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Low-Cost Rural Surface Alternatives: Demonstration Project, Cheng Li, Jeramy C. Ashlock, David White, Pavana Vennapusa Jun 2015

Low-Cost Rural Surface Alternatives: Demonstration Project, Cheng Li, Jeramy C. Ashlock, David White, Pavana Vennapusa

Jeramy C. Ashlock

A field demonstration project was conducted in Hamilton County, Iowa to compare the relative performance, durability, and costs of several stabilization methods for preventing or mitigating freeze-thaw damage to granular surfaced roads.


Low-Cost Rural Surface Alternatives: Demonstration Project, Cheng Li, Jeramy C. Ashlock, David White, Pavana Vennapusa Jun 2015

Low-Cost Rural Surface Alternatives: Demonstration Project, Cheng Li, Jeramy C. Ashlock, David White, Pavana Vennapusa

Jeramy C. Ashlock

The goals of this project were to implement several stabilization methods for preventing or mitigating freeze-thaw damage to granular surfaced roads and identify the most effective and economical methods for the soil and climate conditions of Iowa. Several methods and technologies identified as potentially suitable for Iowa were selected from an extensive analysis of existing literature provided with Iowa Highway Research Board (IHRB) Project TR-632.Using the selected methods, demonstration sections were constructed in Hamilton County on a heavily traveled two-mile section of granular surfaced road that required frequent maintenance during previous thawing periods. Construction procedures and costs of the demonstration …


Assessment Of Nondestructive Testing Technologies For Quality Control/Quality Assurance Of Asphalt Mixtures - Tech Transfer Summary, Shibin Lin, Jeramy C. Ashlock, Hanjun Kim, Jeremy Nash, Hosin David Lee, R. Christopher Williams Mar 2015

Assessment Of Nondestructive Testing Technologies For Quality Control/Quality Assurance Of Asphalt Mixtures - Tech Transfer Summary, Shibin Lin, Jeramy C. Ashlock, Hanjun Kim, Jeremy Nash, Hosin David Lee, R. Christopher Williams

Jeramy C. Ashlock

Asphalt pavements suffer various failures due to insufficient quality within their design lives. The American Association of State Highway and Transportation Officials (AASHTO) Mechanistic-Empirical Pavement Design Guide (MEPDG) has been proposed to improve pavement quality through quantitative performance prediction. Evaluation of the actual performance (quality) of pavements requires in situ nondestructive testing (NDT) techniques that can accurately measure the most critical, objective, and sensitive properties of pavement systems. The purpose of this study is to assess existing as well as promising new NDT technologies for quality control/quality assurance (QC/QA) of asphalt mixtures. Specifically, this study examined field measurements of density …


Optimal Deployment Of Hybrid Alternative Power System At Signalized Intersections, Mo Zhao, Anuj Sharma Jan 2014

Optimal Deployment Of Hybrid Alternative Power System At Signalized Intersections, Mo Zhao, Anuj Sharma

Anuj Sharma

Traffic signal power failures can degrade efficiency and safety at intersections that warrant traffic signal control. Alternative power sources (APSs) are typically used to supply traffic signals in power outages. Agencies that operate signals need a decision-making framework to identify locations and deployment schedules for APS installation. This paper presents a methodology for optimal deployment of APSs at signalized intersections. This methodology can also be used to investigate the economic viability of using wind and solar energy as APSs for signalized intersections. Benefit–cost analysis is used as an economic tool. The primary benefit of an APS is improving traffic operation …


Development Of Preliminary Load And Resistance Factor Design Of Drilled Shafts In Iowa - Tech Transfer Summary, Kam W. Ng, Sri Sritharan, Jeramy C. Ashlock Jan 2014

Development Of Preliminary Load And Resistance Factor Design Of Drilled Shafts In Iowa - Tech Transfer Summary, Kam W. Ng, Sri Sritharan, Jeramy C. Ashlock

Jeramy C. Ashlock

The Federal Highway Administration (FHWA) mandated utilizing the Load and Resistance Factor Design (LRFD) approach for all new bridges initiated in the United States after October 1, 2007. To achieve part of this goal, a database for Drilled Shaft Foundation Testing (DSHAFT) was developed and reported on by Garder, Ng, Sritharan, and Roling in 2012. DSHAFT is aimed at assimilating high-quality drilled shaft test data from Iowa and the surrounding regions. DSHAFT is currently housed on a project website (http://srg.cce.iastate.edu/dshaft) and contains data for 41 drilled shaft tests. The objective of this research was to utilize the DSHAFT database and …


