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Articles 2791 - 2820 of 3662

Full-Text Articles in Physical Sciences and Mathematics

Alaska Aquatic Plant Survey Report 2005, Mary Pfauth, Mark Sytsma Oct 2005

Alaska Aquatic Plant Survey Report 2005, Mary Pfauth, Mark Sytsma

Center for Lakes and Reservoirs Publications and Presentations

Invasive, non-indigenous plants can degrade water quality and fish habitat when they invade lakes, ponds, and streams. Changes in plant community architecture in lakes due to invasion by canopy-forming invasive aquatic plants can result in loss of native plant biodiversity and reduction of the structural complexity of the underwater habitat.


Application Of Information-Theoretic Data Mining Techniques In A National Ambulatory Practice Outcomes Research Network, Adam Wright, Thomas N. Ricciardi, Martin Zwick Oct 2005

Application Of Information-Theoretic Data Mining Techniques In A National Ambulatory Practice Outcomes Research Network, Adam Wright, Thomas N. Ricciardi, Martin Zwick

Systems Science Faculty Publications and Presentations

The Medical Quality Improvement Consortium data warehouse contains de-identified data on more than 3.6 million patients including their problem lists, test results, procedures and medication lists. This study uses reconstructability analysis, an information-theoretic data mining technique, on the MQIC data warehouse to empirically identify risk factors for various complications of diabetes including myocardial infarction and microalbuminuria. The risk factors identified match those risk factors identified in the literature, demonstrating the utility of the MQIC data warehouse for outcomes research, and RA as a technique for mining clinical data warehouses.


High-Resolution Angular Measurement Using Surface-Plasmon-Resonance Via Phase Interrogation At Optimal Incident Wavelengths, Hai-Pang Chiang, Jing-Lun Lin, Railing Chang, Sheng-Yu Su, P.T. Leung Oct 2005

High-Resolution Angular Measurement Using Surface-Plasmon-Resonance Via Phase Interrogation At Optimal Incident Wavelengths, Hai-Pang Chiang, Jing-Lun Lin, Railing Chang, Sheng-Yu Su, P.T. Leung

Physics Faculty Publications and Presentations

It is demonstrated that ultrahigh-resolution angular measurement can be achieved via surface-plasmon-resonance excitation in which the phase difference between p- and s-polarized reflected waves is monitored as a function of the incidence angle. Resolutions down to 1.9 x 10(-6) deg are obtained by performing the measurements at optimal incident wavelengths. This represents an order of magnitude improvement compared with previously reported values.


Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar Oct 2005

Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of …


Can Infopipes Facilitate Reuse In A Traffic Application?, Emerson Murphy-Hill, Chuan-Kai Lin, Andrew P. Black, Jonathan Walpole Oct 2005

Can Infopipes Facilitate Reuse In A Traffic Application?, Emerson Murphy-Hill, Chuan-Kai Lin, Andrew P. Black, Jonathan Walpole

Computer Science Faculty Publications and Presentations

Infopipes are presented as reusable building blocks for streaming applications. To evaluate this claim, we have built a significant traffic application in Smalltalk using Infopipes. This poster presents a traffic problem and solution, a short introduction to Infopipes, and the types of reuse Infopipes facilitate in our implementation.


Towards The Rational Design Of Mri Contrast Agents: A Practical Approach To The Synthesis Of Gadolinium Complexes That Exhibit Optimal Water Exchange, Mark Woods, Mauro Botta, Stefano Avedano, Jing Wang, A. Dean Sherry Sep 2005

Towards The Rational Design Of Mri Contrast Agents: A Practical Approach To The Synthesis Of Gadolinium Complexes That Exhibit Optimal Water Exchange, Mark Woods, Mauro Botta, Stefano Avedano, Jing Wang, A. Dean Sherry

Chemistry Faculty Publications and Presentations

The gadolinium(III) complex of S-SSSS-NO2BnDOTMA exhibits water exchange kinetics that are optimal for use in high relaxivity or targeted contrast agents. However, the synthesis of this ligand is hampered by the steric encumbrance imparted upon the cyclen ring by the nitrobenzyl substituent. A relatively simple modification has been used to enable the synthesis of larger quantities of a bifunctional ligand that retains similar fast water exchange properties. The gadolinium complex of S-SSS-NO2BnDO3MA-1A is shown to retain the rapid water exchange kinetics characteristic of a twisted square antiprismatic (TSAP) …


