Sujit Kumar Nath - Academia.edu (original) (raw)

Papers by Sujit Kumar Nath

Frontiers in Applied Mathematics and Statistics

Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology h... more Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical physics where dislocation patterning of platstically deformed metals and mass transport in nanocomposite materials with high diffusivity paths such as dislocation and grain boundaries, have been traditionally analyzed using the paradigmatic Walgraef-Aifantis (W-A) double-diffusivity (D-D) model. A long standing challenge in these studies has been the inherent nonlinear correlation between the diffusivity paths, making it extremely difficult to analyze their interdependence. Here, we present a novel method of approximating a closed form solution of the ensemble averaged density profiles and correlation statistics of coupled dynamical systems, drawing from a technique used in mathematical biology to calculate a quantity called the basic reproduction n...

arXiv: Quantitative Methods, 2020

Covid-19 is raging a devastating trail with the highest mortality-to-infected ratio ever for a pa... more Covid-19 is raging a devastating trail with the highest mortality-to-infected ratio ever for a pandemic. Lack of vaccine and therapeutic has rendered social exclusion through lockdown as the singular mode of containment. Harnessing the predictive powers of Machine Learning within a 6 dimensional infection kinetic model, depicting interactive evolution of 6 infection stages - healthy susceptible ($H$), predisposed comorbid susceptible ($P$), infected ($I$), recovered ($R$), herd immunized ($V$) and mortality ($D$) - the model, PHIRVD, provides the first accurate mortality prediction of 18 countries at varying stages of strategic lockdown, up to 30 days beyond last data training. PHIRVD establishes mortality-to-infection ratio as the correct pandemic descriptor, substituting reproduction number, and highlights the importance of early and prolonged but strategic lockdown to contain secondary relapse. Significance Statement: 1. Accurate prediction of the day-by-day mortality profiles of...

Scientific Reports, 2021

The devastating trail of Covid-19 is characterized by one of the highest mortality-to-infected ra... more The devastating trail of Covid-19 is characterized by one of the highest mortality-to-infected ratio for a pandemic. Restricted therapeutic and early-stage vaccination still renders social exclusion through lockdown as the key containment mode.To understand the dynamics, we propose PHIRVD, a mechanistic infection propagation model that Machine Learns (Bayesian Markov Chain Monte Carlo) the evolution of six infection stages, namely healthy susceptible (H), predisposed comorbid susceptible (P), infected (I), recovered (R), herd immunized (V) and mortality (D), providing a highly reliable mortality prediction profile for 18 countries at varying stages of lockdown. Training data between 10 February to 29 June 2020, PHIRVD can accurately predict mortality profile up to November 2020, including the second wave kinetics. The model also suggests mortality-to-infection ratio as a more dynamic pandemic descriptor, substituting reproduction number. PHIRVD establishes the importance of early an...

SSRN Electronic Journal, 2020

Background: Covid-19 has raked a devastating trail across continents with the highest mortality t... more Background: Covid-19 has raked a devastating trail across continents with the highest mortality to infected ratio ever for a pandemic. The key containment strategy identified has been social seclusion. Analyzing extensive live statistics with a fully predictive global Covid-19 model, we quantify implications of lockdown and strategic quarantine on Covid-containment. Methods: We analyze Covid-19 infection kinetics using a 6 dimensional (healthy, pre-existing, infected, recovered, immuned, dead) continuum model using a probabilistic Machine Learned (ML) kernel for parameter prediction using data from the Johns Hopkins repository. The ML platform itself uses a double filtration process, first using statistics for infected only, followed by statistics for the infected and dead combined. We use this multi-scale, multivariate ML architecture to categorize 19 countries into 4 different infection classes according to mortality-to-infected ratio. Finding: The model almost unerringly predicts the number of infected and dead (within 1 s.d.) for all infection classes, consistently up to 30 days beyond the last ML training date (10 May 2020). The Reproductive Number R0 estimated from the model makes catastrophic predictions (1.5 < R0 < 2.7) for countries resorting to categorical de-prioritization of lockdown (such as UK, US, Sweden and India). Countries in other infection classes show smaller R0 (1.06 < R0 < 1.5) with faster recovery time, reflecting the impact of variable lockdown measures, with numbers matching almost perfectly with real data. The model also predicts the date of secondary relapse. Interpretation: The model provides robust future estimation for the number of dead for all 19 infected countries that we studied, unfailingly up to 4 following weeks. Early versus later lockdown clearly has major impact on mortality statistics as also on the timelining of secondary relapse, both accurately predicted by the model. The critical importance of correct lockdown span and timing is thus accentuated and quantified. Funding Statement: All authors have been resourced through their affiliating organizations. Declaration of Interests: There is no known conflict of interest. Ethics Approval Statement: This is an epidemiological study with data collected from open access sources. Ethical approval is not required.