Project Complexity Mapping In Five Dimensions For Complex Transportation Projects, Douglas D. Gransberg, Jennifer S. Shane, Carla Lopez Del Puerto Oct 2013

Project Complexity Mapping In Five Dimensions For Complex Transportation Projects, Douglas D. Gransberg, Jennifer S. Shane, Carla Lopez Del Puerto

Douglas D. Gransberg

Traditional three-dimensional project management theory is based on optimizing the cost-schedule-technical dimensions. Recent studies in the United Kingdom, Canada, and Australia have shown that the current project management body of knowledge may not be adequate to address interrelated and dependent variables encountered on complex projects. This paper reports the findings of an international research team’s detailed study of eighteen complex projects, which confirms the findings of the previous research and proposes a framework upon which a complex transportation project’s scope of work can be better conceptualized and a methodology to graphically display a project’s complexity in order to better understand …


Safety Impacts Of Signal-Warning Flashers And Speed Control At High-Speed Signalized Intersections, Zifeng Wu, Anuj Sharma, Fred L. Mannering, Shefang Wang May 2013

Safety Impacts Of Signal-Warning Flashers And Speed Control At High-Speed Signalized Intersections, Zifeng Wu, Anuj Sharma, Fred L. Mannering, Shefang Wang

Anuj Sharma

For many years, to reduce the crash frequency and severity at high-speed signalized intersections, warning flashers have been used to alert drivers of potential traffic-signal changes. Recently, more aggressive countermeasures at such intersections include a speed-limit reduction in addition to warning flashers. While such speed-control strategies have the potential to further improve the crash-mitigation effectiveness of warning flashers, a rigorous statistical analysis of crash data from such intersections has not been undertaken to date. This paper uses 10-year crash data from 28 intersections in Nebraska (all with intersection approaches having signal-warning flashers; some with no speed-limit reduction, and the others …


Structural Health Monitoring System And Method Using Soft Capacitive Sensing Materials, Simon Laflamme, Matthias Kollosche, Guggi H. R. Kofod Feb 2013

Structural Health Monitoring System And Method Using Soft Capacitive Sensing Materials, Simon Laflamme, Matthias Kollosche, Guggi H. R. Kofod

Simon Laflamme

A structural health monitoring system is provided to diagnose and localize crack damage on structural elements. The system uses one or more capacitive sensor assemblies that employ a soft dielectric material. The system can be applied over a large area as a sensing skin, allowing the presence of cracks to be localized.


Modified Friction Device For Control Of Large-Scale Systems, Simon Laflamme, Douglas Taylor, Mohamed Abdellaoui Maane, Jerome J. Connor Jun 2012

Modified Friction Device For Control Of Large-Scale Systems, Simon Laflamme, Douglas Taylor, Mohamed Abdellaoui Maane, Jerome J. Connor

Simon Laflamme

Semi-active control of civil structures has shown to be promising at mitigating vibrations. Those systems typically perform significantly better than passive systems, and only necessitate small power to operate. Nevertheless, semi-active control devices are not yet accepted by the construction and structural engineering communities. Among impeding factors, semi-active devices are not perceived as sufficiently reliable or robust. In this paper, a new semi-active damping device based on existing reliable technology is proposed. It is composed of a stiffness element, a viscous damper, and a braking mechanism in parallel. The device, termed the modified friction device (MFD), is essentially a variable …


Soft Capacitive Sensor For Structural Health Monitoring Of Large-Scale Systems, Simon Laflamme, M. Kollosche, J. J. Connor, G. Kofod Feb 2012

Soft Capacitive Sensor For Structural Health Monitoring Of Large-Scale Systems, Simon Laflamme, M. Kollosche, J. J. Connor, G. Kofod

Simon Laflamme

Structural integrity of infrastructures can be preserved if damage is diagnosed, localized, and repaired in time. During the past decade, there has been a considerable effort to automate the process of structural health monitoring, which is complicated by the inherent large size of civil structures. Hence, a need has arisen to develop new approaches that enable more effective health monitoring.In this paper, a new sensing technique for damage localization on large civil structures is proposed. Specifically, changes in strain are detected using a capacitance sensor built with a soft, stretchable dielectric polymer with attached stretchable metal film electrodes. A change …


