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A Brief Study on Quantum Walks and Quantum Mechanics
Published in Thiruselvan Subramanian, Archana Dhyani, Adarsh Kumar, Sukhpal Singh Gill, Artificial Intelligence, Machine Learning and Blockchain in Quantum Satellite, Drone and Network, 2023
Sapna Renukaradhya, Preethi, Rupam Bhagawati, Thiruselvan Subramanian
Interspersing quantum phenomena with random walks is possible when employing quantum random walks in discrete time, which is one means of doing this. Another use of this principle is continuous random walks, the distinction being that they do not need the additional dimension of a coin space in order for them to work efficiently and effectively. The evolution (Hamiltonian) operator should be utilised for continuous quantum walks because it is capable of being employed without any restrictions, which implies that the walker may walk at any point in the system’s evolutionary history without being restricted. Construction of the mathematical basis for this model is based on the Schrodinger equation, which portrays the process of evolution. Continuous-time in addition to creating discrete state spaces for each state in the state space, a transition rate matrix is also created for each state in the state space, which provides the “jumping rate” or likelihood of transition between any two adjacent states in the state space for every state in the state space. It is feasible to build the walk as a decision tree using the techniques described in Ref. [27], and a quantum operator can be created to traverse it using the methods presented in Ref. [27].
On reliability analysis of a load-sharing k-out-of-n: G system with interacting Markov subsystems
Published in International Journal of Production Research, 2022
After obtaining the transition rate matrix of the system, we apply the theory of aggregated stochastic processes to derive the closed-form formulas for reliability indexes of the system, including the reliability function, the probability density function of the first failure time, the point-wise and interval availabilities. Meanwhile, a case study of multi-engine aircraft systems is provided and some numerical examples are given to illustrate the developed model and obtained results.
Reliability Analysis of Microgrids: Evaluation of Centralized and Decentralized Control Approaches
Published in Electric Power Components and Systems, 2023
Selahattin Garip, Melih Bilgen, Necmi Altin, Saban Ozdemir, Ibrahim Sefa
In [14], by using the Markov chain method, the reliability performances of MGCC and decentralized are contrasted. Markov process is a stochastic progress. The current environment solely influences prospective behavior; historical data are not a factor. A collection of discrete stages is a common way to describe a Markov modeling. At each stage, there are some likely outcomes, and these determine the transition from the current to the following stage of development. On the other hand, it is thought that each stage’s time interval is exponentially distributed. A transition rate matrix is also used for continuous time Markov modeling to describe transitions between states [61]. The Markov chain method could be used to evaluate the reliability of the power system. A state space depiction has two stages for the component stage. These are erratic. Up indicates that something is working, while down indicates that something is not working. The binary-state model is a simple yet effective approach for modeling the health states of system components, which can be extended to include certain addictive behaviors [62]. However, for a more comprehensive analysis of power systems, more complex models are often needed. These extensive models can evaluate the degradation states of various components, perform detailed analyses, and recommend different types of maintenance, repair, and replacement strategies. By incorporating these factors, a more accurate representation of the actual system can be achieved, allowing for more precise predictions of system performance and reliability. In practice, these advanced models are often used by power system engineers and operators to optimize the operation of power systems, improve their efficiency, and minimize downtime and outage costs. Thus, the use of advanced models is crucial for ensuring the long-term sustainability and reliability of power systems in a constantly evolving energy landscape. The results are given in [14]. When the [14] are examined, it is concluded that the reliability function of MGCC decreases to zero under unrepairable microgrid, however the function keep stay over 0.55 under repairable microgrid.