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Prof
Beesham, Aroonkumar
Department: Mathematical Sciences
Research Interest(s): Cosmology, Dark energy, Black holes, Mathematical modelling of Covid-19
Active Community Engagement: South African Maths Society
South African Institute of Physics
International Society of General Relativity & Gravitation
Australasian Society for General Relativity and Gravitation
Royal Astronomical Society, Indian Association for General Relativity and Gravitation
Biography: Prof Beesham is former Senior Professor in the Department of Mathematical Sciences and has been in academia for many years 1979-1989: Lecturer, (now, Westville campus of University of KwaZulu-Natal) and University of Zululand.
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- In the context of f(R,T) modified gravity theory, we consider a homogeneous and anisotropic Bianchi type-I cosmological model which relies on the condition of a constant jerk parameter, j =1, corresponding to a flat ΛCDM model. Under this condition, we obtain two different solutions, one is power-law and the other one is exponential. The power-law solution gives a decelerating model, while the exponential one yields an accelerating cosmology. We discuss the physical and geometric properties of both models, validity of the solutions, and the significance of modified f(R,T) gravity for the models.
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- 2022| Anka PublishersIn this research, we propose a theoretical model which helps us to consider evolutions of some special heart cells by using superconducting quantum interface devices (SQUID) in a magnetocardiography (MCG) technique. In this model, each cell has its own special electrical structure including ions and charges. These charges move within or outside the cell and emit some magnetic fields. Also, some charges have spins which emit spinning magnetic fields. Summing over these biofields produces the real biofield of a cell. All cellular magnetic fields are summed and enter into the sensor (SQUID) and form the observed pulse on the scope. On the other hand, each biofield induces a current on the superconductor of detector. To consider evolutions of a special cell, one can produce some currents, equal and in opposite directions of currents which are induced by other cells. These currents cancel effects of other cells and only the current and magnetic field of a desired cell is remained. Thus, one can analyze the behavior of one special cell. For example, if a cell converts to a tumor one, its radiated charges and magnetic fields are changed. These changes could be detected by SQUID and tumors could be diagnosed fast.
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- 2022| AIMS PressIt is known that differences between potentials of soma, dendrites and different parts of neural structures may be the origin of electroencephalogram (EEG) waves. These potentials may be produced by some excitatory synapses and currents of charges between neurons and then thereafter may themselves cause the emergence of new synapses and electrical currents. These currents within and between neurons emit some electromagnetic waves which could be absorbed by electrodes on the scalp, and form topographic images. In this research, a model is proposed which formulates EEG topographic parameters in terms of the charge and mass of exchanged particles within neurons, those which move between neurons, the number of neurons and the length of neurons and synapses. In this model, by knowing the densities of the frequencies in different regions of the brain, one can predict the type, charge and velocity of particles which are moving along neurons or are exchanged between neurons.
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- 2023| American Astronomica...In previous works, we proposed to estimate cosmological parameters with an artificial neural network (ANN) and a mixture density network (MDN). In this work, we propose an improved method called a mixture neural network (MNN) to achieve parameter estimation by combining ANN and MDN, which can overcome shortcomings of the ANN and MDN methods. Besides, we propose sampling parameters in a hyperellipsoid for the generation of the training set, which makes the parameter estimation more efficient. A high-fidelity posterior distribution can be obtained using ( ) 102 forward simulation samples. In addition, we develop a code named CoLFI for parameter estimation, which incorporates the advantages of MNN, ANN, and MDN, and is suitable for any parameter estimation of complicated models in a wide range of scientific fields. CoLFI provides a more efficient way for parameter estimation, especially for cases where the likelihood function is intractable or cosmological models are complex and resource-consuming. It can learn the conditional probability density p(θ|d) using samples generated by models, and the posterior distribution p(θ|d0) can be obtained for a given observational data d0. We tested the MNN using power spectra of the cosmic microwave background and Type Ia supernovae and obtained almost the same result as the Markov Chain Monte Carlo method. The numerical difference only exists at the level of ( ) s - 10 2 . The method can be extended to higher-dimensional data.
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- In this work, we have developed an FLRW type model of a universe which displays transition from deceleration in the past to the acceleration at the present. For this, we have considered field equations of f(R,T) gravity and have taken f (R, T ) = R + 2λT , λ being an arbitrary constant. We have estimated the λ parameter in such a way that the transition red shift is found similar in the deceleration parameter, pressure and the equation of state parameter ω. The present value of Hubble parameter is estimated on the basis of the three types of observational data set: latest compilation of 46 Hubble data set, SNe Ia 580 data sets of distance modulus and 66 Pantheon data set of apparent magnitude which comprised of 40 SN Ia bined and 26 high redshift data’s in the range 0.014 ≤ z ≤ 2.26. These data are compared with theoretical results through the χ2 statistical test. Interestingly, the model satisfies all the three weak, strong and dominant energy conditions. The model fits well with observational findings. We have discussed some of the physical aspects of the model, in particular the age of the universe.
