Cluster expansions in many-fermion theory. I - ''Factor-cluster'' formalisms.
Cluster expansions in many fermion system for calculating expectation values of observables with respect to dynamically correlated state vectors
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Cluster expansions in many fermion system for calculating expectation values of observables with respect to dynamically correlated state vectors
Factor cluster formalisms in many fermion theory development, discussing primitive decomposition equations rearrangements and linked cluster theorem validity
Galaxy cluster expansion theory, noting dispersion in radial velocities of members
A high-resolution coherent anti-Stokes Raman spectrum of C2H2 in a pulsed molecular beam was obtained and the resolved Q-branch spectrum was used to study the properties of the expansion. Cluster formation limited the minimum observed rotational temperature in the pure-acetylene expansion to 30 K.
The cluster expansion technique is used in combination with first-principles calculations of the total energy of ordered compounds to study the energetics of the disordered phase for a number of alloy systems. The effect of short-range order, as seen in the energy differences between an alloy with the configuration corresponding to finite temperature and the perfectly random one is studied. The role of relaxation due to large size mismatch is discussed in terms of an effective cluster volume approximation. Very good agreement with measured energies of formation is obtained when short-range order and relaxation effects are taken into account.
Displacement correlations and frequency spectra for mass disordered lattices, deriving cluster expansion for phonon Green function
The Ostwald-ripening theory is deduced and discussed starting from the fundamental principles such as Ising model concept, Mayer cluster expansion, Langer condensation point theory, Ginzburg-Landau free energy, Stillinger cutoff-pair potential, LSW-theory and MLSW-theory. Mathematical intricacies are reduced to an understanding version. Comparison of selected works, from 1949 to 1984, on solution of diffusion equation with and without sink/sources term(s) is presented. Kahlweit's 1980 work and Marqusee-Ross' 1954 work are more emphasized. Odijk and Lekkerkerker's 1985 work on rodlike macromolecules is introduced in order to simulate interested investigators.
Full CI (FCI) wave functions are used to compute energies for several electronic states of the same symmetry for SiH2, CH2, and CH2(+). It is found that CASSCF/multireference CI wave functions yield results very similar to FCI, irrespective of whether the CASSCF MOs are optimized independently for each state or using an average of the CASSCF energies for all desired states. The ionization potentials and excitation energies obtained from the FCI calculations should help calibrate methods (such as Green's function approaches, equations of motion and propagator methods, and cluster expansions) in which energy differences are computed directly.
An investigation into the kinetics of molecular clustering processes which occur in the highly supersaturated vapor of a CO2 free jet is described. Terminal cluster concentrations in expansions from room temperature and reservoir pressures in the range from 400 to 900 torr were determined for trimeric CO2 for nozzle diameters of .0076 cm, .015 cm, and .023 cm and in the case of CO2 tetramer and pentamer for .015 cm nozzle diameter. The measurements were made mass spectrometrically in a supersonic molecular beam apparatus. A kinetic analysis was developed from an extension of the critical nucleus concept of nucleation theory and rate equations based on intermolecular collisions. The observed cluster populations could be accounted for by the theory by adopting sticking probabilities of approximately .03 for monomer impinging on dimer, trimer, and tetramer.
The determination of an accurate value of the Hubble constant requires the measurement of accurate galaxy distances and velocities. Both the Virgo and Fornax clusters of galaxies are close enough to be studied in considerable detail.
The core radii of 18 rich star clusters in the LMC with ages from 10 Myr to 1 Gyr. Data for an additional 17 clusters with ages from 1 Myr to 10 Gyr are available in the literature. The combined sample shows that the core radii increase from about 0 to about 5 pc between about 1 Myr and 1 Gyr, and then begin to decrease again. The expansion of the cores is probably driven by mass loss from evolving stars. Models of cluster evolution show that the rate of increase in core radius is sensitive to the slope of the initial mass function. The observed core radius-age relation for the LMC clusters favors an intial mass function with slope slightly flatter than the Salpeter value.
Three examples that illustrate the expected role of the Space Telescope in cosmological investigations are described addressing the distribution of globular star clusters, universe expansion, and other classical cosmological problems.
