A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut‐cell/ghost‐cell method is used together with a direction‐splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second‐order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd.     

Cohomology of normal bundles of special rational varieties

Abstract

We give a new method for calculating the cohomology of the normal bundles over rational varieties which are smooth projections of Veronese embeddings. The method can be used also when the projections are not smooth, in this case it provides information about the critical locus of maps between projective spaces.     

On the viability of local criteria for chaos

Recently, Zscze¸sny and Dobrowolski proposed a geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor sufficient for the occurrence of chaos. To this purpose, we introduce a class of chaotic two-dimensional systems with Gaussian curvature everywhere positive and, hence, locally stable. We show explicitly that chaotic behavior arises from some trajectories that reach certain non-convex parts of the boundary of the effective Riemannian manifold. Our result questions, once more, the viability of local, curvature-based criteria to predict chaotic behavior.     

Van Geemen's families of lines on special quintic threefolds

We study the families of lines on the quintic threefolds of the pencilx ₀ ⁵ +x ₁ ⁵ +x ₂ ⁵ +x ₃ ⁵ +x ₄ ⁵ -5tx ₀ x ₁ x ₂ x ₃ x ₄=0. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone. Partially supported by funds M.P.I.     

A convenient synthetic approach to alpha-amino-beta-lactam synthesis promoted by phenyl dichlorophosphate reagent

The ready and economical phenyl dichlorophosphate, in contrast to many reagents developed for activating carboxyl groups for the beta-lactam synthesis, is shown to be very efficient for the synthesis of alpha-vinylamino-beta-lactams from Dane salts and Schiff bases. Some observations toward the scope of the method are also briefly described. The interaction of acetic acids with ethanolimines afforded beta-lactams and/or oxazolidines according to the synthetic methodology used.     

On a family of models of cell division cycle

The aim of this work is to generalize and study a model of cell division cycle proposed recently by Zheng et al. [Zheng Z, Zhou T, Zhang S. Dynamical behavior in the modeling of cell division cycle. Chaos, Solitons & Fractals 2000;11:2371–8]. Here we study the qualitative properties of a general family to which the above model belongs. The global asymptotic stability (GAS) of the unique equilibrium point E (idest of the arrest of cell cycling) is investigated and some conditions are given. Hopf’s bifurcation is showed to happen. In the second part of the work, the theorems given in the first part are used to analyze the GAS of E and improved conditions are given. Theorem on uniqueness of limit cycle in Lienard’s systems are used to show that, for some combination of parameters, the model has GAS limit cycles.     

Matrix valued Jacobi polynomials

For every value of the parameters α,β>−1 we find a matrix valued weight whose orthogonal polynomials satisfy an explicit differential equation of Jacobi type.     

BAL resin for the preparation of secondary amines

Although amino acids anchored through the amino function to BAL resins can not easily be released from the resin by treatment with neat trifluoroacetic acid, we have shown that secondary amines can be obtained from BAL resins using trifluoroacetic acid solutions.