Self-diffusion in remodelling and growth

Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture

Non-explosive hydrogen and helium burnings: Abundance predictions from the NACRE reaction rate compilation

The abundances of the isotopes of the elements from C to Al produced by the non-explosive CNO, NeNa and MgAl modes of hydrogen burning, as well as by helium burning, are calculated with the thermonuclear rates recommended by the European compilation of reaction rates for astrophysics (NACRE: details about NACRE may be found at http://astro.ulb.ac.be. This electronic address provides many data of nuclear astrophysics interest and also offers the possibility of generating interactively tables of reaction rates for networks and temperature grids selected by the user). The impact of nuclear physics uncertainties on the derived abundances is discussed in the framework of a simple parametric astrophysical model. These calculations have the virtue of being a guide in the selection of the nuclear uncertainties that have to be duly analyzed in detailed model stars, particularly in order to perform meaningful confrontations between abundance observations and predictions. They are also hoped to help nuclear astrophysicists pinpointing the rate uncertainties that have to be reduced most urgently.Comment: 13 pages, 13 figures, Latex, accepted for publication in Astronomy and Astrophysics main journal. Also available at http://astro.ulb.ac.be/Htm/iaa0.ht

Nonlinear Correction to the Euler Buckling Formula for\ud Compressible Cylinders

Euler’s celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as\ud \ud N/(π 3B2)=(E/4)(B/L)2,\ud \ud where E is Young’s modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first nonlinear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of non-linear elasticity for the homogeneous compression of a thick cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants —including Poisson’s ratio— all appear in the coefficient of (B/L)4

Morphoelastic rods Part 1: A single growing elastic rod

A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling

Nonlinear morphoelastic plates II: exodus to buckled states

Morphoelasticity is the theory of growing elastic materials. This theory is based on the multiple decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing nonlinear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed

Symmetry energy: nuclear masses and neutron stars

We describe the main features of our most recent Hartree-Fock-Bogoliubov nuclear mass models, based on 16-parameter generalized Skyrme forces. They have been fitted to the data of the 2012 Atomic Mass Evaluation, and favour a value of 30 MeV for the symmetry coefficient J, the corresponding root-mean square deviation being 0.549 MeV. We find that this conclusion is compatible with measurements of neutron-skin thickness. By constraining the underlying interactions to fit various equations of state of neutron matter calculated {\it ab initio} our models are well adapted to a realistic and unified treatment of all regions of neutron stars. We use our models to calculate the composition, the equation of state, the mass-radius relation and the maximum mass. Comparison with observations of neutron stars again favours a value of J = 30 MeV.Comment: 10 pages, 9 figures, to appear in EPJA special volume on symmetry energ

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XI: Stabilizing neutron stars against a ferromagnetic collapse

We construct a new Hartree-Fock-Bogoliubov (HFB) mass model, labeled HFB-18, with a generalized Skyrme force. The additional terms that we have introduced into the force are density-dependent generalizations of the usual $t_1$ and $t_2$ terms, and are chosen in such a way as to avoid the high-density ferromagnetic instability of neutron stars that is a general feature of conventional Skyrme forces, and in particular of the Skyrme forces underlying all the HFB mass models that we have developed in the past. The remaining parameters of the model are then fitted to essentially all the available mass data, an rms deviation $\sigma$ of 0.585 MeV being obtained. The new model thus gives almost as good a mass fit as our best-fit model HFB-17 ($\sigma$ = 0.581 MeV), and has the advantage of avoiding the ferromagnetic collapse of neutron stars.Comment: accepted for publication in Physical Review

Impact of the phonon coupling on the dipole strength and radiative neutron capture

The E1 strength functions and radiative capture cross sections for several compound Sn isotopes, including unstable 132S n and 150S n, have been calculated using the self-consistent microscopic theory. In addition to the standard RPA or QRPA approaches, the method includes the quasiparticle-phonon coupling and the single-particle continuum. The results obtained show that the phonon contribution is very noticeable for the pygmy-dipole resonance, which, as it is known, is important for a description of the radiative neutron capture. The phonon contribution to the pygmy-dipole resonance and to the radiative neutron capture cross sections is increased with the (N-Z) difference growth. For example, in the (0-10) MeV interval the full theory gives 17% of EWSR for 150S n and 2.8% for 124S n, whereas within the continuum QRPA approach we have 5.1% and 1.7%, respectively. These facts indicate an important role of the self-consistent calculations that are of astrophysical interest for neutron-rich nuclei. The comparison with the phenomenological Generalized Lorentzian approach by Kopecky-Uhl has shown that the (Q)RPA approach gives a significant increase in the cross section by a factor of 2 for 132S n and a factor of 10 for 150S n and inclusion of the phonon coupling increases the cross sections for these nuclei even more, by a factor of 2-3.Comment: 4pages,3figures,International Conference on Nuclear Data for Science and Technology 201