Local sensitivity analysis for the Cucker-Smale model with random inputs

We present pathwise flocking dynamics and local sensitivity analysis for the Cucker-Smale(C-S) model with random communications and initial data. For the deterministic communications, it is well known that the C-S model can model emergent local and global flocking dynamics depending on initial data and integrability of communication function. However, the communication mechanism between agents are not a priori clear and needs to be figured out from observed phenomena and data. Thus, uncertainty in communication is an intrinsic component in the flocking modeling of the C-S model. In this paper, we provide a class of admissible random uncertainties which allows us to perform the local sensitivity analysis for flocking and establish stability to the random C-S model with uncertain communication.Comment: 32 page

Local Sensitivity Analysis of Acute Inflammation

The inflammatory response is the body\u27s response to some pathogen or foreign invader. When infected by a pathogen, a healthy individual will mount a response with immunological factors to eliminate it. An inflammatory response that is either too strong or too weak can be detrimental to the individual\u27s health. We will look at a qualitative mathematical model of the inflammatory response, in scenarios that represent varying disorders of the immune system. Using sensitivity analysis we determine which parameters of this model are most influential in the different scenarios. By determining which parameters are most influential we can suggest possible targets for treatments to these conditions which are traditionally difficult to control

Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling

Compositional data, such as soil texture, are hard to deal with in the geosciences as standard statistical methods are often inappropriate to analyse this type of data. Especially in sensitivity analysis, the closed character of the data is often ignored. To that end, we developed a method to assess the local sensitivity of a model output with resect to a compositional model input. We adapted the finite difference technique such that the different parts of the input are perturbed simultaneously while the closed character of the data is preserved. This method was applied to a hydrologic model and the sensitivity of the simulated soil moisture content to local changes in soil texture was assessed. Based on a high number of model runs, in which the soil texture was varied across the entire texture triangle, we identified zones of high sensitivity in the texture triangle. In such zones, the model output uncertainty induced by the discrepancy between the scale of measurement and the scale of model application, is advised to be reduced through additional data collection. Furthermore, the sensitivity analysis provided more insight into the hydrologic model behaviour as it revealed how the model sensitivity is related to the shape of the soil moisture retention curve

Space shuttle SRM plume expansion sensitivity analysis

The exhaust plumes of the space shuttle solid rocket motors can have a significant effect on the base pressure and base drag of the shuttle vehicle. A parametric analysis was conducted to assess the sensitivity of the initial plume expansion angle of analytical solid rocket motor flow fields to various analytical input parameters and operating conditions. The results of the analysis are presented and conclusions reached regarding the sensitivity of the initial plume expansion angle to each parameter investigated. Operating conditions parametrically varied were chamber pressure, nozzle inlet angle, nozzle throat radius of curvature ratio and propellant particle loading. Empirical particle parameters investigated were mean size, local drag coefficient and local heat transfer coefficient. Sensitivity of the initial plume expansion angle to gas thermochemistry model and local drag coefficient model assumptions were determined

Local sensitivity analysis and bias model selection

PhD ThesisIncomplete data analysis is often considered with other problems such as model uncertainty or non-identi ability. In this thesis I will use the idea of the local sensitivity analysis to address problems under both ignorable and non-ignorable missing data assumptions. One problem with ignorable missing data is the uncertainty for covariate density. At the mean time, the misspeci cation for the missing data mechanism may happen as well. Incomplete data biases are then caused by di erent sources and we aim to evaluate these biases and interpret them via bias parameters. Under non-ignorable missing data, the bias analysis can also be applied to analyse the di erence from ignorability, and the missing data mechanism misspeci cation will be our primary interest in this case. Monte Carlo sensitivity analysis is proposed and developed to make bias model selection. This method combines the idea of conventional sensitivity analysis and Bayesian sensitivity analysis, with the imputation procedure and the bootstrap method used to simulate the incomplete dataset. The selection of bias models is based on the measure of the observation dataset and the simulated incomplete dataset by using K nearest neighbour distance. We further discuss the non-ignorable missing data problem under a selection model, with our developed sensitivity analysis method used to identify the bias parameters in the missing data mechanism. Finally, we discuss robust con dence intervals in meta-regression models with publication bias and missing confounder

A nanoindentation investigation of local strain rate sensitivity in dual-phase Ti alloys

Using nanoindentation we have investigated the local strain rate sensitivity in dual-phase Ti alloys, Ti-6Al-2Sn-4Zr-xMo (x=2 and 6), as strain rate sensitivity could be a potential factor causing cold dwell fatigue. Electron backscatter diffraction (EBSD) was used to select hard and soft grain orientations within each of the alloys. Nanoindentation based tests using the continuous stiffness measurement (CSM) method were performed with variable strain rates, on the order of 10−1 to 10−3s−1. Local strain rate sensitivity is determined using a power law linking equivalent flow stress and equivalent plastic strain rate. Analysis of residual impressions using both a scanning electron microscope (SEM) and a focused ion beam (FIB) reveals local deformation around the indents and shows that nanoindentation tested structures containing both α and β phases within individual colonies. This indicates that the indentation results are derived from averaged α/β properties. The results show that a trend of local rate sensitivity in Ti6242 and Ti6246 is strikingly different; as similar rate sensitivities are found in Ti6246 regardless of grain orientation, whilst a grain orientation dependence is observed in Ti6242. These findings are important for understanding dwell fatigue deformation modes, and the methodology demonstrated can be used for screening new alloy designs and microstructures