Control of neoclassical tearing modes by sawtooth control

The onset of a neoclassical tearing mode (NTM) depends on the existence of a large enough seed island. It is shown in the Joint European Torus that NTMs can be readily destabilized by long-period sawteeth, such as obtained by sawtooth stabilization from ion-cyclotron heating or current drive. This has important implications for burning plasma scenarios, as alpha particles strongly stabilize the sawteeth. It is also shown that, by adding heating and current drive just outside the inversion radius, sawteeth are destabilized, resulting in shorter sawtooth periods and larger beta values being obtained without NTMs.     

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.     

Ricci solitons: the equation point of view

We discuss some classification results for Ricci solitons, that is, self similar solutions of the Ricci Flow. New simpler proofs of some known results will be presented. In detail, we will take the equation point of view, trying to avoid the tools provided by considering the dynamic properties of the Ricci flow.     

The influence of mode coupling on the non-linear evolution of tearing modes

On the basis of tearing mode theory a simple but physically explicit model of the evolution of toroidally coupled rotating magnetic islands has been developed. The basic mechanism identified by the model in the island evolution is the locking in phase of rotating islands that leads to rapid destabilisation of an initially stable mode. Destabilisation of marginally stable (2, 1) and (3, 1) modes is analysed in several scenarios. It is shown that mode coupling is an effective way of destabilising a m=3 island in a low- plasma. The numerical examples presented show the individual roles of coupling, inertia and a resistive wall. The model was applied for the analysis of MHD observations of an ASDEX discharge. Received 4 May 1999 and Received in final form 23 July 1999     

Infrared absorption spectra of Aerosol-OT homologous sodium dialkylsulfosuccinates and the effect of crystal polymorphism on the environment of the succinate segment

A homologous series of sodium dialkylsulfosuccinates, which are straight-chain analogues of Aerosol-OT with various chain lengths (dimethyl, diethyl, dibutyl, dihexyl, diheptyl, dioctyl, didecyl, diundecyl and didodecyl), has been synthesized. In order to assign the IR bands of the CH₂ scissoring and CH deformation modes of the succinate segment, sodium dideuteratedmethylsulfosuccinate and sodium dideuteratedethylsulfosuccinate have also been synthesized. IR absorption spectra have been recorded for these mono-, di- and multihydrate samples in the solid state. In particular, IR bands in the 1250–1500 cm⁻¹ region have been compared for sodium dimethylsulfosuccinate, sodium diethylsulfosuccinate and sodium diheptylsulfosuccinate, whose crystal structures are known. The CH₂ scissoring and CH deformation modes of the succinate CH₂-CH portion strongly depend upon the environment of hydration and on the length of the hydrocarbon portions. Received: 26 April 1999 Accepted in revised form: 15 June 1999     

Direct Numerical Simulation of Liquid Films with Large Interfacial Deformation††

Liquid films are important in many industrial applications, but also from a fundamental point of view, they are important two-phase flow systems. In this paper, we develop a sharp interface/level set method for the Direct Numerical Simulation (DNS) of liquid films with large interfacial deformations, and large density ratio between the liquid and the gas phase. We use the ghost fluid method to capture the interface motion without smoothing properties across it, and adopt a maximization scheme for the implicit treatment of the viscous term in the Navier–Stokes equations. Because liquid films have very low average depth compared to the distance between waves, several innovations are required to handle solving the equations on grid structures of high aspect ratio. Two-dimensional (2D) calculations for wavy films falling down a vertical wall are presented, and good agreement is found when numerical solutions are directly compared with the experiments of Nosoko et al. [ 1 ]. Some results are also presented for falling liquid films transitioning naturally from 2D to 3D surface wave structures demonstrating the potential of the method for 3D fully coupled two-phase liquid films simulations.     

