A Strategy for Teaching an Effective Undergraduate Mineralogy Course

An effective undergraduate mineralogy course provides students with a familiarity and understanding of minerals that is necessary for studying the Earth. This paper describes a strategy for integrating the disparate topics covered in a mineralogy course and for presenting them in a way that facilitates an understanding of mineralogy that enables students to apply it in subsequent courses and research. The course is organized into a well-integrated sequence of lectures, demonstrations and laboratory exercises that unfolds the material logically and at a pace that is responsive to the students’ needs. The course begins with six weeks on crystal chemistry, then five weeks covering analytical methods for characterizing minerals and ends with five weeks on the silicates. This order facilitates a progression of learning from the basic concepts to the more advanced and allows us to reinforce the concepts of crystal chemistry during the final section on the silicates. Optical mineralogy is almost entirely taught in the lab and is aided by use of a mineral identification chart developed to help students learn to identify minerals in thin section. Student performance is assessed through one technical paper and presentation as well as homework, essay exams and lab practicals. Educational levels: Graduate or professional

Some examples and applications of hilbert spaces with reproducing kernel

The purpose of this paper is to exhibit some examples and applications of kernal functions for Hilbert spaces and to illustrate some methods of finding reproducing kernels. This paper will also illustrate relationships between Hilbert space and function theory

Large Area Crop Inventory Experiment (LACIE). Intensive test site assessment report

There are no author-identified significant results in this report

Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems

An approach is proposed to improve the efficiency of fourth-order algorithms for numerical integration of the equations of motion in molecular dynamics simulations. The approach is based on an extension of the decomposition scheme by introducing extra evolution subpropagators. The extended set of parameters of the integration is then determined by reducing the norm of truncation terms to a minimum. In such a way, we derive new explicit symplectic Forest-Ruth- and Suzuki-like integrators and present them in time-reversible velocity and position forms. It is proven that these optimized integrators lead to the best accuracy in the calculations at the same computational cost among all possible algorithms of the fourth order from a given decomposition class. It is shown also that the Forest-Ruth-like algorithms, which are based on direct decomposition of exponential propagators, provide better optimization than their Suzuki-like counterparts which represent compositions of second-order schemes. In particular, using our optimized Forest-Ruth-like algorithms allows us to increase the efficiency of the computations more than in ten times with respect to that of the original integrator by Forest and Ruth, and approximately in five times with respect to Suzuki's approach. The theoretical predictions are confirmed in molecular dynamics simulations of a Lennard-Jones fluid. A special case of the optimization of the proposed Forest-Ruth-like algorithms to celestial mechanics simulations is considered as well.Comment: 12 pages, 3 figures; submitted to Computer Physics Communication

Optimized Verlet-like algorithms for molecular dynamics simulations

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the new algorithms appear to be more efficient than the original Verlet versions which correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the proposed counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the new algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.Comment: 5 pages, 2 figures; submitted to Phys. Rev.

Growth and alteration of uranium-rich microlite

Uranium-rich microlite, a pyrochlore-group mineral, occurs in 440 Ma old lithium pegmatites of the Mozambique Belt in East Africa. Microlite exhibits a pronounced growth zoning, with a U-free core surrounded by a U-rich rim (UO{sub 2} up to 17 wt.%). The core exhibits conjugate sets of straight cracks (cleavage planes) which provided pathways for a late-stage U-enriched pegmatitic fluid which interacted with the U-free microlite to produce a distinct U enrichment along the cracks and led to the formation of the U-rich rim. Following the stage of U incorporation into microlite, a second generation of hydrothermal fluids deposited mica along the cleavage planes. Subsequent to these two hydrothermal stages, the host rock was uplifted and subjected to intense low-temperature alteration during which Na, Ca and F were leached from the microlite crystals. This alteration also led to a hydration of microlite, but there is no evidence of U loss. These low-temperature alteration effects were only observed in the U-rich rim which is characterized by a large number of irregular cracks which are most probably the result of metamictization, as indicated by electron diffraction images and powder X-ray patterns. The pyrochlore-group minerals provide excellent natural analogues for pyrochlore-based nuclear waste forms, because samples of variable age and with high actinide contents are available

Pennsylvania Folklife Special 1960 Festival Issue

• Plain Dutch and Gay Dutch: Two Worlds in the Dutch Country • Pennsylvania Dutch • Displaced Dutchmen Crave Shoo-flies • Hex Signs: A Myth • Lebanon Valley Date Stones • Antiques in Dutchland • Antique or Folk Art: Which? • Folk Festival Program • Religious Patterns of the Dutch Country • The Costumes of the Plain Dutch • Love Feasts • Horse-and-Buggy Mennonites • The Courtship and Wedding Practices of the Old Order Amishhttps://digitalcommons.ursinus.edu/pafolklifemag/1008/thumbnail.jp

Algorithm for numerical integration of the rigid-body equations of motion

A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.