Final Report: Evaluation Of The Morphoedaphic Index And Sediment Diatoms For Inference Of Pre-European Settlement Total Phosphorus Concentration In Epa Region 10 Lakes, Rich Miller, Aaron Hook, Richard Petersen, Mark D. Sytsma Sep 2005

Final Report: Evaluation Of The Morphoedaphic Index And Sediment Diatoms For Inference Of Pre-European Settlement Total Phosphorus Concentration In Epa Region 10 Lakes, Rich Miller, Aaron Hook, Richard Petersen, Mark D. Sytsma

Center for Lakes and Reservoirs Publications and Presentations

Water quality in many Northwest lakes has declined over the past century due, in part, to increased anthropogenic nutrient loading (Edmonson and Lehman, 1981). Under the Clean Water Act, resource managers such as the Washington Department of Ecology, Oregon Department of Environmental Quality, and tribes are responsible for restoring and protecting the integrity of these waters. Targets for restoration or criteria for impairment are not well defined, however, and may naturally vary by geology, hydrology, morphometry, and climate.

One way to determine whether lakes are impaired and to identify restoration targets is to assess lake reference conditions (EPA 2000). Reference …


The Ultrasonic/Shear-Force Microscope: Integrating Ultrasonic Sensing Into A Near-Field Scanning Optical Microscope, Andres H. La Rosa, Xiquan Cui, J. Mccollum, Nan Li, Richard Nordstrom Sep 2005

The Ultrasonic/Shear-Force Microscope: Integrating Ultrasonic Sensing Into A Near-Field Scanning Optical Microscope, Andres H. La Rosa, Xiquan Cui, J. Mccollum, Nan Li, Richard Nordstrom

Physics Faculty Publications and Presentations

An ultrasonic transducer is incorporated into a near-field scanning optical microscope (NSOM) to augment its versatility to characterize the properties of layers adsorbed to a sample's surface. Working under typical NSOM operation conditions, the ultrasonic transducer--attached underneath the sample--demonstrates sufficient sensitivity to monitor the waves generated by the tapered NSOM probe that oscillates in the proximity of, and parallel to, the sample's top surface. This capability makes the newly integrated ultrasonic/shear-force microscope a valuable diagnostic tool in the study of sliding friction and surface phenomena in general. Here, it is used to concurrently and independently monitor the effects that probe-sample …


Street Trees In The Urban Forest Canopy: Portland, Oregon, Joseph Poracsky, David Banis Aug 2005

Street Trees In The Urban Forest Canopy: Portland, Oregon, Joseph Poracsky, David Banis

Geography Faculty Publications and Presentations

Attempts to identify the contribution of street trees to the overall urban forest of a city have been rare and lack consensus on how to measure that contribution – percentage of trees, percentage of canopy cover, or percentage of leaf area. The actual numeric values presented in the literature also vary over a broad range and often are based on estimates, extrapolations from aggregated data, or simply stated with no empirical data referenced. This study was undertaken to evaluate the contribution of street trees to canopy in Portland, Oregon. The study involved both visual and digital analysis of multi-band aerial …


Mathematics, Meaning, And Identity : A Study Of The Practice Of Mathematics Education In A Rural High School, Rick Anderson Jul 2005

Mathematics, Meaning, And Identity : A Study Of The Practice Of Mathematics Education In A Rural High School, Rick Anderson

Dissertations and Theses

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community.