Guaranteed-quality parallel Delaunay refinement for restricted polyhedral domains

We describe a distributed memory parallel Delaunay refinement algorithm for simple polyhedral domains whose constituent bounding edges and surfaces are separated by angles between 90° to 270° inclusive. With these constraints, our algorithm can generate meshes containing tetrahedra with circumradius to shortest edge ratio less than 2, and can tolerate more than 80% of the communication latency caused by unpredictable and variable remote gather operations.

Our experiments show that the algorithm is efficient in practice, even for certain domains whose boundaries do not conform to the theoretical limits imposed by the algorithm. The algorithm we describe is the first step in the development of much more sophisticated guaranteed-quality parallel mesh generation algorithms.     

Total synthesis of (+)-erogorgiaene using lithiation-borylation methodology, and stereoselective synthesis of each of its diastereoisomers

A short (8 steps) synthesis of (+)-erogorgiaene in 44% overall yield from p-methylacetophenone is described. Key steps include lithiation/borylation-protodeboronation to build up the molecule and control the stereochemistry at C1 and C4. The C11 stereochemistry was similarly set up by using lithiation/borylation methodology. The use of a mixed, unhindered borane in the lithiation/borylation reaction proved critical to success in the reaction of the tetralone-derived carbamate to control the C4 stereochemistry. The power of the reagent controlled methodology is illustrated in the stereocontrolled synthesis of all of the diastereomers of (+)-erogorgiaene.     

Analysis of the dynamics of fuel spray using asymptotic methods: The method of integral invariant manifolds

The current research deals with the thermal explosion and ignition of a mixture of carbon and air. The size distribution of the carbon particles is taken to be continuous and is characterized by a probability density function. The chemical reaction term is presented in the Arrhenius form with variable pre-exponential factor. Transforming the new model to a dimensionless form enables us to rewrite the model in a singular perturbed system of ordinary differential equations. This form of the model enables us to apply the method of integral manifold (MIM). As a result of this method we can derive an explicit expression for the thermal explosion limit which depends on the initial probability density function. Comparing our numerical results to the analytical results, we observe that the effect of the thermal radiation is significant, especially at high temperatures, and cannot be ignored in the analysis of the phenomena of the explosion and ignition.     

What is so special about aerosol-OT? Part IV. Phenyl-tipped surfactants

Properties are reported for new phenyl-tipped anionic surfactants, which are aromatic chain relatives of the normal aliphatic aerosol-OT (AOT, sodium bis(2-ethyl-1-hexyl)sulfosuccinate). Variations in chain length and branching with these aromatic surfactants have important effects on aqueous and water-in-oil (w/o) microemulsion phase properties. In dilute aqueous systems, chain structure affects the cmc and surface tension behavior: compared to linear chain analogues, the branched-chain surfactants display lower surface tensions but also reduced packing as measured by molecular area at the cmc a(cmc). Owing to the phenyl-tipped structure, water-in-oil microemulsions were stabilized with aromatic toluene as an oil but not with aliphatic heptane; the latter is commonly used with normal AOT. Contrast variation small-angle neutron scattering (SANS) was used to characterize the microemulsion aggregates and adsorbed films. These SANS data show that water-in-toluene microemulsions stabilized by aromatic-AOTs contain mildly polydisperse spherical nanodroplets of similar structure to those found in systems containing normal AOT. Molecular areas at the air-water and toluene-water interfaces are found to be of similar magnitude and follow a trend that correlates with variations in surfactant chain structure. The new results with aromatic surfactants build on extensive studies of aliphatic AOT analogues (Nave, S.; Eastoe, J.; Penfold, J. Langmuir 2000, 16, 8733. Nave, S.; Eastoe, J.; Heenan, R. K.; Steytler, D.; Grillo, I. Langmuir 2002, 16, 8741. Nave, S.; Eastoe, J.; Heenan, R. K.; Steytler, D.; Grillo, I. 2002, 18, 1505), suggesting that the versatility of normal AOT originates from an optimized head and chain spacer group rather than from any specific effects of the 2-ethyhexyl chain structure.