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- Cosmological models are obtained in a f(R) modified gravity with a coupled Gauss–Bonnet (GB) terms in the gravitational action. The dynamical role of the GB terms is explored with a coupled dilaton field in two different cases (I) where γ, λ and δ are arbitrary constants and (II) f(R) = R and estimate the constraints on the model parameters. In the first case we choose GB terms coupled with a free scalar field in the presence of interacting fluid and in the second case GB terms coupled with scalar field in a self interacting potential to compare the observed Universe. The evolutionary scenario of the Universe is obtained adopting a numerical technique as the field equations are highly non-linear. Defining a new density parameter ΩH, a ratio of the dark energy (DE) density to the present energy density of the non-relativistic matter, we look for a late accelerating Universe. The state finder parameters ΩH, deceleration parameter (q), jerk parameter (j) are plotted. It is noted that a non-singular Universe with oscillating cosmological parameters for a given strength of interactions is admitted in model-I. The gravitational coupling constant λ is playing an important role. The Lagrangian density of f(R) is found to dominate over the GB terms when oscillating phase of DE arises. In model-II, we do not find oscillation of the cosmological parameters as the Universe evolves. In the presence of interaction the energy from radiation sector of matter cannot flow to the other two sectors of fluid. The range of values of the strengths of interaction of the fluids are estimated for a stable Universe assuming the primordial gravitational wave speed equal to unity.
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- 2022| AIMS PressPrevious experiments have shown that extremely low frequency electromagnetic fields could cause serious effects on the evolution of cells. We propose a mathematical model which confirms those results. In our model, electromagnetic waves could cause the motions of ions and charges and the emergence of some currents around and in the interior of cells. These currents produce some waves which interact with the DNAs and remove or attach some repressors. Consequently, some genes could be turned on or off, and cells could obtain some properties or lose them. The frequency of the external waves should be close to the frequency of the exchanged waves between the repressors and DNAs or even bigger than them. We test this idea and did some experiments on quail embryonic cells. We connected a sample of these cells to a battery and considered their evolution. We observed that after connecting the battery and the production of electrical current, some rings around the quail embryonic cells emerged. Maybe, these rings are the response of the cells to changes in electromagnetic waves and electrical currents.
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- In this paper, an attempt is made to construct a Friedmann–Lemaitre–Robertson–Walker model in gravity with a perfect fluid that yields acceleration at late times. We take as . As in the CDM model, we take the matter to consist of two components, viz., and such that . The parameter is the matter density (baryons dark matter), and is the density associated with the Ricci scalar and the trace of the energy–momentum tensor, which we shall call dominant matter. We find that at present is dominant over , and that the two are in the ratio 3:1–3:2 according to the three data sets: (i) 77 Hubble OHD data set, (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range . We have also calculated the pressures and densities associated with the two matter densities, viz., , , and , respectively. It is also found that at present, is greater than . The negative dominant matter pressure creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.
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- In this paper, we have analyzed the significance of bulk viscosity in an axially symmetric Bianchi type-I model to study the accelerated expansion of the universe. We have considered four bulk viscosity parameterizations for the matter-dominated cosmological model. The function of the two significant Hubble 𝐻(𝑧) and deceleration parameters are discussed in detail. The energy parameters of the universe are computed using the most recent observational Hubble data (57 data points) in the redshift range 0.07 ≤ 𝑧 ≤ 2.36. In this model, we obtained all feasible solutions with the viscous component and analyzed the universe’s expansion history. Finally, we analyzed the statefinder diagnostic and found some interesting results. The outcomes of our developed model now properly align with observational results.
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- We get an exact nonlinear electrodynamics (NED) charged black holes endowed with the perfect fluid dark matter (PFDM) in the AdS background-charged PFDM AdS black holes with additional parameter charge parameter q and PFDM parameter β apart from mass M. We investigate the extended phase space thermodynamics wherein we identify the black hole mass with the chemical enthalpy rather than internal energy. We analysed it in a canonical ensemble to probe the effects of the parameter β on the thermodynamic quantities. The behaviour of heat capacity reveals the existence of two secondorder phase transitions for decreasing β, the former occurring at increasing horizon radii xc1 and the latter at reduced values of xc2, where x is ratio of radial coordinate r and AdS length l (x = r/l). Whereas an analysis of Gibbs’ free energy confirms our black hole exhibits first order (small to large black hole) phase transition. The behaviour of the solution is consistent with Van der Waals fluid, which can also result from the P − V criticality describing the liquid/gas phase transition observed by the isotherms for temperatures less than the critical temperature. Thus, we show black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids and can undergo phase transitions.
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