Monotone flows with dense periodic orbits

The main result is Theorem 1: A flow on a connected open set X ⊂ Rd is globally periodic provided (i) periodic points are dense in X, and (ii) at all positive times the flow preserves the partial order defined by a closed convex cone that has nonempty interior and contains no straight line. The proof uses the analog for homeomorphisms due to B. Lemmens et al. [27], a classical theorem of D. Montgomery [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2)

Quantitative analysis of macroevolutionary patterning in technological evolution: Bicycle design from 1800 to 2000

Book description: This volume offers an integrative approach to the application of evolutionary theory in studies of cultural transmission and social evolution and reveals the enormous range of ways in which Darwinian ideas can lead to productive empirical research, the touchstone of any worthwhile theoretical perspective. While many recent works on cultural evolution adopt a specific theoretical framework, such as dual inheritance theory or human behavioral ecology, Pattern and Process in Cultural Evolution emphasizes empirical analysis and includes authors who employ a range of backgrounds and methods to address aspects of culture from an evolutionary perspective. Editor Stephen Shennan has assembled archaeologists, evolutionary theorists, and ethnographers, whose essays cover a broad range of time periods, localities, cultural groups, and artifacts

Primary singularities of vector fields on surfaces

Unless another thing is stated one works in the C∞ category and manifolds have empty boundary. Let X and Y be vector fields on a manifold M. We say that Y tracks X if [Y, X] = fX for some continuous function f: M→ R. A subset K of the zero set Z(X) is an essential block for X if it is non-empty, compact, open in Z(X) and its Poincaré-Hopf index does not vanishes. One says that X is non-flat at p if its ∞-jet at p is non-trivial. A point p of Z(X) is called a primary singularity of X if any vector field defined about p and tracking X vanishes at p. This is our main result: consider an essential block K of a vector field X defined on a surface M. Assume that X is non-flat at every point of K. Then K contains a primary singularity of X. As a consequence, if M is a compact surface with non-zero characteristic and X is nowhere flat, then there exists a primary singularity of X

Wall shear stress and arterial performance: two approaches based on engineering

This is the Abstract of the Article. Copyright @ 2009 Oxford University.This crucially important subject generates a very wide literature and the recent authoritative ‘in vivo’ review of Reneman et al [1] (& [2]), with Vennemann et al [3], are taken as seminal. In this paper we use approaches based on conventional engineering to address two key issues raised in [1]. The first is that of basic theory. To what extent can underlying fluid flow theory complement the in vivo understanding of wall shear stress (WSS)? In [1], which is sub-titled Discrepancies with Theory’, Poiseuille’s Law is used, extended to Murray’s Law in [2]. But they do ’not hold in vivo’ [2] because ‘we are dealing with non-Newtonian fluid, distensible vessels, unsteady flows, and too short entrance lengths’ [1].This comment coincides with the four factors Xu and Collins identified in their early Review of numerical analysis for bifurcations [4]. Subsequently they addressed these factors, with an engineering-based rationale of comparing predictions of Computational Fluid Dynamics (CFD) with Womersley theory, in vitro and in vivo data. This rationale has yet to be widely adopted, possibly due to computing complexities and the wide boundary condition data needed. This is despite uncertainties in current in vivo WSS [2]. Secondly, [1] and [2] focus on endothelial function. WSS is an ‘important determinant of arterial diameter’ and ‘mean (M)WSS is regulated locally’. One pointer is the possible importance of the glycocalyx, so that ‘endothelial cells are not seeing WSS’ and which ‘may be involved in the regulation of the total blood flow’ [3]. A typical glycocalyx is shown in [3]. Such a model should focus on adaptation of arterial diameter by ‘nitric oxide and prostaglandins’ [1]. So, using an engineering approach, can we construct a model for local regulation of MWSS? Again, remarks from [1]-[3] resonate with the conclusions of a review of nanoscale physiological flows [5] undertaken as part of an early Nanotechnology Initiative of the UK’s EPSRC. In [5] is illustrated the fractal nature of the intestinal villi-glycocalyx geometry, together with an engineering-style control loop for nitric oxide release and arterial diameter-flow rate control. Within our discussion we report two studies to obtain CFD predictive data very close to the endothelial surface. In both cases we compared two independent codes, respectively two CFD codes, and CFD and Lattice Boltzmann solvers. We also give an updated version of the endothelium control loop

Genetic algorithm search for stent design improvements

Copyright @ 2002 SpringerThis paper presents an optimisation process for finding improved stent design using Genetic Algorithms. An optimisation criterion based on dissipated power is used which fits with the accepted principle that arterial flows follow a minimum energy loss. The GA shows good convergence and the solution found exhibits improved performance over proprietary designs used for comparison purposes