Search

We prove that both the liquid drop model in ℝ³ with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their groundstates for all masses as long as the external potential V(x) in these models is of long range, that is, it decays slower than Newtonian (e.g., V(χ)>>|χ|-1 for large |χ|.) For the TFDW model, we adapt classical concentration-compactness arguments by Lions, whereas for the liquid drop model with background attraction, we utilize a recent compactness result for sets of finite perimeter by Frank and Lieb. [ABSTRACT FROM AUTHOR]

Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even in presence of a strong quantizing magnetic field. On the other hand, in the Thomas-Fermi-Dirac model a neutral WS cell can have finite radius. Graphical abstract: [ABSTRACT FROM AUTHOR]

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets. [ABSTRACT FROM AUTHOR]

We present an approach for the realization of extreme off-Hugoniot states of matter in laser-driven shock experiments. The method is based on the application of impedance-mismatch effect in sandwich targets. In order to verify this model we have realized numerical simulations using the two-dimensional hydrocode MULTI in three-layer targets (gold-aluminum-gold) with laser intensities ~1014 W/cm² and obtained pressures -10 Mbar. Results show the possibility of obtaining high pressures with relatively small temperatures for a low-impedance material sandwiched between layers with high density material. [ABSTRACT FROM AUTHOR]

Approximation of electronic kinetic energy can be naturally expressed in terms of the one-electron effective potential, namely as a potential functional. Such approximate functionals can lead to linear scaling orbital-free calculations of large systems. For calculation within orbital-free potential functionals, a new optimized effective potential (OEP) method has been developed presently for the direct optimization of electronic ground state energy. This approach parallels the development of OEP for the direct optimization of orbital-dependent exchange-correlation functionals within the Kohn–Sham density functional theory (DFT) framework. It uses the effective one-electron potential as the basic computation variable. This potential is further expanded as a linear combination of basis functions plus a fixed reference potential. Thus, the potential optimization is transformed into the optimization of linear coefficients associated with the basis sets. As a key quantity within the orbital-free potential functionals, the chemical potential controls the correct number of electrons and depends on the trial one-electron potential. The derivatives of the chemical potential with respect to the potential variations have been derived and their use leads to a very efficient electron-number conserving update of the trial potential. The calculations of several atoms and diatomic molecules with the simple Thomas–Fermi–Dirac approximate functional has been carried out to demonstrate our approach. The developed OEP approach should be an efficient computational tool for orbital-free potential functionals. [ABSTRACT FROM AUTHOR]

Abstract: The effect of strong quantizing magnetic field on the equation of state of matter at the outer crust region of magnetars is studied. The density of such matter is low enough compared to the matter density at the inner crust or outer core region. Based on the relativistic version of semi-classical Thomas–Fermi–Dirac model in presence of strong quantizing magnetic field a formalism is developed to investigate this specific problem. The equation of state of such low density crustal matter is obtained by replacing the compressed atoms/ions by Wigner–Seitz cells with nonuniform electron density. The results are compared with other possible scenarios. The appearance of Thomas–Fermi induced electric charge within each Wigner–Seitz cell is also discussed. [Copyright &y& Elsevier]

The tensile stress in CoSi2 films formed by deposition of Co films on Si(1 0 0) substrates and subsequent ex situ rapid thermal annealing was reduced by implantation of carbon ions into Si substrates before the deposition of Co films. It was found that the stress in the CoSi2 films decreases linearly with the increase of the C+ implantation doses. The reason for the reduction in the tensile stress is explained in terms of a new mechanism on the origin of the intrinsic stress in thin solid films based on a refined Thomas–Fermi–Dirac model. The theoretical calculations according to this model agree quite well with the experimental results. [Copyright &y& Elsevier]

The process of high-speed deformation in metals is considered as a propagation of shock-wave with some velocity. The description of this phenomenon is based on microscopic Thomas-Fermi-Dirac and so called "jelly" model of metal with degenerated electron gas and cold ionic subsystem. This model allows to investigate the stationary high-speed deformation structure in metals on microscopic level as a propagation of shock-wave in cold plasma. It is shown that during the shock wave propagation in metals in the shock wave front an effective electrical field is formed which tends to come back the displaced ions to initial equilibrium positions in crystal lattice. This electrostatic energy plays the role of potential energy of ions. The effective electrical field profile and kinetic energy profile for moved ions formed during the short time of shock wave propagation have been obtained. The developed theoretical model allows to suggest a physical mechanism for the explanation of formation of displaced atoms from nodal points during high speed deformation. When the kinetic energy of ions in shock wave front overcomes the threshold displacement energy (the sum of potential energy of ions in electrical field and energy for Frenkel pair formation) the point defects are produced. The obtained results are used to analyze the point defect formation in shock wave front moved with the different velocities. [ABSTRACT FROM AUTHOR]

The article discusses the nonexistence result from a study of energy functional known as Thomas-Fermi-Dirac-von Weizsäcker (TFDW) model for electrons with no external potential. It mentions the emergence of the nonexistence problem when considering the small volume-fraction limit for electrons in a box with uniform background charge. It also notes the isoperimetrical problems with nonlocal interaction.