A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.

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.

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.

Charged Multiplicity Density and Number of Participant Nucleons in Relativistic Nuclear Collisions

The energy and centrality dependencies of charged particle pseudorapidity density in relativistic nuclear collisions were studied using a hadron and string cascade model, JPCIAE. Both the relativistic experimental data and the PHOBOS and PHENIX Au+Au data at RHIC energy could be fairly reproduced within the framework of JPCIAE model and without retuning the model parameters. The predictions for collisions at the LHC energy were also given. We computed the participant nucleon distributions using different methods. It was found that the number of participant nucleons is not a well defined variable both experimentally and theoretically. Thus it may be inappropriate to use the charged particle pseudorapidity density per participant pair as a function of the number of participant nucleons for distinguishing various theoretical models.

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.

Microsegregation and Rayleigh number variation during the solidification of superalloy Inconel 718

The microstructure and composition of the residual liquid at different temperatures were investigated by scanning electron microscopy （SEM） and energy dispersive X-ray spectrometer （EDX） associated with the Thermo-calc software calculation of the equilibrium phase diagrams of Inconel 718 and segregated liquid. The liquid density difference and Rayleigh number variation during solidification were estimated as well. It is found that the heavy segregation of Nb in liquid prompts the precipitation of δ and Laves phase directly from liquid and the resultant quenched liquid microstructure consists of pro-eutectic γ＋eutectic,or complete eutectic according to the content of Nb from low to high. The liquid density increases with decreasing temperature during the solidification of Inconel 718 and the liquid density difference is positive. The largest relative Rayleigh number occurs at 1320°C when the liquid fraction is about 40vol%.

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.

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Studies of Structural and Thermodynamic Properties for Polychlorinated Thianthrenes by Density Functional Theory

The structural and thermodynamic （PCTAs） in the ideal gas state at 298.15 K and 1.013 properties of 75 polychlorinated thianthrenes ×10^5 Pa have been calculated at the B3LYP/6- 31G＊ level using Gaussian 98 program. Based on the output data of Gaussian, the isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fH^θ） of PCTAs congeners. The relations of these thermodynamic parameters with the number and position of C1 atom substitution （Npcs） were discussed, and it was found that there exists high correlation between thermodynamic parameters （total energy （TE）, zero-point vibrational energy （ZPE）, thermal correction to energy （Eth）, heat capacity at constant volume （Cv^θ）, entropy （S^θ）, enthalpy （H^θ）, free energy （G^θ）, standard enthalpies of formation （△fH^θ） and standard Gibbs energies of formation （△fG^θ）） and Npcs. On the basis of the relative magnitude of their △fG^θ, the order of relative stability of PCTA congeners was theoretically proposed. In addition, the correlations between structural parameters and Npcs were also discussed. The good correlations were found between molecular average polarizability （α）, energy of the highest occupied molecular orbital （EHOMO）, molecular volume （Vm） and Npcs, and all R^2 values are larger than 0.95. Moreover, it was supposed that the isomer groups with higher toxicity should be Tri-CTA and TCTA.

Effects of Plant Spacing,Row Spacing and Seedling Number Allocation on the Growth Dynamics of Different Populations of Two Types of Rice Varieties

[Objectives]This study was conducted to construct high-yielding,high-quality,and high-light-efficiency population structures of different types of rice varieties.[Methods]The effects of plant spacing,row spacing and seedling number allocation on stems and tillers,leaf area and dynamic traits of high-yielding rice populations(more than 9750 kg/hm^(2))and low-yielding populations(less than 9750 kg/hm^(2))were studied by two kinds of representative rice varieties with different tiller ability and panicle sizes in cold regions.[Results]Decreasing the plant and row spacing and increasing the number of planted seedlings per hole advanced the heading date and made the number of stems and tillers in the population increase.The impact on the super rice variety with fewer tillers and heavier panicles was greater than that of conventional variety with more tillers and lighter panicles.The stems and tillers of the high-yielding high-quality populations grew steadily in the early stage of development,until an appropriate number of panicles was reached at the critical leaf age for productive tillers(June 25),and the peak seedlings should appear in the jointing stage(July 9)with a small number(that value of Longjing 21,the super rice variety with fewer tillers and heavier panicles,was about 1.2 times the expected panicle number,and that of the conventional variety with more tillers and lighter panicles,Kongyu 131,was about 1.1 times the expected panicle number).The populations gradually declined since then,until reaching an appropriate number of panicles at the heading stage.The high-yielding high-quality populations had a higher leaf area index at the heading stage.The value of Longjing 21,the super rice variety with fewer tiller and heavier panicles,reached about 6.0,and that of Kongyu 131,the conventional variety with more tillers and lighter panicles,reached about 4.5.The values decreased thereafter.At the maturation stage,the leaf area index of Longjing 21 remained above 2.5,and that of Kongyu 131 remained above 2.0.[Conclusions]This study has an important guiding role and significance for their high-yielding and high-quality supporting cultivation in cold regions.

