Failure evolution and disaster prediction of rock under uniaxial compression based on non-extensive statistical analysis of electric potential

Rock failure can cause serious geological disasters,and the non-extensive statistical features of electric potential(EP)are expected to provide valuable information for disaster prediction.In this paper,the uniaxial compression experiments with EP monitoring were carried out on fine sandstone,marble and granite samples under four displacement rates.The Tsallis entropy q value of EPs is used to analyze the selforganization evolution of rock failure.Then the influence of displacement rate and rock type on q value are explored by mineral structure and fracture modes.A self-organized critical prediction method with q value is proposed.The results show that the probability density function(PDF)of EPs follows the q-Gaussian distribution.The displacement rate is positively correlated with q value.With the displacement rate increasing,the fracture mode changes,the damage degree intensifies,and the microcrack network becomes denser.The influence of rock type on q value is related to the burst intensity of energy release and the crack fracture mode.The q value of EPs can be used as an effective prediction index for rock failure like b value of acoustic emission(AE).The results provide useful reference and method for the monitoring and early warning of geological disasters.

Non-extensive statistical distributions of charmed meson production in Pb-Pb and pp(p)collisions

The mid-rapidity transverse momentum spectra of charmed mesons in Pb–Pb and pp(p)collisions are analyzed using the Tsallis–Pareto distribution derived from non-extensive statistics.We provide uniform descriptions of both small and large systems over a wide range of collision energies and hadron transverse momenta.By establishing the relationship between the event multiplicity and Tsallis parameters,we observe that there is a signifi-cant linear relationship between the thermal temperature and Tsallis q parameter in Pb–Pb collisions at √sNN=2.76 TeV and 5.02 TeV.Further,the slope of the T–(q-1)parameter plot is positively correlated with the hadron mass.In addition,charmed mesons have a higher thermal temperature than light hadrons at the same q-1,indicat-ing that the charm flavor requires a higher temperature to reach the same degree of non-extensivity as light flavors in heavy-ion collisions.The same fit is applied to the trans-verse momentum spectra of charmed mesons in pp(p)collisions over a large energy range using the Tsallis–Pareto distribution.It is found that the thermal temperature increases with system energy,whereas the q parameter becomes saturated at the pp(p)limit,q-1=0.142±0.010.In addition,the results of most peripheral Pb–Pb collisions are found to approach the pp(p)limit,which suggests that more peripheral heavy-ion collisions are less affected by the medium and more similar to pp(p)collisions.

Study of obliquely propagating electron acoustic shock waves with non-extensive electron population

Obliquely propagating electron acoustic shock waves in magnetized plasma composed of stationary ions, cold and non-extensive hot electrons are investigated by deriving Korteweg–de Vries Burgers(KdVB) equation. The tangent hyperbolic method is used to solve the KdVB equation in dissipative medium. The dissipation effect is introduced in the model by means of kinematic viscosity term. The analytical calculations of the KdVB equation shows that the structures(amplitude, velocity and width) of the shock waves are modified significantly with kinematic viscosity(η_0), obliqueness(k_z) and magnetic field(ω_c). Since plasmas are ubiquitously permeated with magnetic field, it is pertinent to explore the characteristics of KdVB equation in a magnetized plasmas.

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.

Emergence of non-extensive seismic magnitude-frequency distribution from a Bayesian framework

Non-extensive statistical mechanics has been used in recent years as a framework in order to build some seismic frequency-magnitude models. Following a Bayesian procedure through a process of marginalization, it is shown that some of these models can arise from the result shown here, which reinforces the relevance of the non-extensive distributions to explain the data (earthquake’s magnitude) observed during the seismic manifestation. In addition, it makes possible to extend the non-extensive family of distributions, which could explain cases that, eventually, could not be covered by the currently known distributions within this framework. The model obtained was applied to six data samples, corresponding to the frequency-magnitude distributions observed before and after the three strongest earthquakes registered in Chile during the late millennium. In all cases, fit parameters show a strong trend to a particular non-extensive model widely known in literature.

