Discrete Poincaré Lemma

This paper proves a discrete analogue of the Poincar´e lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone operator, p : Ck(K) -> Ck+1(K), as the geometric cone of a simplex cannot, in general, be interpreted as a chain in the simplicial complex. The corresponding cocone operator H : Ck(K) -> Ck−1(K) can be shown to be a homotopy operator, and this yields the discrete Poincar´e lemma. The generalized cone operator is a combinatorial operator that can be constructed for any simplicial complex that can be grown by a process of local augmentation. In particular, regular triangulations and tetrahedralizations of R2 and R3 are presented, for which the discrete Poincar´e lemma is globally valid

Direct Numerical Simulation of 3D Salt Fingers: From Secondary Instability to Chaotic Convection

The amplification and equilibration of three-dimensional salt fingers in unbounded uniform vertical gradients of temperature and salinity is modeled with a Direct Numerical Simulation in a triply periodic computational domain. A fluid dynamics video of the simulation shows that the secondary instability of the fastest growing square-planform finger mode is a combination of the well-known vertical shear instability of two-dimensional fingers [Holyer, 1984] and a new horizontal shear mode.Comment: APS DFD Gallery of Fluid Motion 200

A Discrete Theory of Connections on Principal Bundles

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition, that takes into account the principal bundle structure, is introduced. Computational issues, such as the order of approximation, are also addressed. Discrete connections provide an intrinsic method for introducing coordinates on the reduced space for discrete mechanics, and provide the necessary discrete geometry to introduce more general discrete symmetry reduction. In addition, discrete analogues of the Levi-Civita connection, and its curvature, are introduced by using the machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure

PRICE, YIELD, AND GROSS REVENUE VARIABILITY FOR SELECTED GEORGIA CROPS

Demand and Price Analysis,

Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary for matching in the discrete context are introduced. The theory is illustrated with the problem of stabilization of the cart-pendulum system on an incline. We also discuss digital and model predictive control.Comment: IEEE Conference on Decision and Control, 2006 6 pages, 4 figure

Calling on Science: Making “Alternatives” the New Gold Standard

All of life’s great journeys start with a goal in mind! The 2007 NAS report, Toxicity Testing in the 21st Century – A Vision and A Strategy, has proposed a clear goal. This report envisions a not-so-distant future where all routine toxicity testing for environmental agents will be conducted in human cells in vitro evaluating perturbations of cellular responses in a suite of toxicity pathway assays. Dose response modeling would utilize computational systems biology models of the circuitry underlying each toxicity pathway; in vitro to in vivo extrapolations would use pharmacokinetic models, ideally physiologically based pharmacokinetic models, to predict human blood and tissue concentrations under specific exposure conditions. Results from these toxicity pathway assays and associated dose response modeling tools rather than those from high dose studies in animals would represent the new gold standard for chemical risk assessment. This talk focuses on some of the scientific challenges required to make this vision a reality, including characteristics of assay design, prospects for mapping and modeling toxicity pathways, assay validation, and biokinetic modeling. All of these tools necessary for this transformation of toxicity testing to an in vitro platform are either available or in advanced development. Science must lead the transformation. The scientific community, animal alternatives groups, regulatory agencies, and funding organizations will also have to muster the resolve to work together to make this vision a reality

Internal Strategies for Assessing Communication Channel Effectiveness

This qualitative multiple case study was designed to explore communication assessment strategies used in three law firms to improve message dissemination and channel efficiency. The findings revealed informal assessment strategies can sustain operations, indirect assessment strategies have a role, and efficient versus timely assessments could improve employee performance and morale.https://scholarworks.waldenu.edu/current/1020/thumbnail.jp