Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models

We measure the critical exponents of the three dimensional Gross-Neveu model with two four-component fermions. The exponents are inferred from the scaling behaviour of observables on different lattice sizes. We also calculate the exponents, through a second order epsilon-expansion around 4d, for the three dimensional Higgs-Yukawa model, which is expected to be in the same universality class and we find that the exponents agree. We conclude that the equivalence of the two models remains valid in 3d at fixed small N_f values.Comment: 14 Latex pages 8 PSfigures included at the end,BI-TP-93/31,AZPH-TH/93-19,SPhT 93/0

spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models

The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site complete graph extended with on-site repulsion is obtained from the underlying spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic ground state is realized for 1 and N+1 electrons only. We identify the large density of states to be responsible for the suppression of the ferromagnetic state and argue that a similar situation is encountered in the Kagome, pyrochlore, and other lattices with flat bands in their one-particle density of states.Comment: 7 pages, 1 figur

A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores

Effect of antimony on the eutectic reaction of heavy section spheroidal graphite castings

There is a strong demand for heavy section castings made of spheroidal graphite with a fully ferritic matrix, e.g. for manufacturing hubs for windmills. Such castings with slow solidification process are prone to graphite degeneration that leads to a dramatic decrease of the mechanical properties of the cast parts. Chunky graphite is certainly the most difficult case of graphite degeneracy, though it has long been known that the limited and controlled addition of antimony may help eliminate it. The drawback of this remedy is that too large Sb additions lead to other forms of degenerate graphite, and also that antimony is a pearlite promoter. As part of an investigation aimed at mastering low level additions to cast iron melts before casting, solidification of large blocks with or without Sb added was followed by thermal analysis. Comparison of the cooling curves and of the microstructures of these different castings gives suggestions to understand the controlling nucleation and growth mechanisms for chunky graphite cells

Thermal analysis applied to estimation of solidification kinetics of Al–Si aluminium alloys

Evaluation of solidification kinetics by thermal analysis is a useful tool for quality control of Al–Si melts before pouring provided it is rapid and highly reproducible. Series of thermal analysis records made with standard cups are presented that show good reproducibility. They are evaluated using a Newton’s like approach to get the instantaneous heat evolution and from it solidification kinetics. An alternative way of calculating the zero line is proposed which is validated by the fact that the latent heat of solidification thus evaluated is within 5% of the value calculated from thermodynamic data. Solidification kinetics was found highly reproducible provided appropriate experimental conditions were achieved: high enough casting temperature for the cup to heat up to the metal temperature well before solidification starts; and equal and homogeneous temperatures of the metal and of the cup at any time in the temperature range used for integration

Phase equilibria and phase transformations in the Ti-rich corner of the Fe-Ni-Ti system

While the main features of the Fe-Ni-Ti system are well known at low Ti content, literature review of the Ti-rich corner revealed inconsistencies between experimental reports. This investigation presents new experimental results, defined to remove the uncertainties concerning melting behavior and solid-state phase equilibria of the (Ni,Fe)Ti2 phase with the adjacent (Fe,Ni)Ti (B2, CsCl-type structure) and Beta-Ti (A2, W-type) phases. Six samples have been prepared and examined by differential thermal analysis performed in yttria and alumina crucibles, and by scanning electron microscopy in the as-cast state as well as equilibrated at 900°C

Tidal instability in a rotating and differentially heated ellipsoidal shell

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows