A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

Strake/delta wing interactions at high angles of attack

The method of vortex discretization is used to analyze the interaction of the vorticity generated by a strake, with the flow over a delta wing. The validity of the approach is first established by making comparisons with established methods for dealing with delta wings, after which compound delta planforms are discussed. An understanding of the favorable interference effects normally associated with this type of configuration is obtained and results are presented to quantify the expected lift increments resulting from the strake interaction

Orientation and solvatochromism of dyes in liquid crystals.

The orientation and solvatochromism of some dye molecules in a liquid crystal have been investigated. Interactions with the host and the structure of the dye molecule affect the macroscopic alignment of dichroic dye molecules in a liquid crystal: It was observed that some dye molecules show a large bathochromic shift of their absorption maxima in the liquid crystal host relative to the situation in isotropic solvents. It is suggested that this is due to the occurrence of a much weaker reaction field in the anisotropic, rigid host. These dye molecules show little or no apparent order in the anisotropic host despite the observation of a reduction in the electro optic switching time when the dye is present. The highest degree of macroscopic alignment was observed for a merocyanine compound, which showed the smallest solvatochromic shift in the liquid crystal host. These results are discussed in terms of the steric, dipolar and hydrogen bond interactions between the guest and the host

A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), for a simple perturbative approximation to the radial distribution functions (RDF), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein ($\beta$-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick (PY) closures have a satisfactory behavior under these regimes, with the HNC being superior throughout. The relevance of our findings for interpreting SAS results is also discussed.Comment: Physical Review E, in press (2005

Analysis of complex trophic networks reveals the signature of land-use intensification on soil communities in agroecosystems

Increasing evidence suggests that agricultural intensification is a threat to many groups of soil biota, but how the impacts of land-use intensity on soil organisms translate into changes in comprehensive soil interaction networks remains unclear. Here for the first time, we use environmental DNA to examine total soil multi-trophic diversity and food web structure for temperate agroecosystems along a gradient of land-use intensity. We tested for response patterns in key properties of the soil food webs in sixteen fields ranging from arable crops to grazed permanent grasslands as part of a long-term management experiment. We found that agricultural intensification drives reductions in trophic group diversity, although taxa richness remained unchanged. Intensification generally reduced the complexity and connectance of soil interaction networks and induced consistent changes in energy pathways, but the magnitude of management-induced changes depended on the variable considered. Average path length (an indicator of food web redundancy and resilience) did not respond to our management intensity gradient. Moreover, turnover of network structure showed little response to increasing management intensity. Our data demonstrates the importance of considering different facets of trophic networks for a clearer understanding of agriculture-biodiversity relationships, with implications for nature-based solutions and sustainable agriculture

Development of a minimal photosystem for hydrogen production in inorganic chemical cells

Inorganic chemical cells (iCHELLs) are compartment structures consisting of polyoxometalates (POMs) and cations, offering structured and confined reaction spaces bounded by membranes. We have constructed a system capable of efficient anisotropic and hierarchical photo‐induced electron transfer across the iCHELL membrane. Mimicking photosynthesis, our system uses proton gradients between the compartment and the bulk to drive efficient conversion of light into chemical energy, producing hydrogen upon irradiation. This illustrates the power of the iCHELL approach for catalysis, where the structure, compartmentalisation and variation in possible components could be utilised to approach a wide range of reactions

Social Effects in Science: Modelling Agents for a Better Scientific Practice

Science is a fundamental human activity and we trust its results because it has several error-correcting mechanisms. Its is subject to experimental tests that are replicated by independent parts. Given the huge amount of information available, scientists have to rely on the reports of others. This makes it possible for social effects to influence the scientific community. Here, an Opinion Dynamics agent model is proposed to describe this situation. The influence of Nature through experiments is described as an external field that acts on the experimental agents. We will see that the retirement of old scientists can be fundamental in the acceptance of a new theory. We will also investigate the interplay between social influence and observations. This will allow us to gain insight in the problem of when social effects can have negligible effects in the conclusions of a scientific community and when we should worry about them.Comment: 14 pages, 5 figure

Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces