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name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2002.11058">arXiv:2002.11058</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/2002.11058">pdf</a>, <a href="https://arxiv.org/format/2002.11058">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.124.214501">10.1103/PhysRevLett.124.214501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Suppression of acoustic streaming in shape-optimized channels </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J+S">Jacob S. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=Bruus%2C+H">Henrik Bruus</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2002.11058v1-abstract-short" style="display: inline;"> Acoustic streaming is an ubiquitous phenomenon resulting from time-averaged nonlinear dynamics in oscillating fluids. In this theoretical study, we show that acoustic streaming can be suppressed by two orders of magnitude in major regions of a fluid by optimizing the shape of its confining walls. Remarkably, the acoustic pressure is not suppressed in this shape-optimized cavity, and neither is the&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2002.11058v1-abstract-full').style.display = 'inline'; document.getElementById('2002.11058v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2002.11058v1-abstract-full" style="display: none;"> Acoustic streaming is an ubiquitous phenomenon resulting from time-averaged nonlinear dynamics in oscillating fluids. In this theoretical study, we show that acoustic streaming can be suppressed by two orders of magnitude in major regions of a fluid by optimizing the shape of its confining walls. Remarkably, the acoustic pressure is not suppressed in this shape-optimized cavity, and neither is the acoustic radiation force on suspended particles. This basic insight may lead to applications, such as acoustophoretic handling of nm-sized particles, which is otherwise impaired by acoustic~streaming. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2002.11058v1-abstract-full').style.display = 'none'; document.getElementById('2002.11058v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 4 figures, RevTex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 124, 214501 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.09976">arXiv:2001.09976</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/2001.09976">pdf</a>, <a href="https://arxiv.org/format/2001.09976">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.101.023107">10.1103/PhysRevE.101.023107 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Theory of acoustic trapping of microparticles in capillary tubes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J+S">Jacob S. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=Bruus%2C+H">Henrik Bruus</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.09976v1-abstract-short" style="display: inline;"> We present a semi-analytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of the quality factor of the two-dimensional (2D) cross-section resonance mode. This axial variation is&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.09976v1-abstract-full').style.display = 'inline'; document.getElementById('2001.09976v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.09976v1-abstract-full" style="display: none;"> We present a semi-analytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of the quality factor of the two-dimensional (2D) cross-section resonance mode. This axial variation is determined analytically based on the numerical solution to the eigenvalue problem in the 2D cross section. The analysis is developed in two steps: First, we generalize a recently published expression for the 2D standing-wave resonance modes in a rectangular cross section to arbitrary shapes, including the viscous boundary layer. Second, based on these 2D modes, we derive analytical expressions in three dimensions for the acoustic pressure, the acoustic radiation and trapping force, as well as the acoustic energy flux density. We validate the theory by comparison to three-dimensional numerical simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.09976v1-abstract-full').style.display = 'none'; document.getElementById('2001.09976v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 7 pdf figures, RevTex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 101, 023107 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.09132">arXiv:1905.09132</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1905.09132">pdf</a>, <a href="https://arxiv.org/format/1905.09132">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.100.023104">10.1103/PhysRevE.100.023104 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Bulk-driven acoustic streaming at resonance in closed microcavities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J+S">Jacob S. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=Bruus%2C+H">Henrik Bruus</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1905.09132v1-abstract-short" style="display: inline;"> Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating a&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.09132v1-abstract-full').style.display = 'inline'; document.getElementById('1905.09132v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.09132v1-abstract-full" style="display: none;"> Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a non-rotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2-by-2, 4-by-4, and 6-by-6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6-by-6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2-by-2 streaming pattern, which is dominated by the boundary-driven streaming. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.09132v1-abstract-full').style.display = 'none'; document.getElementById('1905.09132v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 9 pdf figures, Revtex 4-1</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 100, 023104 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.05802">arXiv:1804.05802</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1804.05802">pdf</a>, <a href="https://arxiv.org/format/1804.05802">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1121/1.5049579">10.1121/1.5049579 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J+S">Jacob S. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=Bruus%2C+H">Henrik Bruus</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1804.05802v1-abstract-short" style="display: inline;"> The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics b&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.05802v1-abstract-full').style.display = 'inline'; document.getElementById('1804.05802v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.05802v1-abstract-full" style="display: none;"> The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.05802v1-abstract-full').style.display = 'none'; document.getElementById('1804.05802v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 5 figures, pdfLatex, RevTex</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.6135">arXiv:1402.6135</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1402.6135">pdf</a>, <a href="https://arxiv.org/format/1402.6135">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1107/S1600577514006857">10.1107/S1600577514006857 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Characterization of Spatial Coherence of Synchrotron Radiation with Non-Redundant Arrays of Apertures </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Skopintsev%2C+P">P. Skopintsev</a>, <a href="/search/physics?searchtype=author&amp;query=Singer%2C+A">A. Singer</a>, <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J">J. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=M%7Fuller%2C+L">L. Muller</a>, <a href="/search/physics?searchtype=author&amp;query=Beyersdorf%2C+B">B. Beyersdorf</a>, <a href="/search/physics?searchtype=author&amp;query=Schleitzer%2C+S">S. Schleitzer</a>, <a href="/search/physics?searchtype=author&amp;query=Gorobtsov%2C+O">O. Gorobtsov</a>, <a href="/search/physics?searchtype=author&amp;query=Shabalin%2C+A">A. Shabalin</a>, <a href="/search/physics?searchtype=author&amp;query=Kurta%2C+R">R. Kurta</a>, <a href="/search/physics?searchtype=author&amp;query=Dzhigaev%2C+D">D. Dzhigaev</a>, <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Glaser%2C+L">L. Glaser</a>, <a href="/search/physics?searchtype=author&amp;query=Sakdinawat%2C+A">A. Sakdinawat</a>, <a href="/search/physics?searchtype=author&amp;query=Liu%2C+Y">Y. Liu</a>, <a href="/search/physics?searchtype=author&amp;query=Gr%7Fubel%2C+G">G. Grubel</a>, <a href="/search/physics?searchtype=author&amp;query=Fr%7Fomter%2C+R">R. Fromter</a>, <a href="/search/physics?searchtype=author&amp;query=Oepen%2C+H+P">H. P. Oepen</a>, <a href="/search/physics?searchtype=author&amp;query=Viefhaus%2C+J">J. Viefhaus</a>, <a href="/search/physics?searchtype=author&amp;query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1402.6135v1-abstract-short" style="display: inline;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamli&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'inline'; document.getElementById('1402.6135v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.6135v1-abstract-full" style="display: none;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring as a function of different beam parameters. To verify the results obtained with the NRAs additional Young&#39;s double pinhole experiments were conducted and show good agreement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'none'; document.getElementById('1402.6135v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 6 figures, 2 tables, 42 references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Synchrotron Rad. 21 Part 4, pages 722-728. (2014) </p> </li> </ol> <div class="is-hidden-tablet"> <!-- feedback for mobile only --> <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>&nbsp;&nbsp;</span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary"> <!-- MetaColumn 1 --> <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div> <!-- end MetaColumn 1 --> <!-- MetaColumn 2 --> <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div> <!-- end MetaColumn 2 --> </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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