Optimal discrete stopping times for reliability growth tests

Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided

Adding flavour to twistor strings

Twistor string theory is known to describe a wide variety of field theories at tree-level and has proved extremely useful in making substantial progress in perturbative gauge theory. We explore the twistor dual description of a class of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding 'flavour' branes to the topological B-model on super-twistor space and comment on the appearance of these objects. Evidence for the correspondence is provided by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3: Typos correcte

Nucleation of NaCl from aqueous solution: critical sizes, ion-attachment kinetics, and rates

Nucleation and crystal growth are important in material synthesis, climate modeling, biomineralization, and pharmaceutical formulation. Despite tremendous efforts, the mechanisms and kinetics of nucleation remain elusive to both theory and experiment. Here we investigate sodium chloride (NaCl) nucleation from supersaturated brines using seeded atomistic simulations, polymorph-specific order parameters, and elements of classical nucleation theory. We find that NaCl nucleates via the common rock salt structure. Ion desolvation - not diffusion - is identified as the limiting resistance to attachment. Two different analyses give approximately consistent attachment kinetics: diffusion along the nucleus size coordinate and reaction-diffusion analysis of approach-to-coexistence simulation data from Aragones et al. [J. Chem. Phys., 2012, 136, 244508]. Our simulations were performed at realistic supersaturations to enable the first direct comparison to experimental nucleation rates for this system. The computed and measured rates converge to a common upper limit at extremely high supersaturation. However, our rate predictions are between 15 and 30 orders of magnitude too fast. We comment on possible origins of the large discrepancies