Structural Health Monitoring System And Method Using Soft Capacitive Sensing Materials, Simon Laflamme, Matthias Kollosche, Guggi H. R. Kofod Oct 2011

Structural Health Monitoring System And Method Using Soft Capacitive Sensing Materials, Simon Laflamme, Matthias Kollosche, Guggi H. R. Kofod

Simon Laflamme

A structural health monitoring system is provided to diagnose and localize crack damage on structural elements. The system uses one or more capacitive sensor assemblies that employ a soft dielectric material. The system can be applied over a large area as a sensing skin, allowing the presence of cracks to be localized.


Quasi-Static Analysis Of Rocking Wall Systems, Douglas Seymour, Simon Laflamme Jun 2011

Quasi-Static Analysis Of Rocking Wall Systems, Douglas Seymour, Simon Laflamme

Simon Laflamme

Rocking wall systems consist of shear walls that are free to rotate at their base. Their purpose is to mitigate seismic structural damage by constraining the structure primarily to its first mode. This constraint prevents weak story failure, and maximizes energy dissipation by activating plastic hinges throughout the structure. The purpose of this paper is to present a methodology for the design of rocking wall systems. A quasi-static analysis model is used for predicting the seismic mitigation performance of rocking walls. The stiffness matrix is generalized for an N-story simplified structure equipped with this structural system. The model presented enables …


Control Of Large-Scale Structures With Large Uncertainties, Simon Laflamme Jun 2011

Control Of Large-Scale Structures With Large Uncertainties, Simon Laflamme

Simon Laflamme

Performance-based design is a design approach that satisfies motion constraints as its primary goal, and then verifies for strength. The approach is traditionally executed by appropriately sizing stiffnesses, but recently, passive energy dissipation systems have gained popularity. Semi-active and active energy dissipation systems have been shown to outperform purely passive systems, but they are not yet widely accepted in the construction and structural engineering fields. Several factors are impeding the application of semi-active and active damping systems, such as large modeling uncertainties that are inherent to large-scale structures, limited state measurements, lack of mechanically reliable control devices, large power requirements, …


Wavelet Network For Semi-Active Control, Simon Laflamme, J.J.E. Slotine, J.J. Connor Jan 2011

Wavelet Network For Semi-Active Control, Simon Laflamme, J.J.E. Slotine, J.J. Connor

Simon Laflamme

This paper proposes a wavelet neurocontroller capable of self-adaptation and self-organization for uncertain systems controlled with semi-active devices, ideal candidates for control of large-scale civil structures. A condition on the sliding surface for cantilever-like structures is defined. The issue of applicability of the control solution to largescale civil structures is made the central theme throughout the text, as this topic has not been extensively discussed in the literature. Stability and convergence of the proposed neurocontroller is assessed through various numerical simulations for harmonic, earthquake, and wind excitations. The simulations consist of semi-active dampers installed as a replacement to the current …


Strongly Enhanced Sensitivity In Elastic Capacitive Strain Sensors, Matthias Kollosche, Hristiyan Stoyanov, Simon Laflamme, Guggi Kofod Jan 2011

Strongly Enhanced Sensitivity In Elastic Capacitive Strain Sensors, Matthias Kollosche, Hristiyan Stoyanov, Simon Laflamme, Guggi Kofod

Simon Laflamme

Strain sensors based on dielectric elastomer capacitors function by the direct coupling of mechanical deformations with the capacitance. The coupling can be improved by enhancing the relative permittivity of the dielectric elastomer. Here, this is carried out through the grafting of conducting polymer (poly-aniline) to the elastomer backbone, leading to molecular composites. An enhancement in capacitance response of 46 times is observed. This could help to extend the possible range of miniaturization towards even smaller device features.


