Extended Density Distribution Research Articles

On the Indispensability of Isogeometric Analysis in Topology Optimization for Smooth or Binary Designs

Recently, isogeometric analysis (IGA), which unifies the computer-aided design (CAD) model and the computer-aided engineering (CAE) model, has been adopted to develop the isogeometric topology optimization (ITO) framework. However, a critical study on the indispensability of IGA in topology optimization to take the place of the conventional finite element method (FEM) is still lacking. In the current work, two important problems are extensively discussed: (1) The lower numerical precision of the FEM resulting from the disunification between the CAD and CAE models damages the effectiveness of the topology optimization, which suggests the indispensability of IGA in the replacement of the FEM in optimization; (2) a material penalization model is required to ensure the generation of a full loading-transmission path during optimization in classic density-based methods, which causes a greater overestimation of structural stiffness and also suggests the necessity of an ersatz material model. The current paper describes a promising ITO method with point-wise design to gain smooth or binary symmetrical topologies, for which an extended density distribution function (DDF) was constructed to describe the structural topology. Two benchmarks of the stiffness-maximization problem and compliant mechanism are studied in the context of the above issues. Finally, several topologically optimized designs with symmetry are obtained using the ITO method.

Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd- A nuclei

To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formula are presented.To perform the integrals of the Green's function properly, the contour paths $C_{\rm b}^{-}$ and $C_{\rm b}^{+}$ introduced for the blocking effects should include the blocked quasi-particle state but can not intrude into the continuum area. By comparing with the box-discretized calculations, the great advantages of the Green's function method in describing the extended density distributions, resonant states, and the couplings with the continuum in exotic nuclei are shown. Finally, taking the neutron-rich odd nucleus $^{159}$Sn as an example, the halo structure is investigated by blocking the quasi-particle state $1p_{1/2}$. It is found that it is mainly the weakly bound states near the Fermi surface that contribute a lot for the extended density distributions at large coordinate space.

Green's function method in covariant density functional theory

This article provides a brief review on the Green's function covariant density functional theory (GF-CDFT), and its appli-cation for the nuclear structure. By reviewing the research status of exotic nuclei and the problems of traditional theory in treating continuum, the Green's function method in nuclear physics is introduced. The GF-CDFT theory is then presented in detail, including a short introduction to the Green's function method, Green's function relativistic mean field (GF-RMF) theory, and Green's function relativistic continuum Hartree-Bogoliubov (GF-RCHB) theory, in which the detailed equa-tions in solving the radial Dirac equation and RCHB equation by Green's function method are given. As to applications, GF-RMF theory is applied to study the single-particle resonant states, in which the energies and widths for the resonant states of 120 Sn are provided; GF-RCHB theory is applied to study the giant halos in the neutron-rich Zr isotopes, in which the extended density distribution as well as the energies and widths of the resonant states playing important roles for giant halos are well described.

Nucleon-nucleon momentum-correlation function as a probe of the density distribution of valence neutrons in neutron-rich nuclei

Proton-neutron, neutron-neutron, and proton-proton momentum-correlation functions (${C}_{pn},\phantom{\rule{0.28em}{0ex}}{C}_{nn}$, and ${C}_{pp}$) are systematically investigated for ${}^{15}\mathrm{C}$ and other C-isotope-induced collisions at different entrance channel conditions within the framework of the isospin-dependent quantum-molecular-dynamics model complemented by the correlation after burner (crab) computation code. ${}^{15}\mathrm{C}$ is a prime exotic nucleus candidate due to the weakly bound valence neutron coupling with closed-neutron-shell nucleus ${}^{14}\mathrm{C}$. To study density dependence of the correlation function by removing the isospin effect, the initialized ${}^{15}\mathrm{C}$ projectiles are sampled from two kinds of density distribution from the relativistic mean-field (RMF) model in which the valence neutron of ${}^{15}\mathrm{C}$ is populated in both $1d5/2$ and $2s1/2$ states, respectively. The results show that the density distributions of the valence neutron significantly influence the nucleon-nucleon momentum-correlation function at large impact parameters and high incident energies. The extended density distribution of the valence neutron largely weakens the strength of the correlation function. The size of the emission source is extracted by fitting the correlation function by using the Gaussian source method. The emission source size as well as the size of the final-state phase space are larger for projectile samplings from more extended density distributions of the valence neutron, which corresponds to the $2s1/2$ state in the RMF model. Therefore, the nucleon-nucleon momentum-correlation function can be considered as a potentially valuable tool to diagnose exotic nuclear structures, such as the skin and halo.

