SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

An improved effective liquid drop model for cluster radioactivity

The effective liquid drop model(ELDM)is improved by introducing an accurate nuclear charge radius formula and an analytic expression for assaulting frequency.Within the improved effective liquid drop model(IMELDM),the experimental cluster radioactivity half-lives of the trans-lead region are calculated.It is shown that the accuracy of the IMELDM is improved compared with that of the ELDM.At last,the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead nuclei are predicted by the IMELDM.These predictions may be useful for searching for new candidates for cluster radioactivity in future experiments.

Systematic study of cluster radioactivity within the generalized liquid drop model

Cluster radioactivity is studied within the generalized liquid drop model(GLDM),in which the shell correction energy,pairing energy,and cluster preformation factor are considered.The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after considering these physical effects.In addition,the systematic trend of the cluster preformation factors is discussed in terms of the N_(p)N_(n)scheme to study the influence of the valence proton-neutron interaction and shell effect on cluster radioactivity.It is found that log10Pcis linearly related to N_(p)N_(n).This is in agreement with a recent study[L.Qi et al.,Phys.Rev.C 108,014325(2023)],in which log10Pc,obtained using different theoretical models and treatment methods than those used in this study,also had a linear relationship with N_(p)N_(n).Combined with the work by Qi et al.,this study suggests that the linear relationship between log10Pcand N_(p)N_(n)is model-independent and both the shell effect and valence proton-neutron interaction play essential roles in cluster radioactivity.An analytical formula is proposed to calculate the cluster preformation factor based on the N_(p)N_(n)scheme.In addition,the cluster preformation factors and the cluster radioactivity half-lives of some heavy nuclei are predicted,which can provide a reference for future experiments.

Topological structure bifurcation of temperature field of deformable drop in Marangoni migration

The unsteady processes of the Marangoni migration of deformable liquid drops are simulated numerically in a wider range of Marangoni number(up to Ma = 500) in the present work.A steady terminal state can always be reached,and the scaled terminal velocity is a monotonic function decreasing with increasing Marangoni number,which is generally in agreement with corresponding experimental data.The topological structure of flow field in the steady terminal state does not change as the Marangoni number increases,while bifurcation of the topological structure of temperature field occurs twice at two corresponding critical Marangoni numbers.A third critical value of Marangoni number also exists,beyond which the coldest point jumps from the rear stagnation to inside the drop though the topological structure of the temperature field does not change.It is found that the inner and outer thermal boundary layers may exist along the interface both inside and outside the drop if Ma>70.But the thickness decreases with increasing Marangoni number more slowly than the prediction of potential flow at large Marangoni and Reynolds numbers.

NUMERICAL INVESTIGATION OF UNSTEADY DROPLET COMBUSTION PROCESS IN HOT QUIESCENT AIR ENVIRONMENTS (HQAE)

A mathematical model has been presented for describing single droplet unsteady processes of vaporization, ignition and combustion in a hot quiescent air environment. The arbitrary Lagrangian Eulerian numerical method, incorporated with an effective adaptive mesh method, is applied. From the obtained time space distributions of gas temperature and species densities, the characteristics of droplet ignition and combustion process are clarified. It is also demonstrated that, due to the strong damping of the high temperature flame region around the droplet, the ambient conditions have little effects on the properties of the drop's surface; and that, due to the unsteady prediction of droplet heating time being much less than the corresponding quasi steady prediction under burning condition, the differences between unsteady and quasi steady results are much greater than those under pure vaporization.

Gravitational Term in Semi Empirical Mass Formula

A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections in the binding energy of a nucleus. The results of our calculations show a straight forward evidence that the gravitational attraction bears a reasonable contribution to the binding energy. On the other hand, employing the gravitational term in the semi empirical mass formula was led to the calculation of gravitational constant at subnuclear level.

