Nonextensive Parameter Research Articles

Effects of a Nonextensive Dust Charge Variation on an Oblique Collision of Dust Acoustic Solitons in a Dusty plasma

In the current study, two-dimensional collision of two dust acoustic solitons in an unmagnetized nonextensive dusty plasma is investigated, including the effect of non-extensive dust charge variation. By using the extended Poincar-Lighthill-Kuo (PLK) method, two Korteweg-de Vries equations that describe the two dust acoustic solitons propagating in two different directions are derived. The phase shifts after a two-dimensional collision of dust acoustic solitons are obtained as well. The effects of parameters of the ratio of ion temperature to electron temperature, the ratio of ion density to electron density and nonextensive parameter of electrons/ions on the phase shifts are discussed with and without dust charge variation. The results show that the phase shift has been significantly influenced by these parameters. Furthermore, the non-extensive dust charge variation has a significant effect on the amplitude, width of a new nonlinear wave, which generates during the oblique collision.

Nonextensive percolation and Lee-Yang edge singularity from nonextensive λϕ3 scalar field theory

We compute the critical exponents for nonextensive λϕ3 scalar field theory for all loop orders and |q−1|<1. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding systems are nonextensive generalizations of their extensive counterparts. For that we employ tools from the recently introduced nonextensive statistical field theory. The results for the nonextensive critical exponents computed depend on the nonextensive parameter q, which encodes global correlations among the degrees of freedom of the system. The extensive results are recovered in the limit q→1. There is an interplay between global correlations and fluctuations, once the nonextensive critical exponents depend on q. This dependence is in agreement with the universality hypothesis.

Study on the characteristics of non-Maxwellian magnetized sheath in Hall thruster acceleration region

The secondary electron emission (SEE) and inclined magnetic field are typical features at the channel wall of the Hall thruster acceleration region (AR), and the characteristics of the magnetized sheath have a significant effect on the radial potential distribution, ion radial acceleration and wall erosion. In this work, the magnetohydrodynamics model is used to study the characteristics of the magnetized sheath with SEE in the AR of Hall thruster. The electrons are assumed to obey non-extensive distribution, the ions and secondary electrons are magnetized. Based on the Sagdeev potential, the modified Bohm criterion is derived, and the influences of the non-extensive parameter and magnetic field on the AR sheath structure and parameters are discussed. Results show that, with the decrease of the parameter q, the high-energy electron leads to an increase of the potential drop in the sheath, and the sheath thickness expands accordingly, the kinetic energy rises when ions reach the wall, which can aggravate the wall erosion. Increasing the magnetic field inclination angle in the AR of the Hall thruster, the Lorenz force along the direction acting as a resistance decelerating ions becomes larger which can reduce the wall erosion, while the strength of magnetic field in the AR has little effect on Bohm criterion and wall potential. The propellant type also has a certain effect on the values of wall potential, secondary electron number density and sheath thickness.

Decoherence limit of quantum systems obeying generalized uncertainty principle: New paradigm for Tsallis thermostatistics

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this Letter, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis' probability amplitudes, whose non-extensivity parameter $q$ monotonically increases with the GUP deformation parameter $\beta$. Secondly, for $\beta < 0$ (i.e., $q < 1$), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi-classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasi-classical regime has relevant observational consequences. We discuss some of the implications.

Non-flat and non-extensive thermodynamic effects of Møller tetradic theory of gravitation on cosmology

We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of Møller’s tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann–Robertson–Walker (FRW) metric. These two models are affected by the free dimensional parameter, λ, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of λ on open and closed universes. We then use the first law of thermodynamics to construct non-flat cosmological models via the non-extensive thermodynamic approach. The resulting models are affected by λ and the extensive parameter, δ, which quantifies the effect of non-extensive thermodynamics. When we set, λ=0 and δ=1, we return to Einstein’s general relativity models. We study the evolution of our models in the presence of collisionless non-relativistic matter and describe precise forms of the dark energy density and equation-of-state parameter constraining the non-extensive thermodynamic parameter. We show that insertion of the non-extensive thermodynamic parameter affects the non-flat FRW universe in a manner that noticeably differs from that observed under normal thermodynamics. We also show that the deceleration of the open universe behaves as dark energy in a future epoch, i.e., when the redshift approaches −1, i.e., z≈−1.

