<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div style="font-family: HelveticaNeue;"><font face="HelveticaNeue">Dear Soft Matter & Complex Systems Colleagues and Friends,</font></div><div style="font-family: HelveticaNeue;"><font face="HelveticaNeue"><br></font></div><div><div style="font-family: HelveticaNeue;"><font face="HelveticaNeue">On Friday 22 November 2024 at 9:30 AM at the UW Faculty of Physics (Pasteura 5, Warsaw; room 1.40) we are hosting a seminar during which </font></div><div style="font-family: HelveticaNeue;"><font face="HelveticaNeue"><br></font></div><div style="font-family: HelveticaNeue; margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"><font face="HelveticaNeue"><b>Stanisław Gepner </b></font><font face="HelveticaNeue">(Warsaw University of Technology</font>)</div><div style="font-family: HelveticaNeue; margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"><font face="HelveticaNeue"><br></font></div><div style="font-family: HelveticaNeue; margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">will give a talk</font></div><div style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"><div><h2 style="margin: 6px 0px 12px; padding: 0px;"><font face="HelveticaNeue"><span style="font-size: 12px;">Is the Laminar-Turbulent Edge Crowded? Exploring Multiple Local </span></font><span style="font-size: 12px; font-family: HelveticaNeue;">Attractors in the Edge of Square-Duct Flow</span></h2></div><h2 style="font-family: HelveticaNeue; margin: 6px 0px 12px; padding: 0px; caret-color: rgb(68, 68, 68);"><b><font face="HelveticaNeue" style="font-size: 12px;">Abstract</font></b></h2><div style="font-family: HelveticaNeue;">In this work, we present the first streamwise-localized invariant<br>solution for turbulent square duct flow in the moderate Reynolds number<br>range. Through heuristic analysis, we demonstrate that during specific<br>periods within the turbulent time evolution, the flow state approaches<br>the identified localized solution. This finding indicates that the<br>localized solution is embedded within the turbulent attractor, making it<br>the first localized solution identified for square duct flow and a<br>the potential building block of turbulence in this configuration.<br><br>We obtain this solution through a bisection process applied within the<br>symmetric subspace of the full state space, which enables the tracking<br>of edge state solutions. Edge states are characterized by a single<br>unstable direction, or a co-dimension one stable manifold, within the<br>symmetric subspace. In the context of the full state space, these<br>solutions are embedded within the turbulent attractor. As relative<br>attractors on the edge of the laminar and turbulent basins, edge states<br>play a significant role in governing the laminar-turbulent transition<br>process. This characteristic makes them particularly interesting for<br>turbulence control applications. In addition to the bisection method, we<br>use Newton-Krylov GMRES-based iterations to converge to invariant<br>solutions. To analyze stability, we apply an Arnoldi-based eigenvalue<br>solver, and an arc-length continuation to track bifurcations. Stability<br>analysis reveals that both branches of our localized solution are<br>unstable in at least one direction. This instability suggests the<br>presence of additional structures that may connect to the branches of<br>the identified solution, indicating that the edge subspace (a<br>co-dimension one subspace of the full space) contains multiple local<br>attractors. Each of these local edge states would have stable manifolds<br>that locally separate initial conditions, leading either toward the<br>laminar attractor, a transient non-laminar excursion or, if it exists,<br>a turbulent attractor. In our ongoing work, we identify and analyze a<br>series of solutions on the edge. We study the positions and potential<br>connections between the lower and upper branches of the identified<br>solutions. By disturbing either the lower or upper branch in the<br>unstable direction, we observe that the system tends either to<br>laminarize smoothly or to experience a transient turbulent excursion.<br>This behavior confirms that both solution branches reside on the edge<br>and that the bifurcation responsible for their creation also lies on the<br>edge. Additionally, we identify a potential heteroclinic connection<br>between these states, which further enriches our understanding of the<br>dynamics governing laminar-turbulent transition in square duct flow.</div><div style="font-family: HelveticaNeue;"><br></div></div><div style="font-family: HelveticaNeue; margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">We warmly welcome everyone to attend the talk and the Soft Matter Coffee Break after the seminar, held in room 2.63 (2nd floor).</font></div></div><div style="font-family: HelveticaNeue;"><font face="HelveticaNeue"><br></font></div><div style="font-family: HelveticaNeue;"><div dir="auto" style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div style="margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">Maria Ekiel-Jeżewska</font></div><div style="margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">Maciej Lisicki</font></div><div style="margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">Piotr Szymczak</font></div><div style="margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">Panagiotis Theodorakis</font></div><div style="margin: 0px; font-stretch: normal; line-height: normal;"><font face="HelveticaNeue">Marek Trippenbach</font></div></div></div><div><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; 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