Asymptotic Properties and Separation Rates for Navier-Stokes Flows

In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay rates for these solutions with locally sub-critical data away from the origin and show improved decay for the `non-linear part\u27 of the flow. We also lower the H\ older regularity required to obtain our maximal decay rate. To achieve improved decay, we use Picard iterates to approximate solutions. We demonstrate a scale of decay rates for Picard approximations which determine upper bounds for how non-unique, discretely self-similar solutions may separate. In subsequent sections, we replace the self-similar condition with local sub-critical regularity and are able to obtain all but the maximal separation rate for Lorentz solutions, a subclass of local energy solutions

Asymptotic Properties and Separation Rates for Navier-Stokes Flows

In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay rates for these solutions with locally sub-critical data away from the origin and show improved decay for the `non-linear part\u27 of the flow. We also lower the H\ older regularity required to obtain our maximal decay rate. To achieve improved decay, we use Picard iterates to approximate solutions. We demonstrate a scale of decay rates for Picard approximations which determine upper bounds for how non-unique, discretely self-similar solutions may separate. In subsequent sections, we replace the self-similar condition with local sub-critical regularity and are able to obtain all but the maximal separation rate for Lorentz solutions, a subclass of local energy solutions

The Interaction of Teacher and Student Social Styles and Learning Styles on Learning Outcomes of the Basic Communication Course

There has been considerable research that indicates the importance of the type and quality of teachers\u27 communication. Too little of this research has considered the possibility of interrelationships between teacher\u27s social and preferred learning styles with the social and preferred learning styles of students. This study examines students in basic communication courses for the effects of actual correspondence in styles as well as students\u27 accuracy in describing the styles of their teachers. The results indicate that accurate perceptions of teachers\u27 social styles influence course grades and actual correspondence influences student evaluations of the course

Correction to: Multi-scale imaging as an essential tool for precision medicine

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How Much Do Schools and Districts Matter? A Production Function Approach to School Accountability

In 1989, President George H.W. Bush convened a first-ever education summit in Charlottesville, Virginia, with the governors of the states and territories

Solar Cell Measurement System for NPS Spacecraft Architecture and Technology Demonstration Satellite, NPSAT1

Rapid changes in semiconductor technologies over the last decade have spawned new interest in developing higher efficiency solar cells which are capable of using a broader part of the light spectrum. The Naval Postgraduate School’s NPSAT1, launching in the Spring of 2006, will include a subsystem which can be used to measure the performance of the new solar cells, providing an ability to combine functions previously available on only individual discrete components onto a single chip. The ability can help make space more accessible by reducing cost and complexity. The Solar Cell Measurement System (SMS) is a radiation hardened microcontroller based system using a radiation hardened FPGA that drives and monitors a collection of sun angle sensors, temperature sensors, a current sink/differential amplifier circuit combination for each of the 22 test cells and 2 control cells to be used in the experiment. The test cells are Triple Junction InGaP/GaAs/Ge cells and the control cells are Dual Junction cells. Triple Redundant Analog-to-Digital Converters, Digital-to-Analog Converters, and memory and interrupt logic will be implemented in the FPGA. The error budget developed for the circuits predicts a maximum error of 0.28%. The controller provides a common controller architecture for NPSAT1’s Electrical Power System and Attitude Control System. Future versions of the system will be able to further reduce costs by implementing a processor core into the FPGA

Reviews

The following publications have been reviewed by the mentioned authors;The Art of the Engineer by Ken Baynes and Francis Pugh, reviewed by Michael SayerVictorian Crafts Revived by Anne Hulbert, reviewed by Andor GommeA Potter's Mexico by Irwin and Emily Whittaker, reviewed by Michael PaffardPainting Without a Brush by Roy Sparkes, reviewed by Edward PhelpsMaking Wooden Toys by Roger Polley, reviewed by Bob NeillMetalwork Theory by R. A. Mold, reviewed by Leslie Deem

Muscle growth in teleost fish is regulated by factors utilizing the activin II B receptor

The activin type IIB receptor (Acvr2b) is the cell surface receptor for multiple transforming growth factor β (TGF-β) superfamily ligands, several of which regulate muscle growth in mammals. To investigate the role of the Acvr2b signaling pathway in the growth and development of skeletal muscle in teleost fish, transgenic rainbow trout (RBT; Oncorhynchus mykiss) expressing a truncated form of the acvr2b-2a (acvr2b▵) in muscle tissue were produced. High levels of acvr2b▵ expression were detected in the majority of P1 transgenic fish. Transgenic P1 trout developed enhanced, localized musculature in both the epaxial and hypaxial regions (dubbed ‘six pack’). The F1 transgenic offspring did not exhibit localized muscle growth, but rather developed a uniform body morphology with greater girth, condition factor and increased muscle fiber hypertrophy. There was a high degree of variation in the mass of both P1 and F1 transgenic fish, with several fish of each generation exhibiting enhanced growth compared with other transgenic and control siblings. The ‘six pack’ phenotype observed in P1 transgenic RBT overexpressing acvr2b▵ and the presence of F1 individuals with altered muscle morphology provides compelling evidence for the importance of TGF-β signaling molecules in regulating muscle growth in teleost fish