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Undetected infectious populations have played a major role in the COVID-19 outbreak across the globe and estimation of this undetected class is a major concern in understanding the actual size of the COVID-19 infections. Due to the asymptomatic nature of some infections, many cases have gone undetected. Also, despite carrying COVID-19 symptoms, most of the infected population kept the infections hidden and stayed unreported, especially in a country like India. Based on these factors, we have added an undetected compartment to the already developed SEIR model [48] to estimate these uncounted infections. In this article, we have applied Physics Informed Neural Network (PINN) to estimate the undetected infectious populations in the 20 worst-affected Indian states as well as India as a whole. The analysis has been carried out for the first as well as second surge of COVID-19 infections in India. A ratio of the active undetected infectious to the active detected infectious population is calculated through the PINN analysis which gives a picture of the real size of the pandemic in India. The rate at which symptomatic infectious population goes undetected and are never reported is also estimated using the PINN method. Toward the end, an artificial neural network (ANN) based forecasting scenario of the pandemic in India is presented. The prediction is found to be reliable as the training of the neural network has been carried out using the unique features, obtained from the state-wide analysis of the newly proposed model as well as from the PINN analysis., Comment: 16 pages, 6 figures, 4 tables

In this work, an 1D electrostatic hybrid-Particle-in-Cell-Monte-Carlo-Collision (h-PIC-MCC) code [1, 2] is used to study the response of a plasma to a moving, external, charged perturbation (debris). We show that the so-called pinned solitons can form only under certain specific conditions through a turbulent regime of the ion-ion counter-streaming electrostatic instability (IICSI). In fact, the pinned solitons are manifestation of the ion phase-space vortices formed around the debris. The simulation shows that the pinned solitons can form only when the debris velocity exceeds a certain critical velocity pushing the instability to a turbulent regime and can then disappear when debris velocity becomes highly supersonic. We further show the existence of a Kolmogorov-type energy cascade scaling [3] for this electrostatic turbulence., Comment: 18 pages, 8 figures

Here, we show that electrostatic solitons in a plasma with turbulent heating of the electrons through an accelerating electric field, can form with very high velocities, reaching up to several order of magnitudes larger than the ion-sound speed. We call these solitons hypersonic solitons. The possible parameter regime, where this work may be relevant, can be found the so-called ``dead zones'' of a protoplanetary disk. These zones are stable to magnetorotational instability but the resultant turbulence can in effect heat the electrons make them follow a highly non-Maxwellian velocity distribution. We show that these hypersonic solitons can also reach very high velocities. With electron velocity distribution described by Davydov distribution function, we argue that these solitons can be an effective mechanism for energy equilibration in such a situation through soliton decay and radiation., Comment: 12 pages, 5 figures

The excitation of nonlinear wave structures in a dusty plasma caused by a moving external charge perturbation is examined in this work, which uses a 1-D flux corrected transport simulation. The plasma responds uniquely to different nature of the moving charge, depending on which, for small amplitude perturbations, pinned envelope solitons are generated and electrostatic dispersive ion-acoustic shock waves are formed for a large amplitude perturbation. The presence of dust particles is found to suppress the formation of dispersive shocks at low velocity of the external charge debris. The results are also investigated theoretically as a solution to the generalized Gross-Piteavskii equation, which broadly supports the simulation results., Comment: 19 pages, 11 figures

Possible existence of chaotic oscillations in ion dynamics in the sheath and pre-sheath regions of a dusty plasma, induced by externally driven dust-charge fluctuation, is presented in this work. In a complex plasma, dust charge fluctuation occurs continuously with time due to the variation of electron and ions current flowing into the dust particles. In most of the works related to dust-charge fluctuation, theoretically it is assumed that the average dust-charge fluctuation follows the the plasma perturbation, while in reality, the dust-charge fluctuation is a semi-random phenomena, fluctuating about some average value. The very cause of dust-charge fluctuation in a dusty plasma also points to the fact that these fluctuations can be driven externally by changing electron and ion currents to the dust particles. With the help of a \emph{hybrid}-Particle in Cell-Monte Carlo (\emph{h}-PIC-MCC) code in this work, we use the plasma sheath as a candidate for driving the dust-charge fluctuation by periodically exposing the sheath-side wall to UV radiation, causing photoemission of electrons, which in turn drive the dust-charge fluctuation. We show that this \emph{driven} dust-charge fluctuation can induce a chaotic response in the ion dynamics in the sheath and the pre-sheath regions., Comment: 16 pages, 11 figures

