Abstract We have performed ab initio molecular-dynamics (MD) calculations for the dependence of the sticking property of a C gas-phase atom ( ) on C(100) on the initial velocity. We have considered initial velocities of 0.0082, 0.0117 and 0.0185 . The largest velocity considered corresponds to a kinetic energy of 0.2142 eV, which is comparable with the chemisorption energy of an order of 1eV. For the three initial velocities considered, can settle on C(100) easily. The relatively quick settlement of even with a large initial velocity can be attributed to an efficient transfer of kinetic energy from to the H atom. We also find that the higher initial velocity, the deeper penetrates into the substrate, which renders to stay closer to the impact position.

This paper will outline some of the key parts of the Statistics course offered through the UTeach Summer Master’s Program as taught by Dr. Martha K. Smith. The paper begins with the introduction of the normal probability density function and is proven with calculus techniques and Euclidean geometry. Probability is discussed at great length in Smith’s course and the importance of understanding probability in statistical analysis is demonstrated through a reference to a study on how medical doctors confuse false positives in breast cancer testing. The frequentist perspective is concluded with a proof that the normal probability density function is zero. The shift from traditional to Bayesian inference begins with a brief introduction to the terminology involved, as well as an example with patient testing. The pros and cons of Bayesian inference are discussed and a proof is shown using the normal probability density function in finding a Bayes estimate for µ. It will be argued that a Statistics course moving from traditional to Bayesian analysis, such as that offered by the UTeach Summer Master’s Program and Smith, would supplement the traditional Statistics course offered at most universities. Such a course would be relevant for the mathematics major, mathematics educator, professionals in the medical industry, and individuals seeking to gain insights into how to understand data sets in new ways. / text

Let (L,h) → (X,ω) be a compact toric polarized Kahler manifold of complex dimension n. For each k ε N, the fibre-wise Hermitian metric hk on Lk induces a natural inner product on the vector space C∞(X,Lk) of smooth global sections of Lk by integration with respect to the volume form ωn /n! . The orthogonal projection Pk : C∞(X,Lk) → H0(X,Lk) onto the space H0(X,Lk) of global holomorphic sections of Lk is represented by an integral kernel Bk which is called the Bergman kernel (with parameter k ε N). The restriction ρk : X → R of the norm of Bk to the diagonal in X × X is called the density function of Bk. On a dense subset of X, we describe a method for computing the coefficients of the asymptotic expansion of ρk as k → ∞ in this toric setting. We also provide a direct proof of a result which illuminates the off-diagonal decay behaviour of toric Bergman kernels. We fix a parameter l ε N and consider the projection Pl,k from C∞(X,Lk) onto those global holomorphic sections of Lk that vanish to order at least lk along some toric submanifold of X. There exists an associated toric partial Bergman kernel Bl,k giving rise to a toric partial density function ρl,k : X → R. For such toric partial density functions, we determine new asymptotic expansions over certain subsets of X as k → ∞. Euler-Maclaurin sums and Laplace’s method are utilized as important tools for this. We discuss the case of a polarization of CPn in detail and also investigate the non-compact Bargmann-Fock model with imposed vanishing at the origin. We then discuss the relationship between the slope inequality and the asymptotics of Bergman kernels with vanishing and study how a version of Song and Zelditch’s toric localization of sums result generalizes to arbitrary polarized Kahler manifolds. Finally, we construct families of induced metrics on blow-ups of polarized Kahler manifolds. We relate those metrics to partial density functions and study their properties for a specific blow-up of Cn and CPn in more detail.

No description available.

Approved for public release; distribution is unlimited / In this thesis a clutter voltage model for scattering from the sea surface is developed. A model for the scattering from a whitecap and a wave breaking occurrence model re combined to simulate the back scattered signal from one radar resolution cell. The simulation performed obtained the probability density function of sea clutter under different assumptions of wind velocities and wave breaking conditions. This model incorporates some measured quantities such as the mean clutter voltage and the correlation time as parameters. The probability density function depends on the parameters of this model. The obtained probability density functions do not confirm to any familiar simple density function. / http://archive.org/details/seaspikemodeling00kuoc / Lieutenant, Taiwan Navy

This papers is divided into numbered sections. The equations are numbered anew in each section, and equation numbers are always enclosed in parentheses. Merely the equation number is given when referring to an equation in the same section as the references; otherwise the section number is prefixed. Thus equation (4) refers to the fourth equation of the same section as the reference, and equation (2.2) refers to the second equation of the second section.

