Primordial Non-Gaussianity: Baryon Bias and Gravitational Collapse of Cosmic String Wakes

I compute the 3-D non-linear evolution of gas and dark matter fluids in the neighbourhood of cosmic string wakes which are formed at high redshift ($z\simeq 2240$) for a ``realistic'' scenario of wake formation. These wakes are the ones which stand out most prominently as cosmological sheets and are expected to play a dominant r\^ole in the cosmic string model of structure formation. Employing a high-resolution 3-D hydrodynamics code to evolve these wakes until the present day yields results for the baryon bias generated in the inner wake region. I find that today, wakes would be $1.5 h^{-1}$ Mpc thick and contain a 70% excess in the density of baryons over the dark matter density in their centre. However, high density peaks in the wake region do not inherit a baryon enhancement. I propose a mechanism for this erasure of the baryon excess in spherically collapsed objects based on the geometry change around the collapsing region. Further, I present heuristic arguments for the consequences of this work for large scale structure in the cosmic string model and conclude that the peculiarities of wake formation are unlikely to have significant import on the discrepancy between power spectrum predictions and observations in this model. If one invokes the nucleosynthesis bound on $\Omega_b$ this could be seen as strengthening the case against $\Omega_m=1$ or for low Hubble constants.Comment: 21 pages, 7 figures, 2 tables, prepared with the AASTeX package. Minor modifications, results unchanged. ApJ in press, scheduled for Vol. 50

Optimal control of martingales in a radially symmetric environment

We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal strategy. We show that it is optimal to switch between two strategies, depending only on the radius of the controlled process. The optimal strategies correspond to purely radial and purely tangential motion. It is notable that the value function exhibits smooth fit even when switching to tangential motion, where the radius of the optimal process is deterministic. Under sufficient regularity on the cost function, we prove optimality via viscosity solutions of a Hamilton-Jacobi-Bellman equation. We extend the results to cost functions that may become infinite at the origin. Extra care is required to solve the control problem in this case, since it is not clear how to define the optimal strategy with deterministic radius at the origin. Our results generalise some problems recently considered in Stochastic Portfolio Theory and Martingale Optimal Transport.Comment: 41 pages, 6 figure. Additional motivating example added, definitions and problem formulations clarified and simplifie

Adapted Wasserstein distance between the laws of SDEs

We consider the adapted optimal transport problem between the laws of Markovian stochastic differential equations (SDE) and establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals an interesting connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes.Comment: 30 pages, 2 figures. Additional example adde

Quick Mobile Power Unit Trailer Connections

This Final Design Review document encompasses the entirety of a sponsored senior project which was conducted by a group of four undergraduate mechanical engineers at California Polytechnic University San Luis Obispo. The primary sponsor of this project was Solar Turbines, a subsidiary of Caterpillar Incorporated. Solar Turbines is in the business of development and application of modern-day energy solutions with a large focus on gas powered turbines. Cal Poly acted as a supplemental support of this project and provide the students with mentorship as well as access to its state-of-the-art facilities for the development of an innovative solution to the design challenge submitted by Solar Turbines. The submittal states a desire to improve the deployment timeline of Solar Turbines’ Titan 130 Gas Turbine Mobile Power Unit. This unit hosts a split drive train with a turbine mounted on one semi-trailer (driving trailer) and a generator mounted on another semi-trailer (driven trailer). These two trailers must be accurately aligned and securely fastened, currently taking roughly 12 hours. Seven of these hours account for aligning and leveling the two trailers and five hours account for securing the trailers using tension bolt fasteners. The process is desired to be reduced to 4 hours without compromising the strength of the connection points. The specified alignment tolerance of the trailers was given as + ¼ inch. The primary stresses in the connection are due to the torsional load resulting from the rotation of the turbine. There are two load conditions that were factored into the design: the normal operating load and the short circuit load. The normal operation load of #### ft-lbf is the torque to be experienced by the bolts as a result of the normal operation of the turbine. The short circuit load (#### ft-lbf) is the resulting torque the system undergoes should the generator seize. This document initially presents the background research and function identification processes followed by the ideation process used to develop various solutions to the problem. The final selection processes are also laid out in detail with the final solution chosen being a hydraulically actuated form of alignment using hydraulic arms and wedge connections between the trailers. Critical component dimensions were then confirmed using hand calculations and ANSYS to conduct FEA. Manufacturing and assembly plans including a bill of materials for a full prototype are provided. In addition, testing plans which can be applied to any scale of prototype are also provided. Due to the emergence of Covid-19 during the third phase of the project, prototype development was unable to be completed. Instead further ANSYS analysis (Rigid Body Dynamic) was done in order to further support the solution provided. The goal of this final document is to provide Solar Turbines with all material listed in the Scope of Work agreement and easily lay out prototype development and testing plans that can be used by Solar Turbines if they decide to build a prototype themselves

