Computer-Assisted Methods for the Study of Stationary Solutions in Dissipative Systems, Applied to the Kuramoto–Sivashinski Equation

We develop some computer-assisted techniques for the analysis of stationary solutions of dissipative partial differential equations, of their stability, and of their bifurcation diagrams. As a case study, these methods are applied to the Kuramoto–Sivashinski equation. This equation has been investigated extensively, and its bifurcation diagram is well known from a numerical point of view. Here, we rigorously describe the full graph of solutions branching off the trivial branch, complete with all secondary bifurcations, for parameter values between 0 and 80. We also determine the dimension of the unstable manifold for the flow at some stationary solution in each branch.     

Bifurcation Instability in Linear Elasticity with the Constraint of Local Injectivity

There are problems in linear elasticity theory whose corresponding deformations, usually associated with singular stress fields, are open to question because they are not one-to-one and predict self-intersection. Recently, a theory has been advanced to handle such situations, which consists in minimizing the quadratic energy functional of linear elasticity subject to the constraint of local injectivity. In particular, the Jacobian of the deformation gradient is required to be not less than an arbitrarily small positive quantity, and, thus, the local orientation is preserved. Here, this theory is applied to the classical Lekhnitskii problem of an elastic aelotropic circular disk which is loaded on its boundary by a uniform radial pressure. Without the injectivity constraint, this classical linear problem has a unique solution. This example, with the injectivity constraint, already has been considered in previous works, but radial symmetry was assumed in order to reduce the problem from 2D to 1D. Here, making use of an interior penalty formulation, a numerical scheme is implemented that solves a full 2D problem. Remarkably, it is shown that there are values of the material moduli for which the minimal potential energy solution is no longer symmetric, producing a strong azimuthal shear and nominally a 180° rotation of an internal central core of the disk. Although the elastic strain energy is quadratic and convex, the strongly nonlinear character of the constraint allows for bifurcation instabilities. We gratefully acknowledge the partial support of the Minnesota Supercomputing Institute and the Italian “Ministero per l’Università e la Ricerca Scientifica” under the program PRIN 2005 “Affidabilità di elementi in vetro strutturale: indagini teoriche e sperimentali sulla risposta termo-meccanica del materiale e di strutture trasparenti di tipo innovativo”. R.F. gratefully acknowledges the Department of Civil and Environmental Engineering at the Politecnico di Bari, Italy, for their kind hospitality and support during his visit of 2006. We appreciate the helpful comments and suggestions of Paolo Podio-Guidugli on an earlier draft of this work.     

Hyperbranched Polymers in Cationic UV Curing

Summary: A wide range of hyperbranched polymers (HBP) was synthesized and investigated as additives in cationic photopolymerization of epoxy systems. The HBP were inserted into the polymeric network either by a copolymerization or through a chain transfer reaction involving the phenolic hydroxyl groups. By varying the type and concentration of HBP a modification of the bulk properties of photocured films was induced. An increase of toughness properties together with a flexibilization was obtained without affecting the processability and the viscosity of the photocurable mixture. In the presence of fluorine-containing HBP, a surface modification was induced.     

Chemical analysis of norrisolide-induced Golgi vesiculation

The chemical origin of the norrisolide-induced irreversible Golgi vesiculation was studied using a variety of norrisolide probes. This natural product was found to bind to a receptor on the Golgi membranes using the perhydroindane core fragment as the recognition element. The acetylated gamma-lactol-gamma-lactone side chain of norrisolide is essential for the irreversible Golgi vesiculation and can be replaced by other electrophilic motifs without loss of biological function. In particular, compound 10 reproduces the cellular phenotype of the natural product.     

A Variational Model for Plastic Slip and Its Regularization via Γ-Convergence

A variational model is presented able to interpret the onset of plastic deformations, here modeled as displacement jumps occurring along slip surfaces at constant yielding stress. The corresponding strain energy functional, leading to a free-discontinuity problem set in the space of SBV functions, is then approximated by a sequence of regularized elliptic functionals following the seminal work by Ambrosio and Tortorelli (Commun. Pure Appl. Math. 43, 999–1036, 1990) within the framework of Γ-convergence. Comparisons between the results obtainable with the free-discontinuity model and its regularized approximation, in terms of stability of the pure elastic phase, irreversibility of plastic slip and response under unloading, are presented, in general, for the 2-D case of antiplane shear and exemplified, in particular, for the 1-D case.     

Time-discretization and global solution for a doubly nonlinear Volterra equation

This note addresses the analysis of an abstract doubly nonlinear Volterra equation with a nonsmooth kernel and possibly unbounded and degenerate operators. By exploiting a suitable implicit time-discretization technique, we obtain the existence of a global strong solution. As a by-product, the discrete scheme is proved to be conditionally stable and convergent.     

Characterization of phospho-proteins in bovine and buffalo caseins using atmospheric pressure ionization mass spectrometry

The specific bovine and buffalo caseins have been characterized with the aim of using atmospheric pressure ionization mass spectrometry as an alternative to electrophoretic and immunological methods in the detection of the fraudulent addition of bovine milk to buffalo milk used in the production of speciality cheeses.     

Novel squalene-hopene cyclase inhibitors derived from hydroxycoumarins and hydroxyacetophenones

Squalene-hopene cyclase (SHC) is a useful model enzyme for predicting molecular interactions with oxidosqualene cyclase (OSC). Structure--activity relationships were investigated for numerous coumarin-derived inhibitors of SHC, and structural simplifications are suggested. Both umbelliferone and 2,4-dihydroxyacetophenone provide convenient starting nuclei for the design of SHC inhibitors. Derivatives bearing an omega-epoxyfarnesyl moiety or just a plain alkyl chain showed an inhibitory effect on a recombinant SHC from Alicyclobacillus acidocaldarius expressed in Escherichia coli.     

Nature optimizes the swirling flow in the human left ventricle

The asymmetry of the blood flow in the human left ventricle is commonly assumed to facilitate the following ejection of blood in the primary circulation. The intraventricular flow is here studied by the numerical solution of the governing equations written in a prolate spheroid geometry with moving walls. The physiological parameters are taken from pediatric clinical data; then, the entering jet is artificially displaced to modify the asymmetry of the flow. The analysis of flow patterns confirms that the physiological case looks to best comply with the transition from the filling to the ejection phase. The flow energy dissipation is found to be minimized about the physiological conditions. An unnatural asymmetry, as given by cardiac diseases or valvular replacement, could reduce the efficiency of the heart pump by over 10%, thus augmenting the work required by the cardiac muscle.