A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.

ESTIMATION OF THE NUMBER OF CORRELATED SOURCES WITH COMMON FREQUENCIES BASED ON POWER SPECTRAL DENSITY

Blind source separation and estimation of the number of sources usually demand that the number of sensors should be greater than or equal to that of the sources, which, however, is very difficult to satisfy for the complex systems. A new estimating method based on power spectral density （PSD） is presented. When the relation between the number of sensors and that of sources is unknown, the PSD matrix is first obtained by the ratio of PSD of the observation signals, and then the bound of the number of correlated sources with common frequencies can be estimated by comparing every column vector of PSD matrix. The effectiveness of the proposed method is verified by theoretical analysis and experiments, and the influence of noise on the estimation of number of source is simulated.

Modeling Density and Anisotropy of Energetic Electrons Along Magnetic Field Lines

The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. The variance of both the number density and anisotropy along the magnetic field line is evaluated systematically by modeling four typically prescribed distribution functions. It is shown that in the case of ＂the positive anisotropy＂ （namely, the perpendicular temperature T⊥ exceeds the parallel temperature T｜｜）, the number density of energetic electrons always decreases with the magnetic latitude for a regular increasing magnetic field and the maximum wave growth is therefore generally confined to the equator where the resonant energy is minimum, and the number density is the largest. However, the ＂loss-cone＂ anisotropy of the electrons with a ＂pancake＂ distribution or kappa distribution keeps invariant or nearly invariant, whereas the ＂temperature＂ anisotropy with a pure bi-Maxwellian distribution or Ashour-Abdalla and Kennel＇s distributions decreases with the magnetic latitude. The results may provide a useful approach to evaluating the number density and anisotropy of the energetic electrons at latitudes where the observation information is not available.

Influence of Jet Angle and Ion Density of Cathode Side on Low Current Vacuum Arc Characteristics

In this study, the influence of the initial jet angles （IJAs） and ion number densities （INDs） at the cathode side on the low current vacuum arc （LCVA） characteristics is simulated and analysed. The results show that the ion temperature, electron temperature, ion number density, axial current density and plasma pressure all decrease with the increase of the cathode IJAs. It is also shown that LCVA can cause a current constriction for lower cathode IND, and the anode sheath potential is more nonuniform, which is mainly related to the nonuniform distribution of the axial current density at the anode side.

An Inquiry into Two Intriguing Values of the Critical Current Density of Bi-2212

The empirically reported values of the critical current density (jc) of Bi-2212 as 2.4 × 105 (jc1;Sample 1) and 1.0 × 106 A/cm2 (jc2;Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 104 G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to jc—a feature to which no heed was paid earlier. The essence of our findings is that the jcs of the two samples differ because they are characterized by different values of the primary variables μi and , where is the effective mass of a charge-carrier and me is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ1 ≈ 12.3 meV, η1 ≈ 0.58;μ2 ≈ 22.7 meV, η2 ≈ 0.94. Following from these and similar estimates when the charge-carriers are e-e pairs, given below for each sample are the detailed results for the values of the secondary variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.

A Study on Numerical Calculation Method of Small Cluster Density in Percolation Model

Percolation theory deals with the numbers and properties of the clusters formed in the different occupation probability. In this Paper, we study the calculation method of small clusters. We calcu-lated the small cluster density of 1, 2 and 3 in the percolation model with the exact method and the numerical method. The results of the two methods are very close, which can be verified by each other. We find that the cluster density of all three kinds of small clusters reaches the highest value when the occupation probability is between 0.1 and 0.2. It is very difficult to get the analytical formula for the exact method when the cluster area is relatively large (such as the area is more than 50), so we can get the density value of the cluster by numerical method. We find that the time required calculating the cluster density is proportional to the percolation area, which is indepen-dent of the cluster size and the occupation probability.

FORMULATION OF STATISTICAL EVOLUTION OF MICROCRACKS IN SOLIDS

The paper presents a principal formulation of statistical evolution of microcracks, occurring in solids, subjected to external loading. In particular, the concept of ideal microcracks is elaborated, in order to describe the fundamental features of damage resulting from nucleation and extension of microcracks. Relevant average damage functions are also discussed.