A model for the formation and stabilization of charged water clathrates is presented which accounts for observed anomalies in H(+)(H2O)n ion distributions. These anomalies are observed in both ion cluster and neutral expansions and are consistent with the sizes expected for clathrate ions. That the same sizes are observed in both ion cluster and neutral expansions strongly suggests that a rapid ionic process is responsible for their formation. The proposed model is based on the high mobility and bonding effects of the excess proton in water. Computer simulations suggest that excess proton movement in a water clathrate would be suitable for stabilizing the clathrate structure as well as giving it access to a large number of nearly degenerate proton configurations. The formation of clathrates in charged water clusters of proper size can be ascribed to the following: rapid excess proton movement, a strong preference of the H3O(+) for a three-coordinate bonding structure (which is compatible with hydrogen bonding), and finally, relatively slow processes leading to thermal disorder.
An important supplementary technique for ion mobility spectrometry (IMS) is mass spectrometry (MS). A mass spectrometer coupled to an ion mobility spectrometer (IMS/MS) can provide significant information on the composition of the ions contributing to an ion mobility peak. On the other hand, the interpretation of IMS/MS results requires knowledge of processes which can occur at the pinhole interface. When the ion composition is a mixture of ion clusters, the observed cluster distribution may not be an accurate representation of the ion clusters in the IMS. Depending on the buffer gas, lower clusters can form by equilibrating with reduced concentrations in the continuum regime of the expansion and larger clusters can form by collisional stabilization in the cooled jet stream. Besides water, nitrogen molecules can also add to the ion clusters. Even though nitrogen is non-polar, this addition is made possible by an ion-induced dipole interaction between the ion and molecule.
The National Aeronautics and Space Administration (NASA) Astronaut Corps is a unique occupational cohort for which vast amounts of measures data have been collected repeatedly in research or operational studies pre-, in-, and post-flight, as well as during multiple clinical care visits. In exploratory analyses aimed at generating hypotheses regarding physiological changes associated with spaceflight exposure, such as impaired vision, it is of interest to identify anomalies and trends across these expansive datasets. Multivariate clustering algorithms for repeated measures data may help parse the data to identify homogeneous groups of astronauts that have higher risks for a particular physiological change. However, available clustering methods may not be able to accommodate the complex data structures found in NASA data, since the methods often rely on strict model assumptions, require equally-spaced and balanced assessment times, cannot accommodate missing data or differing time scales across variables, and cannot process continuous and discrete data simultaneously. To fill this gap, we propose a network-based, multivariate clustering algorithm for repeated measures data that can be tailored to fit various research settings. Using simulated data, we demonstrate how our method can be used to identify patterns in complex data structures found in practice.
A study of the way observable clustering depends on expansion history is reported. Observable shapes that result from evolving otherwise identical systems are intercompared to show differences due to different expansion histories. Four cases are compared: nonexpanding, Omega = 1, and two open universes with 0.10 and 0.03 as final values of Omega. There is remarkably little diffrence in observable forms for the expanding cases. The 0.03 universe expanded by a factor 500 during the experiment. This study is an example of the way numerical experiments can be used in studies of galaxy clustering.
A significant percentage of the carbon inventory of the circumstellar and interstellar media may be in the form of large refractory molecules (or small grains) referred to as carbon clusters. At the small end, uneven numbers of carbon atoms seem to be preferred, whereas above 12 atoms, clusters containing an even number of carbon atoms appear to be preferred in laboratory chemistry. In the lab, the cluster C-60 appears to be a particularly stable form and has been nicknamed Bucky Balls because of its resemblance to a soccer ball and to geodesic domes designed by Buckminster Fuller. In order to investigate the prevalence of these clusters, and their relationship to the polycyclic aromatic hydrocarbons (PAHs) that have become the newest focus of IR astronomy, it is necessary to determine the spectroscopic characteristics of these clusters at near and far infrared wavelengths. Described here is the construction of a near to far IR laser magnetic resonance spectrometer that has been built at the University of California Berkeley in order to detect and characterize these spectra. The equipment produces carbon clusters by laser evaporation of a graphitic target. The clusters are then cooled in a supersonic expansion beam in order to simulate conditions in the interstellar medium (ISM). The expansion beam feeds into the spectrometer chamber and permits concentrations of clusters sufficiently high as to permit ultra-high resolution spectroscopy at near and far IR wavelengths. The first successful demonstration of this apparatus occurred last year when the laboratory studies permitted the observational detection of C-5 in the stellar outflow surrounding IRC+10216 in the near-IR. Current efforts focus on reducing the temperature of the supersonic expansion beam that transport the C clusters evaporated from a graphite target into the spectrometer down to temperatures as low as 1 K.
We have worked on the analysis of the Chandra observations of the nearby and distant clusters of galaxies, and on the expansion of the sample of distant X-ray clusters based on the archival ROSAT PSPC data. Some of the scientific results are discussed.