On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph K _N contains a monochromatic copy of H. A famous result of Chváatal, Rödl, Szemerédi and Trotter states that there exists a constant c(Δ) such that r(H) ≤ c(Δ)n for every graph H with n vertices and maximum degree Δ. The important open question is to determine the constant c(Δ). The best results, both due to Graham, Rödl and Ruciński, state that there are positive constants c and c′ such that $2^{c'\Delta } \leqslant c(\Delta ) \leqslant ^{c\Delta \log ^2 \Delta }$ . We improve this upper bound, showing that there is a constant c for which c(Δ) ≤ 2 ^cΔlogΔ . The induced Ramsey number r _ind (H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd?s conjectured the existence of a constant c such that, for any graph H on n vertices, r _ind (H) ≤ 2 ^cnlogn . We move a step closer to proving this conjecture, showing that r _ind (H) ≤ 2 ^cnlogn . This improves upon an earlier result of Kohayakawa, Prömel and Rödl by a factor of logn in the exponent.     

Resolving 3D magnetism in nanoparticles using polarization analyzed SANS

Utilizing a polarized ³He cell as an analyzer we were able to perform a full polarization analysis on small-angle neutron scattering (SANS) data from an ensemble of 7 nm magnetite nanoparticles. The results led to clear separation of magnetic and nuclear scattering plus a 3D vectorial decomposition of the magnetism observed. At remanence variation in long-range magnetic correlation length was found to be highly dependent on temperature from 50 to 300 K. Additionally, we were able to compare the magnetic scattering from moments along and perpendicular to an applied field at saturation and in remanence.     

Seeing an invisible axion in the supersymmetric particle spectrum

I describe how under favorable circumstances, the existence of an invisible axion could correlate with a distinctive CERN Large Hadron Collider sparticle spectrum, in particular, through a gluino approximately ln(M(P)/m(3/2)) times heavier than other gauginos.     

Construction of 1H-indazoles from ortho-aminobenzoximes by the Mitsunobu reaction

Recently, there has been an upsurge in the occurrence of the indazole motif in drug discovery. Accordingly, newer, milder and more efficient routes towards their synthesis have emerged in the literature. We recently reported the Mitsunobu-triggered cyclodehydration of salicylaldoximes to transient 1,2-benzisoxazoles, and salicylhydroxamic acids to their corresponding 3-hydroxybenzisoxazoles. We hypothesized subjecting ortho-aminobenzoximes to Mitsunobu conditions will likewise induce a cyclodehydration to deliver the corresponding 1H-indazoles. Indeed, secondary anilines afforded the predicted N¹-substituted 1H-indazoles, and primary anilines, after activation with a Boc group, furnished the N¹-Boc 1H-indazoles in good to excellent yields. This work further expands the chemical repertoire of the Mitsunobu reaction, representing its unprecedented use in the construction of the 1H-indazole nucleus.     

On Large Time Behavior and Selection Principle for a Diffusive Carr–Penrose Model

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which singles out a particular self-similar solution of the linear LSW model as determining the large time behavior of the diffusive model. A selection principle is rigorously proven for a model which is a semiclassical approximation to the diffusive model. Upper bounds on the rate of coarsening are also obtained for the full diffusive model.     

An Experimental Investigation of the Liquid Flow Induced by a Pulsed Electrical Discharge Plasma

In this work, particle image velocimetry has been used to visualize and quantify plasma-induced flow fields in liquid water. Experiments were performed in a rod-plane plasma reactor with a thin wire electrode suspended above the surface of the liquid in argon gas and a grounded plate immersed in the liquid. The velocity field has been quantified for two types of solutions: (1) aqueous NaCl solutions of varying solution conductivities and discharge frequencies and (2) aqueous NaCl solutions containing varying concentrations of the following four organic compounds: rhodamine B dye, caffeine, fluoxetine, and perfluorooctanoic acid. Results show that in neat water and aqueous caffeine solutions, the liquid is “pulled” along by the interaction of the gas molecules with the liquid molecules at the free surface and thus the direction of the liquid flow is in the direction of the gas phase flow (i.e., away from the discharge location). However, the flow was reversed (i.e., towards the discharge) for those solutions with strong surfactants such as perfluorooctanoic acid. The magnitude of the reversal depended on the initial concentration of the compound and for some compounds as time progressed the reversed flow pattern weakened and then reverted to a normal flow pattern. To determine the most likely cause of these flow reversals, a simple numerical model of the velocity field was developed to estimate relative contributions of various flow inducing mechanisms. The model indicates that in the presence of surfactants, Marangoni stresses are responsible for inducing the flow in the liquid.     

Extremal results in sparse pseudorandom graphs

Szemerédi's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and Rödl proved an analogue of Szemerédi's regularity lemma for sparse graphs as part of a general program toward extending extremal results to sparse graphs. Many of the key applications of Szemerédi's regularity lemma use an associated counting lemma. In order to prove extensions of these results which also apply to sparse graphs, it remained a well-known open problem to prove a counting lemma in sparse graphs.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.