The findings suggest that high school mathematics education is related to the rural …


Lake Whatcom Water Quality Model, Chris Berger Jul 2005

Lake Whatcom Water Quality Model, Chris Berger

Civil and Environmental Engineering Faculty Publications and Presentations

A water quality model of Lake Whatcom, Washington was developed as part of a Total Maximum Daily Load Study for the Washington Department of Ecology. Lake Whatcom is a large natural lake which is listed on the 1998 Washington State 303(d) list of waterbodies which do not meet the criterion for dissolved oxygen. Located next to the city of Bellingham, it is approximately 10 miles long and has a surface area of approximately 5000 acres and a maximum depth of over 100 meters. Eutrophication processes in the lake have been accelerated in recent years perhaps by the availability of nutrients …


Upper Spokane River Model In Idaho: Boundary Conditions And Model Setup And Calibration For 2001 And 2004, Robert Leslie Annear, Scott A. Wells, Chris Berger Jul 2005

Upper Spokane River Model In Idaho: Boundary Conditions And Model Setup And Calibration For 2001 And 2004, Robert Leslie Annear, Scott A. Wells, Chris Berger

Civil and Environmental Engineering Faculty Publications and Presentations

As a result of a Total Maximum Daily Load (TMDL) study of the Spokane River in Washington, a hydrodynamic and water quality model for the Spokane River was developed by Portland State University (PSU) for the Corps of Engineers and the Washington Department of Ecology from the Washington-Idaho state line to the outlet of Long Lake.

An earlier study of the Spokane River was undertaken by Limno-Tech (2001a, 2001b) for the domain shown in Figure 3. Limno-Tech used an earlier version of CE-QUAL-W2, Version 2, for the Reservoir portion of the Spokane River from Post Falls Dam to Coeur d’Alene …


Waldo Lake Research In 2004, Mark D. Sytsma, John Rueter, Richard Petersen, Roy Koch, Scott A. Wells, Michelle Wood, Yangdong Pan, Robert Leslie Annear, Aaron Hook, Laura Johnson, Rich Miller, Amanda Murphy, Terry Stoltz Jun 2005

Waldo Lake Research In 2004, Mark D. Sytsma, John Rueter, Richard Petersen, Roy Koch, Scott A. Wells, Michelle Wood, Yangdong Pan, Robert Leslie Annear, Aaron Hook, Laura Johnson, Rich Miller, Amanda Murphy, Terry Stoltz

Center for Lakes and Reservoirs Publications and Presentations

The Willamette National Forest has worked with Portland State University, Center for Lakes and Reservoirs (PSU) and the University of Oregon (UO) to investigate ecosystem changes, provide guidance on long-term monitoring methods, assess monitoring data, develop predictive water quality models, and conduct research that will lead to better protection and understanding of the Waldo Lake ecosystem. This report summarizes the second year of collaborative PSU-UO research at Waldo Lake. Research has focused on understanding physical, chemical and biological characteristics of Waldo Lake across a range of spatial and temporal scales. Research tasks that continued from 2003 into 2004 included temperature …


Erratum: "Environmental Swap Energy And Role Of Configurational Entropy In Transfer Of Small Molecules From Water Into Alkanes", Pavel Smejtek, Robert Campbell Word Jun 2005

Erratum: "Environmental Swap Energy And Role Of Configurational Entropy In Transfer Of Small Molecules From Water Into Alkanes", Pavel Smejtek, Robert Campbell Word

Physics Faculty Publications and Presentations

Presents correction to an article related to configurational entropy in transfer of small molecules from water into alkanes, published in the 2005 issue of "The Journal Chemical Physics" and is available online at: http://archives.pdx.edu/ds/psu/8364


Laurance Lake Temperature Model, Chris Berger, Scott A. Wells, Robert Leslie Annear Jun 2005

Laurance Lake Temperature Model, Chris Berger, Scott A. Wells, Robert Leslie Annear

Civil and Environmental Engineering Faculty Publications and Presentations

Laurance Lake is a reservoir located in Hood River County, Oregon (Figure 1). It is located at the base on Mt. Hood in Oregon (see Figure 2 and Figure 3), discharges into the Middle Fork of the Hood River. The reservoir was constructed in 1968 for irrigation storage and has a capacity 3564 acre- feet at full pool. Since the river vio lates temperature standards, this study has been designed to construct a hydrodynamic and temperature model of Laurance reservoir in order to assess strategies for improving temperatures in the Middle Fork River.

