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pro vyhledávání: '"Shipman, Patrick D."'
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 disper
Externí odkaz:
http://arxiv.org/abs/2212.03930
Publikováno v:
CALS Publications Archive. The University of Arizona..
The patterns seen in both the phyllotaxis and surface morphologies in the vicinity of the shoot apical meristems of plants are discussed. We begin with many pictures and a narrative descriptive of both the universal and anomalous features of desert a
Externí odkaz:
http://hdl.handle.net/10150/556802
The anisotropic complex Ginzburg-Landau equation (ACGLE) describes slow modulations of patterns in anisotropic spatially extended systems near oscillatory (Hopf) instabilities with zero wavenumbers. Traveling wave solutions to the ACGLE become unstab
Externí odkaz:
http://arxiv.org/abs/2009.12945
Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers. Hyperbolic n
Externí odkaz:
http://arxiv.org/abs/1901.02085
Autor:
Motta, Francis C., Shipman, Patrick D.
The defect of a complex Hadamard matrix $H$ is an upper bound for the dimension of a continuous Hadamard orbit stemming from $H$. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and apply the C
Externí odkaz:
http://arxiv.org/abs/1609.02829
For positive integers $k,n$, a de Bruijn sequence $B(k,n)$ is a finite sequence of elements drawn from $k$ characters whose subwords of length $n$ are exactly the $k^n$ words of length $n$ on $k$ characters. This paper introduces the unoriented de Br
Externí odkaz:
http://arxiv.org/abs/1608.08480
When the surface of a nominally flat binary material is bombarded with a broad, normally-incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the
Externí odkaz:
http://arxiv.org/abs/1511.01547
Akademický článek
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While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonl
Externí odkaz:
http://arxiv.org/abs/1306.1162
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate that this hyp
Externí odkaz:
http://arxiv.org/abs/1210.7174