Geodesics in the Generalized Schwarzschild Solution

Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for the stationary, spherically-symmetric vacuum metric, which contains one free function. Different choices for the function correspond to common expressions for the line element. From the general metric, we obtain particle and photon trajectories, and use them to specify several time coordinates adapted to physical situations. The most general form of the metric is only slightly more complicated than the Schwarzschild form, which argues effectively for teaching the general line element in place of the diagonal metric.Comment: 7 pages, 1 figure; revised to reflect referee comments; submitted to Am. J. of Phy

Rapid manufacturing technique used in the development of a regenerative pump impeller

This paper presents a method of rapid manufacture used in the development of a regenerative pump impeller. Rapid manufacturing technology was used to create complex impeller blade profiles for testing as part of a regenerative pump optimisation process. Regenerative pumps are the subject of increased interest in industry. Ten modified impeller blade profiles, from the standard radial configuration, were evaluated with the use of computational fluid dynamics and experimental testing. Prototype impellers were needed for experimental validation of the CFD results. The manufacture of the complex blade profiles using conventional milling techniques is a considerable challenge for skilled machinists. The complexity of the modified blade profiles would normally necessitate the use of expensive CNC machining with 5 axis capability. With an impeller less than 75 mm in diameter and a maximum blade thickness of 1.3mm, a rapid manufacturing technique enabled production of complex blade profiles that were dimensionally accurate and structurally robust enough for testing. As more advanced rapid prototyping machines become available in the study in the future, e.g. 3D photopolymer jetting machine, the quality of the parts particularly in terms of surface finish will improve and the amount of post processing operations will reduce. This technique offers the possibility to produce components of increased complexity whilst ensuring quality, strength, performance and speed of manufacture. The ability to manufacture complex blade profiles that are robust enough for testing, in a rapid and cost effective manner is proving essential in the overall design optimisation process for the pump

N-terminal modification of proteins with o-aminophenols.

The synthetic modification of proteins plays an important role in chemical biology and biomaterials science. These fields provide a constant need for chemical tools that can introduce new functionality in specific locations on protein surfaces. In this work, an oxidative strategy is demonstrated for the efficient modification of N-terminal residues on peptides and N-terminal proline residues on proteins. The strategy uses o-aminophenols or o-catechols that are oxidized to active coupling species in situ using potassium ferricyanide. Peptide screening results have revealed that many N-terminal amino acids can participate in this reaction, and that proline residues are particularly reactive. When applied to protein substrates, the reaction shows a stronger requirement for the proline group. Key advantages of the reaction include its fast second-order kinetics and ability to achieve site-selective modification in a single step using low concentrations of reagent. Although free cysteines are also modified by the coupling reaction, they can be protected through disulfide formation and then liberated after N-terminal coupling is complete. This allows access to doubly functionalized bioconjugates that can be difficult to access using other methods

Study of a regenerative pump using numerical and experimental techniques

Regenerative pumps are the subject of increased interest in industry as these pumps are low cost, low specific speed, compact and able to deliver high heads with stable performance characteristics. The complex flow-field within the pump represents a considerable challenge to detailed mathematical modelling as there is significant flow separation in the impeller blading. This paper presents the use of a commercial CFD code to simulate the flow within the regenerative pump and compare the CFD results with new experimental data. The CFD results demonstrate that it is possible to represent the helical flowfield for the pump which has only been witnessed in experimental flow visualisation until now. The CFD performance results also demonstrate reasonable agreement with the experimental tests. The CFD models are currently being used to optimise key geometric features to increase pump efficiency

Development of Peptoid-Based Ligands for the Removal of Cadmium from Biological Media.

Cadmium poisoning poses a serious health concern due to cadmiums increasing industrial use, yet there is currently no recommended treatment. The selective coordination of cadmium in a biological environment-i.e. in the presence of serum ions, small molecules, and proteins-is a difficult task. To address this challenge, a combinatorial library of peptoid-based ligands has been evaluated to identify structures that selectively bind to cadmium in human serum with minimal chelation of essential metal ions. Eighteen unique ligands were identified in this screening procedure, and the binding affinity of each was measured using metal titrations monitored by UV-vis spectroscopy. To evaluate the significance of each chelating moiety, sequence rearrangements and substitutions were examined. Analysis of a metal-ligand complex by NMR spectroscopy highlighted the importance of particular residues. Depletion experiments were performed in serum mimetics and human serum with exogenously added cadmium. These depletion experiments were used to compare and demonstrate the ability of these peptoids to remove cadmium from blood-like mixtures. In one of these depletion experiments, the peptoid sequence was able to deplete the cadmium to a level comparable to the reported acute toxicity limit. Evaluation of the metal selectivity in buffered solution and in human serum was performed to verify minimal off-target binding. These studies highlight a screening platform for of the identification of metal-ligands that are capable of binding in a complex environment. They additionally demonstrate the potential utility of biologically-compatible ligands for the treatment of heavy metal poisoning

The Formation of Networks with Transfers among Players

We examine the formation of networks among a set of players whose payoffs depend on the structure of the network. We focus on games where players may bargain by promising or demanding transfer payments when forming links. We examine several variations of the transfer/bargaining aspect of link formation. One aspect is whether players can only make and receive transfers to other players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in. Another aspect is whether or not transfers related to a given link can be made contingent on the full resulting network or only on the link itself. A final aspect is whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects is related either to accounting for a specific type of externality, or to dealing with the combinatorial nature of network payoffs.Networks, Network games, Network formation, Game theory, Efficient networks, Side payments, Transfers, Bargaining, Externalities

Why the “sacred” is a better resource than “religion” for understanding terrorism

The popular media and many in academia often overstate the role that religion, and its supposedly unique qualities, has played in recent acts of terror. In this article, I argue that the notion of religious violence is unhelpful and that there is a more useful concept that we can utilize to draw out the values and ideas that play a role in the move to violence in both religious and secular groups. From a series of case studies on religious and non-religious groups, I have drawn out an alternative framework for investigating and learning from the role that beliefs play in motivations and justifications for terrorism. This framework uses the concept of non-negotiable (or “sacred”) beliefs. It is as applicable to secular as it is to religious groups, and can show us much more about how such beliefs can contribute to violence