Large N dualities and transitions in geometry

The focus of these lectures is the Gopakumar-Vafa's insight that ``Large N dualities'' (relating gauge theories and closed strings) are realized, in certain cases, by "transition in geometry". In their pivotal 1998 example, the gauge theory is SU(N) Chern-Simons theory on S^3, for large N, and the transition is the "conifold" transition between two Calabi--Yau varieties. Much progress has been made to support Gopakumar and Vafa's conjecture, including the lift of the transition to a transformation between 7-manifolds with G_2 holonomy. In another direction, this set up brings us to consider the uncharted territory of "open Gromov-Witten invariants". The lectures, hence the notes, were prepared for an audience of beginning graduate students, in mathematics and physics, whom we hope to get interested in this subject. Because most of the material presented in these lectures comes from the physics literature, we aimed to build a bridge for the mathematicians towards the physics papers on the subject.Comment: Survey article based on lectures given by the first author in May 2001 during 4th SIGRAV and SAGP2001 Graduate School (Typos corrected, clarifications and references added.

Predator and detritivore niche width helps to explain biocomplexity of experimental detritus-based food webs in four aquatic and terrestrial ecosystems

In the study of food webs, the existence and explanation of recurring patterns, such as the scale invariance of linkage density, predator–prey ratios and mean chain length, constitute long-standing issues. Our study focused on litter-associated food webs and explored the influence of detritivore and predator niche width (as d13C range) on web topological structure. To compare patterns within and between aquatic and terrestrial ecosystems and take account of intra-habitat variability, we constructed 42 macroinvertebrate patch-scale webs in four different habitats (lake, lagoon, beech forest and cornfield), using an experimental approach with litterbags. The results suggest that although web differences exist between ecosystems, patterns are more similar within than between aquatic and terrestrial web types. In accordance with optimal foraging theory, we found that the niche width of predators and prey increased with the number of predators and prey taxa as a proportion of total taxa in the community. The tendency was more marked in terrestrial ecosystems and can be explained by a lower per capita food level than in aquatic ecosystems, particularly evident for predators. In accordance with these results, the number of links increased with the number of species but with a significantly sharper regression slope for terrestrial ecosystems. As a consequence, linkage density, which was found to be directly correlated to niche width, increased with the total number of species in terrestrial webs, whereas it did not change significantly in aquatic ones, where connectance scaled negatively with the total number of species. In both types of ecosystem, web robustness to rare species removal increased with connectance and the niche width of predators. In conclusion, although limited to litter-associated macroinvertebrate assemblages, this study highlights structural differences and similarities between aquatic and terrestrial detrital webs, providing field evidence of the central role of niche width in determining the structure of detritus-based food webs and posing foraging optimisation constraints as a general mechanistic explanation of food web complexity differences within and between ecosystem types

X-ray Photoelectron Spectroscopy Analysis of Tribostressed Samples in the Presence of ZnDTP: A Combinatorial Approach

The influence of load on the chemistry of tribofilms formed on a steel surface in solution of pure di-isopropyl zinc dithiophosphate (i-ZnDTP) in n-decane has been investigated by means of a combinatorial tribological experiment involving X-ray photoelectron spectroscopy. The experiment consisted of the preparation of a set of spatially separated areas, produced under various tribological test conditions, and the subsequent spectroscopic probing of the chemical composition of the tribofilm. The experiment was carried out at room temperature under boundary-lubrication conditions and revealed a physically adsorbed layer of the additive in the non-contact area and a thin (ca. 5 nm), inhomogeneous phosphate film covering the tribostressed areas. The total amount of phosphate present in the tribostressed area was found to increase with increasing load. In the contact areas, iron oxides and metal sulfides have also been detecte

Substituent Effect on the Reactivity of Alkylated Triphenyl Phosphorothionates in Oil Solution in the Presence of Iron Particles

