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pro vyhledávání: '"Hill, Dan"'
The concept of `proximity-based cities' has gained attention as a new urban organizational model. Most prominently, the 15-minute city contends that cities can function more effectively, equitably and sustainably if essential, everyday services and k
Externí odkaz:
http://arxiv.org/abs/2411.12335
Autor:
Hill, Dan J.
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial patterns in g
Externí odkaz:
http://arxiv.org/abs/2405.16927
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and hexagons)
Externí odkaz:
http://arxiv.org/abs/2404.14987
Autor:
Groves, Mark D., Hill, Dan J.
This paper is concerned with complex Banach-space valued functions of the form $$ \hat{f}_k(r\cos\theta,r\sin\theta,z)=\mathrm{e}^{\mathrm{i} k \theta}f_k(r,z), \qquad r \in [0,\infty), \theta \in \mathbb{T}^1, z \in \mathbb{R}, $$ for some $k \in \m
Externí odkaz:
http://arxiv.org/abs/2403.09372
Autor:
Hill, Dan J., Lloyd, David J. B.
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this emergence or c
Externí odkaz:
http://arxiv.org/abs/2403.02949
Autor:
Hill, Dan J.
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that approximations
Externí odkaz:
http://arxiv.org/abs/2309.02956
Publikováno v:
Nonlinearity 37, 035015 (2024)
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns
Externí odkaz:
http://arxiv.org/abs/2210.13122