Predictive capability of RANS and LES models to calculate incipient cavitation of water in a step nozzle is assessed. The RANS models namely, Realizable k-ɛ, SST k-ω and Reynolds Stress Model did not predict any cavitation, due to the limitation of RANS models to predict the low pressure vortex cores. LES WALE model was able to predict the cavitation by capturing the shear layer instability and...

The principal permanent rank characteristic sequence is a binary sequence r0r1 · · · rn where rk = 1 if there exists a principal square submatrix of size k with nonzero permanent and rk = 0 otherwise, and r0 = 1 if there is a zero diagonal entry. A characterization is provided for all principal permanent rank sequences obtainable by the family of nonnegative matrices as well as the family of no...

ceton, NJ The pair correlation function g2ðrÞ provides a basic geometric descriptor for man systems. It must obey two necessary conditions: (i) non-negativity for all distances non-negativity of its associated structure factor SðkÞ for all k. Here we utilize an stochastic construction algorithm for particle configurations to establish conditions (i) and (ii) are also sufficient, i.e., g2ðrÞ is ...

The number |K| of non-isotopic framed knots that correspond to a given unframed knot K ⊂ S is infinite. This follows from the existence of the self-linking number slk of a zerohomologous framed knot. We use the approach of Vassiliev-Goussarov invariants to construct “affine self-linking numbers” that are extensions of slk to the case of nonzerohomologous framed knots. As a corollary we get that...

Introduction The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field Q of rational numbers. We then say that G is realizable over Q. This problem goes back to Hilbert [Hil] who realized Sn and An over Q. Many more groups have been realized over Q since 1892. For example, Shafarevich [Sha] finished in 1958 the work started by Scholz 1936 [Slz] and Rei...

Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras be a set of nonnegative similarity. Also we find all realizable dimensions two semi-commuting matrices. The last result provides solution problem posed M. Kandi?, K. Šivic (2017) [13].

For any simple graph H, let σ(H,n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph. Let Fk denote the friendship graph on 2k+1 vertices, that is, the graph of k triangles intersecting in a single vertex. In this paper, for n sufficiently large, σ(...