The effect of the substituent attached to the phenyl rings on the reactivity of alkylated triphenyl phosphorothionates (t-butyl TPPT (b-TPPT) and p-nonyl TPPT (n-TPPT)) in oil solution at high temperature (423 and 473K) was investigated by means of Fourier-transform infrared spectroscopy (FT-IR), nuclear magnetic resonance (NMR) spectroscopy and X-ray photoelectron spectroscopy (XPS). The FT-IR and NMR results show that the alkylated TPPTs were highly thermally stable and did not completely decompose in oil, even upon heating at 423K for 168h and at 473K for 72h, with and without steel filings and iron particles (both metallic iron and iron oxide particles). The reaction of alkylated TPPTs was found to start with the scission of the P=S bond to yield alkylated triphenyl phosphate. The kinetics of the thermo-oxidative reaction was slower when steel filings and iron particles were added to the oil solutions during the heating experiments. The reactivity of the unsubstituted molecule (TPPT) was higher than that of alkylated TPPTs at 423K, while at 473K TPPT and n-TPPT were more reactive than b-TPPT. In the case of the experiments performed at 473K in the presence of steel filings or metallic iron or iron oxide particles, the reactivity of the alkylated TPPT molecules decreased with the length of the alkyl chain bound to the phenyl rings. The XPS results show that a reaction layer consisting of carbon, oxygen, phosphorus and iron was formed on the 100Cr6 steel filings immersed for 72h in oil solutions containing alkylated TPPTs and heated at 473K. Sulphur was neither detected on the surface nor in the composition vs depth profile. During the heating experiments, the base oil (PAO) was oxidized. At 423K, the alkylated TPPTs had a strong antioxidant effect, which was found to be more pronounced upon increasing the length of the alkyl chain bound to the phenyl rings. At 473K, the TPPTs did not inhibit the oxidation of the base oil as effectively as at 423

A Combinatorial Approach to Elucidating Tribochemical Mechanisms

A new type of combinatorial tribological experiment is presented, which explores a series of tribological conditions, such as load and relative velocity, spatially separated as a "library” on one single sample. As an example, a library displaying the results of tribological testing of an additive under a series of different loads has been prepared and analyzed. The tribological information acquired during the testing has been correlated with spectroscopic information from the tribologically stressed surface. The use of imaging and small-area X-ray photoelectron spectroscopy has allowed the identification of the different tribologically stressed areas and the acquisition of detailed spectroscopic information. The composition and the thickness of the tribofilm were found to be dependent on the applied load. The use of the combinatorial approach shows the potential to greatly facilitate rapid characterization of new lubricant additive

Reactivity of Triphenyl Phosphorothionate in Lubricant Oil Solution

Investigating the thermo-oxidative reactivity of anti-wear additives in lubricant oil solution at high temperature can significantly contribute to an understanding of the mechanism of thermal film and tribofilm formation on metal surfaces. In this study, the reactivity of triphenyl phosphorothionate (TPPT) in lubricant oil solution at high temperature (423 and 473K) has been studied by Fourier transform infrared spectroscopy (FT-IR) and nuclear magnetic resonance (NMR) spectroscopy. The results show that the TPPT molecule was highly thermally stable and did not completely decompose in oil solution even upon heating at 423K for 168h and at 473K for 72h. The degradation of the TPPT molecule, which turned out to be a first-order reaction, started taking place after 6h at both temperatures, leading to the breakage of the P=S bond with the formation of triphenyl phosphate. During these heating experiments, no oil-insoluble compounds were detected. The oxidation of the base oil as a result of the prolonged heating demonstrated that the TPPT molecule did not effectively act as oxidation inhibito

Pressure Dependence of ZnDTP Tribochemical Film Formation: A Combinatorial Approach

Combinatorial testing has been performed on zinc dialkyldithiophosphate (ZnDTP)-containing lubricants, to investigate the effects of contact pressure on the formation of tribochemical films. Contact pressures ranging from 25 to 500MPa were applied in ball-on-disc tribotests with oscillating load. Both the ball and the disc were investigated by means of small-area and imaging X-ray photoelectron spectroscopy (XPS). The thickness and the composition of the reaction layer were estimated from the XPS data. The thickness of the reaction layer in the tribologically stressed areas of the ball and of the disc increased with both temperature and contact pressure. The reaction layer mainly consisted of short-chain poly(thio)phosphates, shorter chains being observed at higher contact pressures. At high pressures, the presence of a thick, high-toughness short-chain poly(thio)phosphate layer can explain the lower friction and dimensional wear coefficients observed. On the ball, similar anti-wear film formation mechanisms were observed as on the disc, zinc sulphide being deposited in the post-contact regio