Ion-scale solitary waves in magnetoplasma with non-thermal electrons

The propagation of ion acoustic (IA) solitary waves (SWs) is investigated in a magnetized electron-ion (EI) plasma with Cairns-Tsallis distributed electrons. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential via a reductive perturbation method (RPM). It is found that increasing values of non-extensive parameter q leads to reduction (enhancement) in amplitude of compressive (rarefactive) solitary structures. The amplitude of compressive (rarefactive) solitary wave (SW) decreases (increases) with increasing values of non-thermality parameter α. Furthermore, it is found that magnetic field strength Ω only affects the width of solitary structures.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this study, we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential based on nonextensive statistical mechanics. A feature of this new statistic is a dimensionless nonextensivity parameter q, which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs (BG) statistics (when , it returns to the BG case). Within the nonextensive Polyakov-Nambu-Jona-Lasinio model, we find that as increases, the critical end point (CEP) in the plane continues to in the plane, and nonextensive effects have a significant impact on the evolution from the CEP to . Generally, with an increase in q, both the CEP and move in the direction of a lower temperature T and larger chemical potential μ (). In addition, we find that chiral charge density generally increases with T, μ, , and q. Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.

Study of midrapidity pt distributions of identified charged particles in Xe+Xe collisions at (snn)1/2 = 5.44TeV using non-extensive Tsallis statistics with transverse flow

The midrapidity transverse momentum [Formula: see text] distributions of the charged pions and kaons, protons, and antiprotons, measured by ALICE Collaboration at nine centrality groups of Xe[Formula: see text]Xe collisions at [Formula: see text], have been reproduced quite well using simultaneous (combined) minimum [Formula: see text] fits with the simple (non-consistent) as well as thermodynamically consistent Tsallis function with included transverse flow. The parameters [Formula: see text], [Formula: see text], and [Formula: see text] extracted in this work using both consistent and non-consistent Tsallis function with included transverse flow demonstrate the similar dependencies on collision centrality [Formula: see text]. The obtained non-extensivity parameter [Formula: see text] values decrease systematically for all studied particle species with increasing Xe[Formula: see text]Xe collision centrality, indicating an increase in degree of system thermalization with increasing centrality of heavy-ion collisions. The average transverse flow velocity demonstrates significantly different growth rates in regions [Formula: see text] and [Formula: see text], and parameter [Formula: see text] stays constant within uncertainties in [Formula: see text] range in Xe[Formula: see text]Xe collisions at [Formula: see text]. It is argued that [Formula: see text] could possibly be a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Xe[Formula: see text]Xe collisions at [Formula: see text]. Depletion (enhancement) of [Formula: see text] ratio at low [Formula: see text] (intermediate [Formula: see text]) has been observed in this work in Xe[Formula: see text]Xe collisions at [Formula: see text], which agrees with the similar results of ALICE Collaboration obtained recently in high-energy Xe[Formula: see text]Xe and [Formula: see text] collisions at the LHC. Analyzing and reflecting the extracted [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] dependencies, we have verified that the depletion (enhancement) of baryon-to-meson ratio at low [Formula: see text] (intermediate [Formula: see text]) values with increasing [Formula: see text] is due to radial flow effects.

The Novel Scaling of Tsallis Parameters from the Transverse Momentum Spectra of Charged Particles in Heavy-Ion Collisions

The transverse momentum (pT) spectra of charged particles measured in Au + Au collisions from the beam energy scan (BES) program, Cu + Cu collisions at sNN=62.4, 200 GeV at the RHIC and Pb + Pb, Xe + Xe collisions at the LHC are investigated in the framework of Tsallis thermodynamics. The theory can describe the experimental data well for all the collision systems, energies and centralities investigated. The collision energy and centrality dependence of the Tsallis distribution parameters, i.e., the temperature T and the nonextensive parameter q, for the A + A collisions are also studied and discussed. A novel scaling between the temperature divided by the natural logarithm of collision energy (T/lns) and the nonextensive parameter q is presented.

