Dr. Prashant R . Dhongle (original) (raw)

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Papers by Dr. Prashant R . Dhongle

International Journal of Mathematics Trends and Technology

The conformally flat spherically symmetric charged perfect fluid distribution model in timeindepe... more The conformally flat spherically symmetric charged perfect fluid distribution model in timeindependent gravitational field is obtained in this paper. The electromagnetic field is present in the model and it is an accelerating universe with negative pressure. The other physical properties of the model are also discussed.

International Journal of Applied Mathematics, 2010

In this note we deduce Bianchi Type I string dust model with magnetic field in stationary space-t... more In this note we deduce Bianchi Type I string dust model with magnetic field in stationary space-time. It is seen that this model goes over to flat space-time. When the cosmological constant Λ ≥ 0, our model does not exist in the presence of magnetic field. Further, it is realized that in the absence of magnetic field, our model goes over to vacuum model, when Λ = 0.

International Journal of Scientific Research in Mathematical and Statistical Sciences, 2019

Bianchi Type I bulk viscous fluid string dust magnetized cosmological model with cosmological con... more Bianchi Type I bulk viscous fluid string dust magnetized cosmological model with cosmological constant term have been evaluated by solving Rosen's field equations. The cosmological constant plays the important role and it affects the physical behavior of the model in the presence as well as in the absence of both the magnetic field and the bulk viscosity. The model is studied for the positive, negative and zero values of cosmological constant. Further in special cases, the physical and geometrical aspects of the model are studied in the absence of magnetic field and in the absence of bulk viscosity.

International Journal of Theoretical & Applied Sciences, 2013

We studied the most general spherically symmetric space-time, in time-independent gravitational f... more We studied the most general spherically symmetric space-time, in time-independent gravitational fields in related to the pre-Hawking radiation, gravitational collapse and stability of the model. It is seen that in stationary space-time, there is no pre-Hawking radiation, and model will continue to collapse due to the gravitational effect. The model is unstable and has no stability phase in stationary spacetime.

American Journal of Pure Applied Mathematics, 2013

In this note, cylindrically symmetric inhomogeneous string cosmological model with magnetic field... more In this note, cylindrically symmetric inhomogeneous string cosmological model with magnetic field in stationary space-time is investigated by assuming that the expansion (�) in the model is proportional to the eigen value � 1 1 of the shear tensor � j i. It is seen that the magnetic field in the model is disappeared and the string tension density � and the rest energy density �, both are negative, which supports the non-existence of the model in stationary space-time. The non-existence of the model is strongly recommended by the negative values of the acceleration vector and the proper volume.

Communications on Applied Nonlinear Analysis, 2024

Blockchain technology depends on consensus mechanisms to assure network agreement on transactions... more Blockchain technology depends on consensus mechanisms to assure network agreement on transactions. State-space modelling and nonlinear analysis offer promising methods for raising knowledge and optimisation of these processes, hence maybe improving their security and efficiency. For modern consensus methods such Proof of Work (PoW) and Proof of Stake (PoS), scalability, energy consumption, and security vulnerabilities all offer challenges. Sometimes typical studies overlook the complexity of dynamics and interactions inherent in these systems, therefore limiting the success of optimising methods. This work presents state-space modelling based representation of blockchain consensus mechanism dynamics. By means of nonlinear analysis techniques, we explore resilience, performance, and stability, so extending this paradigm. By way of Lyapunov functions and bifurcation theory, the method generates state-space representations of consensus protocols and investigates significant areas of failure. Simulations in state-space models show effective capture of the dynamics of several consensus processes, including PoW and PoS. For example, the model in a PoW-based system projects a transition point at roughly 60% network hash rate, beyond which the system stability substantially suffers. Analogously, for PoS, the model recognises a vulnerability threshold when the stake concentration grows above 70%, hence generating probable centralising hazards. These revelations can guide the building of more robust and efficient consensus systems.

International Journal of Applied Physics and Mathematics, 2013

In this note, we have discussed and proved the different properties of double Laplace transforms ... more In this note, we have discussed and proved the different properties of double Laplace transforms like linearity property, change of scale, shifting property, double Laplace transform of partial derivatives, double Laplace transform of integral, multiplication by xt and division by xt.

Journal of Research in Applied Mathematics , 2021

The de-Sitter model with dark energy has been found in stationary space-time and it is realized t... more The de-Sitter model with dark energy has been found in stationary space-time and it is realized that the model is completely filled with dark matter and it represents dark energy star, for the value of M greater than zero. In particular, for zero value of M, the model goes over to de-Sitter empty space-time and then it describes open flat universe of special relativity. The model is the generalization of empty de-Sitter universe. Further geometrical and physical aspects of the model are studied.

International Journal of Physics and Mathematics, 2022

We have evaluated spherically symmetric model with electromagnetic field and with equation of sta... more We have evaluated spherically symmetric model with electromagnetic field and with equation of state   p , where  is arbitrary constant, by solving Einstein's field equations in stationary space-time. It is observed that dust, radiating and stiff dominated spherically symmetric models does not exist. Spherically symmetric dark energy models exist and they are studied in regards with their geometrical and physical aspects in detail.

International Journal of Mathematics Trends and Technology, 2022