A review and critique of UK housing stock energy models, modelling approaches and data sources

The UK housing stock is responsible for some 27% of national energy demand and associated carbon dioxide emissions. 80% of this energy demand is due to heating (60%) and domestic hot water (20%), the former reflecting the poor average thermal integrity of the envelope of the homes comprising this stock. To support the formulation of policies and strategies to decarbonise the UK housing stock, a large number of increasingly sophisticated Housing Stock Energy Models (HSEMs) have been developed throughout the past 25 years. After describing the sources of data and the spatio-temporal granularity with which these data are available to represent this stock, as well as the physical and social phenomena that are modelled and the range of strategies employed to do so, this paper evaluates the 29 HSEMs that have been developed and deployed in the UK. In this we consider the models' predictive accuracy, predictive sensitivity to design parameters, versatility, computational efficiency, the reproducibility of predictions and software usability as well as the models' transparency (how open they are) and modularity. We also discuss their comprehensiveness. From this evaluation, we conclude that current HSEMs are lacking in transparency and modularity, they are limited in their scope and employ simplistic models that limit their utility; in particular, relating to the modelling of heat flow and in the modelling of household behaviours relating to investment decisions and energy using practices. There is a need for an open-source and modular dynamic housing stock energy modelling platform that addresses current limitations, can be readily updated as new (e.g. housing survey) calibration data is released and be readily extended by the modelling community at large: improving upon the utilisation of scarce developmental resources. This would represent a considerable step forward in the formulation of housing stock decarbonisation policy that is informed by sound evidence

Pre-schoolers who stutter score lower in verbal skills than their non-stuttering peers

Purpose: The study aimed at the examination of a link between stuttering and verbal skills (speech comprehension, articulation, grammar, vocabulary, and phonological short-term memory) in three- to five-year-old children.Method: Two samples with a total of 7,217 unselected German children were tested with the validated speech and language test Marburger Sprachscreening – revised version (MSSrev).  Linguistic domains were compared for pre-school children who stuttered (CWS; n=110) and those who did not (CWNS; n=7,107) by means of Mann-Whitney U tests, general linear models, Spearman correlations, and cross-tables.  Results: In both samples, CWS scored lower in grammar, articulation, and overall performance on the MSSrev. Statistically significant associations between stuttering and (a) sex of the child, and (b) language disorders in the family were identified.Conclusions: Taking into account the effect sizes, there appears to be a weak, but statistically significant link between stuttering and verbal skills.

'First, do no harm': are disability assessments associated with adverse trends in mental health? A longitudinal ecological study.

In England between 2010 and 2013, just over one million recipients of the main out-of-work disability benefit had their eligibility reassessed using a new functional checklist-the Work Capability Assessment. Doctors and disability rights organisations have raised concerns that this has had an adverse effect on the mental health of claimants, but there are no population level studies exploring the health effects of this or similar policies. METHOD: We used multivariable regression to investigate whether variation in the trend in reassessments in each of 149 local authorities in England was associated with differences in local trends in suicides, self-reported mental health problems and antidepressant prescribing rates, while adjusting for baseline conditions and trends in other factors known to influence mental ill-health. RESULTS: Each additional 10 000 people reassessed in each area was associated with an additional 6 suicides (95% CI 2 to 9), 2700 cases of reported mental health problems (95% CI 548 to 4840), and the prescribing of an additional 7020 antidepressant items (95% CI 3930 to 10100). The reassessment process was associated with the greatest increases in these adverse mental health outcomes in the most deprived areas of the country, widening health inequalities. CONCLUSIONS: The programme of reassessing people on disability benefits using the Work Capability Assessment was independently associated with an increase in suicides, self-reported mental health problems and antidepressant prescribing. This policy may have had serious adverse consequences for mental health in England, which could outweigh any benefits that arise from moving people off disability benefits