Nonextensive statistical field theory

We introduce a field-theoretic approach for describing the critical behavior of nonextensive systems, systems displaying global correlations among their degrees of freedom, encoded by the nonextensive parameter q. As some applications, we report, to our knowledge, the first analytical computation of both universal static and dynamic q-dependent nonextensive critical exponents for O(N) vector models, valid for all loop orders and |q−1|<1. Then emerges the new nonextensive O(N)q universality class. Both exponents ηq and zq reduce to those when q=1 for N→∞. We employ six independent methods which furnish identical results. Particularly, the results for nonextensive 2d Ising systems, exact within the referred approximation, agree with that obtained from computer simulations, within the margin of error, as better as q is closer to 1. We argue that the present approach can be applied to all models described by extensive statistical field theory as well. The results show an interplay between global correlations and fluctuations.

The ion acoustic solitary waves in the four-component complex plasma with a Cairns-Tsallis distribution

We study the ion acoustic solitary waves in the four-component complex plasma consisting of cold inertial ions, positrons, cold and hot (two-temperature) electrons, where the electrons and positrons are a Cairns-Tsallis distribution and have different nonthermal and nonextensive parameters. Base on the plasma hydrodynamic equations and Sagdeev pseudo-potential theory, we derive the conditions of the solitary waves to exist in the plasma, such as the Sagdeev pseudo- potential, the normalized electrostatic potential, the lower and upper limits of Mach number, and the compressive/rarefactive solitary wave. We show that, according to the present study, the solitary wave solutions exist only if the positrons are a Maxwellian distribution and the two-temperature electrons have the same nonextensive and nonthermal parameters. Numerical analyses are made for the conditions of solitary waves depending on the nonextensive and nonthermal parameters in the Cairns-Tsallis distribution.

Initial measurement of ion nonextensive parameter with geodesic acoustic mode theory

The consideration of nonextensivity effects is crucial to the accurate diagnosis of plasma parameters; common plasma nonextensive parameters include electron nonextensive parameter and ion nonextensive parameter, and the former can be measured, while the ion nonextensive parameter cannot be measured yet. Here we show the measurement of ion nonextensive parameter of plasma based on the theory of nonextensive geodesic acoustic modes. We assume that the plasma to be measured can be described by nonextensive statistical mechanics, and on this basis, the nonextensive geodesic acoustic mode theory is established. Utilizing this theory, we have measured the ion nonextensive parameter {{q}_{{{F}_{mathrm {i}}}}}= 1.565 which cannot be diagnosed even by a nonextensive single electric probe. Our research points out that the proposed measurement method of ion nonextensive parameter may play a role in plasma diagnosis and will help us to grasp the nonextensivity of plasma more precisely. We hope the proposed method of ion nonextensive parameter diagnosis based on the nonextensive geodesic acoustic mode theory can be the starting point of more complex ion nonextensive parameter diagnosis methods. In addition, the measurement of ion nonextensive parameter is closely related to the study of various plasma waves, instabilities, turbulence and abnormal transport, and a defined and quantitative test of nonextensive geodesic acoustic mode theory will bound up deeply with such developments.

Self-Adaptive Image Thresholding within Nonextensive Entropy and the Variance of the Gray-Level Distribution.

In order to automatically recognize different kinds of objects from their backgrounds, a self-adaptive segmentation algorithm that can effectively extract the targets from various surroundings is of great importance. Image thresholding is widely adopted in this field because of its simplicity and high efficiency. The entropy-based and variance-based algorithms are two main kinds of image thresholding methods, and have been independently developed for different kinds of images over the years. In this paper, their advantages are combined and a new algorithm is proposed to deal with a more general scope of images, including the long-range correlations among the pixels that can be determined by a nonextensive parameter. In comparison with the other famous entropy-based and variance-based image thresholding algorithms, the new algorithm performs better in terms of correctness and robustness, as quantitatively demonstrated by four quality indices, ME, RAE, MHD, and PSNR. Furthermore, the whole process of the new algorithm has potential application in self-adaptive object recognition.

