Growth Rates and Explosions in Sandpiles

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ? ^d . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h≤2d?2, the diameter of the set of sites that topple has order n ^1/d . This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification. We can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d?1. On the other hand, we show that if the background height 2d?2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random, then adding finitely many particles creates an explosion (a sandpile that never stabilizes).     

Numerical simulation of flow-induced fiber orientation using normalization of second moment

A normalization scheme for the numerical solution of the moment approximation equation in fiber suspension flows is presented. Here, normalization refers to rescaling the trace of the second moment tensor to unity at each time step. The equivalence between the normalization scheme and the quadratic closure model is analytically proved. The performance of the scheme is investigated in simple shear flow with respect to the quadratic and hybrid closures, and a stochastic Monte-Carlo simulator that provides exact solution. The proposed scheme is a computationally efficient alternative to the quadratic closure: it performs equally well and is more efficient regarding computational time.     

Dissociation of Multisubunit Protein–Ligand Complexes in the Gas Phase. Evidence for Ligand Migration

The results of collision-induced dissociation (CID) experiments performed on gaseous protonated and deprotonated ions of complexes of cholera toxin B subunit homopentamer (CTB₅) with the pentasaccharide (β-D-Galp-(1→3)-β-D-GalpNAc-(1→4)[α-D-Neu5Ac-(2→3)]-β-D-Galp-(1→4)-β-D-Glcp (GM1)) and corresponding glycosphingolipid (β-D-Galp-(1→3)-β-D-GalpNAc-(1→4)[α-D-Neu5Ac-(2→3)]-β-D-Galp-(1→4)-β-D-Glcp-Cer (GM1-Cer)) ligands, and the homotetramer streptavidin (S₄) with biotin (B) and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(biotinyl) (Btl), are reported. The protonated (CTB₅ + 5GM1)ⁿ⁺ ions dissociated predominantly by the loss of a single subunit, with the concomitant migration of ligand to another subunit. The simultaneous loss of ligand and subunit was observed as a minor pathway. In contrast, the deprotonated (CTB₅ + 5GM1)^n- ions dissociated preferentially by the loss of deprotonated ligand; the loss of ligand-bound and ligand-free subunit were minor pathways. The presence of ceramide (Cer) promoted ligand migration and the loss of subunit. The main dissociation pathway for the protonated and deprotonated (S₄ + 4B)^n+/– ions, as well as for deprotonated (S₄ + 4Btl)^n– ions, was loss of the ligand. However, subunit loss from the (S₄ + 4B)ⁿ⁺ ions was observed as a minor pathway. The (S₄ + 4Btl)ⁿ⁺ ions dissociated predominantly by the loss of free and ligand-bound subunit. The charge state of the complex and the collision energy were found to have little effect on the relative contribution of the different dissociation channels. Thermally-driven ligand migration between subunits was captured in the results of molecular dynamics simulations performed on protonated (CTB₅ + 5GM1)¹⁵⁺ ions (with a range of charge configurations) at 800 K. Notably, the migration pathway was found to be highly dependent on the charge configuration of the ion. The main conclusion of this study is that the dissociation pathways of multisubunit protein–ligand complexes in the gas phase depend, not only on the native topology of the complex, but also on structural changes that occur upon collisional activation.