Scientific Research


Editor, [Editor Program]

Journal Publication:

The Reynolds number modulated low frequency dynamical modes of aqueous medium embedded Spherical Virus and implications to detecting and killing viruses

Ujjawal Krishnam, Vaishali Sharma & Prafulla K Jha (2019), Journal of Biomolecular Structure and Dynamics [Taylor & Francis]


The effect of high and low Reynolds number is studied on low frequency dynamical modes of a spherical virus embedded in an aqueous medium using classical Lamb’s model which is based on the elastic continuum model. The elastic continuum model at nanometre scale results in to the two types of quantized dynamical modes. Some of these modes are Raman active and can be observed in low frequency Raman spectroscopic measurements. To calculate the vibrational modes of a virus we have used with material parameters of lysozyme crystal in water. The obvious size effect on the vibrational modes is observed. The estimated damping time which is of the order of picosecond varies with Reynolds number and shows a high value for a critical Reynolds number suggesting the high probability to detect or kill the virus using corresponding virus-water configuration.

Projects Methods [Prerequisites] :

Entropy and thermodynamic probability distribution over phase spaces

Ujjawal Krishnam, Jason Kristiano, Wounsuk Rhee, Sridhar VR Prabhu, Parth D. Pandya, Josephine Melia, Kevin Limanta (2018)


Thermodynamic probability(Ω) distribution over phase spaces is extensively studied. Entropy change(∆S) for reversible motions in the single(μ-space positioning) and multiparticle system is coupled with Schrodinger Equation and fractional fluctuations in thermodynamical ensemble for better approximations. Einstein’s theory on Brownian Motion is treated with Γ-space microstate-macrostate correspondence on experimental relevance. Specifications of classically defined non-meaningful arrangement of particles are supplemented with considerations of degenerate energy levels and distinguishability factor among apparently indistinguishable particles. Further in paper, we investigate equivalence of Sackur-Tetrode equation with classically obtained relation on thermodynamical probability. 3-D Markov Chain and Abel’s summation are introduced over Sterling Approximation for calculation of most probable microstate in the accordance of

Bose-Einstein Distribution. Finally, we introduce abstract algebraic group structurisation on particles’ motion for abelian

and non-abelian characterisation on the contours of phase space shifts.

Mathematical Interpretations On Monochromatic Aberration

Ujjawal KrishnamRitesh S BadgujarParth D. Pandya (2017)

[RG: 314235542]

Theoretical modelling with simulation is done on aberration. Mono wavelength optical rays are treated with marginal and paraxial considerations under ideally normalized conditions for real image plane curvatures. Implications of directional cosines and position coordinates on geometric stability of rays suggest a new approach to study aberration. Para-marginal angular ratio í µí»¼/β is investigated as an important parameter for longitudinal aberration and coma couplings on aplanatic points. Temperature gradient as a parameter suggests proportionality Ω between focal length change xg and longitudinal aberrration xl. Further in paper, authors conclude through linear algebraic interpretations on n-spherical image arc planes under tangentially normalized condition, hence introduce three dimensional linear algebraic-geometric theory on image plane curvatures.

Statistical Analysis And Modification Of Gas Equation

Ujjawal Krishnam (2017)

[Academia: 30504157]

In this paper, thermodynamical variables P, V, T have been taken under consideration of purely statistical implications on thermodynamics. Correlation has been established using Karl pearson coefficient of correlation and cross-check has been subjected to Cauchy-Bunyakovsky-Schwarz inequality for negative correlation, series have been derived for even{ } and odd number{ }of experimentally simulated data sets and have been consecutively put on Spearman’s rank Correlation Coefficient check. Further in paper, author explains the curve join post-critical temperature absolute minima on Van der Waal’s isothermal plot within macroscopic limit with r-th central moment about (PV) i frequency distributions by taking it in use to explain the kurtosis and skewness , as how the curve join refutes the possibility of platykurtic distribution following Bernoulli inequality treatment. Regression between temperature and pressure, i.e. has been studied, and regression coefficient for isochor has been derived using least square method. Centuries old Gas equation has been subjected to statistical cross-checks, and hence finally in the paper, author concludes through statistical treatments, as it will also consider thermodynamical fluctuation in statsitical ensemble, to project a more precise equation to relate gaseous thermodynamical variables preluding to a new approach towards understanding of thermodynamical systems in macrostate.