The influence of regularly distributed disk-like obstacles on the motionof self-propelled particles is investigated within the framework of the Vicsek model. We focus on systems with a large number of self-propelled particles that form ordered structures such as traveling bands. The obstacles are arranged in a square lattice. We investigate the influence of their size and their separation on the formation and stability of ordered patterns of moving particles. We have discovered new structures stabilized by different arrangements of obstacles.
room 1.40, Pasteura 5 at 09:30

Stanisław Gepner (Warsaw University of Technology)
In this work, we present the first streamwise-localized invariant solution for turbulent square duct flow in the moderate Reynolds number range. Through heuristic analysis, we demonstrate that during specific periods within the turbulent time evolution, the flow state approaches the identified localized solution. This finding indicates that the localized solution is embedded within the turbulent attractor, making it the first localized solution identified for square duct flow and a the potential building block of turbulence in this configuration.
We obtain this solution through a bisection process applied within the symmetric subspace of the full state space, which enables the tracking of edge state solutions. Edge states are characterized by a single unstable direction, or a co-dimension one stable manifold, within the symmetric subspace. In the context of the full state space, these solutions are embedded within the turbulent attractor. As relative attractors on the edge of the laminar and turbulent basins, edge states play a significant role in governing the laminar-turbulent transition process. This characteristic makes them particularly interesting for turbulence control applications. In addition to the bisection method, we use Newton-Krylov GMRES-based iterations to converge to invariant solutions. To analyze stability, we apply an Arnoldi-based eigenvalue solver, and an arc-length continuation to track bifurcations. Stability analysis reveals that both branches of our localized solution are unstable in at least one direction. This instability suggests the presence of additional structures that may connect to the branches of the identified solution, indicating that the edge subspace (a co-dimension one subspace of the full space) contains multiple local attractors. Each of these local edge states would have stable manifolds that locally separate initial conditions, leading either toward the laminar attractor, a transient non-laminar excursion or, if it exists, a turbulent attractor. In our ongoing work, we identify and analyze a series of solutions on the edge. We study the positions and potential connections between the lower and upper branches of the identified solutions. By disturbing either the lower or upper branch in the unstable direction, we observe that the system tends either to laminarize smoothly or to experience a transient turbulent excursion. This behavior confirms that both solution branches reside on the edge and that the bifurcation responsible for their creation also lies on the edge. Additionally, we identify a potential heteroclinic connection between these states, which further enriches our understanding of the dynamics governing laminar-turbulent transition in square duct flow.
room 1.40, Pasteura 5 at 09:30

Alina Ciach (IChF PAN)
Concentrated ionic systems can find practical applications in energystorage devices, and in living cells the density of ions is large.Classical theories developed for dilute electrolytes, however, are notvalid when the average distance between the ions becomes comparable withtheir diameters. Different experimental techniques, approximate theoriesand simulations give contradictory results for the distribution of theions and for screening of charged objects, and a commonly acceptedtheory is still to be developed.
I will very briefly present the experimental and simulation results.Next I'll discuss major differences between dilute and concentratedionic systems, and introduce the mesoscopic approach for ionic systemswith any density. In the theory, the finite size of the ions and thevariance of the local charge are taken into account.The correlationfunctions obtained within the theory will be compared with experiments.The remaining open questions will be discussed.
room 1.40, Pasteura 5 at 09:30

Tony Ladd (University of Florida at Gainesville)
DNA is a semi-flexible polyelectrolyte with a persistence length of about 50 nm. At equilibrium, entropic forces cause the individual molecules to form compact spherical coils, which can be easily stretched by a weak shear flow into a cigar-like conformation that is not, on average, aligned with the flow direction. Because the electrophorectic mobility of the sheared polyelectrolyte is no longer isotropic, DNA can be driven to the walls of a confining channel by an electric field that pushes the DNA in the opposite direction to the flow. The migration velocity is sufficient to keep the DNA in a thin layer next to the wall. With a suitable choice of field strengths, the DNA can be driven against the flow (since it is next to the channel walls), while all the other components of a cell lysate are flushed in the opposite direection by the flow. This is a much stronger separation than in typical microfluidic processes, which rely on mobility contrast between the species. A simple microfludic device, assembled from acrylic sheets for less than $1, can provide a chemical-free purification of DNA. In this talk I will outline the physics underpinning the separation and describe experiments that purify DNA in sufficient quantities (up to 40 ng) for PCR amplification and gel electrophoresis.