Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings

Fluctuating parts of nuclear ground state correlation energies

Background: Heavy atomic nuclei are often described using the Hartree-Fock-Bogoliubov (HFB) method. In principle, this approach takes into account Pauli effects and pairing correlations while other correlation effects are mimicked through the use of effective density-dependent interactions. Purpose: Investigate the influence of higher order correlation effects on nuclear binding energies using Skyrme's effective interaction. Methods: A cut-off in relative momenta is introduced in order to remove ultraviolet divergences caused by the zero-range character of the interaction. Corrections to binding energies are then calculated using the quasiparticle-random-phase approximation (QRPA) and second order many-body perturbation theory (MBPT2). Result: Contributions to the correlation energies are evaluated for several isotopic chains and an attempt is made to disentangle which parts give rise to fluctuations that may be difficult to incorporate on the HFB level. The dependence of the results on the cut-off is also investigated. Conclusions: The improved interaction allows explicit summations of perturbation series which is useful for the description of some nuclear observables. However, refits of the interaction parameters are needed to obtain more quantitative results

TOPEX orbital radiation study

The space radiation environment of the TOPEX spacecraft is investigated. A single trajectory was considered. The external (surface incident) charged particle radiation, predicted for the satellite, is determined by orbital flux integration for the specified trajectory. The latest standard models of the environment are used in the calculations. The evaluation is performed for solar maximum conditions. The spacecraft exposure to cosmic rays of galactic origin is evaluated over its flight path through the magnetosphere in terms of geomagnetic shielding effects, both for surface incident heavy ions and for particles emerging behind different material thickness. Limited shielding and dose evaluations are performed for simple infinite slab and spherical geometries. Results, given in graphical and tabular form, are analyzed, explained, and discussed. Conclusions are presented and commented on

AGE AND CHEMISTRY OF BELL CREEK BATHOLITH

The Southern Complex, located near Marquette, Michigan is in the southernmost portion of the Superior Province. This complex consists of granitoids and granitic gneiss that vary in composition. In twentieth century research, Hoffman (1987) and Tinkham (1997) concluded that the Southern Complex contained two units in which the granitoid was emplaced in the granitic gneiss. Recent research conducted by Petryk (2019) determined that the Southern Complex has a U-Pb zircon age of 2600 Ma. Dalle Fratte (2020) concluded that the granitic gneiss migmatite texture was the result of a felsic magma mixing with several generations of mafic intrusions that were later deformed. Data from Petryk (2019) and Dalle Fratte (2020) were mostly from M-95, which only accounts for the western portion of the Southern Complex. More geochemical and isotope data were collected from the eastern portion of the Southern Complex and compared with previous studies. The U-Pb zircon ages from the eastern portion of the Southern Complex were approximately 2600 Ma, similar to data from Petryk (2019) and Tinkham (1997). The eastern side also yielded some data with slight variations in geochemistry, which supports Dalle Fratte (2020) interpretation; magma mixing between a felsic melt and several generations of a more mafic melt intruding the pluton during or later in its crystallization

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

The correlation potential in density functional theory at the GW-level: spherical atoms

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.Comment: 13 pages, 9 figure

The casting and powder-metallurgy forming of precipitation-hardenable stainless steels

Casting and powder metallurgy techniques for shaping precipitation hardened stainless steel

Carbon isotope fractionation during aerobic biodegradation of trichloroethene by Burkholderia cepacia G4: a tool to map degradation mechanisms

The strain Burkholderia cepacia G4 aerobically mineralized trichloroethene (TCE) to CO2 over a time period of similar to20 h. Three biodegradation experiments were conducted with different bacterial optical densities at 540 nm (OD(540)s) in order to test whether isotope fractionation was consistent. The resulting TCE degradation was 93, 83.8, and 57.2% (i.e., 7.0, 16.2, and 42.8% TCE remaining) at OD(540)s of 2.0, 1.1, and 0.6, respectively. ODs also correlated linearly with zero-order degradation rates (1.99, 1.11, and 0.64 mumol h(-1)). While initial nonequilibrium mass losses of TCE produced only minor carbon isotope shifts (expressed in per mille delta C- 13(VPDB)), they were 57.2, 39.6, and 17.0parts per thousand between the initial and final TCE levels for the three experiments, in decreasing order of their OD(540)s. Despite these strong isotope shifts, we found a largely uniform isotope fractionation. The latter is expressed with a Rayleigh enrichment factor, E, and was -18.2 when all experiments were grouped to a common point of 42.8% TCE remaining. Although, decreases of epsilon to -20.7 were observed near complete degradation, our enrichment factors were significantly more negative than those reported for anaerobic dehalogenation of TCE. This indicates typical isotope fractionation for specific enzymatic mechanisms that can help to differentiate between degradation pathways

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio