Density functional theory calculation and thermodynamic analysis of the bridgmanite surface structure

Bridgmanite, a high temperature and pressure form of $MgSiO_3$, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of the chemical potential of oxygen and magnesium. The results presented provide a basis for further theoretical studies of the chemical processes on bridgmanite surfaces in the Earth's mantle and slip plane analysis.Comment: 4 Pages,4 figure

The singularity categories of the Cluster-tilted algebras of Dynkin type

In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence classification of the cluster-tilted algebra of type $A$, $D$ and $E$ respectively.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1012.4661 by other author

A COMPARISON OF LOGISTIC REGRESSION TO RANDOM FORESTS FOR EXPLORING DIFFERENCES IN RISK FACTORS ASSOCIATED WITH STAGE ATDIAGNOSIS BETWEEN BLACK AND WHITE COLON CANCER PATIENTS

Introduction: Colon cancer is one of the most common malignancies in America. According to the American Cancer Society, blacks have lower survival rate than whites. Many previous studies suggested that it is because blacks were more likely to be diagnosed at a late stage. Hence, it is crucial to determine factors that are associated with colon cancer stage at diagnosis. Objectives: The objectives of this study are twofold: 1)To compare logistic regression modeling to Random Forests classification with respect to variables selected and classification accuracy; and 2) To evaluate the factors related to colon cancer stage at diagnosis in a population based study. Many studies have comparedClassification and Regression Trees (CART) to logistic regression and found that they have very similar power with respect to the proportion correctly classified and the variables selected. This study extends previous methodological research by comparing the Random Forests classification techniques to logistic regression modeling using a relatively small and incomplete dataset. Methods and Materials: The data used in this research were from National Cancer Institute Black/White Cancer Survival Study which had 960 cases of invasive colon cancer. Stage at diagnosis was used as the dependent variable for fitting logistic regression models and Random Forests Classification to multiple potential explanatory variables, which included some missing data. Results: Odds ratio (blacks vs. whites) decreased from 1.628 (95%CI: 1.068-2.481) to 1.515 (95% CI: 0.920-2.493) after adjustment was made for patient delay in diagnosis, occupation, histology and grade of tumor. Race became no longer important after these variables were entered in the Random Forests. These four variables were identified as the most important variables associated with racial disparity in colon cancer stage at diagnosis in both logistic regression and Random Forests. The correctclassification rate was 47.9% using logistic regression and was 33.9% using Random Forests. Conclusion: 1). Logistic regression and Random Forests had very similar power in variable selection. 2). Logistic regression had higher classification accuracy than Random Forests with respect to overall correct classification rate

Monopole-Antimonopole Pair Dyons

Monopole-antimonopole pair (MAP) with both electric and magnetic charges are presented. The MAP possess opposite magnetic charges but they carry the same electric charges. These stationary MAP dyon solutions possess finite energy but they do not satisfy the first order Bogomol'nyi equations and are not BPS solutions. They are axially symmetric solutions and are characterized by a parameter, $-1\leq\eta\leq 1$ which determines the net electric charges of these MAP dyons. These dyon solutions are solved numerically when the magnetic charges of the dipoles are $n=\pm 1, \pm 2$ and when the strength of the Higgs field potential $\lambda=0, 1$. When $\lambda=0$, the time component of the gauge field potential is parallel to the Higgs field in isospin space and the MAP separation distance, total energy and net electric charge increase exponentially fast to infinity when $\eta$ approaches $\pm 1$. However when $\lambda=1$, all these three quantities approach a finite critical value as $\eta$ approaches $\pm 1$.Comment: 20 pages, 9 figures, 2 table

Site preference of Fe atoms in the olivine (FexMg2−x)SiO4(Fe_xMg_{2-x})SiO_4 and its surface

Olivine is involved in many natural reactions and industrial reactions as a catalyst. The catalytic ability is highly possible rely on the $Fe^{2+}$ in olivine. We use density functional theory calculation and thermodynamics to investigate the site preference of Fe atom in olivine which composition from iron-rich to iron-poor and its surfaces. The $Fe^{2+}$ always shows its high spin (quintet) state which has larger ion radius than $Mg^{2+}$ in olivine crystal and surfaces. The $Fe^{2+}$ inside the surface slab prefers the smaller M1 site than M2 site by enlarge the metal-oxygen octahedra when occupied the metal site as in the bulk system. Energy contribution of entropies accumulation caused temperature raise stops this preference at the temperature where a cation order-disorder distribution energy crossover happen in olivine. Surface exposed site provide $Fe^{2+}$ large space due its unsaturated nature. This lead a higher level of preference of $Fe^{2+}$ to the surface site than any metal site inside the crystal no matter M1 or M2 site is exposed. This indicate the $Fe^{2+}$ in the bulk system can diffuse to a metal site exposed on the surface driven by the energy difference. Many reactions can use the on surface $Fe^{2+}$ as a catalyst because of the active chemical behavior of Fe. Meanwhile this energetics preference should be considered in the future model to explain the natural observed zoning olivine have a high Fe edge and low Fe center. These microscopic understanding can be essential to many olivine related geochemical and astrochemical reactions.Comment: 8 figure

Free energy conservation in ab initio molecular dynamics simulations and homogeneous melt nucleation

The Z method is a popular atomistic simulation method for determining the melting temperature of solids by using a sequence of molecular dynamics(MD) runs in the microcanonical(NVE) ensemble to target the lowest system energy where the solid always melts. Homogeneous melting at the superheating critical limit($T_h$), is accompanied by a temperature drop to the equilibrium melting temperature($T_m$). Implementation of the Z method interfaced with modern {\it ab initio} electronic structure packages use Hellman-Faynman dynamics to propagate the ions in the NVE ensemble with the Mermin free energy plus the ionic kinetic energy conserved. So the electronic temperature($T_{el}$) is kept fixed along the trajectory which may introduce some spurious ion-electron interactions in MD runs with large temperature changes. We estimate possible systematic errors in evaluating melting temperature with different choices of $T_{el}$. MD runs with the $T_{el}$ = $T_h$ and $T_{el}$ = $T_m$ shows that the difference in melting temperature can be 200-300 K (3-5\% of the melting temperature) for our two test systems. Our results are in good agreement with previous studies with different methods, suggesting the CaSiO$_3$ and SiO$_2$ melts at around 6500 at 100 GPa and 6000 K at 160 GPa. The melting temperature decreases with increasing $T_{el}$ due to the increasing entropic stabilisation of the liquid and the system melts about 3 times faster with $T_{el} = T_h$ than with $T_{el} = T_m$. A careful choice of $T_{el}$ in BOMD is essential for the critical evaluation of the Z method especially at very high temperatures. Inspection of the homogeneous melting process shows that melting occurs via a two-step mechanism: 1) melting of the anion sublattice is accompanied by a small drop in temperature and 2) the formation of small defects which trigger the formation of small liquid clusters and fully melted.Comment: 10 figures, 17 page