skip to main content


Search for: All records

Creators/Authors contains: "Cohen, Itai"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Metamaterials are composite structures whose extraordinary properties arise from a mesoscale organization of their constituents. Here, we introduce a different material class—viscosity metafluids. Specifically, we demonstrate that we can rapidly drive large viscosity oscillations in shear-thickened fluids using acoustic perturbations with kHz to MHz frequencies. Because the timescale for these oscillations can be orders of magnitude smaller than the timescales associated with the global material flow, we can construct metafluids whose resulting time-averaged viscosity is a composite of the thickened, high-viscosity and dethickened, low-viscosity states. We show that viscosity metafluids can be used to engineer a variety of unique properties including zero, infinite, and negative viscosities. The high degree of control over the resulting viscosity, the ease with which they can be accessed, and the variety of exotic properties achievable make viscosity metafluids attractive for uses in technologies ranging from coatings to cloaking to 3D printing.

    Published by the American Physical Society2024 
    more » « less
    Free, publicly-accessible full text available November 1, 2025
  2. An electronically actuated artificial hinged ciliary platform capable of generating efficient bidirectional pumping at the microscale.

     
    more » « less
    Free, publicly-accessible full text available September 24, 2025
  3. Abstract

    Articular joints facilitate motion and transfer loads to underlying bone through a combination of cartilage tissue and synovial fluid, which together generate a low‐friction contact surface. Traumatic injury delivered to cartilage and the surrounding joint capsule causes secretion of proinflammatory cytokines by chondrocytes and the synovium, triggering cartilage matrix breakdown and impairing the ability of synovial fluid to lubricate the joint. Once these inflammatory processes become chronic, posttraumatic osteoarthritis (PTOA) development begins. However, the exact mechanism by which negative alterations to synovial fluid leads to PTOA pathogenesis is not fully understood. We hypothesize that removing the lubricating macromolecules from synovial fluid alters the relationship between mechanical loads and subsequent chondrocyte behavior in injured cartilage. To test this hypothesis, we utilized an ex vivo model of PTOA that involves subjecting cartilage explants to a single rapid impact followed by continuous articulation within a lubricating bath of either healthy synovial fluid, phosphate‐buffered saline (PBS), synovial fluid treated with hyaluronidase, or synovial fluid treated with trypsin. These treatments degrade the main macromolecules attributed with providing synovial fluid with its lubricating properties; hyaluronic acid and lubricin. Explants were then bisected and fluorescently stained to assess global and depth‐dependent cell death, caspase activity, and mitochondrial depolarization. Explants were tested via confocal elastography to determine the local shear strain profile generated in each lubricant. These results show that degrading hyaluronic acid or lubricin in synovial fluid significantly increases middle zone chondrocyte damage and shear strain loading magnitudes, while also altering chondrocyte sensitivity to loading.

     
    more » « less
    Free, publicly-accessible full text available August 25, 2025
  4. Sikkandar, Mohamed Yacin (Ed.)

    In various biological systems, analyzing how cell behaviors are coordinated over time would enable a deeper understanding of tissue-scale response to physiologic or superphysiologic stimuli. Such data is necessary for establishing both normal tissue function and the sequence of events after injury that lead to chronic disease. However, collecting and analyzing these large datasets presents a challenge—such systems are time-consuming to process, and the overwhelming scale of data makes it difficult to parse overall behaviors. This problem calls for an analysis technique that can quickly provide an overview of the groups present in the entire system and also produce meaningful categorization of cell behaviors. Here, we demonstrate the application of an unsupervised method—the Variational Autoencoder (VAE)—to learn the features of cells in cartilage tissue after impact-induced injury and identify meaningful clusters of chondrocyte behavior. This technique quickly generated new insights into the spatial distribution of specific cell behavior phenotypes and connected specific peracute calcium signaling timeseries with long term cellular outcomes, demonstrating the value of the VAE technique.

     
    more » « less
    Free, publicly-accessible full text available May 20, 2025
  5. Free, publicly-accessible full text available September 11, 2025
  6. Systems driven far from equilibrium often retain structural memories of their processing history. This memory has, in some cases, been shown to dramatically alter the material response. For example, work hardening in crystalline metals can alter the hardness, yield strength, and tensile strength to prevent catastrophic failure. Whether memory of processing history can be similarly exploited in flowing systems, where significantly larger changes in structure should be possible, remains poorly understood. Here, we demonstrate a promising route to embedding such useful memories. We build on work showing that exposing a sheared dense suspension to acoustic perturbations of different power allows for dramatically tuning the sheared suspension viscosity and underlying structure. We find that, for sufficiently dense suspensions, upon removing the acoustic perturbations, the suspension shear jams with shear stress contributions from the maximum compressive and maximum extensive axes that reflect or “remember” the acoustic training. Because the contributions from these two orthogonal axes to the total shear stress are antagonistic, it is possible to tune the resulting suspension response in surprising ways. For example, we show that differently trained sheared suspensions exhibit (1) different susceptibility to the same acoustic perturbation, (2) orders of magnitude changes in their instantaneous viscosities upon shear reversal, and (3) even a shear stress that increases in magnitude upon shear cessation. We work through these examples to explain the underlying mechanisms governing each behavior. Then, to illustrate the power of this approach for controlling suspension properties, we demonstrate that flowing states well below the shear jamming threshold can be shear jammed via acoustic training. Collectively, our work paves the way for using acoustically induced memory in dense suspensions to generate rapidly and widely tunable materials.

    <supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> Free, publicly-accessible full text available May 1, 2025</span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10483288-microscale-strain-concentrations-tissue-engineered-osteochondral-implants-dictated-local-compositional-thresholds-architecture" itemprop="url"> <span class='span-link' itemprop="name">Microscale strain concentrations in tissue-engineered osteochondral implants are dictated by local compositional thresholds and architecture</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1016/j.jbiomech.2023.111882" target="_blank" title="Link to document DOI">https://doi.org/10.1016/j.jbiomech.2023.111882  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Kim, Byumsu</span> <span class="sep">; </span><span class="author" itemprop="author">Kelly, Terri-Ann N.</span> <span class="sep">; </span><span class="author" itemprop="author">Jung, Hyung Jin</span> <span class="sep">; </span><span class="author" itemprop="author">Beane, Olivia S.</span> <span class="sep">; </span><span class="author" itemprop="author">Bhumiratana, Sarindr</span> <span class="sep">; </span><span class="author" itemprop="author">Bouklas, Nikolaos</span> <span class="sep">; </span><span class="author" itemprop="author">Cohen, Itai</span> <span class="sep">; </span><span class="author" itemprop="author">Bonassar, Lawrence J.</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-01-01">January 2024</time> , Journal of Biomechanics) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1016/j.jbiomech.2023.111882" target="_blank" title="Link to document DOI" data-ostiid="10483288"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10471990-universal-scaling-shear-thickening-transitions" itemprop="url"> <span class='span-link' itemprop="name">Universal scaling of shear thickening transitions</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1122/8.0000697" target="_blank" title="Link to document DOI">https://doi.org/10.1122/8.0000697  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Ramaswamy, Meera</span> <span class="sep">; </span><span class="author" itemprop="author">Griniasty, Itay</span> <span class="sep">; </span><span class="author" itemprop="author">Liarte, Danilo B.</span> <span class="sep">; </span><span class="author" itemprop="author">Shetty, Abhishek</span> <span class="sep">; </span><span class="author" itemprop="author">Katifori, Eleni</span> <span class="sep">; </span><span class="author" itemprop="author">Del Gado, Emanuela</span> <span class="sep">; </span><span class="author" itemprop="author">Sethna, James P.</span> <span class="sep">; </span><span class="author" itemprop="author">Chakraborty, Bulbul</span> <span class="sep">; </span><span class="author" itemprop="author">Cohen, Itai</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2023-11-01">November 2023</time> , Journal of Rheology) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.</p> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1122/8.0000697" target="_blank" title="Link to document DOI" data-ostiid="10471990"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10472728-bifurcation-instructed-design-multistate-machines" itemprop="url"> <span class='span-link' itemprop="name">Bifurcation instructed design of multistate machines</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1073/pnas.2300081120" target="_blank" title="Link to document DOI">https://doi.org/10.1073/pnas.2300081120  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Yang, Teaya</span> <span class="sep">; </span><span class="author" itemprop="author">Hathcock, David</span> <span class="sep">; </span><span class="author" itemprop="author">Chen, Yuchao</span> <span class="sep">; </span><span class="author" itemprop="author">McEuen, Paul L.</span> <span class="sep">; </span><span class="author" itemprop="author">Sethna, James P.</span> <span class="sep">; </span><span class="author" itemprop="author">Cohen, Itai</span> <span class="sep">; </span><span class="author" itemprop="author">Griniasty, Itay</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2023-08-22">August 2023</time> , Proceedings of the National Academy of Sciences) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We propose a design paradigm for multistate machines where transitions from one state to another are organized by bifurcations of multiple equilibria of the energy landscape describing the collective interactions of the machine components. This design paradigm is attractive since, near bifurcations, small variations in a few control parameters can result in large changes to the system’s state providing an emergent lever mechanism. Further, the topological configuration of transitions between states near such bifurcations ensures robust operation, making the machine less sensitive to fabrication errors and noise. To design such machines, we develop and implement a new efficient algorithm that searches for interactions between the machine components that give rise to energy landscapes with these bifurcation structures. We demonstrate a proof of concept for this approach by designing magnetoelastic machines whose motions are primarily guided by their magnetic energy landscapes and show that by operating near bifurcations we can achieve multiple transition pathways between states. This proof of concept demonstration illustrates the power of this approach, which could be especially useful for soft robotics and at the microscale where typical macroscale designs are difficult to implement.</p> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1073/pnas.2300081120" target="_blank" title="Link to document DOI" data-ostiid="10472728"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> </ol> <div id="pagination-lower" style=""> <div class="pull-right" style="line-height: 30px;"> <div class="btn-group pagination nomargin"> <a href="#" class="btn btn-sm btn-default noborderradius" disabled="disabled">«<span class="hidden-xs"> Prev</span></a> <a class="dropdown-toggle btn btn-sm btn-default paging-dropdown hidden-xs noborderradius" href="#" data-toggle="dropdown"><span class="caret"></span><span class="sr-only">Select page number</span></a> <div class="dropdown-menu pull-right paging-slider-dropdown" style="padding: 15px;"> <small> <div class="text-muted" style="line-height:20px;"><label for="pagination-sel-sptag-2">Go to page: <span class="paging-target">1</span> of <span class="paging-max">6</span></label></div> <div> <table> <tr> <td valign="top"> <input id="pagination-sel-sptag-2" data-range="" value="1" min="1" max="6" name="pagination-sel" type="range" class="pagination-sel noborderradius" style="height:26px;padding:0px;margin-right:5px; width:200px; display:inline-block;" onchange="$(this).closest('.paging-slider-dropdown').find('.paging-target').html(numberWithCommas($(this).val()));" /> </td> <td valign="top"> <button class="btn btn-sm btn-default pagination-go-slider noborderradius" type="button">»</button> </td> </tr> </table> </div> </small> </div> <a href="#" class="btn btn-sm btn-default pagination-go noborderradius" data-page="2"><span class="hidden-xs">Next </span>»</a> </div> </div> <div class="clearfix"></div> </div> </div> </div> </div> <!