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Oscillating edge current in polar active fluid.
Phys Rev E
May 2024
Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.
Dense bacterial suspensions exhibit turbulent behavior called bacterial turbulence. The behavior of the bulk unconstrained bacterial turbulence is described well by the Toner-Tu-Swift-Hohenberg (TTSH) equation for the velocity field. However, it remains unclear how we should treat boundary conditions on bacterial turbulence in contact with some boundaries (e.
View Article and Find Full Text PDFTransverse modulational dynamics of quenched patterns.
Chaos
June 2024
Department of Mathematics and Statistics, Boston University, 665 Commonwealth Ave., Boston, MA 02215, USA.
We study the modulational dynamics of striped patterns formed in the wake of a planar directional quench. Such quenches, which move across a medium and nucleate pattern-forming instabilities in their wake, have been shown in numerous applications to control and select the wavenumber and orientation of striped phases. In the context of the prototypical complex Ginzburg-Landau and Swift-Hohenberg equations, we use a multiple-scale analysis to derive a one-dimensional viscous Burgers' equation, which describes the long-wavelength modulational and defect dynamics in the direction transverse to the quenching motion, that is, along the quenching line.
View Article and Find Full Text PDFGenerative design of large-scale fluid flow structures via steady-state diffusion-based dehomogenization.
Sci Rep
September 2023
Electronics Research Department, Toyota Research Institute of North America, 1555 Woodridge Avenue, Ann Arbor, MI, 48105, USA.
A computationally efficient dehomogenization technique was developed based on a bioinspired diffusion-based pattern generation algorithm to convert an orientation field into explicit large-scale fluid flow channel structures. Due to the transient nature of diffusion and reaction, most diffusion-based pattern generation models were solved in both time and space. In this work, we remove the temporal dependency and directly solve a steady-state equation.
View Article and Find Full Text PDFCollisions of localized patterns in a nonvariational Swift-Hohenberg equation.
Phys Rev E
June 2023
Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.
The cubic-quintic Swift-Hohenberg equation (SH35) has been proposed as an order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use numerical continuation, together with extensive direct numerical simulations (DNSs), to study SH35 with an additional nonvariational quadratic term to model the effects of breaking the midplane reflection symmetry. The nonvariational structure of the model leads to the propagation of asymmetric spatially localized structures (LSs).
View Article and Find Full Text PDFSpatially extended dislocations produced by the dispersive Swift-Hohenberg equation.
Phys Rev E
April 2023
Departments of Physics and Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA.
Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern formation, we study the Swift-Hohenberg equation with an added linear dispersive term, the dispersive Swift-Hohenberg equation (DSHE). The DSHE produces stripe patterns with spatially extended defects that we call seams. A seam is defined to be a dislocation that is smeared out along a line segment that is obliquely oriented relative to an axis of reflectional symmetry.
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