On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Models and methods for the direct simulation of rough and micropatterned surfaces

Friction in hydrodynamic bearings are a major source of losses in car engines ([69]). The extreme loading conditions in those bearings lead to contact between the matching surfaces. In such conditions not only the overall geometry of the bearing is relevant, but also the small-scale topography of the surface determines the bearing performance. The possibility of shaping the surface of lubricated bearings down to the micrometer ([57]) opened the question of whether friction can be reduced by mean of micro-textures, with mixed results. This work focuses in the development of efficient numerical methods to solve thin film (lubrication) problems down to the roughness scale of measured surfaces. Due to the high velocities and the convergent-divergent geometries of hydrodynamic bearings, cavitation takes place. To treat cavitation in the lubrication problem the Elrod- Adams model is used, a mass-conserving model which has proven in careful numerical ([12]) and experimental ([119]) tests to be essential to obtain physically meaningful results. Another relevant aspect of the modeling is that the bearing inertial effects are considered, which is necessary to correctly simulate moving textures. As an application, the effects of micro-texturing the moving surface of the bearing were studied. Realistic values are assumed for the physical parameters defining the problems. Extensive fundamental studies were carried out in the hydrodynamic lubrication regime. Mesh-converged simulations considering the topography of real measured surfaces were also run, and the validity of the lubrication approximation was assessed for such rough surfaces.

Comparative analysis of the visual performance and aberrometric outcomes with a new hybrid and two silicone hydrogel multifocal contact lenses: a pilot study

Background: The aim was to evaluate the visual performance achieved with a new multifocal hybrid contact lens and to compare it with that obtained with two other currently available multifocal soft contact lenses. Methods: This pilot prospective comparative study comprised a total of 16 presbyopic eyes of eight patients ranging in age from 43 to 58 years. All patients were fitted with three different models of multifocal contact lens: Duette multifocal (SynergEyes), Air Optix AQUA multifocal (Alcon) and Biofinity multifocal (CooperVision). Fittings were performed randomly in each patient according to a random number sequence, with a wash-out period between fittings of seven days. At two weeks post-fitting, visual, photopic contrast sensitivity and ocular aberrometry were evaluated. Results: No statistically significant differences were found in distance and near visual acuity achieved with the three different types of multifocal contact lens (p ≥ 0.05). Likewise, no significant differences between lenses were found in the monocular and binocular defocus curve (p ≥ 0.10). Concerning contrast sensitivity, better monocular contrast sensitivities for 6, 12 and 18 cycles per degree were found with the Duette and Air Optix multifocal compared to Biofinity (p = 0.02). Binocularly, differences between lenses were not significant (p ≥ 0.27). Furthermore, trefoil aberration was significantly higher with Biofinity multifocal (p < 0.01) and Air Optix (p = 0.01) multifocal compared to Duette. Conclusions: The Duette multifocal hybrid contact lens seems to provide similar visual quality outcomes in presbyopic patients with low corneal astigmatism, when compared with other soft multifocal contact lenses. This preliminary result should be confirmed in studies with larger samples.

A Case of Anatomical Models

Daybook, image #40

Constructing and evaluating alternative prediction models for identifying clinically relevant cases in an STD clinic

Thesis (Master's)--University of Washington, 2016-06

Noise in detection of qubit states using a quantum point contact

We present a model for detection of the states of a coupled quantum dots (qubit) by a quantum point contact. Most proposals for measurements of states of quantum systems are idealized. However in a real laboratory the measurements cannot be perfect due to practical devices and circuits. The models using ideal devices are not sufficient for describing the detection information of the states of the quantum systems. Our model therefore includes the extension to a non-ideal measurement device case using an equivalent circuit. We derive a quantum trajectory that describes the stochastic evolution of the state of the system of the qubit and the measuring device. We calculate the noise power spectrum of tunnelling events in an ideal and a non-ideal quantum point contact measurement respectively. We found that, for the strong coupling case it is difficult to obtain information of the quantum processes in the qubit by measurements using a non-ideal quantum point contact. The noise spectra can also be used to estimate the limits of applicability of the ideal model.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Use of imaging technology to better understand soft contact lens fit dynamics

