Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric

The new Italian SIDAPA Baseline Series for patch testing (2023): an update according to the new regulatory pathway for contact allergens

Allergic contact dermatitis (ACD) is a common inflammatory skin disease caused by delayed hypersensitivity to chemical and biotic contact allergens. ACD significantly affects the patients' quality of life negatively impacting both occupational and non-occupational settings. Patch testing is the gold standard diagnostic in vivo test to precise the ACD etiology and to correctly perform prevention. According to the Italian Medicines Agency (AIFA) legislative decree no. 178 of 29th May 1991, allergens are defined as medicines and therefore they are subject to strict regulation. In 2017, AIFA (decree no. 2130/2017) started a procedure to regulate contact allergens on the Italian market and actually the contact allergens temporarily authorized are reported in AIFA decree no. 98/2022, valid until November 2023. The availability on the market of contact allergens to diagnose ACD and continuous updating on the basis of new epidemiological trends are mandatory, jointly with the continuous update of the baseline and integrative series for patch testing. For this reason, the scientific community represented in Italy by the Skin Allergies Study Group of SIDeMaST (Italian Society of Dermatology and Venereology) and SIDAPA (Italian Society of Allergological, Occupational and Environmental Dermatology) are constantly working, in close relationship with the European scientific communities with large expertise in this important sector of the modern Dermatology. Herein, we report the setting up of regulatory legislation by AIFA and the new Italian Adult Baseline Series for patch testing