The current generation of climate models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) is used to assess the future changes in daily precipitation and its extremes. The simple average of all the models, i.e. the multi-model ensemble mean (MMEM), has been widely used due to its simplicity and better performance than most individual models. Weighting techniques are also proposed to deal with the systematic biases within the models. However, both methods are designed to reduce the uncertainties for the study of climate mean state. They will induce problems when the climate extremes are of interest. We utilize a Bayesian weighting method to investigate the rainfall mean state and perform a probability density function based assessment of daily rainfall extremes. Satellite measurement is used to evaluate the short historical period. The weighting method can be only applied to regions rather than hemispheric scale, and thus three tropical regions including the Amazon, Congo, and Southeast Asia are studied. The method based on the Gamma distribution for daily precipitation is demonstrated to perform much better than the MMEM with respect to the extreme events. A use of the Kolmogorov-Smirnov statistic for the distribution assessment indicates the method is more applicable in three tropical wet regions over land mentioned above. This is consistent with previous studies showing the Gamma distribution is more suitable for daily rainfall in wet regions. Both methods provide consistent results. The three regions display significant changes at the end of the 21st century. The Amazon will be drier, while the Congo will not have large changes in mean rainfall. However, both of the Amazon and Congo will have large rainfall variability, implying more droughts and floods. The Amazon will have 7.5% more little-rain days (defined as > 0.5 mm/d) and 4.5 mm/d larger 95th percentile for 2092-2099, and the Congo will have 2.5% more little-rain days and 1 mm/d larger 95th percentile. Southeast Asia will be dryer in the western part and wetter in the eastern part, which is consistent with the different changes in the 5th percentile. It will also experience heavier rainfall events with much larger increases in the 95th percentile. The future changes, especially the increase in rainfall extremes, are very likely associated with the strengthening of hydrological cycle. / text

Our understanding of the nature of Earth’s D” region was changed significantly by a recent finding by Murakami et al. (2004), who revealed a phase transition from perovskite to post-perovskite structure in MgSiO3 at about 125 GPa and 2500 K, corresponding to conditions of the lowermost mantle. A perovskite to post-perovskite phase transition accounts for many unusual features of the D” region, including its notable seismic anisotropy, and also accounts for the unusual topology of the D” discontinuity. However, the experimentally synthesised post-perovskite phase of MgSiO3 is not quenchable to ambient conditions, which means that many of its physical properties remain difficult to determine. On the other hand, there are several post-perovskite oxides, CaIrO3, CaPtO3, CaRhO3 and CaRuO3, which can be quenched to ambient conditions, maintaining their structure. High pressure synthesis of CaIr1-xPtxO3 solid solutions (x = 0, 0.3, 0.5, 0.7) and CaIr0.5Rh0.5O3 was conducted at the University of Edinburgh and Geodynamics Research Center, Ehime University, and structures and physical properties of these novel post-perovskite materials determined. Substantial [100] grain growth was observed in all solid solutions leading to pronounced texture even in powdered materials. Temperature-independent paramagnetism above 150 K and small magnetic entropy observed in heat capacity measurements suggest that CaIrO3 is an intrinsically weak itinerant ferromagnetic metal, while electrical resistivity measurements show that it is a narrow bandgap semiconductor, possibly due to grain boundary effects. CaIrO3 undergoes a magnetic transition at 108K and possesses a saturated magnetic moment of 0.04 μB. Doping with Pt or Rh induces Curie-Weiss paramagnetism and suppresses the magnetic transition. The anisotropic structure and morphology of CaIrO3 combined with the Ir4+ spin-orbit coupling results in a large magnetic anisotropy constant of 1.77 x 106 Jm-3, comparable to values for permanent magnet materials. A new high-pressure phase of CaIr0.5Pt0.5O3 was synthesised at 60GPa, 1900K using a laser-heated DAC (diamond anvil cell) at GRC, Ehime University. Its Raman spectra resemble those of perovskite phases of CaIrO3 and CaMnO3, implying that CaIr0.5Pt0.5O3 undergoes a post-perovskite to perovskite phase transition with increasing pressure. I estimate an increase in thermodynamic Grüneisen parameter γth across the post-perovskite to perovskite transition of 34 %, with similar magnitude to (Mg,Fe)SiO3 and MgGeO3, suggesting that CaIr0.5Pt0.5O3 is a promising analogue for experimentally simulating the competitive stability between perovskite and post-perovskite phase of magnesium silicates in Earth’s lowermost mantle. Such estimation is reliable since the estimated and directly calculated thermodynamic Grüneisen parameter γth from heat capacity show consistent values. The marked effect that Pt has on stabilising the post-perovskite structure in CaIr1-xPtxO3 solid solutions explains why the post-perovskite to perovskite phase transition has not been observed for CaPtO3 in contrast to other quenchable post-perovskite oxides: CaIrO3, CaRhO3 and CaRuO3.Work presented here demonstrates that CaIrO3 solid solutions can be used to provide new insight into factors stabilising post-perovskite structures in Earth’s lowermost mantle.

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The goals of the research presented in this dissertation were to create algorithms that produce images of complex phenomena, to study the efficacy of the algorithms, and to apply these algorithms to important mineralogical problems. The algorithms that were created include the Sphere Projection method, the Chicken Wire method, and methods for calculating the curvature at any point on a surface. The Sphere Projection method is best applied to roughly spherical surfaces. A theorem about the "fit" to a sphere determines the accuracy of the model in this special case and gives some insight into the limitations of this method. The Chicken Wire method was developed to model those surfaces for which the Sphere Projection method was ineffective. The effectiveness of the Chicken Wire method was also determined. The algorithms were used to produce images of equi-value surfaces of the Laplacian of the electron density function in selected molecules. The water molecule, H2O, was studied to demonstrate that these new methods are capable of reproducing known features. The disiloxane molecule, H6Si2O7, was studied because it serves as a model for bonding in quartz and other important silicates. Lastly, the molecule NaLi2Si2OF9 was examined as a molecular model for low albite. A new discovery suggests that these algorithms will be an important tool in mineralogy. / Ph. D.