Systematic study ofαdecay half-lives within the Generalized Liquid Drop Model with various versions of proximity energies

It is universally acknowledged that the Generalized Liquid Drop Model(GLDM)has two advantages over otherαdecay theoretical models:introduction of the quasimolecular shape mechanism and proximity energy.In the past few decades,the original proximity energy has been improved by numerous works.In the present work,the different improvements of proximity energy are examined when they are applied to the GLDM for enhancing the calculation accuracy and prediction ability ofαdecay half-lives for known and unsynthesized superheavy nuclei.The calculations ofαhalf-lives have systematic improvements in reproducing experimental data after choosing a more suitable proximity energy for application to the GLDM.Encouraged by this,theαdecay half-lives of even-even superheavy nuclei with Z=112-122 are predicted by the GLDM with a more suitable proximity energy.The predictions are consistent with calculations by the improved Royer formula and the universal decay law.In addition,the features of the predictedαdecay half-lives imply that the next double magic nucleus after ^(208)Pb is ^(298)Fl.

Capillary wrinkling scaling laws of floating elastic thin film with a liquid drop

The deformation patterns of elastic membranes under tension is called wrinkling.Wrinkling,which is caused by capillary surface tension,is called capillary wrinkling(Figure 1).In recent years wrinkling patterns have drawn particular attention[1-11],since it can be an useful tool to infer material parameters that might otherwise be inaccessible.For example,the commonly observed tearing instability of an

Investigation of proton radioactivity with the effective liquid drop model

Proton radioactivity has been investigated using the effective liquid drop model with varying mass asymmetry shapes and effective inertial coefficients. An effective nuclear radius constant formula replaces the old empirical one in the calculations. The theoretical half-lives are in good agreement with the available experimental data. All the deviations between the calculated logarithmic half-lives and the experimental values are less than 0.8. The root-mean-square （rms） deviation is 0.523. Predictions for the half-lives of proton radioactivity are made for elements across the periodic table. From the theoretical results, there are 11 candidate nuclei for proton radioactivity in the region Z〈51. In the region Z〉83, no nuclei are suggested as probable candidate nuclei for proton radioactivity within the selected range of half-lives studied.

Systematic study of theαdecay preformation factors of the nuclei around the Z=82,N=126 shell closures within the generalized liquid drop model

In this study,we systematically investigate theαdecay preformation factors,Pα,and theαdecay half-lives of 152 nuclei around Z=82,N=126 closed shells based on the generalized liquid drop model(GLDM)with Pαbeing extracted from the ratio of the calculatedαdecay half-life to the experimental one.The results show that there is a remarkable linear relationship between Pαand the product of valance protons(holes)Np and valance neutrons(holes)Nn.At the same time,we extract theαdecay preformation factor values of the even–even nuclei around the Z=82,N=126 closed shells from the study of Sun et al.[J.Phys.G:Nucl.Part.Phys.,45:075106(2018)],in which theαdecay was calculated by two different microscopic formulas.We find that theαdecay preformation factors are also related to NpNn.Combining with our previous studies[Sun et al.,Phys.Rev.C,94:024338(2016);Deng et al.,ibid.96:024318(2017);Deng et al.,ibid.97:044322(2018)]and that of Seif et al.,[Phys.Rev.C,84:064608(2011)],we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent.This may be caused by the effect of the valence protons(holes)and valence neutrons(holes)around the shell closures.Finally,using the formula obtained by fitting theαdecay preformation factor data calculated by the GLDM,we calculate theαdecay half-lives of these nuclei.The calculated results agree with the experimental data well.

Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Qα value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the DensityDependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.

Parametric Instability of a Liquid Metal Sessile Drop Under a High Frequency Amplitude-Modulate Magnetic Field

The parametric instability behavior of a liquid mercury sessile drop under high frequency Amplitude-Modulate Magnetic Field(AMMF),i.e.a high frequency magnetic field(carder wave)modulated by a low frequency sine wave(modulate wave),is investigated experimentally.The free surface contour of the mercury drop is observed by a CCD camera while varying the frequency and amplitude of the high frequency AMMF.At a given frequency and amplitude,the edge deformations with an azimuthal wave numbers(modes n=3,4,5,6)were excited.

α-decay half-lives of superheavy nuclei and general predictions

The generalized liquid drop model （GLDM） and the cluster model have been employed to calculate the α-decay half-lives of superheavy nuclei （SHN） using the experimental α-decay Q values. The results of the cluster model are slightly poorer than those from the GLDM if experimental Q values are used. The prediction powers of these two models with theoretical Q values from Audi et al. （QAudi） and Muntian et al. （QM） have been tested to find that the cluster model with QAudi and QM could provide reliable results for Z 〉 112 but the GLDM with QAudi for Z 112. The half-lives of some still unknown nuclei are predicted by these two models and these results may be useful for future experimental assignment and identification.