The principal theme of this thesis is the identification of additional factors affecting, and consequently to better allow, the prediction of soft contact lens fit. Various models have been put forward in an attempt to predict the parameters that influence soft contact lens fit dynamics; however, the factors that influence variation in soft lens fit are still not fully understood. The investigations in this body of work involved the use of a variety of different imaging techniques to both quantify the anterior ocular topography and assess lens fit. The use of Anterior-Segment Optical Coherence Tomography (AS-OCT) allowed for a more complete characterisation of the cornea and corneoscleral profile (CSP) than either conventional keratometry or videokeratoscopy alone, and for the collection of normative data relating to the CSP for a substantial sample size. The scleral face was identified as being rotationally asymmetric, the mean corneoscleral junction (CSJ) angle being sharpest nasally and becoming progressively flatter at the temporal, inferior and superior limbal junctions. Additionally, 77% of all CSJ angles were within ±50 of 1800, demonstrating an almost tangential extension of the cornea to form the paralimbal sclera. Use of AS-OCT allowed for a more robust determination of corneal diameter than that of white-to-white (WTW) measurement, which is highly variable and dependent on changes in peripheral corneal transparency. Significant differences in ocular topography were found between different ethnicities and sexes, most notably for corneal diameter and corneal sagittal height variables. Lens tightness was found to be significantly correlated with the difference between horizontal CSJ angles (r =+0.40, P =0.0086). Modelling of the CSP data gained allowed for prediction of up to 24% of the variance in contact lens fit; however, it was likely that stronger associations and an increase in the modelled prediction of variance in fit may have occurred had an objective method of lens fit assessment have been made. A subsequent investigation to determine the validity and repeatability of objective contact lens fit assessment using digital video capture showed no significant benefit over subjective evaluation. The technique, however, was employed in the ensuing investigation to show significant changes in lens fit between 8 hours (the longest duration of wear previously examined) and 16 hours, demonstrating that wearing time is an additional factor driving lens fit dynamics. The modelling of data from enhanced videokeratoscopy composite maps alone allowed for up to 77% of the variance in soft contact lens fit, and up to almost 90% to be predicted when used in conjunction with OCT. The investigations provided further insight into the ocular topography and factors affecting soft contact lens fit.

Imagined intergroup contact and common ingroup identity:an integrative approach

We conducted two studies involving two different age groups (elementary school children and adults) aimed at integrating imagined contact and common ingroup identity models. In the first study, Italian elementary school children were asked to imagine interacting with an unknown immigrant peer as members of a common group. Results revealed that common ingroup imagined contact, relative to a control condition, improved outgroup helping intentions assessed 1 week and 2 weeks after the intervention. In the second study, common ingroup imagined contact led Italian university students to display higher intentions to have contact with immigrants compared to control conditions. In conclusion, results from both studies demonstrate that imagining an intergroup interaction as members of the same group strengthens the effects of imagined contact. These findings point to the importance of combining the common ingroup identity model and the imagined contact theory in order to increase the potentiality of prejudice reduction interventions.

Exploring business models to provide a foundation for enhanced eye care services in high street optometric practice

High street optometric practices are for-profit businesses. They mostly provide sight testing and eye examination services and sell optical products, such as spectacles and contact lenses. The sight testing services are often sold at a vastly reduced price and profits are generated primarily through high margin spectacle sales, in a loss leading strategy. Published literature highlights weaknesses in this strategy as it forms a barrier to widening the scope of services provided within optometric practices. This includes specialist non-refraction based services, such as shared care. In addition this business strategy discourages investment in advanced diagnostic equipment and higher professional qualifications. The aim of this thesis was to develop a greater understanding of the traditional loss-leading strategy. The thesis also aimed to assess the plausibility of alternative business models to support the development of specialist non-refraction services within high street optometric practice. This research was based on a single independent optometric practice that specialises in advanced retinal imaging and offers a broad range of shared care services. Specialist non-refraction based services were found to be poor generators of spectacle sales likely due to patient needs and presenting concerns. Alternative business strategies to support these services included charging more realistic professional fees via cost-based pricing and monthly payment plans. These strategies enabled specialist services to be more self-sustainable with less reliance on cross-subsidy from spectacle sales. Furthermore, improving operational efficiency can increase stand-alone profits for specialist services.Practice managers may be reluctant to increase professional fees due to market pressures and confidence. However, this thesis found that patients were accepting of increased professional fees. Practice managers can implement alternative business models to enhance eye care provision in high street optometric practices. These alternative business models also improve revenues and profits generated via clinical services and improve patient loyalty.

Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.