Actuator disc methods for open propellers: assessments of numerical methods

The paper describes the assessment of two different actuator disc models as applied to the flow around open propellers. The first method is based on a semi-analytical approach returning the solution for the nonlinear differential equation governing the axisymmetric, steady, inviscid and incompressible flow around an actuator disc. Despite its low computational cost, the method does not require simplifying assumptions regarding the shape of the slipstream, e.g. the wake contraction is not disregarded or prescribed in advance. Moreover, the presence of a tangential velocity in the wake as well as the spanwise variation of the load are taken into account. The second one is a commonly used procedure based on CFD techniques in which the effects of the propeller are synthetically described through a set of body forces distributed over the disc surface. Both methods avoid the difficulties and the computational costs associated with the resolution of the propeller blades geometrical details. The comparison is based on an in-depth error analysis of the two procedures which results in a set of reference data with controlled accuracy. An excellent agreement has been documented between the two methods while the computational complexity is obviously very different. Among other things the comparison is also aimed at verifying the accuracy of the semi-analytical approach at each point of the computational domain and at quantifying the effect of the errors embodied in the two methods on the quality of the solution, both in terms of global and local performance parameters. Furthermore, the paper provides a set of reference solutions with controlled accuracy that could be used for the verification of new and existing computational methods. Finally, the computational cost of the semi-analytical model is quantified, thus providing a valuable information to designers who need to select a cost effective and reliable analysis tool

Sandpile model on an optimized scale-free network on Euclidean space

Deterministic sandpile models are studied on a cost optimized Barab\'asi-Albert (BA) scale-free network whose nodes are the sites of a square lattice. For the optimized BA network, the sandpile model has the same critical behaviour as the BTW sandpile, whereas for the un-optimized BA network the critical behaviour is mean-field like.Comment: Five pages, four figure

Self-Structuring of Granular Media under Internal Avalanches

We study the phenomenon of internal avalanching within the context of recently proposed ``Tetris'' lattice models for granular media. We define a recycling dynamics under which the system reaches a steady state which is self-structured, i.e. it shows a complex interplay between textured internal structures and critical avalanche behavior. Furthermore we develop a general mean-field theory for this class of systems and discuss possible scenarios for the breakdown of universality.Comment: 4 pages RevTex, 3 eps figures, revised version to appear in Phys. Rev. Let

Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg--de Vries hierarchy, we show that the solitary--wave of the Boussinesq equation is a solitary--wave satisfying simultaneously all equations of the Korteweg--de Vries hierarchy, each one in an appropriate slow time variable.Comment: 12 pages, RevTex (to appear in J. Math Phys.

The Role of Specific Mitogen-Activated Protein Kinase Signaling Cascades in the Regulation of Steroidogenesis

Mitogen-activated protein kinases (MAPKs) comprise a family of serine/threonine kinases that are activated by a large variety of extracellular stimuli and play integral roles in controlling many cellular processes, from the cell surface to the nucleus. The MAPK family includes four distinct MAPK cascades, that is, extracellular signal-regulated kinase 1/2 (ERK1/2), p38 MAPK, c-Jun N-terminal kinase or stress-activated protein kinase, and ERK5. These MAPKs are essentially operated through three-tiered consecutive phosphorylation events catalyzed by a MAPK kinase kinase, a MAPK kinase, and a MAPK. MAPKs lie in protein kinase cascades. The MAPK signaling pathways have been demonstrated to be associated with events regulating the expression of the steroidogenic acute regulatory protein (StAR) and steroidogenesis in steroidogenic tissues. However, it has become clear that the regulation of MAPK-dependent StAR expression and steroid synthesis is a complex process and is context dependent. This paper summarizes the current level of understanding concerning the roles of the MAPK signaling cascades in the regulation of StAR expression and steroidogenesis in different steroidogenic cell models

Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

On the computational complexity of dynamic slicing problems for program schemas

This is the preprint version of the Article - Copyright @ 2011 Cambridge University PressGiven a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program that preserves part of the behaviour of the original program. All program slicing algorithms take account of the structural properties of a program, such as control dependence and data dependence, rather than the semantics of its functions and predicates, and thus work, in effect, with program schemas. The dynamic slicing criterion of Korel and Laski requires only that program behaviour is preserved in cases where the original program follows a particular path, and that the slice/quotient follows this path. In this paper we formalise Korel and Laski's definition of a dynamic slice as applied to linear schemas, and also formulate a less restrictive definition in which the path through the original program need not be preserved by the slice. The less restrictive definition has the benefit of leading to smaller slices. For both definitions, we compute complexity bounds for the problems of establishing whether a given slice of a linear schema is a dynamic slice and whether a linear schema has a non-trivial dynamic slice, and prove that the latter problem is NP-hard in both cases. We also give an example to prove that minimal dynamic slices (whether or not they preserve the original path) need not be unique.This work was partly supported by the Engineering and Physical Sciences Research Council, UK, under grant EP/E002919/1