New behaviors ofα-particle preformation factors near doubly magic ^(100)Sn

Theα-particle preformation factors of nuclei above doubly magic nuclei ^(100)Sn and ^(208)Pb are investigated within the generalized liquid drop model.The results show that theα-particle preformation factors of nuclei near self-conjugate doubly magic ^(100)Sn are significantly larger than those of analogous nuclei just above ^(208)Pb,and they will be enhanced as the nuclei move towards the N=Z line.The proton-neutron correlation energy E_(p-n) and two protons-two neutrons correlation energy E_(2p-2n) of nuclei near ^(100)Sn also exhibit a similar situation,indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance theα-particle preformation factors and result in superallowed a decay.This also provides evidence of the significant role of the proton-neutron interaction onα-particle preformation.Also,the linear relationship betweenα-particle preformation factors and the product of valence protons and valence neutrons for nuclei around ^(208)Pb is broken in the100 Sn region because theα-particle preformation factor is enhanced when a nucleus near 100 Sn moves towards the N=Z line.Furthermore,the calculatedαdecay half-lives fit well with the experimental data,including the recent observed self-conjugate nuclei ^(104)Te and ^(108)Xe[Phys.Rev.Lett.121,182501(2018)].

α particle preformation and shell effect for heavy and superheavy nuclei

The α particle preformation factor is extracted within a generalized liquid drop model for Z=84-92 isotopes and N=126, 128, 152, 162, 176, 184 isotones. The calculated results show clearly that the shell effects play a key role in α particle preformation. The closer the proton and neutron numbers are to the magic numbers, the more difficult the formation of the α cluster inside the mother nucleus is. The preformation factors of the isotopes reflect that N=126 is a magic number for Po, Rn, Ra, and Th isotopes, but for U isotopes the weakening of the influence of the N=126 shell closure is evident. The trend of the factors for N=126 and N=128 isotones also support this conclusion. We extend the calculations for N=152, 162, 176, 184 isotones to explore the magic numbers for heavy and superheavy nuclei, which are probably present near Z=108 to N=152, 162 isotones and Z=116 to N=176, 184 isotones. The results also show that another subshell closure may exist after Z=124 in the superheavy nuclei. This is useful for future experiments.

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model（GLDM）, whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.

Improved empirical formula for α particle preformation factor

In this contribution,the α preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model(GLDM).Through the systematic analysis of the α preformation factors of even-even Po-U isotopes,we found that there is a significant weakening of influence of N=126 shell closure in uranium,which is consistent with the results of a recent experiment [J.Khuyagbaatar et al.,Phys.Rev.Lett.115,242502(2015)],implying that N=126 may not be the magic number for U isotopes.Furthermore,we propose an improved formula with only 7 parameters to calculate α preformation factors suitable for all types of α-decay;it has fewer parameters than the original formula proposed by Zhang et al.[H.F.Zhang et al.,Phys.Rev.C 80,057301(2009)]with higher precision.The standard deviation of the α preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3,indicating that our improved formula can accurately reproduce the α preformation factors.Encouraged by this,the α-decay half-lives of actinide elements are predicted,which could be useful in future experiments.Notably,the predicted α-decay half-lives of two new isotopes 220 Np [Z.Y.Zhang,et al.,Phys.Rev.Lett.122,192503(2019)] and 219 Np [H.B.Yang et al.,Phys.Lett.B 777,212(2018)] are in good agreement with the experimental α-decay half-lives.

Proton Radioactivity Within a Hybrid Method

The proton radioactivity half-lives are investigated theoretically within a hybrid method.The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model(GLDM). The penetrability is calculated with the WentzelKramers-Brillouin(WKB) approximation. The spectroscopic factor has been taken into account in halflife calculation, which is obtained by employing the relativistic mean field(RMF) theory combined with the Bardeen-Cooper-Schrieffer(BCS) method. The half-lives within the present hybrid method reproduced the experimental data very well. Some predictions for proton radioactivity are made for future experiments.