Study of a collisionless magnetized plasma sheath with nonextensively distributed species

A weakly magnetized sheath for a collisionless, electronegative plasma comprising positive ions,electrons, and negative ions is investigated numerically using the fluid approach. The electrons are considered to be non-Maxwellian in nature and are described by Tsalli's distribution. Such electrons have a substantial effect on the sheath properties. The study also reveals that non-Maxwellian distribution is the most realistic description for negative ions in the presence of an oblique magnetic field. In addition to the negative ion temperature, the sheath potential is also affected by the nonextensive parameters. The present research finds application in the plasma processing and semiconductor industry as well as in space plasmas.

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU(3)quark mean field model

In the present study,we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3)quark mean field model.Within this model,the properties of the quark matter were modified through the scalar fieldsσ,ζ,δ,χ,vector fieldsω,ρ,ϕ,and Polyakov fieldsΦandΦ¯at finite temperature and chemical potential.Non-extensive effects were introduced through a dimensionless parameter q,and the results were compared to those of the extensive case(q→1).In the non-extensive case,the exponential in the Fermi-Dirac(FD)function was modified to a q-exponential form.The influence of the q parameter on the thermodynamic properties,pressure,energy,and entropy density,as well as trace anomaly,was investigated.The speed of sound and specific heat with non-extensive effects were also studied.Furthermore,the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of u,d,and s quarks was explored.We found that the critical end point(CEP),which defines the point in the(T−μ)phase diagram where the order of the phase transition changes,shifts to a lower value of temperature,TCEP,and a higher value of chemical potential,μCEP,as the non-extensivity is increased,that is,q>1.

Modelling of electronegative collisional warm plasma for plasma-surface interaction process

An electronegative collisional plasma having warm and massive positive ions,non-extensive distributed electrons and Boltzmann distributed negative ions is modelled for the plasma-surface interaction process that is used for the surface nitriding.Specifically the sheath formation is evaluated through the Bohm’s criterion,which is found to be modified,and the variation of the sheath thickness and profiles of the density of plasma species and the net space charge density in the sheath region in addition to the electric potential.The effect of ion temperature,nonextensivity and collisional parameter is examined in greater detail considering the collisional cross-section to obey power-law dependency on the positive ion velocity.The positive ions are found to enter in the sheath region at lower velocities in the collisional plasma compared to the case of collision-less plasma;this velocity sees minuscule reduction with increasing nonextensivity.The increasing ion temperature and collisional parameter lead to the formation of sheath with smaller thickness.

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 x 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.

Dependence of thermodynamic quantities at freeze-out on pseudorapidity and collision energy in p-p collisions at LHC energies

The transverse momentum distributions of charged hadrons produced in proton-proton collisions at center-of-mass energies(√s)of 0.9 TeV and 2.36 TeV,as measured by the CMS detector at the Large Hadron Collider(LHC),have been analyzed within various pseudorapidity classes utilizing the thermodynamically consistent Tsallis distribution.The fitting procedure resulted in the key parameters,namely,effective temperature(T),non-extensivity parameter(q),and kinetic freezeout volume(V).Additionally,the mean transverse momentum(<pT>)and initial temperature(T_(i))of the particle source are determined through the fit function and string percolation method,respectively.An alternative method is employed to calculate the kinetic freezeout temperature(T_(0))and transverse flow velocity(β_(T))from T.Furthermore,thermodynamic quantities at the freezeout,including energy density(ε),particle density(n),entropy density(s),pressure(P),and squared speed of sound(C_(s)^(2)),are computed using the extracted T and q.It is also observed that,with a decrease in pseudorapidity,all thermodynamic quantities except V and q increase.This trend is attributed to greater energy transfer along the mid pseudorapidity.q increases towards higher values of pseudorapidity,indicating that particles close to the beam axis are far from equilibrium.Meanwhile,V remains nearly independent of pseudorapidity.The excitation function of these parameters(q)shows a direct(inverse)correlation with collision energy.The ε,n,s,and P show a strong dependence on collision energies at low pseudorapidities.Explicit verification of the thermodynamic inequality ε≥3P suggests the formation of a highly dense droplet-like Quark-Gluon Plasma(QGP).Additionally,the inequality T_(i)>T>T_(0)is explicitly confirmed,aligning with the evolution of the produced fireball.