Self-Organizing Inputs For Adaptive Neurocontrol Of Large-Scale Systems, Simon Laflamme, Jerome J. Connor Oct 2010

Self-Organizing Inputs For Adaptive Neurocontrol Of Large-Scale Systems, Simon Laflamme, Jerome J. Connor

Simon Laflamme

Black-box modeling for system identification and control can be constrained by the geometric scale of a plant. Those constrains arise from a technical or economical issue in obtaining input-output data sets for training purposes. A solution is sequential adaptation, which must be achieved in real time in the case of control systems, because a prescribed level of performance is required while external excitations are occurring. A major challenge is the proper selection of inputs that would lead to a quick and optimal adaptation. This paper proposes a new method for selection of inputs in black-box modeling. The method, termed the …


Proteomic Analysis Of Ethene-Enriched Groundwater Microcosms From A Vinyl Chloride-Contaminated Site, Adina S. Chuang, Yang Oh Jin, Laura S. Schmidt, Yalan Li, Samuel Fogel, Donna Smoler, Timothy E. Mattes Mar 2010

Proteomic Analysis Of Ethene-Enriched Groundwater Microcosms From A Vinyl Chloride-Contaminated Site, Adina S. Chuang, Yang Oh Jin, Laura S. Schmidt, Yalan Li, Samuel Fogel, Donna Smoler, Timothy E. Mattes

Adina Howe

Contamination of groundwater with vinyl chloride (VC), a known human carcinogen, is a common environmental problem at plastics manufacturing, dry cleaning, and military sites. At many sites, there is the potential to cleanup VC groundwater plumes with aerobic VC-oxidizing microorganisms (e.g., methanotrophs, etheneotrophs, and VC-assimilating bacteria). Environmental biotechnologies that reveal the presence and activity of VC-oxidizing bacteria in contaminated groundwater samples would provide valuable lines of evidence that bioremediation of VC is occurring at a site. We applied targeted shotgun mass spectrometry-based proteomic methods to ethene-enriched groundwater microcosms from a VC-contaminated site. Polypeptides from the enzymes alkene monooxygenase (EtnC) and …


Effects Of Damping Device Nonlinearity On The Performance Of Semiactive Tuned Mass Dampers, C Lindh, Simon Laflamme, Jerome J. Connor Jan 2010

Effects Of Damping Device Nonlinearity On The Performance Of Semiactive Tuned Mass Dampers, C Lindh, Simon Laflamme, Jerome J. Connor

Simon Laflamme

Studies have already demonstrated the successful use of linear semiactive damping devices, such as variable orifice (VO) dampers, for semiactive TMD systems. More recently, nonlinear semiactive damping devices, such as magnetorheological (MR) dampers, have also been shown to be effective for semiactive control of TMDs. Though semiactive dampers differ widely, with responses ranging from linear (VO) to nonlinear (MR), criteria for choosing an optimal semiacive device for a TMD have not been rigorously developed. This paper expands knowledge of semiactive TMD systems by assessing the effect of nonlinearity in the damping device on the effectiveness of a semiactive TMD. This …


Large-Scale Capacitance Sensor For Health Monitoring Of Civil Structures, Simon Laflamme, Matthias Kollosche, Jerome J. Connor, Guggi Kofod Jan 2010

Large-Scale Capacitance Sensor For Health Monitoring Of Civil Structures, Simon Laflamme, Matthias Kollosche, Jerome J. Connor, Guggi Kofod

Simon Laflamme

In this paper, a new type of sensing technique for damage localization on large civil structures is proposed. Specifically, changes in strain are detected using a capacitance sensor built with a soft-stretchable dielectric polymer with attached stretchable metal film electrodes. This sensor is sensitive to a change in strain that causes a change in its capacitance. Fixed to a structure, small changes in the strain can be monitored directly by measuring the change in the capacitance of the unit. This technology allows for simple yet highly accurate measurements of cracks occurring due to deformation, aging, or other structural failures. The …


Intelligent Controller For Smart Base Isolation Of Masonry Structures, Simon Laflamme, T.Y. Yu, Jerome J. Connor Oct 2009

Intelligent Controller For Smart Base Isolation Of Masonry Structures, Simon Laflamme, T.Y. Yu, Jerome J. Connor

Simon Laflamme

In this paper, an intelligent controller to control a smart base-isolated masonry structure is proposed. The smart base isolation consists of rubber bearings and a magnetorheological damper. This semi-active scheme takes advantage of the low power requirement of magnetorheological devices to achieve structural control. The controller is capable of mapping the behaviour of the controlled structure sequentially, using a self-organizing neural network which has time-varying learning rates. This neurocontroller is augmented by a sliding mode controller to account for the uncertainty on the semi-active damping forces. Wavelets are used as functions in the single hidden layer for their capability of …


