Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

Effect of media polarity on the photoisomerisation of substituted stilbene, azobenzene and imine chromophores

The influence of substituents and media polarity on the photoinducedE→Z geometrical isomerisation of the stilbene, azobenzene and N-benzylideneaniline chromophores has been compared and assessed. The efficiency of the process in all three systems is markedly dependent on the presence and characteristics of electron-donor and electron-acceptor substituents at the 4- and 4′-positions. The results are discussed in terms of relaxation of the E-excited singlet state. In the absence of a nitro substituent, relaxation to the S1 orthogonal state competes effectively with non-productive intramolecular electron transfer; in the presence of a nitro substituent, the T1 orthogonal state is formed from inter-system crossing. For systems with a 4-nitro and a 4′-electron-donor substituent, access to the triplet state is inhibited by polar solvents promoting formation of the inactive charge-transfer state from the S1 state, and no isomerisation is observed. Similar effects are observed in both solution and polymer films. Such variations in behaviour have important implications for the utilisation of the chromophores in nonlinear optical phenomena including photorefractivity.

A carbamazepine-indomethacin (1:1) cocrystal produced by milling

An X-ray amorphous mixture of carbamazepine and indomethacin transforms upon annealing to produce a novel 1:1 cocrystal, whose structure has been determined from laboratory powder X-ray diffraction (PXRD) data.

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

A comparison of two identification and tracking methods for polar lows

In this study, we compare two different cyclone-tracking algorithms to detect North Atlantic polar lows, which are very intense mesoscale cyclones. Both approaches include spatial filtering, detection, tracking and constraints specific to polar lows. The first method uses digital bandpass-filtered mean sea level pressure (MSLP) fieldsin the spatial range of 200�600 km and is especially designed for polar lows. The second method also uses a bandpass filter but is based on the discrete cosine transforms (DCT) and can be applied to MSLP and vorticity fields. The latter was originally designed for cyclones in general and has been adapted to polar lows for this study. Both algorithms are applied to the same regional climate model output fields from October 1993 to September 1995 produced from dynamical downscaling of the NCEP/NCAR reanalysis data. Comparisons between these two methods show that different filters lead to different numbers and locations of tracks. The DCT is more precise in scale separation than the digital filter and the results of this study suggest that it is more suited for the bandpass filtering of MSLP fields. The detection and tracking parts also influence the numbers of tracks although less critically. After a selection process that applies criteria to identify tracks of potential polar lows, differences between both methods are still visible though the major systems are identified in both.

Comparative study of the performance of the M-cycle counter-flow and cross-flow heat exchangers for indirect evaporative cooling - paving the path towards sustainable cooling of buildings

This paper provides a comparative study of the performance of cross-flow and counter-flow M-cycle heat exchangers for dew point cooling. It is recognised that evaporative cooling systems offer a low energy alternative to conventional air conditioning units. Recently emerged dew point cooling, as the renovated evaporative cooling configuration, is claimed to have much higher cooling output over the conventional evaporative modes owing to use of the M-cycle heat exchangers. Cross-flow and counter-flow heat exchangers, as the available structures for M-cycle dew point cooling processing, were theoretically and experimentally investigated to identify the difference in cooling effectiveness of both under the parallel structural/operational conditions, optimise the geometrical sizes of the exchangers and suggest their favourite operational conditions. Through development of a dedicated computer model and case-by-case experimental testing and validation, a parametric study of the cooling performance of the counter-flow and cross-flow heat exchangers was carried out. The results showed the counter-flow exchanger offered greater (around 20% higher) cooling capacity, as well as greater (15%–23% higher) dew-point and wet-bulb effectiveness when equal in physical size and under the same operating conditions. The cross-flow system, however, had a greater (10% higher) Energy Efficiency (COP). As the increased cooling effectiveness will lead to reduced air volume flow rate, smaller system size and lower cost, whilst the size and cost are the inherent barriers for use of dew point cooling as the alternation of the conventional cooling systems, the counter-flow system is considered to offer practical advantages over the cross-flow system that would aid the uptake of this low energy cooling alternative. In line with increased global demand for energy in cooling of building, largely by economic booming of emerging developing nations and recognised global warming, the research results will be of significant importance in terms of promoting deployment of the low energy dew point cooling system, helping reduction of energy use in cooling of buildings and cut of the associated carbon emission.

