Renormalisation of q-Regularised Multiple Zeta Values

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the quasi-shuffle product are obtained using an Hopf-algebraic Birkhoff factorisation together with minimal subtraction.     

Essential countability of treeable equivalence relations

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E   is essentially countable if and only if there is no continuous embedding of _E1${\mathbb{E}}_1$ into E. Our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations, and allow us to show that up to continuous Kakutani embeddability, there is a minimum Borel function which is not essentially countable-to-one.     

Direct Numerical Simulations of Hotspot-induced Ignition in Homogeneous Hydrogen-air Pre-mixtures and Ignition Spot Tracking

A systematic study relying on Direct Numerical Simulations (DNS) of premixed hydrogen-air mixtures has been performed to investigate the hotspot ignition characteristics and ignition probability under turbulent conditions. An ignition diagram is first obtained under laminar conditions by a parametric study. The impact of turbulence intensity on ignition delays and ignition probability is then quantified in a statistically-significant manner by repeating a large number of independent DNS realizations. By tracking in a Lagrangian frame the ignition spot, the balance between heat diffusion and heat of chemical reaction is observed as function of time. The evolution of each chemical species and radicals at the ignition spot is checked and the mechanism leading to ignition or misfire are analyzed. It is observed that successful ignition is mostly connected to a sufficient build-up of a HO₂ pool, ultimately initiating production of OH. Turbulence always delays ignition, and ignition probability goes to zero at sufficiently high turbulence intensity when keeping temperature and size of the initial hotspot constant.     

Turbulence Models and Large Eddy Simulations Applied to Ascending Mixed Convection Flows

Coolant flows in the cores of current gas-cooled nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be significantly modified from the forced convection condition by the action of buoyancy, and the thermal-hydraulic regime is no longer one of pure forced convection. These modifications are associated primarily with changes to the turbulence structure. Flow laminarization may occur, and in that event heat transfer rates may be as low as 40% of those in the corresponding forced convection case. The present work is concerned with the modelling of such ??mixed?? convection flows in a vertical heated pipe. All fluid properties are assumed to be constant and buoyancy is accounted for within the Boussinesq approximation. Six different Eddy Viscosity Models (EVMs) are examined against experimental measurements and the direct numerical simulation (DNS) data of You et?al. (Int J Heat Mass Transfer 46:1613?C1627, 2003). The EVMs selected for study embody distinct physical refinements with respect to the parent high-Reynolds-number k-?? model. Large Eddy Simulations employing the classical Smagorinsky sub-grid-scale model are also presented. It is found that the early EVM scheme of Launder and Sharma (1974) is the turbulence model in the closest agreement with direct simulation results for the ratio of mixed-to-forced convection Nusselt number, Nu/Nu ₀; the model in the poorest accord with the DNS data is a k-??-SST formulation. However, in relation to comparisons with both numerical and experimental data for forced convection Nusselt number, Nu ₀, the present work reveals that some of the more recent models perform better than the Launder-Sharma scheme. No single scheme is in consistently close agreement with the numerical simulation flow profiles.     

Covalently Trapped Triarylamine-Based Supramolecular Polymers

C₃-Symmetric triarylamine trisamides (TATAs), decorated with three norbornene end groups, undergo supramolecular polymerization and further gelation by π–π stacking and hydrogen bonding of their TATA cores. By using subsequent ring-opening metathesis polymerization, these physical gels are permanently crosslinked into chemical gels. Detailed comparisons of the supramolecular stacks in solution, in the physical gel, and in the chemical gel states, are performed by optical spectroscopies, electronic spectroscopies, atomic force microscopy, electronic paramagnetic resonance spectroscopy, X-ray scattering, electronic transport measurements, and rheology. The results presented here clearly evidence that the core structure of the functional supramolecular polymers can be precisely retained during the covalent capture whereas the mechanical properties of the gels are concomitantly improved, with an increase of their storage modulus by two orders of magnitude.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

Direct angle resolved photoemission spectroscopy and superconductivity of strained high-T c films

Since 1997 we systematically perform direct angle resolved photoemission spectroscopy (ARPES) on in-situ grown thin (<30 nm) cuprate films. Specifically, we probe low-energy electronic structure and properties of high-T _c superconductors (HTSC) under different degrees of epitaxial (compressive vs. tensile) strain. In overdoped and underdoped in-plane compressed (the strain is induced by the choice of substrate) ≈15 nm thin La_{2 − x} Sr _x CuO₄ (LSCO) films we almost double T _c to 40 K, from 20 K and 24 K, respectively. Yet the Fermi surface (FS) remains essentially two-dimensional. In contrast, ARPES data under tensile strain exhibit the dispersion that is three-dimensional, yet T _c drastically decreases. It seems that the in-plane compressive strain tends to push the apical oxygen far away from the CuO₂ plane, enhances the two-dimensional character of the dispersion and increases T _c, while the tensile strain acts in the opposite direction and the resulting dispersion is three-dimensional. We have established the shape of the FS for both cases, and all our data are consistent with other ongoing studies, like EXAFS. As the actual lattice of cuprates is like a ‘Napoleon-cake’, i.e. rigid CuO₂ planes alternating with softer ‘reservoir’, that distort differently under strain, our data rule out all oversimplified two-dimensional (rigid lattice) mean field models. The work is still in progress on optimized La-doped Bi-2201 films with enhanced T _c.      

Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.