The objectives of the study are then …


When Scoundrels Rule: Review Of The Last Refuge: Patriotism, Politics, And The Environment In An Age Of Terror, By David W. Orr, Robert Costanza May 2005

When Scoundrels Rule: Review Of The Last Refuge: Patriotism, Politics, And The Environment In An Age Of Terror, By David W. Orr, Robert Costanza

Institute for Sustainable Solutions Publications and Presentations

Book Review of The Last Refuge: Patriotism, Politics, and the Environment in an Age of Terror. David W. Orr. Island Press, Washington, DC, 2004.


The Potential For Mitten Crab Colonization Of Estuaries On The West Coast Of North America, Erik Hanson, Mark Sytsma Apr 2005

The Potential For Mitten Crab Colonization Of Estuaries On The West Coast Of North America, Erik Hanson, Mark Sytsma

Center for Lakes and Reservoirs Publications and Presentations

Mitten crabs are invasive species that pose a risk to the aquatic environments of the Pacific Northwest and the economic and social activities that depend upon intact aquatic systems. The recent establishment of a large population in the San Francisco Bay and the potential for introductions from California, Asia and Europe pose a significant invasion potential for esturaires and rivers from Catifornia to Alaska.


The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger Mar 2005

The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger

Mathematics and Statistics Faculty Publications and Presentations

Let Y denote a D-class symmetric association scheme with D≥3, and suppose Y is almost-bipartite P- and Q-polynomial. Let x denote a vertex of Y and let T=T(x) denote the corresponding Terwilliger algebra. We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the isomorphism class of W as a T-module is determined by two parameters, the dual endpoint and diameter of W. We find a recurrence which gives the multiplicities with which the …


Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan Mar 2005

Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …


Potential Economic Impacts Of Zebra Mussels On The Hydropower Facilities In The Columbia River Basin, Stephen Phillips, Tim Darland, Mark Sytsma Feb 2005

Potential Economic Impacts Of Zebra Mussels On The Hydropower Facilities In The Columbia River Basin, Stephen Phillips, Tim Darland, Mark Sytsma

Center for Lakes and Reservoirs Publications and Presentations

The purpose of this study was to estimate costs to the Federal Columbia River Power System hydroelectric projects in the event of a zebra mussel infestation.


Ecological Science And Sustainability For The 21st Century, Margaret A. Palmer, Emily S. Bernhardt, Elizabeth A. Chornesky, Scott L. Collins, Andrew P. Dobson, Clifford S. Duke, Barry D. Gold, Robert B. Jacobson, Sharon E. Kingsland, Rhonda H. Kranz, Michael J. Mappin, M. Luisa Martinez, Florenza Micheli, Jennifer L. Morse, Michael L. Pace, Mercedes Pascual, Stephen S. Palumbi, Oj Reichman, Alan R. Townsend, Monica G. Turner Feb 2005

Ecological Science And Sustainability For The 21st Century, Margaret A. Palmer, Emily S. Bernhardt, Elizabeth A. Chornesky, Scott L. Collins, Andrew P. Dobson, Clifford S. Duke, Barry D. Gold, Robert B. Jacobson, Sharon E. Kingsland, Rhonda H. Kranz, Michael J. Mappin, M. Luisa Martinez, Florenza Micheli, Jennifer L. Morse, Michael L. Pace, Mercedes Pascual, Stephen S. Palumbi, Oj Reichman, Alan R. Townsend, Monica G. Turner

Environmental Science and Management Faculty Publications and Presentations

Ecological science has contributed greatly to our understanding of the natural world and the impact of humans on that world. Now, we need to refocus the discipline towards research that ensures a future in which natural systems and the humans they include coexist on a more sustainable planet. Acknowledging that managed ecosystems and intensive exploitation of resources define our future, ecologists must play a greatly expanded role in communicating their research and influencing policy and decisions that affect the environment. To accomplish this, they will have to forge partnerships at scales and in forms they have not traditionally used. These …


First Season Effects Of Managed Flooding On The Invasive Species Phalaris Arundinacea L. And Shoreline Vegetation Communities In An Urban Wetland, Noah John Jenkins Jan 2005

