Adjoint Equation-Based Methods for Control Problems in Incompressible, Viscous Flows

A review of adjoint equation-based methodologies for viscous,incompressible flow control and optimization problems is given and illustrated by a drag minimization example. A number of approaches to ameliorating the high storage and CPU costs associated with straightforward implementations of adjoint equation based methodologies are discussed. Other issues, including the relative merits of the differentiate-then-discretize and discretize-then-differentiate approaches to deriving discrete adjoint equations, the incorporation of side constraints into adjoint equation-based methodologies, and inaccuracies that occur due to differentiations at the boundary, are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Boolean and fuzzy logic implemented at the molecular level

In this work, it is shown how to implement both hard and soft computing by means of two structurally related heterocyclic compounds: flindersine (FL) and 6(5H)-phenanthridinone (PH). Since FL and PH have a carbonyl group in their molecular skeletons, they exhibit Proximity Effects in their photophysics. In other words, they have an emission power that can be modulated through external inputs such as temperature (T) and hydrogen-bonding donation (HBD) ability of solvents. This phenomenology can be exploited to implement both crisp and fuzzy logic. Fuzzy Logic Systems (FLSs) wherein the antecedents of the rules are connected through the AND operator, are built by both the Mamdani’s and Sugeno’s models. Finally, they are adopted as approximators of the proximity effect phenomenon and tested for their prediction capabilities. Moreover, FL as photochromic compound is also a multiply configurable crisp logic molecular element.     

Theoretical study of neutral and protonated triple bonded molecules formed between C, N, Si, P, B and Al

A theoretical study of the possible protonation sites of simple molecules formed by C, N, Si, P, B and Al that present a triple bond between those atoms has been carried out. The calculations performed include MP2 and CCSD(T) methods with the aug-cc-pVTZ basis set. The nature of the protonated species has been analyzed with the Atoms In Molecules methodology. To Serafin, a free spirit and a good friend. Contribution to the Serafin Fraga Memorial Issue.     

Kink band propagation in layered structures

Confined layered structures in layer-parallel compression exhibit kink band deformation that has an associated severe initial instability. However, once the first kink band forms the system restabilizes and the bands then propagate in two mechanisms: band broadening and band progression. Previous work on triggering the initial instability and band broadening is now extended to include band progression. A new model for this propagation mechanism that successfully accounts for the modulating restabilizing response is presented and quantitative comparisons with the physical experiments yield excellent results.     

Liquid vorticity computation in non‐spherical bubble dynamics

The purpose of this work is to compare efficiency of a number of numerical techniques of computation of liquid vorticity from non‐spherical bubble oscillations. The techniques based on the finite‐difference method (FDM), the collocation method (one with differentiating (CMd) the integral boundary condition and another without it (CM)) and the Galerkin method (GM) have been considered. The central‐difference approximations are used in FDM. Sinus functions are chosen as the basis in GM. Problems of decaying a small distortion of the spherical shape of a bubble and dynamics of a bubble under harmonic liquid pressure variation with various parameters are used for comparison. The FDM technique has been found to be most efficient in all the cases. Copyright © 2004 John Wiley & Sons, Ltd.     

过氧亚硝酸的细胞生物学效应及其分析方法研究进展

对过氧亚硝酸的细胞生物学效应做了简单阐述，全面回顾和总结了近年来用于过氧亚硝酸测定的各种分析方法，并对各种方法的优缺点及其适用范围进行了比较．过氧亚硝酸的相关研究已取得很大进展，但其在线准确检测仍存在一定困难．     

Reducibility and contractivity of Runge–Kutta methods revisited

The exact relation between a Cooper-like reducibility concept and the reducibilities introduced by Hundsdorfer, Spijker and by Dahlquist and Jeltsch is given. A shifted Runge–Kutta scheme and a transplanted differential equation is introduced in such a fashion that the input/output relation remains unchanged under these transformations. This gives a technique to prove stability and contractivity results. This is demonstrated on the example of contractivity disks. AMS subject classification (2000) 65L07     

Existence and nonexistence of curved front solution of a biological equation

This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential.     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.