Review of R&D progress and practical application of the solar photovoltaic/thermal (PV/T) technologies

In this paper, the global market potential of solar thermal, photovoltaic (PV) and combined photovoltaic/thermal (PV/T) technologies in current time and near future was discussed. The concept of the PV/T and the theory behind the PV/T operation were briefly introduced, and standards for evaluating technical, economic and environmental performance of the PV/T systems were addressed. A comprehensive literature review into R&D works and practical application of the PV/T technology was illustrated and the review results were critically analysed in terms of PV/T type and research methodology used. The major features, current status, research focuses and existing difficulties/barriers related to the various types of PV/T were identified. The research methods, including theoretical analyses and computer simulation, experimental and combined experimental/theoretical investigation, demonstration and feasibility study, as well as economic and environmental analyses, applied into the PV/T technology were individually discussed, and the achievement and problems remaining in each research method category were described. Finally, opportunities for further work to carry on PV/T study were identified. The review research indicated that air/water-based PV/T systems are the commonly used technologies but their thermal removal effectiveness is lower. Refrigerant/heat-pipe-based PV/Ts, although still in research/laboratory stage, could achieve much higher solar conversion efficiencies over the air/water-based systems. However, these systems were found a few technical challenges in practice which require further resolutions. The review research suggested that further works could be undertaken to (1) develop new feasible, economic and energy efficient PV/T systems; (2) optimise the structural/geometrical configurations of the existing PV/T systems; (3) study long term dynamic performance of the PV/T systems; (4) demonstrate the PV/T systems in real buildings and conduct the feasibility study; and (5) carry on advanced economic and environmental analyses. This review research helps finding the questions remaining in PV/T technology, identify new research topics/directions to further improve the performance of the PV/T, remove the barriers in PV/T practical application, establish the standards/regulations related to PV/T design and installation, and promote its market penetration throughout the world.

Synthesis and spectroscopic properties of cobalt(III) complexes of some aroyl hydrazones: x-ray crystal structures of one cobalt(III) complex and two aroyl hydrazone ligands

Cobalt(III) complexes of diacetyl monooxime benzoyl hydrazone (dmoBH(2)) and diacetyl monooxime isonicotinoyl hydrazone (dmoInH(2)) have been synthesized and characterized by elemental analyses and spectroscopic methods. The X-ray crystal structures of the two hydrazone ligands, as well as that of the cobalt(III) complex [Co(III)(dmoInH)(2)]Cl center dot 2H(2)O, are also reported. It is found that in the cobalt(III) complexes the Co(III) ion is hexa-coordinated, the hydrazone ligands behaving as mono-anionic tridentate O,N,N donors. In the [Co(III)(dmoInH) (2)]Cl center dot 2H(2)O complex, the amide and the oxime hydrogens are deprotonated for both the ligands, while the isonicotine nitrogens are protonated. In the [Co(III)(d-moBH)(2)] Cl complex, only the amide nitrogens are deprotonated. It is shown that the additional hydrogen bonding capability of the isonicotine nitrogen results in different conformation and supramolecular structure for dmoInH(2), compared to dmoBH(2), in the solid state. Comparing the structure of the [CoIII(dmoInH)(2)]Cl center dot 2H(2)O with that of the Zn(II) complex of the same ligand, reported earlier, it is seen that the metal ion has a profound influence on the supramolecular structure, due to change in geometrical dispositions of the chelate rings.

