Search results for "Energy functional"
showing 10 items of 34 documents
Adaptive Bias Field Correction: Application on Abdominal MR Images
2017
Segmentation of medical images is one of the most important phases for disease diagnosis. Accuracy, robustness and stability of the results obtained by image segmentation is a major concern. Many segmentation methods rely on absolute values of intensity level, which are affected by a bias term due to in-homogeneous field in magnetic resonance images. The main objective of this paper is two folded: (1) To show efficiency of an energy minimization based approach, which uses intrinsic component optimization, on abdominal magnetic resonance images. (2) To propose an adaptive method to stop the optimization automatically. The proposed method can control the value of the energy functional and sto…
Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
2021
We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda u - \gamma (|x|^{-1} * |u|^2) u - a |u|^{p-2}u = 0 \quad \text{in} \quad \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx = c \end{equation*} for some prescribed $c>0$. Here $ u \in H^1(\mathbb{R}^3)$, $\gamma \in \mathbb{R},$ $ a \in \mathbb{R}$ and $p \in (\frac{10}{3}, 6]$. When $\gamma >0$ and $a > 0$, both in the Sobolev subcritical case $p \in (\frac{10}{3}, 6)$ and in the Sobolev critical case $p=6$, we show that there exists a $c_1>0$ such that, for any $c \in (0,c_1)$, the equation admits two solutions $u_c^+$ and $u_c^-$ which can be characterized respectively…
Energy dissipative solutions to the Kobayashi-Warren-Carter system
2017
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\Gamma$-convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions togethe…
Continuous theory of switching in geometrically confined ferroelectrics
2014
A theory of ferroelectric switching in geometrically confined samples like thin films and multilayers with domain structure has been proposed. For that we use Landau–Khalatnikov (LK) equations with free energy functional being dependent on polarization gradients. In this case, the consistent theory can be developed as for thin ferroelectric films and multilayers the domain structure reduces to Fourier series in ferroelectric polarization. The specific calculations are presented for thin film ferroelectric with dead layers and ferro-/paraelectric multilayer. Our theory is generalizable to ferroelectrics and multiferroics with other geometries.
Geometry and analysis of Dirichlet forms (II)
2014
Abstract Given a regular, strongly local Dirichlet form E , under assumption that the lower bound of the Ricci curvature of Bakry–Emery, the local doubling and local Poincare inequalities are satisfied, we obtain that: (i) the intrinsic differential and distance structures of E coincide; (ii) the Cheeger energy functional Ch d E is a quadratic norm. This shows that (ii) is necessary for the Riemannian Ricci curvature defined by Ambrosio–Gigli–Savare to be bounded from below. This together with some recent results of Ambrosio–Gigli–Savare yields that the heat flow gives a gradient flow of Boltzman–Shannon entropy under the above assumptions. We also obtain an improvement on Kuwada's duality …
Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data
2002
We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in $L^1$ for these solutions. To prove the existence we use the nonlinear semigroup theory.
Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)
2017
Let be a bounded smooth domain in RN. We prove a general existence result of least energy solutions and least energy nodal ones for the problem −u = f(x, u) in u = 0 on ∂ (P) where f is a Carathéodory function. Our result includes some previous results related to special cases of f . Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type f(x, u) = λ|u| s−2u − μ|u| r−2u, with s, r ∈ (1, 2) and λ,μ > 0.
Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems
2013
We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these re…
Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
2018
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $\Omega [\mathbf{G}]$ regarded as variational functional of the Green's function $G$ based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger-Ward form. By restricting the input Green's function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To establish the one-to-one mapping we use that, at any finite temperature and for a given 1RDM $\…
Finite-range separable pairing interaction within the new N3LO DFT approach
2011
For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N3LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N3LO energy …