Formal Analysis of Geometrical Optics using Theorem Proving

Geometrical optics is a classical theory of Physics which describes the light propagation in the form of rays and beams. One of its main advantages is efficient and scalable formalism for the modeling and analysis of a variety of optical systems which are used in ubiquitous applications including telecommunication, medicine and biomedical devices. Traditionally, the modeling and analysis of optical systems have been carried out by paper-and-pencil based proofs and numerical algorithms. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent incompleteness of numerical algorithms. In this thesis, we propose a higher-order logic theorem proving based framework to analyze optical systems. The main advantages of this framework are the expressiveness of higher-order logic and the soundness of theorem proving systems which provide unrivaled analysis accuracy. In particular, this thesis provides the higher-order logic formalization of geometrical optics including the notion of light rays, beams and optical systems. This allows us to develop a comprehensive analysis support for optical resonators, optical imaging and Quasi-optical systems. This thesis also facilitates the verification of some of the most interesting optical system properties like stability, chaotic map generation, beam transformation and mode analysis. We use this infrastructure to build a library of commonly used optical components such as lenses, mirrors and optical cavities. In order to demonstrate the effectiveness of our proposed approach, we conduct the formal analysis of some real-world optical systems, e.g., an ophthalmic device for eye, a Fabry-P\'{e}rot resonator, an optical phase-conjugated ring resonator and a receiver module of the APEX telescope. All the above mentioned work is carried out in the HOL Light theorem prover

On numerical investigation of semi-empirical relation representing development length for a fluid flow in a closed conduit

The development of the velocity gradient at the opening of a closed conduit plays an essential role in monitoring the heat transfer behavior. Hence it is indispensable to examine the minimum critical length at which the velocity gradient is fully developed. Ultimately the flow is fully developed. The developing length determination is very useful for many industrial problems. This can be concluded from the literature survey. The role played by the wall shear in creating the profile is of strong consideration against the Reynold number of flowing fluid. Therefore, the development length for laminar and turbulent flow are defined separately. The determination of average Reynold number through the conduit is mandatory to be known in terms of developing length. In the latter part of the article, semi-empirical relations are defined for developing length separately for laminar and turbulent flow. In order to minimize the effort on experimentation, simulations are carried out in the present studies in ANSYS CFX 18. The developing length carries 1/6th power to the Reynold number. For determination of developing length in terms of Reynold number, SST turbulence model was used

Some visions for designing Mozambican low cost roads based on new alternative construction techniques

Paper presented at the 33rd Annual Southern African Transport Conference 7-10 July 2014 "Leading Transport into the Future", CSIR International Convention Centre, Pretoria, South Africa.Low cost road (LCR) initiatives are often concerned with supporting of the sustainable improvements of roads and creating the basic access to support poverty reduction initiatives in rural communities. In southern Africa low cost roads are those built with thin asphalt surfacings for low volume road traffic and also referred to as improved unpaved roads. LCR can be built or kept maintained cost effectively by using appropriate types of equipment suited to small-scale contractors. The objectives of this essay are to evaluate alternative pavement solutions for low volume roads. In order to evaluate the performance of different LCR, the KENLAYER program was used to evaluate the pavements. The deformation responses of unpaved and surface treated roads before and after surface treatments, at critical locations (bottom of base, top of selected subgrade and top of subgrade) are nearly the same; that means, the use of surface treatment over unpaved roads, does not increase the structural capacity, but it may only improve the riding quality and the drainage of the roads. The comparison of the cost of different LCR different pavement models (untreated, treated with ECOLOPAVI and treated with cement) found that the roads treated with ECOLOPAVI may cost less. Previous research has investigated the use of the ECOLOPAVI road treatment solution for improving roads and suggested, for consistency, further studies may be needed with an aim to investigate its use as an LCR alternative in Mozambican roads.This paper was transferred from the original CD ROM created for this conference. The material was published using Adobe Acrobat 10.1.0 Technology. The original CD ROM was produced by CE Projects cc. Postal Address: PO Box 560 Irene 0062 South Africa. Tel.: +27 12 667 2074 Fax: +27 12 667 2766 E-mail: [email protected]

Numerical investigation of mathematical non-dimensional constant representing smoothness in the Nusselt profile

Cooling of devices using air-jet and other fluid impingement has acquired pace in the manufacturing and electronic device industries. The cooling of the surface using liquid jets is studied using the Nusselt distribution profile. The pattern of the Nusselt profile becomes non-uniform when some parameters are wrongly selected. This may lead to heating of some locations instead of cooling of the surface. Thus research for keeping the Nusselt profile uniform is a primary task. The Nusselt profile depends mainly on the Reynolds number (Re) and nozzle-target spacing (Z/d). Therefore, the current study numerically evaluates the value of constant, which is a ratio of Reynolds number and nozzle-target spacing (C = Re/ (Z/d)) up to which the Nusselt profile remains uniform. The value of constant C is found to be 7400. Also, the present work uses a computational model for study, which is validated using grid independence test and turbulence modeling.The Research Creativity and Management Office, Universiti Saint Malaysiahttps://www.akademiabaru.com/submit/index.php/cfdl/indexpm2021Mechanical and Aeronautical Engineerin

On numerical investigation of semi-empirical relations representing local nusselt number at lower nozzle-target spacing’s

Examining the cooling rate using impingement of air jet finds a wide application in electronic packaging and micro-scale fluid heat interaction systems, While the prediction of Nusselt profile at low nozzle-target spacing is a big issue. The plot of area average Nusselt number magnitude against the nozzle-target spacing (Z/d) shows a gradual decrement in the profile up to Z/d = 1 and beyond that is steady. The present work aims to anticipate the profile of Nusselt number using semi-empirical relations. These semi-empirical relations are derived using regression analysis which is carried out between Re, Z/d and local Nusselt number. The data required for regression are obtained through computation. Numerical simulations are accomplished for different impinging and geometric parameters. The semi-empirical power-law relations are correlated between Z/d and Re. These are predicted differently for four distinct regions of the heat sink (stagnant point, near jet region, far jet region, near wall region). The developed correlations are found to bear negative exponent with Z/d and positive exponent with Re. The negative power of r/d and Z/d varies from 0.23 – 0.64 and 0.0025 – 0.38, respectively, While the exponents of Re varies in the positive range of 0.4-0.76

Formal Modeling and Analysis of the MAL-Associated Biological Regulatory Network: Insight into Cerebral Malaria

The discrete modeling formalism of René Thomas is a well known approach for the modeling and analysis of Biological Regulatory Networks (BRNs). This formalism uses a set of parameters which reflect the dynamics of the BRN under study. These parameters are initially unknown but may be deduced from the appropriately chosen observed dynamics of a BRN. The discrete model can be further enriched by using the model checking tool HyTech along with delay parameters. This paves the way to accurately analyse a BRN and to make predictions about critical trajectories which lead to a normal or diseased response. In this paper, we apply the formal discrete and hybrid (discrete and continuous) modeling approaches to characterize behavior of the BRN associated with MyD88-adapter-like (MAL) – a key protein involved with innate immune response to infections. In order to demonstrate the practical effectiveness of our current work, different trajectories and corresponding conditions that may lead to the development of cerebral malaria (CM) are identified. Our results suggest that the system converges towards hyperinflammation if Bruton's tyrosine kinase (BTK) remains constitutively active along with pre-existing high cytokine levels which may play an important role in CM pathogenesis