Target genes discovery through copy number alteration analysis in human hepatocellular carcinoma

High-throughput short-read sequencing of exomes and whole cancer genomes in multiple human hepatocellular carcinoma(HCC)cohorts confirmed previously identified frequently mutated somatic genes,such as TP53,CTNNB1 and AXIN1,and identified several novel genes with moderate mutation frequencies,including ARID1A,ARID2,MLL,MLL2,MLL3,MLL4,IRF2,ATM,CDKN2A,FGF19,PIK3CA,RPS6KA3,JAK1,KEAP1,NFE2L2,C16orf62,LEPR,RAC2,and IL6ST.Functional classification of these mutated genes suggested that alterations in pathways participating in chromatin remodeling,Wnt/β-catenin signaling,JAK/STAT signaling,and oxidative stress play critical roles in HCC tumorigenesis.Nevertheless,because there are few druggable genes used in HCC therapy,the identification of new therapeutic targets through integrated genomic approaches remains an important task.Because a large amount of HCC genomic data genotyped by high density single nucleotide polymorphism arrays is deposited in the public domain,copy number alteration(CNA)analyses of these arrays is a cost-effective way to reveal target genes through profiling of recurrent and overlapping amplicons,homozygous deletions and potentially unbalanced chromosomal translocations accumulated during HCC progression.Moreover,integration of CNAs with other high-throughput genomic data,such as aberrantly coding transcriptomes and non-coding gene expression in human HCC tissues and rodent HCC models,provides lines of evidence that can be used to facilitate the identification of novel HCC target genes with the potential of improving the survival of HCC patients.

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.

Mathematical modeling of electromagnetic dimensionless number for electromagnetic casting of metals and its application

In order to estimate the feasibility of electromagnetic casting (EMC) for different metals, a mathematical model named the electromagnetic dimensionless number (EMDN) was presented, and its validity was proved by the experiments of aluminum and Sn-3%Pb alloy. From the experiment and the analysis of EMDN it can be concluded that the EMC of steel can be attained only when the magnetic flux density is larger than 0.09T, while that required for aluminum is only 0.04T. The mathematical expression of the electromagnetic dimensionless number was given out.

Particle Density in Zero Temperature Symmetry Restoring Phase Transitions in Four-Fermion Interaction Models

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μc in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μc but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.

Ensuring Quality of Random Numbers from TRNG: Design and Evaluation of Post-Processing Using Genetic Algorithm

Random numbers generated by pseudo-random and true random number generators (TRNG) are used in a wide variety of important applications. A TRNG relies on a non-deterministic source to sample random numbers. In this paper, we improve the post-processing stage of TRNGs using a heuristic evolutionary algorithm. Our post-processing algorithm decomposes the problem of improving the quality of random numbers into two phases: (i) Exact Histogram Equalization: it modifies the random numbers distribution with a specified output distribution;(ii) Stationarity Enforcement: using genetic algorithms, the output of (ii) is permuted until the random numbers meet wide-sense stationarity. We ensure that the quality of the numbers generated from the genetic algorithm is within a specified level of error defined by the user. We parallelize the genetic algorithm for improved performance. The post-processing is based on the power spectral density of the generated numbers used as a metric. We propose guideline parameters for the evolutionary algorithm to ensure fast convergence, within the first 100 generations, with a standard deviation over the specified quality level of less than 0.45. We also include a TestU01 evaluation over the random numbers generated.

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.

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.

Ultrafast Laser Energy Density and Retinal Absorption Cross-Section Determination by Saturable Absorption Measurements

Laser pulse nonlinear transmission measurements through saturable absorbers of known absorption parameters allow the measurement of their energy density. On the other hand, nonlinear transmission measurements of laser pulses of known energy density through absorbing media allow their absorption parameter determination. The peak energy density w0P of second harmonic pulses of a mode-locked titanium sapphire laser at wavelength λP = 400 nm is determined by nonlinear energy transmission measurement TE through the dye ADS084BE (1,4-bis(9-ethyl-3-car-bazovinylene)-2-methoxy-5-(2’-ethyl-hexyloxy)-benzene) in tetrahydrofuran. TE(w0P) calibration curves are calculated for laser pulse peak energy density reading w0P from measured pulse energy transmissions TE. The ground-state absorption cross-section σP and the excited-state absorption cross-section σex at λP, and the number density N0 of the retinal Schiff base isoform RetA in pH 7.4 buffer of the blue-light adapted recombinant rhodopsin fragment of the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii were determined by picosecond titanium sapphire second harmonic laser pulse energy transmission measurement TE through RetA as a function of laser input peak energy density w0P. The complete absorption cross-section spectrum