Effect of dust polarity on transcritical bifurcation of dust ion-acoustic waves in a nonextensive dusty plasma

In this paper, we combine bifurcation techniques and numerical simulations to fully analyze the nonlinear propagation of dust ion-acoustic waves in a complex dusty plasma consisting of warm adiabatic ions, nonextensive electrons, and negatively (positively) charged dust particles. An autonomous dynamical system is derived which captures the main features of traveling wave solutions and transition between nonlinear modes. It is shown that for a range of electron nonextensivity and negative (positive) dust concentration, there are different existence domains of stability regions. At the critical points of nonextensivity parameter and dust concentration, we show that the motion dynamics of low-frequency dust ion-acoustic traveling waves undergoes a transcritical bifurcation, where two equilibrium points coalesce, and then switch their stability. A new kind of solitary structure is also observed which is characterized by the transcritical bifurcation parameters with half-stable equilibrium points. It is found that an increase in negative (positive) dust concentration leads to the appearance of bifurcation points at larger (smaller) values of electron nonextensivity. In accordance with the phase portraits analysis, the coexistence of homoclinic orbits, nonlinear periodic and supernonlinear periodic orbits are also investigated for different conditions. It is shown that the nonextensive parameter and dust polarity play a crucial role in the transition between nonlinear traveling waves.

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

We describe a procedure to obtain the plasma parameters from the I-V Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, q and r, to the usual plasma parameters: plasma potential (V p ), floating potential (V f ), electron density (n), and electron temperature (T). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the I-V Langmuir curve with the q-Weibull distribution function, and is motivated by recent works which use the q-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the q-exponential distribution function, and the q-Weibull distribution function. We explain the limitations of the q-exponential function, where the experimental data V > V p needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the q-Weibull function is introduced as a natural generalization to the q-exponential distribution, and it has greater flexibility in order to represent the concavity change around V p . We apply this procedure to analyze the measurements corresponding to a nitrogen N 2 cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the q parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.

A Modified SIR Model for the COVID-19 Epidemic in China

The analysis of the coronavirus disease 2019 (COVID-19) is of great importance to deeply understand the dynamics of this coronavirus spread. Based on the complexity of it, a modified susceptible-infected-removed (SIR) model is applied to analyse the time dependence of active and hospitalized cases in China. The time evolution of the virus spread in different provinces was adequately modelled. Changeable parameters among them have been obtained and turned to be not naively independent with each other. The non-extensive parameter was found to be strongly connected with the freedom of systems. Taken into the prevention and treatment of disease, more measures by the government lead to higher values of it.

Researches on the COVID-19 epidemic in the world within a nonextensive SIR model

The coronavirus disease 2019 (COVID-19) epidemic was investigated within a general Susceptible-Infectious-Removed (SIR) model, especially the distributions of its dead cases and infectious ones. This paper applied its nonextensive modification with respect to more realistic situations. A time-dependent SIR model was modified when particularly regarding control and mitigation measures in response to the societal impacts of epidemics and pandemics. We validated all the theoretical results by fitting the derived q -distributions with data from the COVID-19 pandemic in the world. It was found that not all the changeable fit parameters are independent, some of which shared common properties, a result corroborated by our model prediction. Our modified SIR model was proved to be effective in fitting the COVID-19 epidemic distributions. The relative non-extensive parameter was strongly connected with the freedom of systems, which thus threw a light upon the prevention and treatment of disease next in the world.

The overtaking interaction of electron acoustic solitary waves in a plasma with hot non-extensive electrons

In the present work, we investigate the propagation and overtaking interaction of electron-acoustic solitary waves (EASWs) in a plasma comprising cold electron fluid, hot nonextensive electrons and immobile ions. For this purpose, the Korteweg–de Vries (KdV) equation is derived for this model. Then Hirota’s direct method is used to the KdV equation to obtain multisoliton solution for studying the interaction process. Our one-dimensional plasma model supports rarefactive EASWs. For both single soliton and multisoliton solutions, the amplitude and velocity of the solitons increase with the increase of nonextensivity or superthermality of hot electrons. It is found that the temporal scale of collision between two solitons decreases with the decrease of nonextensive parameter . The choice of propagation vectors on the interaction of the solitons is also significant. The present analysis may be helpful for further study of the modified bipolar or tripolar electric field signatures observed in the auroral zone.

First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises

We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis’ q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge–Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed.

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems.