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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
Publikováno v:
Nonlinearity 36, 2567 (2023)
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular patterns from
Externí odkaz:
http://arxiv.org/abs/2203.09363