Nonextensive Parameter Research Articles

Event Shape and Multiplicity Dependence of Freeze-Out Scenario and System Thermodynamics in Proton+Proton Collisions at s = 13 TeV Using PYTHIA8

Recent observations of QGP-like conditions in high-multiplicity pp collisions from ALICE experiment at the LHC warrant an introspection whether to use pp collisions as a baseline measurement to characterize heavy-ion collisions for the possible formation of a Quark-Gluon Plasma. A double differential study of the particle spectra and thermodynamics of the produced system as a function of charged-particle multiplicity and transverse spherocity in pp collisions would shed light on the underlying event dynamics. Transverse spherocity, one of the event shape observables, allows to separate the events in terms of jetty and isotropic events. We analyse the identified particle transverse momentum ( p T ) spectra as a function of charged-particle multiplicity and transverse spherocity using Tsallis nonextensive statistics and Boltzmann-Gibbs Blast-Wave (BGBW) model in pp collisions at s = 13 TeV using PYTHIA8 event generator. The extracted parameters such as temperature ( T ), radial flow ( β ), and nonextensive parameter ( q ) are shown as a function of charged-particle multiplicity for different spherocity classes. We observe that the isotropic events approach thermal equilibrium while the jetty ones remain far from equilibrium. We argue that, while studying the QGP-like conditions in small systems, one should separate the isotropic events from the spherocity-integrated events, as the production dynamics are different.

Role of electrons non-extensivity on the fully nonlinear dust-ion acoustic solitary waves

Fully nonlinear dust-ion acoustic solitary waves are investigated in a multi-species plasma model comprised of warm positive mobile ions with a non-zero ion temperature, non-extensive electrons and negatively charged dust particles. Basic plasma system is reduced to a single energy integral using pseudopotential analysis without sorting to any perturbations or approximation scheme. Existence regions of positive and negative dust-ion acoustic waves as well as soliton profile are determined through phase portrait analysis and numerical investigations. Effects of the electrons non-extensivity parameter, temperature ratios, fractional densities and soliton speeds on both soliton polarities profiles and their corresponding pseudopotentials show that existence domains and soliton characteristics are inherently affected in the considered plasma regime. Bifurcation analysis as well as numerical investigations, revealed that only negative soliton polarities exist for plasma parameters observed in the Earth’s auroral ionosphere.

Characteristics of supernonlinear and coexistence features for electron-acoustic waves in an adiabatic quantum plasma

Bifurcation of quantum electron-acoustic waves (QEAWs) is studied in an adiabatic quantum plasma with nonextensively distributed hot electrons. Using reductive perturbation technique, modified Kortweg de Vries (KdV) equation is derived with dual power nonlinearity for highly nonlinear QEAWs. Using Galilean transformation the modified KdV equation is reduced to a planar dynamical system with three equilibrium points. Applying phase plane analysis periodic wave solutions and supernonlinear periodic wave solutions for QEAWs are perceived. It is found that the amplitude of the nonlinear structures is indirectly proportional to the ratio of number densities ( $$\mu $$ ), the cold to hot electron temperature ratio ( $$\sigma $$ ) and the nonextensivity parameter (q), we have explained physically that confronts our results. In addition, coexistence of superperiodic and quasiperiodic phenomena, quasiperiodic and chaotic phenomena and chaotic, superperiodic and quasiperiodic phenomena for QEAWs are observed for appropriate initial values.

Non-Extensive Thermodynamics Effects in the Cosmology of f(T) Gravity

Using f(T) gravitational theory, we construct modified cosmological models via the first law of thermodynamics by using the non-extensive thermodynamics framework, the effects of which are captured by the parameter δ. The resulting cosmological equations are modified compared to the standard Einstein-Hilbert ones, with the modifications coming from the f(T) gravitational theory and from the non-extensive parameter which quantifies the non-extensive thermodynamics effects quantified by the parameter δ, which when is set equal to unity, one recovers the field equations of f(T) gravity. We study in detail the cosmological evolution of the model in the presence of collisionless non-relativistic matter case, and we derive the exact forms of the dark energy density parameter and of the dark energy equation of state parameter, from which we impose constraints on the non-extensive thermodynamics parameter, δ, by using the Planck 2018 data on cosmological parameters. Accordingly, we repeat our calculations after including the relativistic matter along with the non-relativistic one, and we derive the new forms of the dark energy density parameter and of the dark energy equation of state parameter. Our study shows that the inclusion of non-extensive thermodynamic effects, quantified by the parameter δ, for a flat Friedmann-Robertson-Walker Universe, has measurable differences compared with the normal thermodynamics case. We confront our results with Type Ia supernovae observations for z≥0.4 and we obtain reasonably agreement with the observational data.