Effect of Chain-Length and Countersurface on the Tribochemistry of Bulk Zinc Polyphosphate Glasses

Zinc polyphosphate glasses are considered to be chiefly responsible for the anti-wear efficiency of ZnDTP tribofilms. In this work, the tribochemical properties of amorphous bulk zinc polyphosphates of different chain lengths (ranging from zinc metaphosphate to zinc pyrophosphate) have been investigated. Tribological tests on bulk polyphosphate discs have been carried out using steel and quartz balls as counter-surfaces in a poly-α-olefin (PAO) bath at room temperature. The composition in the wear track and on the contact region of the balls has been monitored by small-area and imaging X-ray photoelectron spectroscopy (i-XPS). The XPS analysis revealed that the composition of short-chain-length polyphosphates remained unchanged following tribological stress. Long-chain-length polyphosphates are depolymerized in the wear track as a consequence of a tribochemical reaction. By comparing the results obtained using quartz and steel balls, it could be observed that while the reaction of iron oxide with the polyphosphates certainly plays a role in the depolymerization of the samples under sliding conditions, pressure and shear stress alone and also in the presence of water or oil-oxidized species are able to depolymerize the glass when an inert material is used as counterpart; the composition of the wear track, in this case, is dependent on the applied load. All samples were able to form an adhesive, glassy transfer film on both steel and quartz balls, but the short-chain-length polyphosphates showed a lower friction coefficient and wear coefficient. The results suggest a third-body mechanism with the polyphosphates acting as a solid lubricant. Differences in tribological behavior of the different-chain-length polyphosphates are attributable to their mechanical and rheological propertie

In Situ Attenuated Total Reflection (ATR/FT-IR) Tribometry: A Powerful Tool for Investigating Tribochemistry at the Lubricant-Substrate Interface

To investigate the chemical changes occurring at metal/lubricant interfaces under tribological conditions in the boundary-lubrication regime, an in situ system for conducting quantitative tribological measurements has been constructed by combining an attenuated total reflection Fourier-transform infrared (ATR/FT-IR) spectrometer with a reciprocating tribometer. By periodically acquiring ATR/FT-IR spectra during sliding, spectroscopic changes due to thermal and/or tribochemical reactions occurring at the metal/oil interface can be monitored and correlated with friction measurements. The usefulness of this tribological test system has been demonstrated by performing ATR tribological experiments in the presence of a poly-α-olefin base oil at high temperature (423K) on iron-coated germanium ATR crystal

Stainless steels: passive film composition, pitting potentials and critical chloride content in concrete

Stainless steel reinforcing bars show excellent corrosion resistance in concrete structures exposed to harsh environments. Only little information on the surface chemistry of these materials in alkaline media is available. This work reports XPS surface analytical results (thickness, composition of the passive film and of the interface beneath the film) obtained on black steel, FeCr alloys, DIN 1.4301, DIN 1.4462 and the nickel-free DIN 1.4456 after exposure to alkaline solutions simulating concrete. The pitting potentials of the steels could be related to the Cr(III)oxy-hydroxide and Mo(VI) content in the passive film. Ccrit, the critical chloride content for corrosion initiation in concrete, necessary for life-time predictions can be determined only with time consuming tests, especially for high-alloyed stainless steels. This work reports a correlation between Ccrit in concrete (made with CEM II A/LL and CEM I) and the pitting potential for carbon steel, Fe12%Cr alloy, DIN 1.4301 and DIN 1.4571 stainless steels. This could allow for the first time a quantitative estimation of Ccrit for stainless steels in concrete based on short-term solution tests