Optical Emission Spectroscopy Analysis of the Early Phase During Femtosecond Laser-Induced Air Breakdown

Single-pulse and double-pulse optical emission spectroscopy （OES） analyses were carried out in air by using ultrashort laser pulses at atmospheric pressure. The aim of this work is to use spectroscopic methods to analyze the early phase of laser-induced plasma after the femtosecond laser pulse. The temporal behavior of emission spectra of air plasma has been characterized. In comparison with the single-pulse scheme, the plasma emission obtained in the double-pulse scheme presents a more intense continuum along with several additional ionic lines. As only one line is available in the single-pulse scheme, the plasma temperature measurements were performed using only the relative line-to-continuum intensity ratio method, whereas the relative line-to-line intensity ratio method and the relative line-to-continuum intensity ratio method were used simultaneously to estimate the electron temperature in the double-pulse scheme. The results reveal that the temperature values obtained by the two methods in the double-pulse scheme agree. Moreover, this shows that the relative line-to-continuum intensity ratio method is suitable for early phase of laser-induced plasma diagnostics. The electron number density was estimated using the Stark broadening method. In the early phase of laser-induced plasma, the temporal evolution of the electron number density exhibits a power law decrease with delay time.

Time-Resolved Emission Spectroscopic Study of Laser-Induced Steel Plasmas

Laser-induced steel plasma is generated by focusing a Q-switched Nd：YAG visible laser（532 nm wavelength） with an irradiance of 1 x 109 W/cm2 on a steel sample in air at atmospheric pressure.An Echelle spectrograph coupled with a gateable intensified charge-coupled detector is used to record the plasma emissions.Using time-resolved spectroscopic measurements of the plasma emissions,the temperature and electron number density of the steel plasma are determined for many times of the detector delay.The validity of the assumption by the spectroscopic methods that the laser-induced plasma（LIP） is optically thin and is also in local thermodynamic equilibrium（LTE） has been evaluated for many delay times.From the temporal evolution of the intensity ratio of two Fe I lines and matching it with its theoretical value,the delay times where the plasma is optically thin and is also in LTE are found to be 800 ns,900 ns and 1000 ns.

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.

Electro-optic Properties of DR1 Doped SiO_2 Organic/inorganic Guest-host Films

We made a comprehensive investigation on the electro-optic（EO） properties of hybrid sol-gel silica film doped with Dispersed Red 1 dye（DR1/SiO2）. An important finding is that the dipoles which don＇t orient along the direction of corona poling field in the films can be instantaneously poled by alternate modulation electrical field. This instant poling effect results in the EO coefficients dependent on the frequency and intensity of alternate modulation electric field, and some experiments have proved it. We also investigated the electro-optic coefficients and thickness of films at different stir temperatures（Ts） of start solution and at different number densities of DR1. Experimentally the DR1 number density was optimized to an order of 1021/cm^3 and a large EO coefficient of γ33= 37 pm/V for DR1/SiO2 film was measured by simple reflection technique at 1 kHz frequencies of modulation electric field. These findings may benefit the practical application of DR1/SiO2 films in the field of EO modulator and EO probing.

Plasma characteristics and broadband electromagnetic wave absorption in argon and helium capacitively coupled plasma

A one-dimensional self-consistent calculation model of capacitively coupled plasma(CCP)discharge and electromagnetic wave propagation is developed to solve the plasma characteristics and electromagnetic wave transmission attenuation.Numerical simulation results show that the peak electron number density of argon is about 12 times higher than that of helium,and that the electron number density increases with the augment of pressure,radio frequency(RF)power,and RF frequency.However,the electron number density first increases and then decreases as the discharge gap increases.The transmission attenuation of electromagnetic wave in argon discharge plasma is 8.5-dB higher than that of helium.At the same time,the transmission attenuation increases with the augment of the RF power and RF frequency,but it does not increase or decrease monotonically with the increase of gas pressure and discharge gap.The electromagnetic wave absorption frequency band of the argon discharge plasma under the optimal parameters in this paper can reach the Ku band.It is concluded that the argon CCP discharge under the optimal discharge parameters has great potential applications in plasma stealth.

Study on the Size Distribution and Similarity Law of Bubble Nuclei in Water

To study the distribution characteristics and similarity laws of nuclei under different pressures,based on the selfdesigned decompression chamber and the acoustic measuring system,the size distributions of nuclei in the degassed tap water under negative ambient pressures were measured.A number density distribution function of nuclei based on the modified Weibull distribution function was proposed and verified by the experimental measurement results and some published data of nuclei size distribution.Based on this nuclei number density distribution function,the similarity law of the nuclei size distribution was analyzed:in the scale experiment,the value of exponential in the similarity law of the nuclei number density should be determined by the nuclei size distribution of the water in the prototype experiment and the actual nuclei size distribution of the water in the model experiment.And a precondition is that the nuclei size distributions are similar.