Nonextensive Analysis of Aftershocks Following Moderate Earthquakes in Tien Shan and North Pamir

Aftershock sequences have been identified for 60 earthquakes (K ≥ 11) from the catalog of the Institute of Seismology, National Academy of Sciences, Kyrgyz Republic (to be referred to as KIS in what follows). The catalog includes 56 259 events that have occurred in Tien Shan and North Pamir during the period from 1980 to 2001. We have obtained some statistical characteristics of the catalog and determined its completely reported part. A map of seismic activity has been made. We determined some parameters of main events and aftershock sequences. The lowest number of aftershocks was 3 events, the largest number was 2370, the shortest duration of the aftershock process was 2 days and the longest 2046 days. The earthquake catalog and the aftershock sequences were treated from the standpoint of nonequilibrium thermodynamics using the Tsallis statistic (the parameters q and a). We sought to obtain a description of earthquakes over energy using a modified stick-slip earthquake source model and the principle of maximum entropy. This approach was used to obtain a quantitative estimate of the nonextensive Tsallis parameter q for seismicity, as well as to estimate the variation of that parameter just before a large earthquake and during aftershocks. It was shown that seismicity is a system with memory and long-range spatial correlations. The Tsallis parameter q for aftershock sequences exceeds the value of q based on the entire catalog, thus indicating an unstable state of the earthquake-generating system during aftershocks. One observed a sharp increase in the Tsallis parameter q in an area that includes the precursory area before the main event and a sharp drop at once after it, gradually returning to the average level observed before the main event.

Characteristics of non-Maxwellian magnetized sheath with secondary electron emission

In this paper, the effects of non-Maxwellian distribution of electrons on the characteristics of magnetized plasma sheath with secondary electron emission are investigated by using a magnetic fluid model of one-dimensional velocity and three-dimensional space. The velocity of electrons follows the non-extensive distribution, and the ions are magnetized in a magnetic field with a certain tilt angle relative to the wall. The effects of the non-extensive electron distribution parameter <i>q</i> and the magnetic field strength and angle on the Bohm criterion, the floating wall potential, the secondary electron number density at the sheath edge, the sheath thickness and the ion velocity are studied by establishing the self-consistent equations. When the electron velocity distribution deviates from the Maxwellian distribution, the results show that as the <i>q</i>-parameter increases, the value of the Bohm criterion decreases, the floating wall potential increases, the number of secondary electrons at the sheath increases, the sheath thickness decreases, the number density of ions and electrons decline faster, the number density of ions near the wall is higher, and the velocities of the ions in the three directions are all reduced. In addition, as the magnetic field strength increases, the sheath thickness decreases, and the number density of ions and electrons in the sheath area decrease rapidly; the larger the magnetic field angle, the more significant the influences of the parameter <i>q</i> on the wall potential and the sheath thickness are, while the velocity component of the ion in the <i>x</i>-direction decreases with the increase of the magnetic field angle, but in the case of super-extensive distribution (<i>q</i> < 1), the velocity change near the wall presents an opposite trend, the increase of magnetic field angle causes wall velocity to increase; when it is close to Maxwellian distribution (<i>q</i> → 1), the velocity near the wall does not depend on the change of the magnetic field angle and basically tends to be identical; in the case of sub-extensive distribution (<i>q</i> > 1), the velocity near the wall decreases with the magnetic field angle increasing.

Magnetic Fields Observed by Voyager 2 in the Heliosheath

Abstract We present observations of the magnetic field in the outermost region of the heliosheath made by Voyager 2 (V2) from 2016 to 2018.6, just before V2 entered the magnetic barrier inside of the heliopause. The average magnetic field strength (B) during this interval was relatively large, 0.135 nT, mainly due to numerous merged interaction regions. Sector structure was observed, and the direction of azimuthal angle λ was primarily close to the Parker spiral magnetic field directions 90° and 270°. Thus, the heliospheric current sheet extended to relatively high southern latitudes poleward of V2 (>30°). On smaller scales, distributions of daily increments in B and the components of from 2016 to 2018.6 were accurately described by q-Gaussian distributions. The average values of the nonextensivity parameter q for one-day increments of the components decreased from q = 1.7 ± 0.01 during 2016 (near solar maximum) to q = 1.3 ± 0.1 during 2017 and 2018, as solar activity declined. The BT direction was close to the average magnetic field direction, and V2 measured primarily compressible fluctuations. These new results are also presented in the context of an overview of the observations of the magnetic field in the heliosheath from the termination shock crossing to the heliopause.