The Astrophysical Journal, 2016

We provide a possible resolution for the century-old problem of hydrodynamic shear flows, which a... more We provide a possible resolution for the century-old problem of hydrodynamic shear flows, which are apparently stable in linear analysis but shown to be turbulent in astrophysically observed data and experiments. This mismatch is noticed in a variety of systems, from laboratory to astrophysical flows. There are so many uncountable attempts made so far to resolve this mismatch, beginning with the early work of Kelvin, Rayleigh, and Reynolds toward the end of the nineteenth century. Here we show that the presence of stochastic noise, whose inevitable presence should not be neglected in the stability analysis of shear flows, leads to pure hydrodynamic linear instability therein. This explains the origin of turbulence, which has been observed/interpreted in astrophysical accretion disks, laboratory experiments, and direct numerical simulations. This is, to the best of our knowledge, the first solution to the long-standing problem of hydrodynamic instability of Rayleigh-stable flows.

Physical Review E, 2015

We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks... more We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks. It is known that molecular viscosity is negligible in accretion disks. Hence, it has been argued that a mechanism, known as Magnetorotational Instability (MRI), is responsible for transporting matter in the presence of weak magnetic field. However, there are some shortcomings, which question effectiveness of MRI. Now the question arises, whether other hydromagnetic effects, e.g. transient growth (TG), can play important role to bring nonlinearity in the system, even at weak magnetic fields. Otherwise, whether MRI or TG, which is primarily responsible to reveal nonlinearity to make the flow turbulent? Our results prove explicitly that the flows with high Reynolds number (Re), which is the case of realistic astrophysical accretion disks, exhibit nonlinearity by TG of perturbation modes faster than that by modes producing MRI. For a fixed wavevector, MRI dominates over transient effects, only at low Re, lower than its value expected to be in astrophysical accretion disks, and low magnetic fields. This seriously questions (overall) suasiveness of MRI in astrophysical accretion disks.

Physical Review E, 2014

Origin of linear instability resulting in rotating sheared accretion flows has remained a controv... more Origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for long. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay, et al where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross-correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross-correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross-correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Physical Review E, 2013

We investigate the evolution of magnetohydrodynamic perturbations in presence of stochastic noise... more We investigate the evolution of magnetohydrodynamic perturbations in presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable, but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations/experiments. The mismatch seems to have been resolved, atleast in certain regimes, in presence of weak magnetic field revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and hence large energy dissipations of perturbation, which generate instability.

Journal of Physics A: Mathematical and Theoretical, 2021

We study the effects of an intermittent harmonic potential of strength µ = µ 0 ν-that switches on... more We study the effects of an intermittent harmonic potential of strength µ = µ 0 ν-that switches on and off stochastically at a constant rate γ, on an overdamped Brownian particle with damping coefficient ν. This can be thought of as a realistic model for realisation of stochastic resetting. We show that this dynamics admits a stationary solution in all parameter regimes and compute the full time dependent variance for the position distribution and find the characteristic relaxation time. We find the exact non-equilibrium stationary state distributions in the limits-(i) γ µ 0 which shows a non-trivial distribution, in addition as µ 0 → ∞, we get back the result for resetting with refractory period; (ii) γ µ 0 where the particle relaxes to a Boltzmann distribution of an Ornstein-Uhlenbeck process with half the strength of the original potential and (iii) intermediate γ = 2nµ 0 for n = 1, 2. The mean first passage time (MFPT) to find a target exhibits an optimisation with the switching rate, however unlike instantaneous resetting the MFPT does not diverge but reaches a stationary value at large rates. MFPT also shows similar behavior with respect to the potential strength. Our results can be verified in experiments on colloids using optical tweezers.

We model the propagation of an infection, in a population, as a simplified age-dependent branchin... more We model the propagation of an infection, in a population, as a simplified age-dependent branching process. We analytically estimate the fraction of population, needed to be infected or immuned, to achieve herd immunity for an infection. We calculate this estimation as a function of the incubation period of the contagion, contact probability among the infected and susceptible population, and the probability of disease transmission from an infected to a susceptible individual. We show how herd immunity is strongly dependent on the incubation period, and it may be extremely difficult to achieve herd immunity in case of large incubation period. We derive the distribution of generation time from basic principles, which, by far, has been assumed in an ad hoc manner in epidemiological studies. We quantify the success probability of quarantine measures before achieving herd immunity, and discuss a novel method for designing effective quarantine measures in the absence of any pharmaceutical...