A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation

We present a numerical investigation of a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression of limestones under the attack of SO₂, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as well as some examples of the numerical behavior of the solutions.     

Numerical algorithms for simulations of a traffic model on road networks

We introduce a simulation algorithm based on a fluid-dynamic model for traffic flows on road networks, which are considered as graphs composed by arcs that meet at some junctions. The approximation of scalar conservation laws along arcs is made by three velocities Kinetic schemes with suitable boundary conditions at junctions. Here we describe the algorithm and we give an example.     

The Dirichlet problem for the Laplace equation in a starlike domain of a Riemann surface

We consider the Dirichlet problem for the Laplace equation in a starlike domain, i.e. a domain which is normal with respect to a suitable polar co-ordinates system. Such a domain can be interpreted as a non-isotropically stretched unit circle. We write down the explicit solution in terms of a Fourier series whose coefficients are determined by solving an infinite system of linear equations depending on the boundary data. Numerical experiments show that the same method works even if the considered starlike domain belongs to a two-fold Riemann surface.     

Double-cut of scattering amplitudes and Stokes' Theorem

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.     

Last ten years (2008–2018) of chiral ligand‐exchange chromatography in HPLC: An updated review

Chiral ligand‐exchange chromatography is one of the elective strategies for the direct enantioresolution of small chelating compounds: amino acids, diamines, amino alcohols, diols, small peptides, etc. Unlike other methods, the interaction between chiral selector and analyte enantiomers is mediated by a cation, thus producing diastereomeric ternary complexes. Two main approaches are conventionally applied in chiral ligand‐exchange chromatography. The first relies upon chiral stationary phases where the chiral selector is either covalently immobilized or physically adsorbed onto suitable packing materials (coated phases). In the second approach, chiral molecules are added to the eluent, thus generating chiral eluent systems. Among the advantages of chiral ligand‐exchange chromatography, the generation of UV/vis‐active metal complexes, and the use of commercially available or easy‐to‐synthesize chiral selectors, in combination to rather inexpensive achiral columns for coated phases and chiral eluents, are noteworthy. Besides amino acids and amino alcohols, other species have proven suitable for chiral ligand‐exchange chromatography applications. Recently, the use of either chiral ionic liquids or micellar liquid chromatography systems as well as the successful off‐column formation of diastereomeric complexes have expanded the selectivity profiles and application fields. All of these issues are touched in the review, shedding light to the contributions appeared in the last decade.     

On Relaxation Hyperbolic Systems Violating the Shizuta–Kawashima Condition

In this paper, we start a general study on relaxation hyperbolic systems which violate the Shizuta–Kawashima ([SK]) coupling condition. This investigation is motivated by the fact that this condition is not satisfied by various physical systems, and almost all the time in several space dimensions. First, we explore the role of entropy functionals around equilibrium solutions, which may not be constant, proposing a stability condition for such solutions. Then we find strictly dissipative entropy functions for one dimensional 2 × 2 systems which violate the [SK] condition. Finally, we prove the existence of global smooth solutions for a class of systems such that condition [SK] does not hold, but which are linearly degenerated in the non-dissipative directions.     

Sharp non-resonance conditions for periodically perturbed Liénard systems

Archiv der Mathematik -     

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saito?-Mun?oz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.