We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse. Furthermore, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given, and the relationship between this fractal dimension and a conserved quantity is pointed out.

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DeclarationWe, hereby declare that this thesis is based on results we have found ourselves.Materials of work from researchers conducted by others are mentioned in references. AbstractThe Internet of Things (IOT) is a network formed by electronic objects which have embedded sensors, software and network connectivity in them. They can collect and exchange and are prone to both cyber-attack and physical tampering. Thus, it is essential to encrypt their communications, by addressing new challenges such as impersonating "things" or nodes, denial-of-sleep attacks that drain batteries, to denial-of-service attacks (DoS). A peer-to-peer model can eliminate the dependency of a centralized data center. A Blockchain is a model for a distributed database of records of all transactions or digital events that have been executed and shared among participating nodes. In it, digital signatures are validated instead of physical signatures. With a decentralized approach implemented through cryptographic algorithms, blockchainoversees a secure transaction betweenIOT devices and coordinate them. This paper explores one of the process of incorporating blockchain with a very vulnerable centralized IOT data transactions.IOT devices are represented as Aircrafts in which the engine data and various data from the aircrafts' sensors are sent to the airports for analysis. After analysis, the analyzed data is sent to nearby airports and also to that particular aircraft. The paper analyzes how the blockchain network is created, the time latency of sending the data of the IOT devices through this blockchain network and some parts of the analysis process which is required for the Aircraft maintenance. AcknowledgementWe would like to express our utmost gratitude and appreciation to our supervisor Dr. MahbubAlamMajumdarfor his attention and time. We would also like to thank him for giving us the opportunity to work on this topic and assisting us throughout the process. Secondly, we would also like to thank our co-advisor MonzurMorshed for his guidance and time.Chapter 1: Literature ReviewThe Internet of Things (IOT) refers to the "networked interconnection of everyday objects, which are often equipped with ubiquitous intelligence" [7]. Its purpose is to provide an infrastructure that facilitates "the exchange of "things" in a secure and reliable manner, by overcoming the gap between objects in the physical world and therein information systems" [6]. Objects in the physical world that are inter-networked in the IOT includes vehicles, home appliances, and buildings.These devices are embedded with electronics, software, sensors, and actuators and have network connectivity that allows them to connect to the network.Due to the technological boom of today, there is a rise in technology-assisted crimes. It may be possible for a hacker to override the electricity in the home and cause equipment to malfunction and create major problems. Therefore, it is absolutely necessary to ensure a physical object to be secured so that it does not malfunction. The IOT ...

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