Self-consistent Shapes Research Articles

Nuclear DFT electromagnetic moments in heavy deformed open-shell odd nuclei

Within the nuclear DFT approach, we determined the magnetic dipole and electric quadrupole moments for paired nuclear states corresponding to the proton (neutron) quasiparticles blocked in the π11/2− (ν13/2+) intruder configurations. We performed calculations for all deformed open-shell odd nuclei with 63≤Z≤82 and 82≤N≤126. Time-reversal symmetry was broken in the intrinsic reference frame and self-consistent shape and spin core polarizations were established. We determined spectroscopic moments of angular-momentum-projected wave functions and compared them with available experimental data. We obtained good agreement with data without using effective g-factors or effective charges in the dipole or quadrupole operators, respectively. We also showed that the intrinsic magnetic dipole moments, or those obtained for conserved intrinsic time-reversal symmetry, do not represent viable approximations of the spectroscopic ones.

Limitation of symmetry breaking by gravitational collapse: the revisit of Lin–Mestel–Shu instability

ABSTRACT We revisit the topic of shape evolution during the spherical collapse of an N-body system. Our main objective is to investigate the critical particle number below which, during a gravitational collapse, the amplification of triaxiality from initial fluctuations is effective, and above which it is ineffective. To this aim, we develop the Lin–Mestel–Shu theory for a system of particles initially with isotropic velocity dispersion and with a simple power-law density profile. We first determine, for an unstable cloud, two radii corresponding to the balance of two opposing forces and their fluctuations: such radii fix the sizes of the non-collapsing region and the triaxial seed from density fluctuations. We hypothesize that the triaxial degree of the final state depends on which radius is dominant prior to the collapse phase leading to a different scheme of the self-consistent shape evolution of the core and the rest of the system. The condition where the two radii are equal therefore identifies the critical particle number, which can be expressed as the function of the parameters of initial state. In numerical work, we can pinpoint such a critical number by comparing the virialized flattening with the initial flattening. The difference between these two quantities agrees with the theoretical predictions only for the power-law density profiles with an exponent in the range [0, 0.25]. For higher exponents, results suggest that the critical number is above the range of simulated N. We speculate that there is an additional mechanism, related to strong density gradients that increases further the flattening, requiring higher N to further weaken the initial fluctuations.

The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn’s tidal response

We extend to three dimensions the Concentric Maclaurin Spheroid method for obtaining the self-consistent shape and gravitational field of a rotating liquid planet, to include a tidal potential from a satellite. We exhibit, for the first time, an important effect of the planetary rotation rate on tidal response of gas giants, whose shape is dominated by the centrifugal potential from rapid rotation. Simulations of planets with fast rotation rates like those of Jupiter and Saturn, exhibit significant changes in calculated tidal love numbers knm when compared with non-rotating bodies. A test model of Saturn fitted to observed zonal gravitational multipole harmonics yields k2=0.413, consistent with a recent observational determination from Cassini astrometry data (Lainey et al., 2016.). The calculated love number is robust under reasonable assumptions of interior rotation rate, satellite parameters, and details of Saturn’s interior structure. The method is benchmarked against several published test cases.

Effects of solute concentration in liquid on pore shape in solid

The effects of initial solute gas concentration in the liquid on the shape of a pore, resulting from a nucleated bubble entrapped by a solidification front, are predicted in this work. Solute concentration in liquid is responsible for solute transfer across the bubble cap, gas pressure in the pore, and shapes of the cap and pore in solid. Distributions and shapes of pores in solids influence not only microstructure of materials, but also contemporary issues of biology, engineering, foods, geophysics and climate change, etc. In this work, the relevant pore shape delineated by tracing contact angle of the cap to a first approximation is determined by accounting for mass and momentum transport across a self-consistent shape of the cap whose surface is satisfied by physico-chemical equilibrium, as proposed previously. This work finds that there exist three different mechanisms for pore formation, depending on directions and magnitude of solute transfer across the cap. Case 1 is subject to solute transport from the pore into surrounding liquid as a result of the cap emerged from a thin concentration boundary layer on the solidification front. An increase in initial solute concentration in liquid decreases pore radius and times for bubble entrapment. Opposite directions of solute transport across the cap submerged into a thick concentration boundary layer along the solidification front, however, cannot result in bubble entrapment, because solute concentration at the cap increases and decreases rapidly in late stage in Cases 2a and 2b, respectively. The predicted pore shape in solid agrees with experimental data. The pore shape therefore can be controlled by initial solute concentration to change directions and magnitudes of solute transport across the cap.

Modeling high speed growth of large rods of cesium iodide crystals by edge-defined film-fed growth (EFG)

A thermocapillary model of edge-defined film-fed growth (EFG) is developed to analyze an experimental system for high speed growth of cesium iodide as a model system for halide scintillator production. The model simulates heat transfer and fluid dynamics in the die, melt, and crystal under conditions of steady growth. Appropriate mass, force, and energy balances are used to compute self-consistent shapes of the growth interface and melt–vapor meniscus. The model is applied to study the effects of growth rate, die geometry, and furnace heat transfer on the limits of system operability. An inverse problem formulation is used to seek operable states at high growth rates by adjusting the overall temperature level and thermal gradient in the furnace. The model predicts that steady growth is feasible at rates greater than 20mm/h for crystals up to 18mm in diameter under reasonable furnace gradients.

