Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

Designing atmospheric-pressure plasma sources for surface engineering of nanomaterials

Atmospheric-pressure plasma processing techniques emerge as efficient and convenient tools to engineer a variety of nanomaterials for advanced applications in nanoscience and nanotechnology. This work presents different methods, including using a quasi-sinusoidal high-voltage generator, a radio-frequency power supply, and a uni-polar pulse generator, to generate atmospheric-pressure plasmas in the jet or dielectric barrier discharge configurations. The applicability of the atmospheric-pressure plasma is exemplified by the surface modification of nanoparticles for polymeric nanocomposites. Dielectric measurements reveal that representative nanocomposites with plasma modified nanoparticles exhibit notably higher dielectric breakdown strength and a significantly extended lifetime.

Carbon nanostructures for hard tissue engineering

The primary goal in hard tissue engineering is to combine high-performance scaffold materials with living cells to develop biologically active substitutes that can restore tissue functions. This requires relevant knowledge in multidisciplinary fields encompassing chemical engineering, material science, chemistry, biology and nanotechnology. Here we present an overview on the recent progress of how two representative carbon nanostructures, namely, carbon nanotubes and graphene, aid and advance the research in hard tissue engineering. The article focuses on the advantages and challenges of integrating these carbon nanostructures into functional scaffolds for repairing and regenerative purposes. It includes, but is not limited to, the critical physico-chemical properties of carbon nanomaterials for enhanced cell interactions such as adhesion, morphogenesis, proliferation and differentiation; the novel designs of two- and three-dimensional nanostructured scaffolds; multifunctional hybrid materials; and the biocompatible aspects of carbon nanotubes and graphene. Perspectives on the future research directions are also given, in an attempt to shed light on the innovative and rational design of more effective biomedical devices in hard tissue engineering.

Loading of a very tall building in a simulated downburst wind field

Thunderstorm downbursts are important for wind engineers as they have been shown to produce the design wind speeds for mid to high return periods in many regions of Australia [1]. In structural design codes (e.g. AS/NZS1170.02-02) an atmospheric boundary layer (ABL) is assumed, and a vertical profile is interpolated from recorded 10 m wind speeds. The ABL assumption is however inaccurate when considering the complex structure of a thunderstorm outflow, and its effects on engineered structures. Several researchers have shown that the downburst, close to its point of divergence is better represented by an impinging wall jet profile than the traditional ABL. Physical modelling is the generally accepted approach to estimate wind loads on structures and it is therefore important to physically model the thunderstorm downburst so that its effects on engineered structures may be studied. An advancement on the simple impinging jet theory, addressed here is the addition of a pulsing mechanism to the jet which allows not only the divergent characteristics of a downburst to be produced, but also it allows the associated leading ring vortex to be developed. The ring vortex modelling is considered very important for structural design as it is within the horizontal vortex that the largest velocities occur [2]. This paper discusses the flow field produced by a pulsed wall jet, and also discusses the induced pressures that this type of flow has on a scaled tall building.

Influence of jet inclination on structural loading in an experimentally simulated microburst

Steady and pulsed flow stationary impinging jets have been employed to simulate the wind field produced by a thunderstorm microburst. The effect on the low level wind field due to jet inclination with respect to the impingement surface has been studied. A single point velocity time history has been compared to the full-scale Andrews AFB microburst for model validation. It was found that for steady flow, jet inclination increased the radial extent of high winds but did not increase the magnitude of these winds when compared to the perpendicular impingement case. It was found that for inclined pulsed flow the design wind conditions could increase compared to perpendicular impingement. It was found that the location of peak winds was affected by varying the outlet conditions.

Discussion on full-scale internal pressure measurements

The wind loading on most structural elements is made up of both an external and internal pressure. Internal pressures are also important for the design of naturally ventilated buildings. The internal pressure is the interaction between the external pressure propagating through the building envelope and any internal plant causing building pressurization. Although the external pressure field can be well defined through a series of wind tunnel tests, modeling complexities makes accurate prediction of the internal pressure difficult. For commercial testing for the determination of design cladding pressures, an internal pressure coefficient is generally assumed from wind loading standards. Several theories regarding the propagation of internal pressures through single and multiple dominant openings have been proposed for small and large flexible buildings (Harris (1990), Holmes, (1979), Liu & Saathoff (1981 ), Vickery (1986, 1994), Vickery & Bloxham (1992), Vickery & Georgiou (1991))...

Nanoscale surface and interface engineering : why plasma-aided?

This contribution provides arguments why and in which cases low-temperature plasmas should be used for nanoscale surface and interface engineering and discusses several advantages offered by plasma-based processes and tools compared to neutral gas fabrication routes. Relevant processes involve nanotexturing (etching, sputtering, nanostructuring, pre-patterning, etc.) and composition/structure control at nanoscales (phases, layering, elemental presence, doping, functionalization, etc.) and complex combinations thereof. A case study in p-Si/n-Si solar cell junction exemplifies a successful use of inductively coupled plasma-assisted RF magnetron sputtering for nanoscale fabrication of a bi-layered stack of unconventionally doped highly-crystalline silicon nanofilms with engineered high-quality interfaces.

Workflow patterns as a means to model task succession in games – a preliminary case study

Over about the last decade, people involved in game development have noted the need for more formal models and tools to support the design phase of games. It is argued that the present lack of such formal tools is currently hindering knowledge transfer among designers. Formal visual languages, on the other hand, can help to more effectively express, abstract and communicate game design concepts. Moreover, formal tools can assist in the prototyping phase, allowing designers to reason about and simulate game mechanics on an abstract level. In this paper we present an initial investigation into whether workflow patterns – which have already proven to be effective for modeling business processes – are a suitable way to model task succession in games. Our preliminary results suggest that workflow patterns show promise in this regard but some limitations, especially in regard to time constraints, currently restrict their potential.