Assembly and analysis of fragmentation data for liquid propellant vessels

Fragmentation data was assembled and analyzed for exploding liquid propellant vessels. These data were to be retrieved from reports of tests and accidents, including measurements or estimates of blast yield, etc. A significant amount of data was retrieved from a series of tests conducted for measurement of blast and fireball effects of liquid propellant explosions (Project PYRO), a few well-documented accident reports, and a series of tests to determine auto-ignition properties of mixing liquid propellants. The data were reduced and fitted to various statistical functions. Comparisons were made with methods of prediction for blast yield, initial fragment velocities, and fragment range. Reasonably good correlation was achieved. Methods presented in the report allow prediction of fragment patterns, given type and quantity of propellant, type of accident, and time of propellant mixing

Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He)2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.Comment: 22 page

Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional

Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $\lambda$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced coupling constant, $\lambda<1$, is defined to reproduce $n_{GS}({\bf r})$ and the ground state energy. Fixing the charge density, possible phase transitions as level crossings detected in a value of the reduced density functional happen only at discrete points along the $\lambda$ axis. If the density is $v$-representable also for $\lambda<1$, accumulation of phase transition points is forbidden when $\lambda\rightarrow 1$. Relevance of the theorems for the multi-reference density functional theory is discussed.Comment: 19 page

Dynamical coherent-potential approximation approach to excitation spectra in 3d transition metals

First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied to the investigations of a systematic change of excitation spectra in $3d$ transition metals from Sc to Cu at finite temperatures. It is shown that the dynamical effects damp main peaks in the densities of states (DOS) obtained by the local density approximation to the density functional theory, reduce the band broadening due to thermal spin fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc Fe, and create a small hump corresponding to the `6 eV' satellite in the case of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it is found that screening effects on the exchange energy parameters are significant for understanding the spectra in magnetic transition metals.Comment: To be published in Phys. Rev.

A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations

The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.Comment: 7 pages, RevTeX4, revise

Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods

Spectroscopic and optical properties of nanosystems and point defects are discussed within the framework of Green's function methods. We use an approach based on evaluating the self-energy in the so-called GW approximation and solving the Bethe-Salpeter equation in the space of single-particle transitions. Plasmon-pole models or numerical energy integration, which have been used in most of the previous GW calculations, are not used. Fourier transforms of the dielectric function are also avoided. This approach is applied to benzene, naphthalene, passivated silicon clusters (containing more than one hundred atoms), and the F center in LiCl. In the latter, excitonic effects and the $1s \to 2p$ defect line are identified in the energy-resolved dielectric function. We also compare optical spectra obtained by solving the Bethe-Salpeter equation and by using time-dependent density functional theory in the local, adiabatic approximation. From this comparison, we conclude that both methods give similar predictions for optical excitations in benzene and naphthalene, but they differ in the spectra of small silicon clusters. As cluster size increases, both methods predict very low cross section for photoabsorption in the optical and near ultra-violet ranges. For the larger clusters, the computed cross section shows a slow increase as function of photon frequency. Ionization potentials and electron affinities of molecules and clusters are also calculated.Comment: 9 figures, 5 tables, to appear in Phys. Rev. B, 200

Scanning Electron Microscopic Studies of the Oral Tissue Responses to Dental Implants

Scanning electron microscopy ( SEM) and its associated technologies have proven invaluable in elucidating the interfacial oral tissue responses to dental implants. Since the dental implant must extend from the mandibular or maxillary jaw, through the oral mucosa, and into the oral cavity, these tissue responses include epithelium, connective tissue and bone. The continual occlusal forces acting upon these tissues reinforce the dynamic character of these tissue responses. Immediately upon implantation, a healing phase begins as a response to the implanted biomaterial. Following this immediate response a longer healing phase occurs, beginning approximately 1 week after implantation, resulting in the modeling of bone to the implant as well as the formation of epithelial attachment to the implant. This later, delayed healing continues throughout the lifetime of the implant since these tissues must die and be replaced by similar tissues. Current dental research employing scanning electron microscopy is now documenting these tissue responses. This paper reviews, in detail, SEM observations of these tissue responses

Inter-cluster reactivity of Metallo-aromatic and anti-aromatic Compounds and Their Applications in Molecular Electronics: A Theoretical Investigation

Local reactivity descriptors such as the condensed local softness and Fukui function have been employed to investigate the inter-cluster reactivity of the metallo-aromatic (Al4Li- and Al4Na-) and anti-aromatic (Al4Li4 and Al4Na4) compounds. We use the concept of group softness and group Fukui function to study the strength of the nucleophilicity of the Al4 unit in these compounds. Our analysis shows that the trend of nucleophilicity of the Al4 unit in the above clusters is as follows; Al4Li- > Al4Na- > Al4Li4 > Al4Na 4 For the first time we have used the reactivity descriptors to show that these clusters can act as electron donating systems and thus can be used as a molecular cathode.Comment: 23 pages, 1 figure and 1 table of conten

Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms

The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime. It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.Comment: Resubmitted to PRA in response to referee's comments. Abstract is changed. Added new figure

Particle-Number Restoration within the Energy Density Functional Formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.Comment: 37 pages, 14 figures, accepted for publication in PR