Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors, because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute $\epsilon(i \xi)$. By making important improvements in the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersions relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulae presented in this paper permit to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need of uncontrolled data extrapolations towards zero frequency that are instead necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate viability of the new dispersion formulae.Comment: 18 pages, 15 encapsulated figures. In the revised version important improvements have been made, which affect the main conclusions of the pape

Seeing the wood for the trees: the role of woody resources for the construction of gender specific household cultural artefacts in non-traditional communities in the Eastern Cape, South Africa

There is a growing wealth of data capturing the direct-use values of the environment and recognition of forests and wild resources as representing ‘‘the poor man’s overcoat’’. This focus has however resulted in an emphasis on the utilitarian values of wild resources for rural livelihoods and has for the most part overlooked their cultural values. In tangent to these developments within the field of anthropology there has been increased attention directed towards the relationship between biodiversity and human diversity over the past decade. This has resulted in the recognition of what the Declaration of Belem calls an ‘inextricable link’ between biological and cultural diversity. The term bio-cultural diversity has been introduced as a concept denoting this link. Consequently there is a need for more elaborate assessments of the various ways in which different groups of people find value in biodiversity. The aim of this paper is to demonstrate the cultural significance of wild harvested plant resources for the maintenance of two gender specific cultural artefacts for amaXhosa people in South Africa, to assess the persistence of these practices in rapidly modernizing communities. We demonstrate the endurance of these ancient cultural artefacts in present-day peri-urban communities and suggest that they point to the need for improved understanding of the significance of bio-cultural diversity. The findings of the study should not be interpreted as illustrating stagnation in the traditional past, but rather as pointing at the need for improved understanding of the significance of bio-cultural diversity in a dynamic sense

Boceprevir in combination with HIV protease inhibitors in patients with advanced fibrosis-altered drug-drug interactions?

In HIV/HCV co-infected patients improved treatment outcomes have been reported for the HCV protease inhibitors (PIs) boceprevir (BOC) and telaprevir (TVR), reaching SVR rates of up to 70% in pilot trials. Due to complex drug-drug-interactions triple therapy is substantially limited in HIV/HCV-coinfected individuals. Co-administration of BOC with the commonly available HIV PIs has been reported not only to decrease the level of BOC but also to lead to relevant decreases in the respective HIV PI. Here, we report on two patients who received BOC-containing HCV triple therapy in combination with a HIV PI. Patient 1 was on darunavir 800 mg/ritonavir 100 mg once-daily mono-therapy. Using FibroScan a liver stiffness of 34 kPa suggested liver cirrhosis prior to start of HCV triple therapy. At week 5 of HCV triple therapy darunavir trough concentration was measured in the reference range with 3777 ng/ml (reference trough concentration 2400–4600 ng/ml). HCV-RNA became negative at week 10 and HIV-RNA was below detection limit (<40 copies/ml) at all times. Patient 2 was on a simplified FTC qd and fos-amprenavir 700 mg/ritonavir 100 mg bid regimen. Liver disease had also progressed to liver cirrhosis, confirmed in FibroScan, with a liver stiffness of 32 kPa. At week 8 of HCV triple therapy fos-amprenavir trough level was measured in the normal reference range with 1699 ng/ml (reference trough concentration 750–2500 ng/ml). At week 11 HCV-RNA was <12 IU/ml and HIV viral load was below detection limit of <40 copies/ml at all times. Our clinical data suggest that in patients with advanced liver disease possibly drug levels of HIV PIs which are coadministered with BOC may be within the normal range. In order to better understand the true amount of drug interactions between BOC and commonly used HIV PIs in HIV/HCV-coinfected patients with more advanced liver fibrosis, urgently more PK studies are required to make HCV triple therapy accessible for a wider number of HIV/HCV-coinfected patients in desperate need of these drugs

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of nonadiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the nonadiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero and a standing combustion wave is formed as the extinction condition is reached. Prospects of further work are also discussed.Comment: pages 32, figures 2

Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number

A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full reactive Navier-Stokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers

Ignition of thermally sensitive explosives between a contact surface and a shock

The dynamics of ignition between a contact surface and a shock wave is investigated using a one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing and contrasting the solutions with those of the ignition process between a piston and a shock, considered previously. The large activation energy asymptotic solutions are found to be qualitatively different from the piston driven shock case, in that thermal runaway first occurs ahead of the contact surface, and both forward and backward moving reaction waves emerge. These waves take the form of quasi-steady weak detonations that may later transition into strong detonation waves. For the finite activation energies considered in the numerical simulations, the results are qualitatively different to the asymptotic predictions in that no backward weak detonation wave forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance of the contact surface. The above conclusions are relevant to gas phase equation of state models. However, when a large polytropic index more representative of condensed phase explosives is used, the large activation energy asymptotic and finite activation energy numerical results are found to be in quantitative agreement

Assessment of investments towards digitalised production

Since 2011 the term “Industrie 4.0” represents the process of digital transformation for industrial production. The discussion in regard to this transformation is dominated by technological aspects but neglects the economical rational for investments in many cases. However, the necessary investments in digitalised technical equipment creates new challenges in solid judgement on ROI and priorities. The complexity related to digital transformation confronts companies with new aspects of uncertainty. Therefore, a paradox situation is observed by a “digital gap” between investment in technology and where the added value is captured and monetised. This thesis investigates how complexity of digitalisation, respectively the “digital gap” can be understood and bridged by the usage of value-constructs originated from recent business model research. The moderating role of constructs like value proposition, value network and value capture towards decision for investments is investigated in relation with digitalisation initiatives, technology and measurement of industrial productivity. Based on differences between industries in their digital maturity level the survey primarily focuses on Food, Beverage, Pharma, Life science and FMCG companies. A second survey sample covers other industries, mainly machine builders and automotive companies, to see differences or possible generalisable elements in the results. The research method is based on a mixed-method design, combining qualitative research results with quantitative analyses by triangulation. An intensive literature research of four related scientific disciplines delivers theory for the paradigmatic coding and formulation of a Grounded Theory. The results of Grounded Theory deliver the theoretical rational to build a structural model to use within statistical factor analysis methods. The thesis delivers a wide range of results and insights into the complex relations of transformation within the context of digitalised production. It shows innovative research design in using value-constructs for the moderation of value within an organisation. Finally, the mixed-method design complements the results by the combination of diverse disciplines of science. Results to explain how moderation of value does bridge the “digital gap”, how data is enabling monetisation of value generated and how standardisation shows relevance in successful investments are delivered within the thesis

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction