Search

Boij-Söderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring S = k [ x 1 , ... , x n ]. We posit that a similar combinatorial description can be given for analogous numerical invariants of graded differential S-modules , which are natural generalizations of chain complexes. We prove several results that lend evidence in support of this conjecture, including a categorical pairing between the derived categories of graded differential S -modules and coherent sheaves on P n − 1 and a proof of the conjecture in the case where S = k [ t ]. [ABSTRACT FROM AUTHOR]

Three-dimensional Direct Numerical Simulations (DNS) of turbulent premixed lean H 2 -air flames are performed for different equivalence ratios and initial turbulence intensities to investigate the influence of differential diffusion on the invariants of the velocity gradient tensor and local flow topologies. It is found that the effects of differential diffusion strengthen with a decrease in equivalence ratio. This difference results in more frequent super-adiabatic temperatures and higher positive dilatation rates for smaller values of equivalence ratio, having a significant impact on the flow topology distributions and their contributions to the scalar-turbulence interaction and vortex-stretching terms. The topologies associated with positive dilatation rates tend to occur at the curvatures associated with super-adiabatic temperatures for highly lean H 2 -air premixed flames. However, this tendency weakens with increasing equivalence ratio. These findings suggest that the chemical timescale must be accounted for in the modelling of viscous and scalar dissipation rates in lean hydrogen-air premixed flames. • Statistically planar flame DNS of equivalence ratios of 0.4 and 0.7 considered. • Effects of equivalence ratio on flow topology distributions analysed. • The non-unity Lewis number effects strengthen with deceasing equivalence ratio. • Dilatation effects strengthen with deceasing equivalence ratio. • Topologies specific to positive dilatation strengthen for small equivalence ratio. [ABSTRACT FROM AUTHOR]