An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

Signal recognition particle prevents N-terminal processing of bacterial membrane proteins.

Bacterial proteins are synthesized with an N-formylated amino-terminal methionine, and N-formylated peptides elicit innate-immunity responses against bacterial infections. However, the source of these formylated peptides is not clear, as most bacterial proteins are co-translationally deformylated by peptide deformylase. Here we develop a deformylation assay with translating ribosomes as substrates, to show that the binding of the signal recognition particle (SRP) to signal sequences in nascent proteins on the ribosome prevents deformylation, whereas deformylation of nascent proteins without signal sequence is not affected. Deformylation and its inhibition by SRP are not influenced by trigger factor, a chaperone that interacts with nascent chains on the ribosome. We propose that bacterial inner-membrane proteins, in particular those with N-out topology, can retain their N-terminal formyl group during cotranslational membrane insertion and supply formylated peptides during bacterial infections