A Class of Non-associated Materials: n-Monotone Materials—Hooke’s Law of Elasticity Revisited

Generalized Standard Materials are governed by maximal cyclically monotone operators and modeled by convex potentials. Géry de Saxcé’s Implicit Standard Materials are modeled by biconvex bipotentials. We analyze the intermediate class of n-monotone materials governed by maximal n-monotone operators and modeled by Fitzpatrick’s functions. Revisiting the model of elastic materials initiated by Robert Hooke, and insisting on the linearity, coaxiality and monotonicity properties of the constitutive law, we illustrate that Fitzpatrick’s representation of n-monotone operators coming from convex analysis provides a constructive method to discover the best bipotential modeling a n-monotone material. Giving up the symmetry of the linear constitutive laws, we find out that n-monotonicity is a relevant criterion for the materials characterization and classification.     

Direct Oxidation of Propylene with Molecular Oxygen Over Ti-Modified Sulfated Zirconia Catalyst, 2. In Situ Diffuse Reflectance FT-IR Study

During the reaction of propylene with O₂, in situ Diffuse Reflectance FT-IR measurements were performed over Ti-modified SZ and SZ catalysts. Without O₂, the main bands characteristic of (branched) hydrocarbons, formed by oligomerization leading to, finally, carbonaceous residue, appeared within the range of 3900-2750 cm^-1, which was affected by the bands of surface OH groups. Investigation of these IR bands showed the role of molecular oxygen not only to limit the formation of carbonaceous species on the catalyst surface, but also to form oxygenates and these findings were in good agreement with the results of catalytic reaction.     

Modelling by a planar map: Lyapunov-type numbers in the presence of spiral points

Lyapunov-type numbers are usually defined for diffeomorphisms with a smooth invariant manifold. We consider here the case of a planar diffeomorphism with an invariant curve that contains spiral points. The limits defining the Lyapunov-type numbers are shown to exist. Numerical results for the delayed logistic map illustrate the analysis.     

Increasing peptide identification in tandem mass spectrometry through automatic function switching optimization

Comprehensive proteomic studies that employ MS directed peptide sequencing are limited by optimal peptide separation and MS and tandem MS data acquisition routines. To identify the optimal parameters for data acquisition, we developed a system that models the automatic function switching behavior of a mass spectrometer using an MS-only dataset. Simulations were conducted to characterize the number and the quality of simulated fragmentation as a function of the data acquisition routines and used to construct operating curves defining tandem mass spectra quality and the number of peptides fragmented. Results demonstrated that one could optimize for quality or quantity, with the number of peptides fragmented decreasing as quality increased. The predicted optimal operating curve indicated that significant improvements can be realized by selecting the appropriate data acquisition parameters. The simulation results were confirmed experimentally by testing 10 LC MS/MS data acquisition parameter sets on an LC-Q-TOF-MS. Database matching of the experimental fragmentation returned peptide scores consistent with the predictions of the model. The results of the simulations of mass spectrometer data acquisition routines reveal an inverse relationship between the quality and the quantity of peptide identifications and predict an optimal operating curve that can be used to select an optimal data acquisition parameter for a given (or any) sample.     

Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

A dynamical approach to symplectic and spectral invariants for billiards

The Lazutkin parameter for curves which are invariant under the billiard ball map is viewed symplectically in a way which makes it analogous to the sum of the values of a generating function over a closed orbit. This leads to relations among lengths of closed geodesics, lengths of invariant curves for the billiard map, rotation numbers, and the Lazutkin parameter. These relations establish the Birkhoff invariant and the expansion for the lengths of invariant curves in terms of the Lazutkin parameter as symplectic and spectral invariants (for the Dirichlet spectrum) and provide invariants which characterize a family of ellipses among smooth curves with positive curvature. Geodesic flow on a bounded planar region gives rise to several geometric objects among which are closed reflected geodesics and invariant curves-closed curves whose tangents are invariant under reflection at the boundary. On a bounded domain, the map that assigns to each geodesic segment its successor after reflection at the boundary is called the billiard ball map and its dual (in the cotangent bundle for the boundary) is called the boundary map.     

Balancing aspects of numerical dissipation,dispersion, and aliasing in time-accurate simulations

The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.     

Location of the shoulder joint centre and identification of the body segment parameters

This paper presents two methods for human body modelisation: the location of the joint centre and the identification of the body segment inertial parameters. These methods require only tools usually used in biomechanics (force plate and motion analysis system) and allow to have precise and personal parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform convergence of nonparametric regressions in competing risk models with right censoring

We consider, in the presence of covariates, non-independent competing risks that are subject to right censoring. We define a nonparametric estimator of the incident regression function through the generalized product-limit estimator of the conditional censorship distribution function. Under suitable conditions, we establish the almost sure uniform convergence of those estimators with an appropriate rate.     

Rhodopsin in a new model bilayer membrane

In search of a planar and uniform model membrane presenting a wide interaction-surface for the study of photobiological processes, we have succeeded in depositing lipid bilayer on a single face of a porous disc. Using a method that combines the Langmuir-Blodgett dipping and the touching procedures, a symmetrical or asymmetrical bilayer membrane has been obtained. The illumination of rhodopsin-containing membranes appears to increase the permeability to K⁺, Na⁺, and Ca²⁺ with a high selectivity for Ca²⁺. The bilayer adsorption on the porous disc is discussed and an attempt is made to explain the failure of the dipping method in our experimental conditions for preparing an artificial membrane. A comparative look at model membranes is also presented.