor Installation in Rigid Pavement

This unique approach for installing strain gages in PCC pavement sections in the Ohio SHRP Test Road was very successful. All sensors were installed during construction with no delays to the contractor, and all gages performed well in controlled vehicle tests which followed. After two and one-half years, more than 90% of the gages continue to balance electronically and function properly. Data from these sensors are expected to provide engineers with an in-depth understanding of how PCC pavements respond to traffic loads and environmental factors.