We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws for the wave number in the bulk of the domain. Scalings are based on a description of striped patterns in semibounded domains via strain-displacement relations. We compare predictions with direct simulations in the Swift-Hohenberg, the complex Ginzburg-Landau, the Cahn-Hilliard, and reaction-diffusion equations.
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http://dx.doi.org/10.1103/PhysRevE.94.022219 | DOI Listing |
Phys Rev E
August 2024
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland.
We analyze the three-dimensional (3D) buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Péclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for a small perturbation of a thin filament from a straight position of arbitrary orientation.
View Article and Find Full Text PDFPhys Rev Lett
July 2024
Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA.
The leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins can develop closed loops forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales.
View Article and Find Full Text PDFJ Chem Phys
August 2023
School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 62 Nanyang Drive, Singapore 637459.
Phys Rev Lett
August 2023
Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA.
The mechanisms that generate "seed" magnetic fields in our Universe and that amplify them throughout cosmic time remain poorly understood. By means of fully kinetic particle-in-cell simulations of turbulent, initially unmagnetized plasmas, we study the genesis of magnetic fields via the Weibel instability and follow their dynamo growth up to near-equipartition levels. In the kinematic stage of the dynamo, we find that the rms magnetic field strength grows exponentially with rate γ_{B}≃0.
View Article and Find Full Text PDFPhys Rev Lett
March 2022
Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-0840, USA.
In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations.
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