Jeans instability of Eddington-inspired Born-Infield gravitational systems in the context of nonextensive statistics

Criterion of the Jeans modes for self-gravitational systems in Eddington-inspired Born-Infeld (EiBI) gravity is revisited based on the framework of nonextensive statistics and kinetic theory. The results show the nonextensive parameter q has significant effects on the growth rate and critical wave-number of Jeans instability for the EiBI-gravitational systems. Also, we prove that the standard dispersion relationship proposed by Binney can be recovered if q→1 and τ→0. Concept of Jeans critical value (that is, the Jeans thresholds of EiBI gravitational systems) obtains a more tight emendation and the results of present work may provide theoretical references for the evolution of stars such as neutron stars, accretion disks, and relevant plasma physics, etc.

A two-dimensional Weibel instability simulation using the non-extensive distribution function

In this paper, the analysis of Weibel instability for electron–positron plasma is carried out by applying the q non-extensive velocity distribution function. Our analysis is based on two dimensional fully kinetic electromagnetic relativistic electromagnetic (EM) particles in cell simulation. The simulation results show the steepening of the distribution function by increasing the q-factor and decreasing the total energy of the system. From plots it can be manifested that in all cases, the particles give energies to the EM fields, and hence, the strength of magnetic tubes decreases. For the non-extensive parameter q = 10, the electron energy levels are higher than the positron energy levels and give energy to both positrons and EM fields.

Three-dimensional dissipative ion-acoustic rogue waves in magnetized plasma with adiabatic ions and nonextensive electrons

ABSTRACT The modulational instability of ion-acoustic rogue waves in a three-dimensional magnetized, dissipative plasma consisting of inertial warm positive ions and nonextensive electrons has been theoretically investigated. Using the well-known reductive perturbation method, the (3+1)-dimensional modified nonlinear Schrödinger equation (mNLSE), i.e. the standard NLSE in addition to the dissipative term has been derived and then solved to obtained instability criteria, as well as first- and second-order rogue wave solutions. It is found that increasing viscosity results in dissipation of energy which makes the IARW shorter and thinner as was reported in the literature. Furthermore effects of relevant parameters such as nonextensive parameter, and magnetic field on growth rate and rogue waves solutions were discussed in detail. The results of the present investigation may be useful in understanding and predicting the nonlinear excitations that occur in space and laboratory dissipative plasma systems.

Systematic analysis of midrapidity transverse momentum spectra of identified charged particles in p + p collisions at (snn)1/2 = 2.76, 5.02, and 7 TeV at the LHC

The experimental transverse momentum spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in inelastic [Formula: see text] collisions at [Formula: see text], 5.02, and 7 TeV, measured by ALICE collaboration, are analyzed systematically using the thermodynamically consistent Tsallis distribution function as well as Hagedorn function with the embedded transverse flow. To compare directly the results obtained from combined (simultaneous) fits with the above theoretical model functions of midrapidity spectra of the charged pions and kaons, protons and antiprotons in [Formula: see text] collisions at [Formula: see text], 5.02, and 7 TeV, we use the optimal identical fitting [Formula: see text] ranges [Formula: see text] in [Formula: see text] collisions at [Formula: see text], 5.02, and 7 TeV. The parameter [Formula: see text] increases consistently for all the particle species with increasing [Formula: see text] of [Formula: see text] collisions from 2.76 to 5.02 TeV, remaining practically constant within fit errors in the collision energy range [Formula: see text] TeV, suggesting probably a saturation and limiting behavior of the [Formula: see text] value in [Formula: see text] collisions at [Formula: see text] TeV. Approximate equality of the extracted nonextensivity parameter [Formula: see text] for the pions and kaons ([Formula: see text]) and relation [Formula: see text] are obtained in [Formula: see text] collisions at [Formula: see text], 5.02, and 7 TeV. Very negligible transverse (radial) flow velocity (consistent with zero value within the fit errors) is obtained in [Formula: see text] collisions at [Formula: see text], 5.02, and 7 TeV from fitting the [Formula: see text] distributions of the charged pions and kaons, protons and antiprotons with the Hagedorn formula with the embedded transverse flow in the selected optimal identical [Formula: see text] ranges as well as in the full measured [Formula: see text] ranges.

