Cup and cap products in intersection (co)homology

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.     

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

Synthesis of Novel Bisphosphono-Pyrimidinediones Via Pentacovalent Organophosphorus Methodology

Abstract

The synthesis of bisphosphono-pyrimidinediones from the condensations of pentacovalent oxaphospholenes with isocyanates is discussed.     

Synthetic Studies Toward the Preparation of Phosphonate Analogs of Sphingomyelins and Ceramide 1 -Phosphate Using Pentacovalent Organophosphorus Methodology

Abstract

Non-isosteric phosphonate analogs of sphingomyelin and ceramide 1-phosphate are being synthesized from the condensation product of a pentacovalent oxaphospholene and azodicarboxylates. Model studies are initially described.     

Synthesis of Acyclic γ-Amino Mono-or Bisphosphonates Via Pentacovalent Oxaphosphorane Chemistry

Abstract

Geminal bisphosphonic acids and their salu have long been known to he effective inhibitors of bone resorption and mineralization. which arc common symptoms of diseases such as osteoporosis and Paget's disease [I]. Utilizing penlacovalent nxaphosphoranc chemistry, a variety of acyclic γ-amino mono- and bisphosphonates can be efficiently hynthesizcd. Hydrolysis of the P(V) oxaphospholenes, I and 2. followed by reductive amination [2] of the multing ketones, kds directly to the γ-amino mono and bisphosphonateh 5 and 6. The reaction of secondary amincs with ketones 3 and 4 are slow and low yielding. In reactions with ketones containing a bisphosphonatc. The primary product is the cyclic bisphosphonates. 7. Reactions of primary amines with ketones containing a mono-phosphonate M generally hencr, giving higher yields of the desired prcduct in a rhoncr rcaciion time. Syntheses of compounds, 9–11 were also performed (R₁ ? H, R₂ ? pentyl, cyclohexyl, benzyl, phenyl) in good yields.     

Qualitative Identification of an Unknown Pesticide Using GC-MS and Online Resources

A senior-level instrumental analysis experiment is described in which students examine fruit for pesticide residues. This experiment involves fundamental instruction in sample preparation, the use of gas chromatography (GC) to resolve and deduce important components of a commercial pesticide preparation by matching against a certified standard, and unambiguous identification of the active pesticide by using mass spectrometry in conjunction with public data available on the Internet.     

Beyond Anisotropy: Examining Non-Darcy Flow in Asymmetric Porous Media

Accepted theory for anisotropic flow in porous media establishes that the properties of a particular flow may depend upon the flow orientation, but generally assumes that flow properties are invariant for a reversal of the flow direction. By simulating simple two-dimensional and three-dimensional flows from the pore-scale, we demonstrate that while this assumption holds true when flow is slow such that the approximations supporting Darcy’s law apply, reversal of the flow direction can have a significant impact on nonlinear corrections to Darcy’s law that become important at higher flow rates. In this study, we consider flow through simple periodic porous media consisting of oriented, asymmetrical grains for Reynolds numbers <150. Analysis of the pore-scale flow structure demonstrates that direction-dependent effects can be linked with asymmetry. We present a nonlinear correction to Darcy’s law that accounts for this extended anisotropy and propose a macroscopic morphological measure to quantify asymmetry of the solid phase.     

A statistical model to evaluate analyte homogeneity for a material.

An underlying assumption for collaborative studies is that the analyte variation among test samples of the material (i.e., matrix and analyte concentration combination) under study has a negligible influence on the estimates of precision for the method. This assumption is expected to be fulfilled when the material under study is prepared (i.e., thoroughly mixed) such that the analyte is distributed uniformly throughout the matrix. Statistical design and intra-class correlation analysis procedures are proposed to assess the similarity or agreement among analytical results among- and within-containers for single and multiple occasions of use (e.g., collaborative and proficiency studies).