Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients

A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method

Boundary conditions for finite element simulations of convective flows with artificial boundaries

We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors

An experience in modelling business process architecture

We present a mapping of a previously designed Business Process Architecture (BPA) meta-model onto ArchiMate, i.e., the de facto standard Enterprise Architecture (EA) modelling language. This construct mapping allows developing process maps, i.e., descriptions of (views of) the business process architecture of an organization. We demonstrate the development of these process maps using the Signavio Business Process Management (BPM) modelling platform. The developed process maps are part of the organization’s enterprise architecture model and are linked to BPMN process diagrams that detail the functional, control-flow, data and resource aspects of the business processes included in the process map. Our research contributes to the integration of BPM and EA by researching BPA as a concept common to both disciplines

Definition of the σW regulon of Bacillus subtilis in the absence of stress

Bacteria employ extracytoplasmic function (ECF) sigma factors for their responses to environmental stresses. Despite intensive research, the molecular dissection of ECF sigma factor regulons has remained a major challenge due to overlaps in the ECF sigma factor-regulated genes and the stimuli that activate the different ECF sigma factors. Here we have employed tiling arrays to single out the ECF σW regulon of the Gram-positive bacterium Bacillus subtilis from the overlapping ECF σX, σY, and σM regulons. For this purpose, we profiled the transcriptome of a B. subtilis sigW mutant under non-stress conditions to select candidate genes that are strictly σW-regulated. Under these conditions, σW exhibits a basal level of activity. Subsequently, we verified the σW-dependency of candidate genes by comparing their transcript profiles to transcriptome data obtained with the parental B. subtilis strain 168 grown under 104 different conditions, including relevant stress conditions, such as salt shock. In addition, we investigated the transcriptomes of rasP or prsW mutant strains that lack the proteases involved in the degradation of the σW anti-sigma factor RsiW and subsequent activation of the σW-regulon. Taken together, our studies identify 89 genes as being strictly σW-regulated, including several genes for non-coding RNAs. The effects of rasP or prsW mutations on the expression of σW-dependent genes were relatively mild, which implies that σW-dependent transcription under non-stress conditions is not strictly related to RasP and PrsW. Lastly, we show that the pleiotropic phenotype of rasP mutant cells, which have defects in competence development, protein secretion and membrane protein production, is not mirrored in the transcript profile of these cells. This implies that RasP is not only important for transcriptional regulation via σW, but that this membrane protease also exerts other important post-transcriptional regulatory functions

Floral temperature and optimal foraging: is heat a feasible floral reward for pollinators?

As well as nutritional rewards, some plants also reward ectothermic pollinators with warmth. Bumble bees have some control over their temperature, but have been shown to forage at warmer flowers when given a choice, suggesting that there is some advantage to them of foraging at warm flowers (such as reducing the energy required to raise their body to flight temperature before leaving the flower). We describe a model that considers how a heat reward affects the foraging behaviour in a thermogenic central-place forager (such as a bumble bee). We show that although the pollinator should spend a longer time on individual flowers if they are warm, the increase in total visit time is likely to be small. The pollinator's net rate of energy gain will be increased by landing on warmer flowers. Therefore, if a plant provides a heat reward, it could reduce the amount of nectar it produces, whilst still providing its pollinator with the same net rate of gain. We suggest how heat rewards may link with plant life history strategies

Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution

Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integrated over the phase space in order to provide solid numerical control of the MC codes and for the discussion of the differences between the standard $\bar{MS}$ factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.Comment: 34 pages, 3 figure

Strong and Tunable Nonlinear Optomechanical Coupling in a Low-Loss System

A major goal in optomechanics is to observe and control quantum behavior in a system consisting of a mechanical resonator coupled to an optical cavity. Work towards this goal has focused on increasing the strength of the coupling between the mechanical and optical degrees of freedom; however, the form of this coupling is crucial in determining which phenomena can be observed in such a system. Here we demonstrate that avoided crossings in the spectrum of an optical cavity containing a flexible dielectric membrane allow us to realize several different forms of the optomechanical coupling. These include cavity detunings that are (to lowest order) linear, quadratic, or quartic in the membrane's displacement, and a cavity finesse that is linear in (or independent of) the membrane's displacement. All these couplings are realized in a single device with extremely low optical loss and can be tuned over a wide range in situ; in particular, we find that the quadratic coupling can be increased three orders of magnitude beyond previous devices. As a result of these advances, the device presented here should be capable of demonstrating the quantization of the membrane's mechanical energy.Comment: 12 pages, 4 figures, 1 tabl

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

The novel mTOR inhibitor RAD001 (Everolimus) induces antiproliferative effects in human pancreatic neuroendocrine tumor cells

Background/Aim: Tumors exhibiting constitutively activated PI(3) K/Akt/mTOR signaling are hypersensitive to mTOR inhibitors such as RAD001 (everolimus) which is presently being investigated in clinical phase II trials in various tumor entities, including neuroendocrine tumors (NETs). However, no preclinical data about the effects of RAD001 on NET cells have been published. In this study, we aimed to evaluate the effects of RAD001 on BON cells, a human pancreatic NET cell line that exhibits constitutively activated PI(3) K/Akt/mTOR signaling. Methods: BON cells were treated with different concentrations of RAD001 to analyze its effect on cell growth using proliferation assays. Apoptosis was examined by Western blot analysis of caspase-3/PARP cleavage and by FACS analysis of DNA fragmentation. Results: RAD001 potently inhibited BON cell growth in a dose-dependent manner which was dependent on the serum concentration in the medium. RAD001-induced growth inhibition involved G0/G1-phase arrest as well as induction of apoptosis. Conclusion: In summary, our data demonstrate antiproliferative and apoptotic effects of RAD001 in NET cells in vitro supporting its clinical use in current phase II trials in NET patients. Copyright (c) 2007 S. Karger AG, Basel