Analytical mass formula and nuclear surface properties in the ETF approximation

The problem of the determination of the nuclear surface and surface symmetry energy is addressed in the framework of the Extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. For the case of symmetric nuclei, the resulting ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed, which cannot be simply deduced from the local part of the functional. In the case of asymmetric nuclei, we propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves over previous models and leads to a precision better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.Comment: 27 pages, 18 figures, submitted to PR

Clusterized nuclear matter in the (proto-)neutron star crust and the symmetry energy

Though generally agreed that the symmetry energy plays a dramatic role in determining the structure of neutron stars and the evolution of core-collapsing supernovae, little is known in what concerns its value away from normal nuclear matter density and, even more important, the correct definition of this quantity in the case of unhomogeneous matter. Indeed, nuclear matter traditionally addressed by mean-field models is uniform while clusters are known to exist in the dilute baryonic matter which constitutes the main component of compact objects outer shells. In the present work we investigate the meaning of symmetry energy in the case of clusterized systems and the sensitivity of the proto-neutron star composition and equation of state to the effective interaction. To this aim an improved Nuclear Statistical Equilibrium (NSE) model is developed, where the same effective interaction is consistently used to determine the clusters and unbound particles energy functionals in the self-consistent mean-field approximation. In the same framework, in-medium modifications to the cluster energies due to the presence of the nuclear gas are evaluated. We show that the excluded volume effect does not exhaust the in-medium effects and an extra isospin and density dependent energy shift has to be considered to consistently determine the composition of subsaturation stellar matter. The symmetry energy of diluted matter is seen to depend on the isovector properties of the effective interaction, but its behavior with density and its quantitative value are strongly modified by clusterization.Comment: A contribution to the upcoming EPJA Special Volume on Nuclear Symmetry Energ

Bifurcation analysis and steady state patterns in reaction-diffusion systems augmented with self- and cross-diffusion

In this article, a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion is done, using an augmented Gray-Scott system as a generic example. The methodology remains general, and is therefore applicable to other systems. Simulations of the temporal model (nonlinear parabolic system) reveal the presence of steady states, often associated with energy dissipation. A Newton method based on a mixed finite element method is provided, in order to directly evaluate the steady states of the temporal system (nonlinear elliptic system), and validated against its solutions. Linear stability analysis (LSA) using Fourier analysis is carried out, as well as a numerical stability analysis, emphasizing the limitation of the latter. A multi-parameter birfurcation is reported, where LSA predicts only stability. Original steady state patterns are unveiled, not observable with linear diffusion only. Two key observations are made: a dependency of the pattern on the initial condition of the system, and a dependency on the geometry of the domain

Neuroscience, Materialism, and the Soul: Limit Questions

In light of recent discoveries in neuroscience linking the mind to physical processes, Christian philosophers have resorted to a more materialistic view of the human person, using neuroscience as support for their view that an immaterial soul does not exist. In this essay, I will point out a major flaw in the logic for defending a materialistic view, argue that either a bipartite or tripartite view of the human person is more aligned with Scripture, and hopefully point towards a more reliable means for attaining truth regarding human nature and the soul

Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems

We show that the sublinearity hypothesis of some well-known existence results on multipoint Boundary Value Problems (in short BVPs) may allow the existence of infinitely many solutions by using Tietze extension theorem. This is a qualitative result which is of concern in Applied Analysis and can motivate more research on the conditions that ascertain the existence of multiple solutions to sublinear BVPs. The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions