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• W1553695993 abstract "The field of stochastic growth encompasses various different processes whichare ubiquitously seen across the physical world. In many systems, stochasticityappears quite naturally, where inherent randomness provides the right setting for thetone of motion and interaction, whose symphony leads to the surprising emergenceof interesting patterns and structure. Although on the microscopic scale one can beoverwhelmed by the randomness arising from the fluctuating interactions betweencomponents, on the macroscopic scale, however, one is mesmerized by the emergenceof mathematical beauty and symmetry, leading to complex structures with fractalarchitecture.Competition between components adds an extra degree of complexity andleads to the possibility of critical behaviour and phase transitions. It is an importantaspect of many systems, and in order to provide a full explanation of many naturalphenomena, we have to understand the role it plays on modifying behaviour. Thecombination of stochastic growth and competition leads to the emergence of interestingcomplex patterns. They occur in various systems and in many forms, andthus we treat competition in growth models driven by different laws for the stochasticnoise. As a consequence our results are widely applicable and we encourage thereader to find good use for them in their respective field.In this thesis we study stochastic systems containing interacting particleswhose motion and interplay lead to directed growth structures on a particular geometry.We show how the effect of the overall geometry in many growth processescan be captured elegantly in terms of a time dependent metric. A natural examplewe treat is isoradial growth in two dimensions, with domain boundaries of competingmicrobial species as an example of a system with a homogeneously changingmetric. In general, we view domain boundaries as space-time trajectories of particlesmoving on a dynamic surface and map those into more easily tractable systemswith constant metric. This leads to establishing a generic relation between locallyinteracting, scale invariant stochastic space-time trajectories under constant andtime dependent metric. Indeed “the book of nature is written in the language ofmathematics” (Galileo Galilei) and we provide a mathematical framework for varioussystems with various interactions and our results are backed with numericalconfirmation." @default.
• W1553695993 created "2016-06-24" @default.
• W1553695993 creator A5045995727 @default.
• W1553695993 date "2012-09-01" @default.
• W1553695993 modified "2023-09-27" @default.
• W1553695993 title "Stochastic pattern formation in growth models with spatial competition" @default.
• W1553695993 cites W1484033701 @default.
• W1553695993 cites W1486447486 @default.
• W1553695993 cites W1494779996 @default.
• W1553695993 cites W1501631266 @default.
• W1553695993 cites W1534544220 @default.
• W1553695993 cites W1549240140 @default.
• W1553695993 cites W1569791555 @default.
• W1553695993 cites W1583323312 @default.
• W1553695993 cites W1591798773 @default.
• W1553695993 cites W1672907864 @default.
• W1553695993 cites W1677703250 @default.
• W1553695993 cites W168596846 @default.
• W1553695993 cites W1793793548 @default.
• W1553695993 cites W1865525050 @default.
• W1553695993 cites W1872853220 @default.
• W1553695993 cites W1876293409 @default.
• W1553695993 cites W1963897110 @default.
• W1553695993 cites W1964255989 @default.
• W1553695993 cites W1965052062 @default.
• W1553695993 cites W1966475467 @default.
• W1553695993 cites W1971912858 @default.
• W1553695993 cites W1972476295 @default.
• W1553695993 cites W1974120868 @default.
• W1553695993 cites W1975642142 @default.
• W1553695993 cites W1981425595 @default.
• W1553695993 cites W1982115118 @default.
• W1553695993 cites W1983813591 @default.
• W1553695993 cites W1984034197 @default.
• W1553695993 cites W1985997303 @default.
• W1553695993 cites W1986033475 @default.
• W1553695993 cites W1987302215 @default.
• W1553695993 cites W1987907424 @default.
• W1553695993 cites W1991037583 @default.
• W1553695993 cites W1992334438 @default.
• W1553695993 cites W1997385990 @default.
• W1553695993 cites W1997722194 @default.
• W1553695993 cites W1999080762 @default.
• W1553695993 cites W2000071663 @default.
• W1553695993 cites W2002882118 @default.
• W1553695993 cites W2003691173 @default.
• W1553695993 cites W2004734978 @default.
• W1553695993 cites W2007570141 @default.
• W1553695993 cites W2007993714 @default.
• W1553695993 cites W2009905627 @default.
• W1553695993 cites W2010517136 @default.
• W1553695993 cites W2013324823 @default.
• W1553695993 cites W2013612669 @default.
• W1553695993 cites W2013731294 @default.
• W1553695993 cites W2014188567 @default.
• W1553695993 cites W2016437223 @default.
• W1553695993 cites W2020956300 @default.
• W1553695993 cites W2021059415 @default.
• W1553695993 cites W2021929999 @default.
• W1553695993 cites W2022197635 @default.
• W1553695993 cites W2023987479 @default.
• W1553695993 cites W2024060531 @default.
• W1553695993 cites W2026501291 @default.
• W1553695993 cites W2027716584 @default.
• W1553695993 cites W2028838633 @default.
• W1553695993 cites W2029774109 @default.
• W1553695993 cites W2029894197 @default.
• W1553695993 cites W2036030799 @default.
• W1553695993 cites W2037451010 @default.
• W1553695993 cites W2039551846 @default.
• W1553695993 cites W2040109383 @default.
• W1553695993 cites W2041289996 @default.
• W1553695993 cites W2042815070 @default.
• W1553695993 cites W2042847139 @default.
• W1553695993 cites W2042977597 @default.
• W1553695993 cites W2046866397 @default.
• W1553695993 cites W2048615939 @default.
• W1553695993 cites W2049795184 @default.
• W1553695993 cites W2050595181 @default.
• W1553695993 cites W2051330050 @default.
• W1553695993 cites W2051884660 @default.
• W1553695993 cites W2053425700 @default.
• W1553695993 cites W2054704061 @default.
• W1553695993 cites W2057788561 @default.
• W1553695993 cites W2058077745 @default.
• W1553695993 cites W2061693681 @default.
• W1553695993 cites W2064166468 @default.
• W1553695993 cites W2065096983 @default.
• W1553695993 cites W2066359652 @default.
• W1553695993 cites W2066620359 @default.
• W1553695993 cites W2067983805 @default.
• W1553695993 cites W2067995211 @default.
• W1553695993 cites W2071063963 @default.
• W1553695993 cites W2076405005 @default.
• W1553695993 cites W2078041165 @default.
• W1553695993 cites W2078068324 @default.
• W1553695993 cites W2078206416 @default.
• W1553695993 cites W2079439973 @default.
• W1553695993 cites W2080477605 @default.
• W1553695993 cites W2081003444 @default.

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