The structure of an electronegative magnetized plasma sheath with non-extensive electron distribution

In this paper, an electronegative magnetized plasma sheath model with non-extensive electron distribution is established, and the Bohm criterion affected by the non-extensive parameter q is theoretically derived. The ion Mach number varies with q. The numerical simulation results show that compared with electronegative magnetized plasma sheath with Maxwell distribution (q = 1), the sheath structures with super-extensive distribution (q < 1) and sub-extensive distribution (q > 1) are different. The physical quantities including the sheath potential distribution, ion density distribution, the electron density distribution, negative ion density distribution and the net space charge density distribution are discussed. It is shown that the non-extensive parameter q has a significant influence on the structure of the electronegative magnetized plasma sheath. Due to the Lorentz force, both the magnitude and the angle of the magnetic field affect the structure of the sheath, whether the electrons are Maxwell distributed or non-extensively distributed.

Modulation of the Nonlinear Ion Acoustic Waves in a Weakly Relativistic Warm Plasma with Nonextensively Distributed Electrons

A reductive perturbation technique (multiple scales) is applied to a weakly relativistic warm unmagnetized adiabatic plasma system consisting of inertial ions fluid and nonextensively distributed electrons. A nonlinear Schrodinger-type (NST) equation for finite wave number at the second order is derived. Using the reductive perturbation technique we derived the corresponding Korteweg-de Vries (K-dV) equation. For small wavenumber limit the K-dV equation is transformed into NST equation. It is found that the coefficient of the NST equation obtained from the K-dV equation agree with the corresponding coefficients of NST equation obtained by the multiple scales. Moreover we investigated the effect of the physical parameters of the system namely temperature ratio of the ion temperature T_i to electron temperature T_e, the relativistic factor u_0/C as well as the nonextensive parameter (q) of the distribution on the stability/instability of the system. It is found that these parameters affect strongly on the stability/instability regions. Finally, the validity of our results in astrophysical plasma is briefly discussed.

Thermodynamics and Van der Waals phase transition of charged black holes in flat spacetime via Rényi statistics

The phase structure and critical phenomena of the 3+1 dimensional charged black holes in asymptotically flat spacetime are investigated in terms of thermodynamic properties within the R\'enyi statistics. With this approach as the non-extensive parameter above zero, we find that the charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation, and have a Hawking-Page phase transition in the same way in the case of AdS charged black hole. This gives more evidence supporting the proposal that there exists an equivalence between the black hole thermodynamics in asymptotically flat spacetime via R\'enyi statistics and that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics, proposed by Czinner et al. However, the present work also provides another aspect of supporting evidence through exploring the extended phase space within the R\'enyi statistics. Working on a modified version of Smarr formula, the thermodynamic pressure $P$ and volume $v$ of a charged black hole are found to be related to the non-extensive parameter. The resulting $P-v$ diagram indicates that the thermodynamics of charged black holes in asymptotically flat spacetime via R\'enyi statistics has the Van der Waals phase structure, equivalent to that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics.

Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma

Bifurcation analysis of ion-acoustic wave (IAWs) solutions of the nonlinear Schrödinger equation (NLSE) is explored for the first time in an electron-ion (e-i) magnetized solar wind plasma. The existence of ion-acoustic (IA) periodic, superperiodic, kink, antikink, compressive and rarefactive solitary wave solutions are revealed. Special values of Solar wind plasma parameters at a normalized distance from the Sun are considered for numerical simulation. The IA wave solutions are derived analytically. These solutions are analyzed numerically considering the influence of parameters, namely, wave number (k), velocity (V) of traveling wave and nonextensive parameter (q). Computational simulation reveals that only IA periodic wave grows in amplitude as waves moves from the Sun.

Similarities in Multiparticle Production Processes in pp Collisions as Imprints of Nonextensive Statistics

The transverse momentum pT spectra of both hadrons and jets produced in pp collisions at beam energies from hundreds GeV to a few TeV exhibit power-law behavior of 1/pTn at high pT, with similar power indices n. The respective nonextensivity parameters for transverse momenta distributions and the global nonextensivity parameter obtained from multiplicities are compared. In particular, data on kaon to pion (charged particles) multiplicity ratio are analyzed, assuming that the reaction occurs in some nonextensive environment. The values of the corresponding nonextensivity parameters were found to be similar, strongly indicating the existence of a common mechanism behind all these observables.