File Transfer Protocol

The discourse surrounding the virtual has moved away from the utopian thinking accompanying the rise of the Internet in the 1990s. The Cyber-gurus of the last decades promised a technotopia removed from materiality and the confines of the flesh and the built environment, a liberation from old institutions and power structures. But since then, the virtual has grown into a distinct yet related sphere of cultural and political production that both parallels and occasionally flows over into the old world of material objects. The strict dichotomy of matter and digital purity has been replaced more recently with a more complex model where both the world of stuff and the world of knowledge support, resist and at the same time contain each other. Online social networks amplify and extend existing ones; other cultural interfaces like youtube have not replaced the communal experience of watching moving images in a semi-public space (the cinema) or the semi-private space (the family living room). Rather the experience of viewing is very much about sharing and communicating, offering interpretations and comments. Many of the web’s strongest entities (Amazon, eBay, Gumtree etc.) sit exactly at this juncture of applying tools taken from the knowledge management industry to organize the chaos of the material world along (post-)Fordist rationality. Since the early 1990s there have been many artistic and curatorial attempts to use the Internet as a platform of producing and exhibiting art, but a lot of these were reluctant to let go of the fantasy of digital freedom. Storage Room collapses the binary opposition of real and virtual space by using online data storage as a conduit for IRL art production. The artworks here will not be available for viewing online in a 'screen' environment but only as part of a downloadable package with the intention that the exhibition could be displayed (in a physical space) by any interested party and realised as ambitiously or minimally as the downloader wishes, based on their means. The artists will therefore also supply a set of instructions for the physical installation of the work alongside the digital files. In response to this curatorial initiative, File Transfer Protocol invites seven UK based artists to produce digital art for a physical environment, addressing the intersection between the virtual and the material. The files range from sound, video, digital prints and net art, blueprints for an action to take place, something to be made, a conceptual text piece, etc. About the works and artists: Polly Fibre is the pseudonym of London-based artist Christine Ellison. Ellison creates live music using domestic devices such as sewing machines, irons and slide projectors. Her costumes and stage sets propose a physical manifestation of the virtual space that is created inside software like Photoshop. For this exhibition, Polly Fibre invites the audience to create a musical composition using a pair of amplified scissors and a turntable. http://www.pollyfibre.com John Russell, a founding member of 1990s art group Bank, is an artist, curator and writer who explores in his work the contemporary political conditions of the work of art. In his digital print, Russell collages together visual representations of abstract philosophical ideas and transforms them into a post apocalyptic landscape that is complex and banal at the same time. www.john-russell.org The work of Bristol based artist Jem Nobel opens up a dialogue between the contemporary and the legacy of 20th century conceptual art around questions of collectivism and participation, authorship and individualism. His print SPACE concretizes the representation of the most common piece of Unicode: the vacant space between words. In this way, the gap itself turns from invisible cipher to sign. www.jemnoble.com Annabel Frearson is rewriting Mary Shelley's Frankenstein using all and only the words from the original text. Frankenstein 2, or the Monster of Main Stream, is read in parts by different performers, embodying the psychotic character of the protagonist, a mongrel hybrid of used language. www.annabelfrearson.com Darren Banks uses fragments of effect laden Holywood films to create an impossible space. The fictitious parts don't add up to a convincing material reality, leaving the viewer with a failed amalgamation of simulations of sophisticated technologies. www.darrenbanks.co.uk FIELDCLUB is collaboration between artist Paul Chaney and researcher Kenna Hernly. Chaney and Hernly developed together a project that critically examines various proposals for the management of sustainable ecological systems. Their FIELDMACHINE invites the public to design an ideal agricultural field. By playing with different types of crops that are found in the south west of England, it is possible for the user, for example, to create a balanced, but protein poor, diet or to simply decide to 'get rid' of half the population. The meeting point of the Platonic field and it physical consequences, generates a geometric abstraction that investigates the relationship between modernist utopianism and contemporary actuality. www.fieldclub.co.uk Pil and Galia Kollectiv, who have also curated the exhibition are London-based artists and run the xero, kline & coma gallery. Here they present a dialogue between two computers. The conversation opens with a simple text book problem in business studies. But gradually the language, mimicking the application of game theory in the business sector, becomes more abstract. The two interlocutors become adversaries trapped forever in a competition without winners. www.kollectiv.co.uk

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Haptics in medicine and clinical skill acquisition

THE clinical skills of medical professionals rely strongly on the sense of touch, combined with anatomical and diagnostic knowledge. Haptic exploratory procedures allow the expert to detect anomalies via gross and fine palpation, squeezing, and contour following. Haptic feedback is also key to medical interventions, for example when an anaesthetist inserts an epidural needle, a surgeon makes an incision, a dental surgeon drills into a carious lesion, or a veterinarian sutures a wound. Yet, current trends in medical technology and training methods involve less haptic feedback to clinicians and trainees. For example, minimally invasive surgery removes the direct contact between the patient and clinician that gives rise to natural haptic feedback, and furthermore introduces scaling and rotational transforms that confuse the relationship between movements of the hand and the surgical site. Similarly, it is thought that computer-based medical simulation and training systems require high-resolution and realistic haptic feedback to the trainee for significant training transfer to occur. The science and technology of haptics thus has great potential to affect the performance of medical procedures and learning of clinical skills. This special section is about understanding

The creativity of action: Property, Kin and the social in African artisanal mining

Analyses of neo-liberal change in African mining tend to frame discussion through the lens of an overarching structural perspective. Far less attention has been paid to the way change is enacted within social relations in mining communities. To this end, our chapter considers how development in the Tanzanian mineral sector transforms people’s relationships and stimulates new iterations of power and agency within local trajectories of development, focusing on the case of artisanal gold mining in Mgusu village in Geita region, Tanzania. The aim is to trace how neo-liberal change configures market rationality and property relations in ways that can fundamentally alter social relationships within the local community, occupational groups and families, raising both opportunities for wealth accumulation and the potential to entrench poverty. The creative action involved in these processes generates new associational ties and repertoires of practice, as miners’ respond to change and the need to protect their livelihoods.