Isospin effect in the nuclear reaction induced by neutron-halo nuclei

We study the average property of the isospin effect of reaction induced by halo-neutron nuclei 8He and 10He in the intermediate energy heavy ion collisions using the isospin-dependent quantum molecular dynamics model (IQMD). This study is based on the extended neutron density distribution for the halo-neutron nuclei, which includes the average property of the isospin effect of reaction mechanism and loose inner structure. The extended neutron density distribution brings an important isospin effect into the average property of reaction mechanism because the interaction potential and nucleon-nucleon(N-N)cross section in IQMD model depend sensitively on the density distribution of colliding system. In order to see clearly the average properties of reaction mechanism induced by halo-neutron nuclei we also compare the results for the neutron-halo colliding systems with those for the corresponding stable colliding systems under the same incident channel condition. We found that the extended density distribution for the neutron-halo projectile brings an important isospin effect to the reaction mechanism, which leads to the decrease of nuclear stopping R, yet induces obvious increase of the neutron-proton ratio of nucleon emissions and isospin fractionation ratio for all beam energies studied in this work, compared to the corresponding stable colliding system. In this case, nuclear stopping, the neutron-proton ratio of nucleon emissions and isospin fractionation ratio induced by halo-neutron nuclei can be used as possible probes for studying the average property of the isospin effect of reaction mechanism and extracting the information of symmetry potential and in-medium N-N cross section by the neutron-halo nuclei in heavy ion collisions.

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei**The project supported by the State Key Basic Research Development Program of China under Contract No. G2000077400, the “100- Person Project” of the Chinese Academy of Sciences, National Natural Science Foundation of China under Grant Nos. 10175080, 10175082 10004012, and 19847002, and CAS Knowledge Innovation Project under Grant No.

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy.The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially, it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.

Effect of Break-Up Processes on Fusion Reactions with Weakly Bound Projectiles

The possible effects of break-up channels on fusion reactions in collisions induced by weakly-bound projectiles are discussed. In addition to the static effects due to variation in the potential following the extended density distributions, attention is devoted to dynamical effects due to coupling to reaction channels, in primis the break-up channels. The key issues and the still controversial open problems are discussed.

Electronic Structure of Fe+X Alloys (X = Si, Ge, Co)

The electronic structure of Fe–Ge, Fe–Si, and Fe–Co alloys has been investigated by X-ray photoelectron spectroscopy. In Fe–Ge alloys with less than 10 at.% Ge, the Fe–Ge bond is mainly formed by the Fe 4sp- and Ge 4p-electrons. The results obtained for this system are identical to those for the Fe–Si system. The form of the valence band reflects the density distribution of both iron d-electronic states the and p-electronic states of the second component, having more extended density distribution of valence electrons. In FeCo alloys, strong spatial localization of d-electron density takes place in the vicinity of the corresponding atoms, which is stronger on the iron atoms compared to pure iron; the valence band has a two-band structure reflecting the density distribution of the d-states of each component. X-ray photoelectron spectroscopy data are in good agreement with kinetic data for the alloys.

Study of halo structure in light nuclei with a multicluster model

Abstract Detailed structure of light exotic nuclei is described with a multicluster model comprising α, t , 3 He, p and n clusters. The multicluster dynamics is fully taken into account with the stochastic variational method. The model enables us to describe the non-uniform and spatially extended density distribution of the halo structure. It is discussed that light stable nuclei have halo-like structure as the isospin increases.

Mira model photospheres

The temperature stratifications and the emitted fluxes of Mira model photospheres based upon the extended density distribution of a pulsation model differ substantially from those of conventional model photospheres based upon a hydrostatic density distribution. Hence, the interpretation of Mira spectra by means of hydrostatic models is inadequate, and the spectral characteristics of Miras may deviate significantly from those of non-Miras.

Diffusion and reaction in random media and models of evolution processes

A diffusion equation including source terms, representing randomly distributed sources and sinks is considered. For quasilinear growth rates the eigenvalue problem is equivalent to that of the quantum mechanical motion of electrons in random fields. Correspondingly there exist localized and extended density distributions dependent on the statistics of the random field and on the dimension of the space. Besides applications in physics (nonequilibrium processes in pumped disordered solid materials) a new evolution model is discussed which considers evolution as hill climbing in a random landscape.