A Modulus Variation Model of Concrete under External Sulfate Attack:New Perspective from Statistical Evolution of Microcracks

A numerical model was proposed to describe the modulus variation of mortar exposed to external sulfate attack and the effectivity was verified by experiments. The model joints statistical evolution of microcracks to effective elastic modulus with microcracks and is applied to predict the damage degree of mortar attacked by sulfate. The experimental results show that the model can predict the modulus variation development of the specimen and the microcraks density. The elastic modulus values calculated by the model are consistent with that measured by experiments. The model focuses on nucleation of microcracks and finds that the theoretical results of microcracks number density show a linear growth over time in mortar. Compared with other sulfate attack damage model, this model provides a more suitable damage evolution equation that can be used to analyze the chemically assisted damage.

Diagnostic Study of an Fe-Ni Alloy Plasma Generated by the Fundamental (1064 nm) and Second (532 nm) Harmonics of an Nd: YAG Laser

We studied the spatial evolution of the Fe-Ni plasma generated by the fundamental （1064 nm） and second （532 nm） harmonics of a Q-switched Nd： YAG laser. The experimentally observed line profiles of the neutral iron （Fe I） have been used to extract the plasma temperature （T e ） using the Boltzmann plot method, whereas the electron number density （N e ） has been deter- mined from the Stark broadening. In addition, we studied the spatial behavior of T e and N e with the variation of laser energy for iron plasma by placing the target material （iron-nickel alloy） in air at atmospheric pressure for both modes of the Nd： YAG laser.

Analysis of choked two-phase flows of gas and particle in a C-D nozzle

Particle-gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent-divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of nozzle performance. In the present studies, theoretical analysis and numerical simulations were carried out to investigate particle-gas flows in a C-D nozzle. Homogeneous equilibrium model that no lag in velocity and temperature occurs between particles and gas phase was used to derive mass flow rate and sound speed of multiphase flows. Two-phase flows are regarded as isentropic flows that isentropic relations can be used for homogeneous equilibrium model. Discrete phase model （DPM） where interaction with continuous phase and discrete random walk model were considered was used to calculate particle- gas flows. Particle mass loadings were varied to investigate their effects on choking phenomena of particle-gas flows. Mass flow rate and sound speed of mixture flows were theoretically calculated by homogeneous equilibrium model and compared with numerical results. Shock wave structure and particle number density were also obtained to be different at different particle mass loading and operating pressure conditions.

Laser induced photo-detachment of O2 in DC discharge

Determination of the negative ion number density of O2 and O in a DC discharge of oxygen plasma was made employing Langmuir probe in conjunction with eclipse laser photo- detachment technique. The temporal evolution of the extra electrons resulting from the photo- detachment of O2- and O- were used to evaluate the negative ion number density. The ratio of O2 number density to O varied from 0.03 to 0.22. Number density of both O~ and O increased with increasing power and decreased as the pressure was increased. Electron number density was evaluated from the electron energy distribution function （EEDF） using the I-V recorded characteristic curves. Electron temperature between 2 and 2.7 eV were obtained. Influence of the 02（al△g） metastable state is discussed.

About the Reliability of Particle in Cell Methods and the Notion of a“Local”Temperature of Ionized Species Around a Spacecraft in the Ionosphere

The development of space science has generated important computer codes for the simulation of the interaction between complex space structures(artificial satellites,solar panels,etc.)and the surrounding plasma.The basic equation to be solved is the Poisson equation for the electric potential around a structure.Here,we try to study analytically the shadowing effect of a spacecraft on an electrode for the electron number density and the electron temperature.We suggest that the electron temperature should be taken as a variable and not as a parameter.However,its computation involves the knowledge of the histogram of the distribution of the frequencies of the electron velocities inside the computational cells.Also,we have illustrated the possibilities of artefacts due to the design and geometry of scientific instruments for the measurement of the electron number density and the electron temperature in the ionosphere.We suggest an optimal design for an electrode and its guard ring.

Size distribution of inclusions in 12%Cr stainless steel with a wide range of solidification cooling rates

The effect of solidification cooling rate on the size and distribution of inclusions in 12%Cr stainless steel was investigated. A wide range of solidification cooling rates（from 0.05 to 106 K·s^-1） was achieved using various solidification processes, including conventional casting, laser remelting, and melt spinning. The size and distribution of inclusions in the steel were observed and statistically collected. For comparison, mathematical models were used to calculate the sizes of inclusions at different solidification cooling rates. Both the statistical size determined from observations and that predicted from calculations tended to decrease with increasing cooling rate; however, the experimental and calculated results did not agree well with each other at excessively high or low cooling rate. The reasons for this discrepancy were theoretically analyzed. For the size distribution of inclusions, the effect of cooling rate on the number densities of large-sized（〉 2 μm） inclusions and small-sized（≤ 2 μm） inclusions were distinct. The number density of inclusions larger than 1 μm was not affected when the cooing rate was less than or equal to 6 K·s^-1 because inclusion precipitation was suppressed by the increased cooling rate.