First Season Effects Of Managed Flooding On The Invasive Species Phalaris Arundinacea L. And Shoreline Vegetation Communities In An Urban Wetland, Noah John Jenkins

Dissertations and Theses

Recent management efforts in the Smith and Bybee Lakes Wildlife Area (SBL), a 700-ha preserve in north Portland, Oregon, have included using a water control structure to suppress invasive reed canarygrass (Phalaris arundinacea L.) by flooding during spring and early summer growth periods. For the first year of managed flooding, I sought to determine: (a) the extent and distribution of reed canarygrass at SBL; (b) the effectiveness of the change in water level at suppressing reed canarygrass; and ( c) the effects of the change in water level on other plant species.

I established 30 vegetation transects throughout SBL before …


Preliminary Study Comparing Precipitation Quality Between Nominal Land Uses In Portland, Oregon, Lacey Sullivan Jan 2005

Preliminary Study Comparing Precipitation Quality Between Nominal Land Uses In Portland, Oregon, Lacey Sullivan

Environmental Science and Management Professional Master's Project Reports

The purpose of this study is to analyze the precipitation quality in various land use categories throughout Portland. Because of its significance in the removal of atmospheric pollutants, wet deposition is an important component to study. In addition to its significant role in cleansing the atmosphere, wet deposition can have a direct impact on the ecosystem due to its potential pollutant load. Various land uses may provide different emission sources, each uniquely affecting the composition of the atmosphere. A literature review found few studies comparing precipitation quality between local land uses within an urban area. Wet deposition studies seem to …


Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan Jan 2005

Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …


A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman Jan 2005

A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Fix nonnegative integers n1,…,nd and let L denote the lattice of integer points (a1,…,ad)∈Zd satisfying 0⩽ai⩽ni for 1⩽i⩽d. Let L be partially ordered by the usual dominance ordering. In this paper we offer combinatorial derivations of a number of results concerning chains in L. In particular, the results obtained are established without recourse to generating functions or recurrence relations. We begin with an elementary derivation of the number of chains in L of a given size, from which one can deduce the classical expression for the total number …


A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman Jan 2005

A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We discuss a toy model to study the dynamics of individual particles in avalanches. The model describes a particle launched from an inclined infinite staircase. The particle is not allowed to bounce when it collides with the staircase. During the collision, the particle loses some energy, and after that slides on to the end of the step it landed on. The process then repeats itself. The dynamics of this no-bounce model can essentially be completely understood. Partial versions of some results were stated and argued in previous work. Here we give a full description together with all the proofs. We …


Marine Ice Modification Of Fringing Ice Shelf Flow, Christina L. Hulbe, R. Johnston, Ian R. Joughin, Ted A. Scambos Jan 2005

Marine Ice Modification Of Fringing Ice Shelf Flow, Christina L. Hulbe, R. Johnston, Ian R. Joughin, Ted A. Scambos

Geology Faculty Publications and Presentations

Locally derived ice is often observed to fill through-cutting rifts and uneven fronts in ice shelves. That ice may nucleate as fast ice at the shelf front, by growth at the sea surface within rifts, or by basal accretion. Here, we investigate the role of such ice in the flow of the Brunt Ice Shelf and adjacent Stancomb-Wills ice tongue, along the Caird Coast of Antarctica. Much of the shelf system is severely rifted, with locally derived ice filling the space between rift walls and around ice rafts. A series of numerical experiments that account for thermal properties of the …


Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz Jan 2005

Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.


Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan Jan 2005

Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We introduce a method that gives exactly incompressible velocity approximations to Stokes ow in three space dimensions. The method is designed by extending the ideas in Part I (http://archives.pdx.edu/ds/psu/10914) of this series, where the Stokes system in two space dimensions was considered. Thus we hybridize a vorticity-velocity formulation to obtain a new mixed method coupling approximations of tangential velocity and pressure on mesh faces. Once this relatively small tangential velocity-pressure system is solved, it is possible to recover a globally divergence-free numerical approximation of the fluid velocity, an approximation of the vorticity whose tangential component is continuous across …


Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman Jan 2005

Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature …