Energy functional
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On Dipolar Quantum Gases in the Unstable Regime Open
We study the nonlinear Schr\\"odinger equation arising in dipolar\nBose-Einstein condensate in the unstable regime. Two cases are studied: the\nfirst when the system is free, the second when gradually a trapping potential\nis added. In bot…
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Fusion-based Variational Image Dehazing Open
We propose a novel image-dehazing technique based on the minimization of two energy functionals and a fusion scheme to combine the output of both optimizations. The proposed fusion-based variational image-dehazing (FVID) method is a spatia…
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Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions Open
Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free-energy functional accurate over a wide range of state conditions. Unl…
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Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative Open
Orbital-free approaches might offer a way to boost the applicability of density functional theory by orders of magnitude in system size. An important ingredient for this endeavor is the kinetic energy density functional. Snyder et al. [ Ph…
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The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases Open
We study the ground state of a trapped Bose gas, starting from the full\nmany-body Schr{\\"o}dinger Hamiltonian, and derive the nonlinear Schr{\\"o}dinger\nenergy functional in the limit of large particle number, when the interaction\npote…
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Spherical harmonics based descriptor for neural network potentials: Structure and dynamics of Au147 nanocluster Open
We propose a highly efficient method for fitting the potential energy surface of a nanocluster using a spherical harmonics based descriptor integrated with an artificial neural network. Our method achieves the accuracy of quantum mechanics…
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The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory Open
Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional fo…
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Gradient dynamics models for liquid films with soluble surfactant Open
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Fractional elliptic problems with critical growth in the whole of $\R^n$ Open
We study the following nonlinear and nonlocal elliptic equation in~$\R^n$ $$ (-Δ)^s u = ε\,h\,u^q + u^p \ {\mbox{ in }}\R^n, $$ where~$s\in(0,1)$, $n>2s$, $ε>0$ is a small parameter, $p=\frac{n+2s}{n-2s}$, $q\in(0,1)$, and~$h\in L^1(\R^n)\…
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Topological Function Optimization for Continuous Shape Matching Open
We present a novel approach for optimizing real‐valued functions based on a wide range of topological criteria. In particular, we show how to modify a given function in order to remove topological noise and to exhibit prescribed topologica…
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Multiconfiguration Pair-Density Functional Theory Open
Kohn-Sham density functional theory with the available exchange–correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated…
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Consistent multiphase-field theory for interface driven multidomain dynamics Open
We present a new multiphase-field theory for describing pattern formation in\nmulti-domain and/or multi-component systems. The construction of the free\nenergy functional and the dynamic equations is based on criteria that ensure\nmathemat…
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Status of free-energy representations for the homogeneous electron gas Open
Renewed interest in the homogeneous electron gas (HEG) has been stimulated by recent accurate simulations of it over a wide range of densities and temperatures. Those data, combined with known theoretical limits, have led to analytical rep…
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Primal Dual Methods for Wasserstein Gradient Flows Open
Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science, …
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Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings Open
In this paper we study the ground state solutions for a nonlinear elliptic system of three equations which comes from models in Bose-Einstein condensates. Comparing with existing works in the literature which have been on purely attractive…
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Machine-learning-based exchange correlation functional with physical asymptotic constraints Open
Density functional theory is the standard theory for computing the electronic structure of materials, which is based on a functional that maps the electron density to the energy. However, a rigorous form of the functional is not known and …
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Tetrahedral shapes of neutron-rich Zr isotopes from a multidimensionally constrained relativistic Hartree-Bogoliubov model Open
We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be…
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Fuzzy Region-Based Active Contours Driven by Weighting Global and Local Fitting Energy Open
Active contour model (ACM) has been a successful method for image segmentation. The existing ACMs poorly segment the images with intensity inhomogeneity or non-homogeneity, and the results highly depend on the initial position of the conto…
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Machine learning density functional theory for the Hubbard model Open
The solution of complex many-body lattice models can often be found by\ndefining an energy functional of the relevant density of the problem. For\ninstance, in the case of the Hubbard model the spin-resolved site occupation is\nenough to d…
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Augmented Lagrangian method for an Euler's elastica based segmentation model that promotes convex contours Open
In this paper, we propose an image segmentation model where an $L^1$ variant of the Euler's elastica energy is used as boundary regularization. An interesting feature of this model lies in its preference for convex segmentation contours. H…
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From gas dynamics with large friction to gradient flows describing diffusion theories Open
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flo…
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Active contours driven by local and global fitted image models for image segmentation robust to intensity inhomogeneity Open
This paper presents a region-based active contour method for the segmentation of intensity inhomogeneous images using an energy functional based on local and global fitted images. A square image fitted model is defined by using both local …
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Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory Open
Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the app…
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Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning Open
We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron d…
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Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density Open
We introduce an approximation to the short-range correlation energy functional with multideterminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, t…
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Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria Open
We present a framework for the multiscale modeling of finite strain magneto-elasticity based on physics-augmented neural networks (NNs). By using a set of problem specific invariants as input, an energy functional as the output and by addi…
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Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy Open
From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fu…
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Vector solitons in a spin-orbit-coupled spin-2 Bose-Einstein condensate Open
Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a mean-…
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Discrete Optimization for Shape Matching Open
We propose a novel discrete solver for optimizing functional map‐based energies, including descriptor preservation and promoting structural properties such as area‐preservation, bijectivity and Laplacian commutativity among others. Unlike …
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Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation Open
We seek to obtain a usable form of the nuclear energy density functional that\nis rooted in the modern theory of nuclear forces. We thus consider a functional\nobtained from the density matrix expansion of local nuclear potentials from\nch…