Tungsten and Molybdenum Surfaces Exposed to Warm Deuterium Ion Plasma with Q-Nonextensive Distribution of Electrons

This work is concerned with the effect of non-Maxwellian electrons and obliqueness of magnetic field on magnetized plasma sheath characteristics, in which plasma interacts with tungsten (W) and molybdenum (Mo) surfaces via non-neutral plasma sheath using two fluids model. It is assumed that the singly charged positive ions are treated as warm fluid whereas the electrons obey q-nonextensive distribution. It is found that the q-nonextensive distributed electrons and the temperature of ions affect the entrance velocity of positive ions, which is a key parameter in the plasma sheath formation. Also, the nonextensive parameter q affects the distribution of ions and electrons in the sheath region and their distributions explicitly related with the electrostatic potential variation. The parallel and perpendicular components of ions velocity are affected by the obliqueness of magnetic field. As the nonextensivity of electrons increases, the gradient in electric potential increases towards the wall and hence the impact energy also increases. The obliqueness of magnetic field and impact energy of ions is a key factor that determines the physical sputtering rate, particle reflection and absorption from the target surface. Furthermore, the probability of particle reflection coefficient from the W-surface is higher than that of Mo-surface.

Nonplanar ion acoustic waves in dusty plasma with two temperature electrons: Application to Saturn's E ring

In the present paper, we have studied the cylindrical/spherical ion acoustic waves in dusty plasma consisting of positive ions, immobile dust particles, and q nonextensive distributed cold and hot electrons. A multiple scale expansion method is employed to derive a modified Korteweg–de Vries (mKdV) equation. Exact analytical solution for the mKdV equation in nonplanar geometry is obtained using the weighted residual method. This solution is, then, plotted for different physical parameters relevant to Saturn's E ring through 2D figures. We show that the amplitude of the wave decreases faster as one departs away from the axis of the cylinder or the center of the sphere. Such a decaying behavior continues as time progresses. This is expected from the obtained solution where the cylindrical (spherical) amplitude component (τ∞/τ)m decreases as the time progresses. We have also studied the role of the nonadiabatic dust charging fluctuating dissipation process and analyzed the resulting damped mKdV equation. Furthermore, the parametric dependence of wave properties (amplitude and width) on the q nonextensive parameter, density, and temperature of cold and hot electrons, concentration of dust particles, and thermal effects of ions has been studied in detail, and findings obtained here will be beneficial to further astrophysical investigations.

Numerical investigation of secondary electron emission effect on the dusty plasma sheath with superextensive electrons

We have investigated the structure of a magnetized sheath of dusty plasma in the presence of secondary electrons emitted by the micro-size dust particles in the context of the Tsallis statistics. The fluid model is used to analyze numerically the effects of the nonextensivity parameter q on the emission of secondary electrons and therefore, on the sheath structure as well as the dust dynamics. The results show that the secondary emission yield increases with the decrease of the parameter of nonextensivity q and consequently, the dust charge becomes less negative with its range of values playing a primordial role in the secondary electron emission rate. The quantities characterizing the sheath are significantly affected by the secondary electron emission (SEE) from the dust. It is seen that as the SEE rises at a given value of q(q&amp;lt;0.91), the sheath potential decreases as well as its absolute value at the wall. In addition, the dynamics of the dust particles is also affected by the emission of secondary electrons.

Ordinary and extraordinary waves in hot nonextensive plasma

In this paper, a kinetic method based on particle velocity distribution function in the context of the nonextensive Tsallis statistics is presented for ordinary and extraordinary waves in a collisionless magnetized hot plasma. The components of the generalized dielectric tensor for perpendicular propagation in hot nonextensive plasma are derived in terms of generalized hypergeometric functions. The components are expressed as functions of different values of the nonextensive parameter q, which quantifies the degree of nonextensivity of the system. The dispersion relations of ordinary and extraordinary waves in hot plasma are obtained in the context of the nonextensive statistics. It is shown that in hot nonextensive plasma the generalized dispersion relations of these waves depend on q parameter, which means that the initial distribution function alters the properties of ordinary and extraordinary waves. For the hot nonextensive plasma, the ordinary and extraordinary wave experience resonances at cyclotron harmonics, whilst the upper hybrid resonance is eliminated due to thermal effects. However, cutoff frequencies shift to higher values as q parameter increases.