scholarly journals Variational Method for Nuclear Matter with an Explicit Energy Functional

2013 ◽  
Author(s):  
Masatoshi Takano
Keyword(s):  
Variational Method ◽  
Nuclear Matter ◽  
Energy Functional

scholarly journals Non-empirical pairing energy functional in nuclear matter and finite nuclei

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
K. Hebeler ◽  
T. Duguet ◽  
T. Lesinski ◽  
A. Schwenk
Keyword(s):  
Nuclear Matter ◽  
Energy Functional ◽  
Pairing Energy ◽  
Finite Nuclei

scholarly journals On a nonlinear PDE involving weighted $p$-Laplacian

2019 ◽  
Vol 38 (5) ◽  
pp. 131-145
Author(s):  
A. El Khalil ◽  
M. D. Morchid Alaoui ◽  
Mohamed Laghzal ◽  
A. Touzani
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Method ◽  
Nonlinear Partial Differential Equation ◽  
Weighted Sobolev Spaces ◽  
Point Theory ◽  
Energy Functional ◽  
Nonlinear Pde ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions

In the present paper, we study the nonlinear partial differential equation with the weighted $p$-Laplacian operator\begin{gather*}- \operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u) = \frac{ f(x)}{(1-u)^{2}},\end{gather*}on a ball ${B}_{r}\subset \mathbb{R}^{N}(N\geq 2)$. Under some appropriate conditionson the functions $f, w$ and the nonlinearity $\frac{1}{(1-u)^{2}}$, we prove the existence and the uniqueness of solutions of the above problem. Our analysis mainly combines the variational method and critical point theory. Such solution is obtained as a minimizer for the energy functional associated with our problem in the setting of the weighted Sobolev spaces.

scholarly journals Equation of state for nuclear matter in core-collapse supernovae by the variational method

2014 ◽  
Vol 569 ◽  
pp. 012058
Author(s):  
H Togashi ◽  
Y Takehara ◽  
S Yamamuro ◽  
K Nakazato ◽  
H Suzuki ◽  
...  
Keyword(s):  
Equation Of State ◽  
Variational Method ◽  
Nuclear Matter ◽  
Core Collapse

The Correlated Basis Function Method and its Application to Liquid 3He, Nuclear Matter and Neutron Matter

1975 ◽  
Vol 30 (8) ◽  
pp. 923-936
Author(s):  
J. Nitsch
Keyword(s):  
Correlation Function ◽  
Nuclear Matter ◽  
Lagrange Equation ◽  
Expansion Method ◽  
Liquid Structure ◽  
Energy Functional ◽  
Basis Functions ◽  
Neutron Matter ◽  
Expectation Values ◽  
Energy Expectation

Abstract The method of correlated basis functions is studied and applied to the Fermi systems: liquid 3 He, nuclear matter and neutron matter. The reduced cluster integrals xijkl... and so the sub-normalization integrals Iijkl... are generalized to coinciding quantum numbers out of the set {i, j, k, I,...}. This generalization has an important consequence for the radial distribution function g (r) (and then for the liquid structure function) ; g(r) has no contributions of the order O (A-1). For 3 He the state-independent two-body correlation function g(r) is calculated from the Euler-Lagrange equation (in the limit of r → 0) for the unrenormalized two-body energy functional. For nuclear matter and neutron matter we adopt the three-parameter correlation function of Bäckman et al. Then the energy expectation values are calculated by including up to the three-body terms in the unrenormalized and renormalized version of the correlated basis functions method. The experimental ground-state energy and density of liquid s He can be well reproduced by the present method with the Lennard-Jones-(6 -12) potential. The same method is applied to the nuclear matter and neutron matter calculations with the OMY-potential. The results of the energy expectation values indicate a practical superiority of the unrenormalized cluster expansion method over the renormalized one.

Variational method for the Hartree equation of the helium atom

1978 ◽  
Vol 82 (1-2) ◽  
pp. 27-39 ◽  
Author(s):  
Peter Bader
Keyword(s):  
Variational Method ◽  
Helium Atom ◽  
Energy Functional ◽  
Hartree Equation ◽  
Hartree Approximation

SynopsisIt is shown that in the Hartree approximation the energy functional of the helium atom reaches its minimum and that the corresponding minimizing function is a solution of the Hartree equation.

Sign in / Sign up

Export Citation Format

Share Document