Abstract Simulating viscoelastic fluids at high Weissenberg numbers is challenging due to numerical instabilities, especially in flows with singularities. The natural stress formulation (NSF) is a robust technique designed to overcome these issues. Separately, the generalized Phan-Thien and Tanner (gPTT) model offers enhanced rheological flexibility by using the Mittag-Leffler function. This work develops and validates an in-house, finite-difference NSF-gPTT solver. The method is first validated against the traditional HiG-Flow solver in channel flow and 1:4 sudden expansion geometries, showing excellent agreement for velocity/stress profiles and vortex reattachment lengths. We then apply the framework to the L-shaped channel benchmark, which features a re-entrant corner. The NSF-gPTT solver remains stable and accurate up to a Weissenberg number ( Wi ) of 100. The results reveal a counter-intuitive decrease in the peak of the first normal stress difference ( $$N_1$$ N 1 ) at the corner with increasing Wi , a direct result of the gPTT model’s shear-thinning. Furthermore, we demonstrate the NSF’s stability by showing that at $$Wi=100$$ W i = 100 , the internal conformation tensor trace grows to $$\approx 100$$ ≈ 100 , while the elastic stress trace remains small ( $$\approx 0.48$$ ≈ 0.48 ). This study demonstrates that the NSF-gPTT formulation is a stable and powerful tool for probing complex viscoelastic phenomena in high- Wi regimes.

Abstract Bipolar fuzzy relation equations with join-irreducible right-hand side have been recently studied in the literature, considering a complete distributive residuated lattice endowed with an involutive negation as the underlying algebraic structure. This manuscript elevates the study of these equations to the multi-adjoint paradigm, by significantly weakening the underlying algebraic structure and allowing the use of conjunctions of adjoint pairs instead of triangular norms. Specifically, the resolution of systems of bipolar multi-adjoint relation equations with join-irreducible right-hand side is investigated, the whole solution set is determined, paying particular attention to maximal and minimal solutions, and different examples illustrating the theoretical development are given.

Abstract We study the inverse problem for singular, irreducible, symmetric M -matrices that consists in characterizing those for which the group inverse is again an M -matrix. We solve the problem for a structured class of such matrices arising from star graphs by employing both matrix-theoretic tools and potential theory on networks. Our approach yields explicit criteria for the M -property of the group inverse in terms of conductances and Doob potentials, and provides a constructive procedure to obtain such families of matrices with the desired property.