A low dimensional nonlinear model based on the basic lighting mechanism of a firefly is proposed. The basic assumption is that the firefly lighting cycle can be thought to be a nonlinear oscillator with a robust periodic cycle. We base our hypothesis on the well known light producing reactions involving enzymes, common to many insect species, including the fireflies. We compare our numerical findings with the available experimental results which correctly predicts the reaction rates of the underlying chemical reactions. Toward the end, a time-delay effect is introduced for possible explanation of appearance of multiple-peak light pulses, especially when the ambient temperature becomes low., Comment: 18 pages, 7 figures, 1 table

The results of an analysis of the physics of levitation of negatively charged dust particles over a surface (wall) in an inverse sheath are reported. It is shown that under suitable parameter regime, the ion-drag force may balance the combined electrostatic and gravitational force on the dust particles owing to its hollow profile as one moves away from the surface. Our analysis shows that the parameter regimes in which such a situation may result is realizable in laboratory and space plasma environments, particularly the near-surface dayside lunar plasma. The lunar surface and dust grains are electrostatically charged due to the interaction with the solar wind plasma environment and the photoemission of electrons due to solar UV radiation. This results in a process that charges the surface positively and generates a near-surface photoelectron inverse plasma sheath. The potential structure changes from a monotonic classical sheath to an inverse sheath as the emitted electron density becomes larger than the plasma electron density. In a relatively newer, recently developed charging model, called the Patched Charge Model, it has shown both theoretically and experimentally that even in photoelectron-rich environment, dust particles lying on a regolith surface can attain large negative potential due to formation of micro cavities. This negative potential may reach such values so that dust mobilization and lofting may become possible. In our work, we have assumed the existence of such negatively charged dust particles in a photoelectron-rich environment and argue that once the dust lofting is effected, the levitation can be sustained through the ion-drag force. The conditions of levitation are investigated for these dust particles and the levitation distances from the lunar surface are calculated., Comment: 11 pages, 4 figures

Formation of electrostatic solitary structures are analysed for a magnetised plasma with ion and electron thermal anisotropies. The ion thermal anisotropy is modelled with the help of the Chew-Goldberger-Low (CGL) double adiabatic equations of state while the electrons are treated as inertia-less species with an anisotropic bi-Maxwellian velocity distribution function. A negative electron thermal anisotropy $(T_{e\perp}/T_e{\parallel}>1)$ is found to help form large amplitude solitary structures which are in agreement with observational data., Comment: 15 pages, 4 figures

We consider a van der Pol-Mathieu (vdPM) equation with parametric forcing, which arises in a simplified model of dusty plasma with dust-charge fluctuation. We make a detailed numerical investigation and show that the system can be driven to chaos either through a period doubling cascade or though a subcritical pitchfork bifurcation over an wide range of parameter space. We also discuss the frequency entrainment or frequency-locked phase of the dust-charge fluctuation dynamics and show that the system exhibits 2:1 parametric resonance away from the chaotic regime., Comment: 10 pages, 16 figures

We present an analysis of radiation induced instabilities in an expanding plasma with considerable presence of dust particles and equilibrium cooling. We have shown that the equilibrium expansion and cooling destabilize the radiation condensation modes and the presence of dust particles enhances this effect. We have examined our results in the context of ionized, dusty-plasma environments such as those found in planetary nebulae (PNe). We show that due to the non-static equilibrium and finite equilibrium cooling, small-scale localized structures formed out of thermal instability, become transient, which agrees with the observational results. The dust-charge fluctuation is found to heavily suppress these instabilities, though in view of non-availability of convincing experimental data, a definitive conclusion could not be made., Comment: 23 pages, 14 figures

A minimal (low-dimensional) dynamical model of the sawtooth oscillations is presented. It is assumed that the sawtooth is triggered by a thermal instability which causes the plasma temperature in the central part of the plasma to drop suddenly, leading to the sawtooth crash. It is shown that this model possesses an isolated limit cycle which exhibits relaxation oscillation, in the appropriate parameter regime, which is the typical characteristics of sawtooth oscillations. It is further shown that the invariant manifold of the model is actually the slow manifold of the relaxation oscillation., Comment: 26 pages, 14 EPS figures. accepted for publication in Communications in Nonlinear Science and Numerical Simulations

We investigate the role of thermal instability, arising from radiative cooling of an optically thin, dusty plasma, by linear stability analysis. The corresponding isobaric stability condition for condensation mode is found to be modified significantly by the degree of ionization and concentration of finite sized, relatively heavy, and negatively charged dust particles. It has been shown that though the fundamental wave mode is similar in nature to the one in absence of dust particles, a new dust-wave mode can propagate in such a plasma. It is conjectured that the presence of negatively charged dust particles may considerably affect the stability of various astrophysical structures against thermal instability, which can not be explained with the help of gravitational instability., Comment: 9 pages, 5 eps figures