Application Of Self-Tuning Gaussian Networks For Control Of Civil Structures Equipped With Magnetorheological Dampers, Simon Laflamme, Jerome J. Connor Apr 2009

Application Of Self-Tuning Gaussian Networks For Control Of Civil Structures Equipped With Magnetorheological Dampers, Simon Laflamme, Jerome J. Connor

Simon Laflamme

This paper proposes an adaptive neural network composed of Gaussian radial functions for mapping the behavior of civil structures controlled with magnetorheological dampers. The online adaptation takes into account the limited force output of the semi-active dampers using a sliding mode controller, as their reaction forces are state dependent. The structural response and the actual forces from the dampers are used to adapt the Gaussian network by tuning the radial function widths, centers, and weights. In order to accelerate convergence of the Gaussian radial function network during extraordinary external excitations, the learning rates are also adaptive. The proposed controller is …


Study Of A Nanoscale Water Cluster By Atomic Force Microscopy, Manhee Lee, Baekman Sung, Nicole N. Hashemi, Wonho Jhe Jan 2009

Study Of A Nanoscale Water Cluster By Atomic Force Microscopy, Manhee Lee, Baekman Sung, Nicole N. Hashemi, Wonho Jhe

Nastaran Hashemi

We present a novel method for investigating a nanometric cluster of water molecules, which includes the formation and manipulation of nanometric water, and the measurement of its mechanical properties. The atomic force microscope based on the quartz tuning-fork sensor is employed to form and manipulate the nanometric water, and the theoretical tool of amplitude-modulation atomic force microscopy is used to obtain the elasticity, viscosity and dissipation energy of it. With high vertical resolution less than [similar]0.1 nm and high force sensitivity of [similar]0.01 N m−1, this tool facilitates the stable formation and manipulation of a nano-water cluster ([similar]104 molecules) in …


Quantifying Uncertainty Of Construction Material Price Volatility Using Monte Carlo, Douglas D. Gransberg, Erin J. Kelly Jun 2008

Quantifying Uncertainty Of Construction Material Price Volatility Using Monte Carlo, Douglas D. Gransberg, Erin J. Kelly

Douglas D. Gransberg

This study uses Monte Carlo simulation to derive a quantitative measure of construction price volatility for two case study projects in Oklahoma. In the past four years, the impact of events like Hurricane Katrina and the economic growth in China have induced unprecedented volatility in US construction prices. This has caused a huge number of public construction project bids to exceed the owners' estimates, making it difficult for public construction agencies to be able to predict construction budgets. Construction prices are a function of many factors beyond pure material costs. This study broke down the pay items from a typical …


The Nonlinear Dynamics Of Tapping Mode Atomic Force Microscopy With Capillary Force Interactions, Nicole N. Hashemi, H. Dankowicz, M.R. Paul Jan 2008

The Nonlinear Dynamics Of Tapping Mode Atomic Force Microscopy With Capillary Force Interactions, Nicole N. Hashemi, H. Dankowicz, M.R. Paul

Nastaran Hashemi

We study the nonlinear dynamics of a tapping mode atomic force microscope with tip-surface interactions that include attractive, repulsive, and capillary force contributions using numerical techniques tailored for hybrid or discontinuous dynamical systems that include forward-time simulation with event handling and numerical pseudo-arclength continuation. We find four branches of periodic solutions that are separated by windows of complex and irregular dynamics. The branches of periodic solutions end where the cantilever comes into grazing contact with event surfaces in state space, corresponding to the onset of capillary interactions and the onset of repulsive forces associated with contact. These windows of irregular …


Repetitive Impact Response Of A Beam Structure Subjected To Harmonic Base Excitation, Elizabeth K. Ervin, Jonathan A. Wickert Oct 2007

Repetitive Impact Response Of A Beam Structure Subjected To Harmonic Base Excitation, Elizabeth K. Ervin, Jonathan A. Wickert

Jonathan A. Wickert

This paper investigates the forced response dynamics of a clamped–clamped beam to which a rigid body is attached, and in the presence of periodic or non-periodic impacts between the body and a comparatively compliant base structure. The assembly is subjected to base excitation at specified frequency and acceleration, and the potentially complex responses that occur are examined analytically. The two sets of natural frequencies and vibration modes of the beam-rigid body structure (in its in-contact state, and in its not-in-contact state), are used to treat the forced response problem through a series of algebraic mappings among those states. A modal …