Link between self-consistent pressure profiles and electron internal transport barriers in tokamaks

Tokamak plasmas have a tendency to self-organization: the plasma pressure profiles obtained in different operational regimes and even in various tokamaks may be represented by a single typical curve, called the self-consistent pressure profile. About a decade ago local zones with enhanced confinement were discovered in tokamak plasmas. These zones are referred to as internal transport barriers (ITBs) and they can act on the electron and/or ion fluid. Here the pressure gradients can largely exceed the gradients dictated by profile consistency. So the existence of ITBs seems to be in contradiction with the self-consistent pressure profiles (this is also often referred to as profile resilience or profile stiffness). In this paper we will discuss the interplay between profile consistency and ITBs. A summary of the cumulative information obtained from T-10, RTP and TEXTOR is given, and a coherent explanation of the main features of the observed phenomena is suggested. Both phenomena, the self-consistent profile and ITB, are connected with the density of rational magnetic surfaces, where the turbulent cells are situated. The distance between these cells determines the level of their interaction, and therefore the level of the turbulent transport. This process regulates the plasma pressure profile. If the distance is wide, the turbulent flux may be diminished and the ITB may be formed. In regions with rarefied surfaces the steeper pressure gradients are possible without instantaneously inducing pressure driven instabilities, which force the profiles back to their self-consistent shapes. Also it can be expected that the ITB region is wider for lower dq/dρ (more rarefied surfaces).

Topomers: a validated protocol for their self-consistent generation.

The hypothesis underlying topomer development is that describing molecular structures consistently may be at least as productive as describing them more realistically but incompletely. A general protocol is detailed for deterministically generating self-consistent shapes of molecular fragments from their topologies. These and other extensions to the topomer methodology are validated by repetition of earlier benchmark studies.

Irregular eutectic solidification

A numerical calculation is presented for irregular eutectic growth which takes into account the increased difficulty of solute diffusion at a curved interface and the change in temperature of the interface with position. The validity of using a steady state growth model is questioned. The solute distribution for planar and curved interface shapes is calculated using the boundary element method. These distributions are used to calculate interface shapes and self-consistent shapes for steady state growth. Steady state shapes are not found for the experimentally measured average Si flake spacings in the AlSi eutectic. The largest spacing for which a self-consistent interface shape exists is much smaller than the measured average flake spacing. This suggests that a steady state model cannot be used to describe irregular eutectic growth. A time-dependent model must be developed.

Level densities in mean-field theory versus the independent particle model

We point out that nuclear level densities at moderate excitation are systematically greater in mean-field theory than in the independent-particle model because self-consistency lowers the energies of excited states. We estimate the effect using a harmonic-oscillator model for 40Ca and find a 10% change in the level density parameter a, which is a disappointingly small effect. The main effect of self-consistent shapes is a substantial smearing of shell structure.

A Numerical Finite Difference Model of Steady State Cellular and Dendritic Growth

A theoretical model is developed to treat the steady state growth of an array of cells and dendrites in a positive temperature gradient using finite difference techniques. The coupled three dimensional heat and solute flow equations have been solved in a ‘half-cell’ repeat unit with radial symmetry using the conservation boundary conditions at the solid-liquid interface. As, however, the problem is a free boundary one, there is an additional condition to be satisfied at the solid-liquid interface. Using this ‘equilibrium’ condition, self-consistent cell shapes have been obtained. Calculations have been carried out at several different growth velocities for fixed values of alloy content and liquid gradient. At each velocity self-consistent shapes have been found up to a maximum value of the cell spacing. The effect of surface energy and the kinetic coefficient on growth behavior has also been examined.

The shape of liquid droplets in the presence of a quantized vortex

The self-consistent shapes are calculated for small superfluid drops containing a vortex, and for normal fluid drops attached to a vortex. Surface energies which depend on the local curvature and the distance from the vortex axis are given in terms of the bulk superfluid density, and the coherence length.

An extended cranked shape-consistent oscillator model for rotations of triaxial nuclei: Application to 24Mg

The shape-consistent oscillator model is extended to triaxial nuclei. An application to 24Mg shows results similar to those from a variation-after-projection Hartree-Fock calculation with realistic forces. The observed trends of B(E2) values within a band seem to be consistent with self-consistent shape changes but greater experimental accuracy is needed for a more definite conclusion.

Note on the Single-Closed-Shell Nuclei

Assuming the existence of a spherical $^{16}\mathrm{O}$ core, self-consistent Hartree-Fock, Hartree-Fock-Bogoliubov, and spherical BCS calculations for the even oxygen isotopes are carried out for Kuo-Brown and a number of other effective interactions. In agreement with the finding of Chandra and Rustgi for the even Ca and Ni isotopes, the spherical BCS approximation is found to yield the actual minimum-energy solution for the even oxygen isotopes as well. The present calculation thus adds credibility to the general inferences made by Chandra and Rustgi that for single-closed-shell structures, the self-consistent shape will always be spherical BCS.