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We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…

Numerical Analysis · Mathematics 2025-10-23 Agus L. Soenjaya , Ping Lin , Thanh Tran

We present relativistic many-body calculations of total electron binding energy of neutral atoms up to element $Z=120$. Binding energy for ions may be found by subtracting known ionization potentials. Accuracy of the results for $17<Z…

Atomic Physics · Physics 2025-03-25 V. A. Dzuba , V. V. Flambaum , A. V. Afanasjev

We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…

Atomic Physics · Physics 2013-05-29 Gillian Peach , Ian B Whittingham , Timothy J Beams

The semi-classical Wigner-Kirkwood $\hbar$ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in $\hbar$. A systematic study of Wigner-Kirkwood averaged…

Nuclear Theory · Physics 2010-12-23 A. Bhagwat , X. Viñas , M. Centelles , P. Schuck , R. Wyss

We report the density-functional calculations that systematically clarify the stable forms of carbon-related defects and their energy levels in amorphous SiO$_2$ using the melt-quench technique in molecular dynamics. Considering the…

Materials Science · Physics 2018-12-03 Yu-ichiro Matsushita , Atsushi Oshiyama

Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…

Materials Science · Physics 2009-11-11 Florian R. Krajewski , Michele Parrinello

Starting from the total energy expressions within density functional theory, we are able to perform a comparison of several currently used charged-defect finite-size supercell correction schemes in a unified manner. This approach also…

Mesoscale and Nanoscale Physics · Physics 2009-06-09 Hannu-Pekka Komsa , Tapio T. Rantala

We present a symmetry-based calculation of the electronic structure of a compound semiconductor quantum dot (QD) in the sp^3s* tight-binding model including the spin-orbit interaction. The Hamiltonian matrix is diagonalized exactly for CdTe…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 J. Perez-Conde , A. K. Bhattacharjee

The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calculation of formation energies in one-dimensional nanostructures, which overcomes the…

Materials Science · Physics 2015-05-13 Riccardo Rurali , Xavier Cartoixa

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…

Analysis of PDEs · Mathematics 2022-08-10 Julian Braun , Thomas Hudson , Christoph Ortner

We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…

We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QD's) within the empirical $s p^{3} s^{*}$ tight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit…

Materials Science · Physics 2009-11-10 R. Santoprete , Belita Koiller , R. B. Capaz , P. Kratzer , Q. K. K. Liu , M. Scheffler

The electron and photon transport processes in spectroscopy techniques described by the invariant embedding theory is here revisited. We report a convergence method to obtain closed analytical solutions to the 3D integro-differential…

Materials Science · Physics 2010-06-22 Carlos Figueroa , Horacio Brizuela , Silvia P. Heluani

Energetic disorder has been known for decades to limit the performance of structurally disordered semiconductors such as amorphous silicon and organic semiconductors. However, in the past years, high performance organic solar cells have…

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified…

Nuclear Theory · Physics 2011-01-04 B. Alex Brown , Angelo Signoracci , Morten Hjorth-Jensen

We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and…

Materials Science · Physics 2009-11-07 Matthew D. Jones , R. C. Albers

We apply a hard-core version of the Faddeev differential equations to the ^3He^4He_2 three-atomic system. Employing the TTY interatomic potential by Tang, Toennies and Yiu we calculate the binding energy of the ^3He^4He_2 trimer and the…

Atomic and Molecular Clusters · Physics 2007-05-23 E. A. Kolganova , Y. K. Ho , A. K. Motovilov , W. Sandhas

Methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In one method, the electron density is…

Chemical Physics · Physics 2022-05-16 Jerry L. Whitten

An efficient method for calculating the electronic structure in large systems with a fully converged BZ sampling is presented. The method is based on a k.p-like approximation developed in the framework of the density functional perturbation…

Computational Physics · Physics 2009-11-07 Marcella Iannuzzi , Michele Parrinello

For a previously published study of the titanium hcp (alpha) to omega (omega) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron…

Materials Science · Physics 2008-07-24 D. R. Trinkle , M. D. Jones , R. G. Hennig , S. P. Rudin , R. C. Albers , J. W. Wilkins
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