There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

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Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, ∆R ch , is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability αD. In particular, this quantity correlates poorly with both the neutron skin and L. We demonstrate that ∆R ch is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on ∆R ch , we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.

Information content of the differences in the charge radii of mirror nuclei

We employ the structure-averaged jellium model (SAJM) to obtain the selfconsistent LDA Kohn-Sham ground state of axially deformed sodium clusters with broken leftright symmetry, and calculate the dipole-response of the low-energy isomers using the local RPA (LRPA) scheme in the range 7 < Z ≤ 59. We choose the multipole operators rPYLM (p=1,...,10; L=1,...,4, M=0,1) as coupled intrinsic modes of the electron system. The collective spectra are compared with recent measurements of the dipole absorption cross section performed by Meibom et al., and we find very good agreement of the positions and strengths of the leading collective modes in the measured range 47 < Z ≤ 59.

The collective response of deformed sodium clusters

The main goal of the paper is to investigate the experimentally observed spectral fragmentation of the isovector $M1$ resonance in $^{208}\mathrm{Pb}$ within a self-consistent model based on an energy-density functional (EDF) of the Skyrme type. This fragmentation is not reproduced in a conventional one-particle--one-hole $(1\mathrm{p}1\mathrm{h})$ random-phase approximation (RPA) and thus has to be investigated in the framework of models including complex configurations. However, previously applied models of this type were not self-consistent. In the present work, we use a recently developed renormalized version of the self-consistent time-blocking approximation (RenTBA) in which $1\mathrm{p}1\mathrm{h}\ensuremath{\bigotimes}\mathrm{phonon}$ configurations are included on top of the RPA $1\mathrm{p}1\mathrm{h}$ configurations. We have investigated several parameter sets of modified Skyrme EDFs which were fitted within the RenTBA and RPA to reproduce the basic experimental characteristics of the low-energy $M1$ excitations in $^{208}\mathrm{Pb}$. We have found as a necessary condition for producing the appropriate fragmentation of the $M1$ resonance in $^{208}\mathrm{Pb}$ that the minimum energy of the intermediate $1\mathrm{p}1\mathrm{h}\ensuremath{\bigotimes}\mathrm{phonon}$ configurations comes close to the mean energy of the $M1$ resonance. We present also results of the RenTBA and RPA calculations for the first excited states of the natural parity modes in $^{208}\mathrm{Pb}$ obtained with the modified parametrizations.

M 1 resonance in Pb 208 within the self-consistent phonon-coupling model

We analyze the relation between isoscalar toroidal modes and so-called pygmy dipole resonance (PDR) which both appear in the same region of low-energy dipole excitations. To this end, we use a theoretical description within the fully self-consistent Skyrme quasiparticle random-phase approximation (QRPA). Test cases are spherical nuclei $^{40,48}$Ca, $^{58,72}$Ni, $^{90,100}$Zr, and $^{100,120,132}$Sn which cover four different elements and for each element at least two isotopes with different neutron excess, one small and another large. The structure of the modes is investigated in terms of strength functions, transition densities (TD) and transition currents (TC). For all considered nuclei, we see that, independently on whether PDR strength exists or not, the flow pattern in the lower part of the "PDR energy region" is basically the isoscalar vortical toroidal motion with a minor irrotational fraction. A one-to-one correspondence between calculated TD and TC can be established. The toroidal flow appears already in the uncoupled two-quasiparticle (2qp) excitations and becomes definitively strong for the QRPA modes. Altogether, we find that low-lying dipole strength often denoted as isoscalar PDR is actually an oversimplified imitation of the basically toroidal motion in nuclei with a sufficient neutron excess.

Paul-Gerhard Reinhard

Papers

Information content of the differences in the charge radii of mirror nuclei

The collective response of deformed sodium clusters

M 1 resonance in Pb 208 within the self-consistent phonon-coupling model

Systematics of toroidal dipole modes in Ca, Ni, Zr, and Sn isotopes

Cluster Dynamics in Strong Laser Fields