Effect of Electron and/or Ion Nonthermality on Dust Acoustic Wave Propagation in a Complex Plasma in Presence of Positively Charged Dust Grains Generated by Secondary Electron Emission Process

In this paper we have developed a model to study the role of both electron and ion nonthermalities on dust acoustic wave propagation in a complex plasma in presence of positively charged dust grains. Secondary electron emission from dust grains has been considered as the source of positive dust charging. As secondary emission current depends on the flux of primary electrons, nonthermality of primary electrons changes the expression of secondary emission current from that of earlier work where primary electrons were thermal. Expression of nonthermal electron current flowing to the positively charged dust grains and consequently the expression of secondary electron current flowing out of the dust grains have been first time calculated in this paper, whereas the expression for nonthermal ion current flowing to the positively charged dust grains is present in existing literature. Dispersion relation of dust acoustic wave has been derived. From this dispersion relation real frequency and growth rate of the wave have been calculated. Results have been plotted for different strength of nonthermalities of electrons and ions.

Study of the Characteristics of Dust Acoustic Solitary Waves and Dust Acoustic Shock Waves in Electron Free Dusty Space Plasma

A theoretical investigation has been done for the study of dust acoustic solitary waves and dust acoustic shock waves propagating in an unmagnetized, collisionless Lorentzian dusty plasma considering adiabatic and non-adiabatic dust charge variation. Plasma under consideration is composed of inertialess Lorentzian positive and negative ions along with inertial positively charged dust grains. Such dust grains are charged by the flow of positive ion and negative ion current over the grain surface. Adiabatic grain charge variation shows the existence of compressive soliton whose amplitude decreases and width increases with increasing number of suprathermal particles. Non-adiabatic dust charge variation is concerned with the propagation of monotonic dust acoustic shock waves which do not loose monotonicity even when a number of suprathermal particles are very large.

Ion Nonthermality Induced Nonlinear Dust Acoustic Wave Propagation in a Complex Plasma in Presence of Weak Secondary Electron Emission from Dust Grains

In this paper we have investigated the effect of ion nonthermality on nonlinear dust acoustic wave propagation in a complex plasma in presence of weak secondary electron emission from dust grains. Equilibrium dust charge in this case is negative. Dusty plasma under our consideration consists of inertialess nonthermal ions, Boltzman distributed primary and secondary electrons and negatively charged inertial dust grains. Both adiabatic and nonadiabatic dust charge variations have been taken into account. Our analysis shows that in case of adiabatic dust charge variation, at a fixed non-zero ion nonthermality increasing secondary electron emission decreases amplitude and increases width of the rarefied dust acoustic soliton whereas for a fixed secondary electron yield increasing ion nonthermality increases amplitude and decreases width of such rarefied dust acoustic soliton. Thus shape of the soliton may be retained if strength of both the secondary electron yield and the ion nonthermality are increased. Nonadiabatic dust charge variation shows that, at fixed non-zero ion nonthermality, increasing secondary electron emission suppresses oscillation of oscillatory dust acoustic shock at weak nonadiabaticity and pronounces monotonicity of monotonic dust acoustic shock at strong nonadiabaticity. On the other hand at a fixed value of the secondary electron yield, increasing ion nonthermality enhances oscillation of oscillatory dust acoustic shock at weak nonadiabaticity and reduces monotonicity of monotonic dust acoustic shock at strong nonadiabaticity. Thus nature of dust acoustic shock may also remain unchanged if both secondary electron yield and ion nonthermality are increased.

Fractional Weierstrass Function by Application of Jumarie Fractional Trigonometric Functions and Its Analysis

The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.

Mathematical model of zika virus dynamics with vector control and sensitivity analysis

In this paper,we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death.To formulate the model,we assume that the Zika virus is being first transmitted to human by mosquito bite,and then it is being transmitted to his or her sexual partner.The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points,exists under certain conditions.The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one.Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one.The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value.We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia.Furthermore,using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate,recruitment rate of mosquito,transmission probability per biting of Susceptible(infected)humans with infected(susceptible)mosquito,rate of awareness in host population,recovery rates of infected human are most sensitive parameters of the considered Zika model.Lastly,some conclusions are given to control the spreading of the Zika disease.