-- / basic search results --> </div> </div> <input type='hidden' id='schtype' value=''/> </div> </div> <footer class="row" id="footer-wrapper"> <div class="footer-content"> <div id="footerOSTI" class=" hidden-print"> <ul> <li><a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/">Website Policies</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/about/performance/">Budget and Performance</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/oig/">Inspector General</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/privacy.jsp">Privacy</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/foia.jsp">FOIA</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/od/odi/notice.jsp">No FEAR Act</a> | <a target="_blank" rel="noreferrer" href="http://usa.gov">USA.gov</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/access.jsp">Accessibility</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/nsf_plain_language.jsp">Plain Language</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/help/contact.jsp">Contact</a> | <a target="_blank" rel="noreferrer" href="https://nsf.gov/help/">Help</a> </li> </ul> The National Science Foundation, 2415 Eisenhower Avenue, Alexandria, Virginia 22314, USA Tel: (703) 292-5111, FIRS: (800) 877-8339 | TDD: (800) 281-8749 </div> </div> </footer> </div> <div id="authorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="authorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="authorselect_label">Author Select</div> </div> <form id="authorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="authorselect-pg" value="1" /> <div class="modal-body" id="authorselect_body"> <div class="row"> <div class="col-md-4"> <label for="authorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="authorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="authorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="authorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#authorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#authorselect-tab-res" id="authorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#authorselect-tab-sel" id="authorselect-tab-sel-btn" data-toggle="tab">Selected Authors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="authorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match authors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="authorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-sel-content">No authors are currently selected. Choosing "Select These Authors" will enter a blank value for author search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_review" onclick="$('#authorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_submit" onclick="authorSelectAddToForm(); $('#authorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div id="editorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="editorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="editorselect_label">Editor Select</div> </div> <form id="editorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="editorselect-pg" value="1" /> <div class="modal-body" id="editorselect_body"> <div class="row"> <div class="col-md-4"> <label for="editorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="editorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="editorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="editorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#editorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#editorselect-tab-res" id="editorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#editorselect-tab-sel" id="editorselect-tab-sel-btn" data-toggle="tab">Selected Editors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="editorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match editors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="editorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-sel-content">No editors are currently selected. Choosing "Select These Editors" will enter a blank value for editor search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_review" onclick="$('#editorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_submit" onclick="editorSelectAddToForm();$('#editorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div class="push_top"></div> <!-- External Link Modal --> <div class="modal fade" id="external-link-modal" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close nsf-close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> <h4 class="modal-title"><strong>Warning: Leaving National Science Foundation Website</strong></h4> </div> <div class="modal-body"> <div> <img src="https://par.nsf.gov/img/nsf/nsf_logo.png" width="292" height="53" alt="National Science Foundation Logo" border="0" /> </div> <br> <span>You are now leaving the National Science Foundation website to go to a non-government website.</span> <br> <br> Website: <a id="external-link-url" rel='noopener noreferrer' target='_blank'></a> <br> <br> <span> NSF takes no responsibility for and exercises no control over the views expressed or the accuracy of the information contained on this site. Also be aware that NSF's privacy policy does not apply to this site. </span> <br> <br> </div> <div class="modal-footer"> <div class="pull-right"> <button id="external-link-continue" type="button" data-extlink="" class="btn btn-primary" data-dismiss="modal"><u>Continue to Site</u></button> <button type="button" class="btn btn-default" data-dismiss="modal"><u>Cancel</u></button> </div> </div> </div> </div> </div> <!-- /content --> <input type='hidden' id='webtrend-id' value='dcsngbilzcxafpc7vw2qgbbij_3j2v'/> <input type='hidden' id='js-context-path' value='https://par.nsf.gov/'/> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/latest.js?config=TeX-MML-AM_CHTML" defer></script> <script type="text/x-mathjax-config" defer> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]} }); </script> <noscript></noscript> <script src="https://par.nsf.gov/js/context.js" type="text/javascript" defer></script> <noscript>You must have javascript enabled</noscript> <script src="https://par.nsf.gov/js/libraries/jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/chosen/chosen.jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.extras.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.min.js" type="text/javascript" defer></script> <noscript></noscript> <!--$$$$$$$$$ the following blocks are for WebTrends $$$$$$$$--> <!-- START OF SmartSource Data Collector TAG --> <!-- Copyright (c) 1996-2009 WebTrends Inc. All rights reserved. --> <!-- Version: 8.6.2 --> <!-- Tag Builder Version: 3.0 --> <!-- Created: 5/7/2009 8:32:37 PM --> <script src="https://par.nsf.gov/js/webtrends.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- ----------------------------------------------------------------------------------- --> <!-- Warning: The two script blocks below must remain inline. Moving them to an external --> <!-- JavaScript include file can cause serious problems with cross-domain tracking. --> <!-- ----------------------------------------------------------------------------------- --> <script src="https://par.nsf.gov/js/webtrend-script.min.js" type="text/javascript" defer></script> <noscript> <div><img alt="" id="DCSIMG" width="1" height="1" src="http://wt.research.gov/dcsngbilzcxafpc7vw2qgbbij_3j2v/njs.gif?dcsuri=/nojavascript&WT.js=No&DCS.dcscfg=1&WT.tv=8.6.2"/></div> </noscript> <script src="https://par.nsf.gov/js/webtrendsactions.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- $$$$$$$$ End WebTrends $$$$$ --> <!-- /scripts --> </body> <!-- NSF PAGES v.@project.version@ --> </html>