Identification Of Polypeptides Expressed In Response To Vinyl Chloride, Ethene, And Epoxyethane In Nocardioides Sp. Strain Js614 By Using Peptide Mass Fingerprinting, Adina S. Chuang, Timothy E. Mattes Jul 2007

Identification Of Polypeptides Expressed In Response To Vinyl Chloride, Ethene, And Epoxyethane In Nocardioides Sp. Strain Js614 By Using Peptide Mass Fingerprinting, Adina S. Chuang, Timothy E. Mattes

Adina Howe

Enzymes expressed in response to vinyl chloride, ethene, and epoxyethane by Nocardioides sp. strain JS614 were identified by using a peptide mass fingerprinting (PMF) approach. PMF provided insight concerning vinyl chloride biodegradation in strain JS614 and extends the use of matrix-assisted laser desorption-ionization time of flight mass spectrometry as a tool to enhance characterization of biodegradation pathways.


Online Learning Algorithm For Structural Control Using Magnetorheological Actuators, Simon Laflamme Jun 2007

Online Learning Algorithm For Structural Control Using Magnetorheological Actuators, Simon Laflamme

Simon Laflamme

Magnetorheological actuators are promising devices for mitigating vibrations because they only require a fraction of energy for a similar performance to active control. Conversely, these semi-active devices have limited maximum forces and are hard to model due to the rheological properties of their fluid. When considering structural control, classical theories necessitate full knowledge of the structural dynamic states and properties most of which can only be estimated when considering large-scale control, which may be difficult or inaccurate for complicated geometries due to the non-linear behaviour of structures. Additionally, most of these theories do not take into account the response delay …


Artificial Neural Networks For Analyzing Concrete Airfield Pavements Serving The Boeing B-777 Aircraft, Halil Ceylan, Erol Tutumluer, Ernest J. Barenberg Jan 2007

Artificial Neural Networks For Analyzing Concrete Airfield Pavements Serving The Boeing B-777 Aircraft, Halil Ceylan, Erol Tutumluer, Ernest J. Barenberg

Halil Ceylan

An artificial neural network (ANN) model has been trained with the results of the ILLI-SLAB finite element program and has been used to predict stresses and deflections in jointed concrete airfield pavements serving the Boeing B-777 aircraft. The trained ANN model produces stresses and deflections with average errors of less than 0.5 percent of those obtained directly from the finite element analyses. Use of the ANN model has been found to be very effective for correctly predicting ILLI-SLAB stresses and deflections, in less than 1 s, with no requirements of complicated finite element inputs. On the other hand, elastic layered …


Computational And Experimental Modeling Of Dynamic Foundation Interactions With Sand, Phd Thesis, Jeramy C. Ashlock Jan 2006

Computational And Experimental Modeling Of Dynamic Foundation Interactions With Sand, Phd Thesis, Jeramy C. Ashlock

Jeramy C. Ashlock

The subject of dynamic soil-structure interaction (SSI) is fundamental to the design of structures and foundations to withstand dynamic events such as earthquakes, explosions and vibrations from traffic, wind, waves and machinery. With the tools of modern experimental and computational methods, a critical evaluation of current concepts and capabilities for the dynamic characterization of both surface foundations and embedded piles in granular soils is the first target. Well suited for this kind of fundamental study, a variety of scaled-model surface and pile foundations are designed and tested in a large geotechnical centrifuge using dynamic forced excitations. Used as a rigorous …


Small-Scale Structure Of Strongly Stratified Turbulence, Jin Hwan Hwang, Chris R. Rehmann Feb 2005

Small-Scale Structure Of Strongly Stratified Turbulence, Jin Hwan Hwang, Chris R. Rehmann

Chris R. Rehmann

The small-scale structure of turbulence subjected to strong stratification is analyzed with rapid distortion theory to evaluate the performance of formulas for predicting dissipation of turbulent kinetic energy and dissipation of scalar variance. The approach is restricted to weak turbulence in strong stratification, like that in the thermocline or the abyssal ocean. Flows with and without mean shear are considered. For unsheared turbulence, the small scales are axisymmetric about the vertical axis, as others have previously assumed. The calculations here complement and extend previous work because they can be used to compute errors in dissipation estimates, develop simpler formulas, and …