Spatiotemporal Pattern Formation

The evolution of spatiotemporal patterns of water footprint economic benefits (WFEB) in the 32 counties (cities and districts) of the Poyang Lake City Group in Jiangxi Province was evaluated based on panel data. Where after, the spatial spillover effects of the regional WFEB in the Poyang Lake City Group were investigated using the spatial Durbin model (SDM). The results showed a rising trend in the total water footprint (WF) and WFEB of the Poyang Lake City Group from 2010 to 2013, and the number of cities at the levels of high efficiency in the Poyang Lake City Group increased steadily. Clear local spatial autocorrelations were found in WFEB, the degree of spatial clustering of WFEB gradually strengthened during 2010–2013, and the spatial agglomeration of WFEB in the Poyang Lake City Group mainly showed Low-High and LowLow types of trends, which accounted for 9.4% and 12.5%, respectively, of the four types of trends. Our SDM analysis further confirmed significant spatial dependenc...

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Water scarcity is an important factor limiting agricultural development in arid areas. Clarifying and evaluating the current situation of water resources in arid regions is helpful for decision-makers in the rational use of water resources. This study takes a typical arid region located at the edge of Taklamakan Desert-Hotan region as the study area. The water footprint (WF) of the Hotan region was calculated based on 20 years of data information from 2000–2019. An evaluation system was established using four aspects of the WF: structural indicators, efficiency indicators, ecological safety indicators, and sustainability indicators. The results show that the WF of the study area is mainly dominated by blue water consumption, with a proportion of 65.74%. The WF of crop production is larger than that of livestock production. The produced WF of grain crops is the highest of all products with a share of 44.21%. The increase in the local agricultural WF reached 53.18% from 2000 to 2019, ...

One of the most surprising mechanisms to explain the symmetry breaking phenomenon linked to pattern formation is known as Turing instabilities. These patterns are self-organising spatial structures resulting from the interaction of at least two diffusive species in specific conditions. The ideas of Turing have been used extensively in the specialised literature both to explain developmental patterns, as well as synthetic biology design. In the present work we study a previously proposed morphogenetic synthetic circuit consisting of two genes controlled by the same regulatory system. The spatial homogeneous version of this simple model presents a rich phase diagram, since it has a saddle-node bifurcation, spirals and limit cycle. Linear stability analysis and numerical simulations of the complete model allow us to determine the conditions for the development of Turing patterns, as well as transient patterns. We found that the parameter region where Turing patterns are found is much s...

We study Turing pattern formation in a system undergoing radial growth in two dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL Multiphysics and solved on domains growing at different speeds while sweeping other parameters to examine a wide range of Turing pattern morphologies. By altering the configuration of the finite element mesh, we examine patterning in several simulation growth modes. The observed pattern morphologies match previously observed trends for Turing pattern growth modes. Fast growth leads to pattern formation parallel to the growing boundary, intermediate growth leads to pattern formation perpendicular to the growing boundary, and slow growth leads to pattern growth from the interior. Exponential growth leads to the expected fast-growth mode of pattern formation parallel to the moving boundary. Simulations to replicate interior growth using logistic illumination do not show simple pattern trends due to the effects of partial pattern suppr...

We have carried out the first systematic study of the effects of ultraviolet light, both alone and in combination with visible white light, on Turing patterns in the chlorine dioxide-iodine-malonic acid (CDIMA) reaction. The ultraviolet light used has a sharp peak at 368 nm and can perturb the system selectively. It primarily decomposes chlorine dioxide in a zeroth-order reaction and, when it is used to illuminate Turing patterns, shrunken spots are formed with an imperfect hexagonal arrangement. The ultraviolet light competes directly with the visible white light via the photoreaction with dissolved chlorine dioxide, which prevents the total suppression of patterns at intermediate intensities of white light. These results suggest that specific wavelengths of light in the ultraviolet spectrum selectively modify the chemistry behind the pattern formation and can be utilized to generate novel self-organized structures under forcing conditions. We propose a modified Lengyel-Epstein model to incorporate the effect of ultraviolet illumination and obtain good qualitative agreement between simulations and experiments. These results support the idea that chlorine dioxide photoreaction is a key step in modulating CDIMA patterns under ultraviolet illumination.

Abstract. This article reviews the development of the concept of reactiondiffusion leading to pattern formation in living organisms. The article commences with an historical background and then describes biological development, and ideas of the formation of patterns using dynamic activator inhibitor systems. In addition to this, different models to represent such systems and their computer simulations are discussed.

The evolution of spatiotemporal patterns of water footprint economic benefits (WFEB) in the 32 counties (cities and districts) of the Poyang Lake City Group in Jiangxi Province was evaluated based on panel data. Where after, the spatial spillover effects of the regional WFEB in the Poyang Lake City Group were investigated using the spatial Durbin model (SDM). The results showed a rising trend in the total water footprint (WF) and WFEB of the Poyang Lake City Group from 2010 to 2013, and the number of cities at the levels of high efficiency in the Poyang Lake City Group increased steadily. Clear local spatial autocorrelations were found in WFEB, the degree of spatial clustering of WFEB gradually strengthened during 2010–2013, and the spatial agglomeration of WFEB in the Poyang Lake City Group mainly showed Low-High and LowLow types of trends, which accounted for 9.4% and 12.5%, respectively, of the four types of trends. Our SDM analysis further confirmed significant spatial dependenc...

It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction−diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells. 1 The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose−response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction−diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

Socioeconomic development has led to increased consumption of both blue and green water. Consequently, China is facing serious water scarcity issue. However, few studies have investigated interactions of blue and green water footprints, as well as driving forces underlying the changes in water footprints across provinces and sectors. To fill in this knowledge gap, we quantified the spatial-temporal dynamics of the blue and green water footprint (BWF and GWF, respectively), and analyzed the key factors that drive the provincial-level changes in BWF and GWF from 2002 to 2012. The analysis is facilitated by the approaches of multi-region input-output analysis and structural decomposition analysis, and we developed one decoupling index to quantify the watereconomy relation and substitution between green and blue water. The results show that China's BWF averaged at 161 billion m 3 /yr, about one-third the size of the GWF. In addition, water scarce provinces in Northern China were moving towards decoupling between economic growth and blue water consumption, with GWF playing an increasingly important role. The changes in the WFs were mainly influenced by changes in affluence (final demand per capita), technological improvements (decreased direct water consumption intensity), and consumption pattern (composition of the final demand) rather than changes in the population and export. Technology improvement, consumption pattern shift and industrial structure adjustment contribute to WF reductions, thus help improve water security and sustainability in China. This study provides a new approach to analyze water-economy relations for water scarce countries.

The development of renewable clean energy such as hydropower can not only ensure energy security, but also help achieve the United Nation’s Sustainable Development Goals. This paper uses the annual data of 30 provinces in China from 2000 to 2017, and constructs a dynamic spatial Durbin model and a geographically weighted regression model to empirically test the dynamic impact of hydropower on haze pollution and economic growth at the national and provincial levels. The empirical results show that the promoting effect of hydropower on economic growth in Western China is less than that in Eastern China, which further aggravates the economic development gap between the eastern and western regions. In addition, the suppression effect of hydropower on the haze pollution in the western region is greater than that in the eastern region, where the haze pollution is serious. From the national level, hydropower can promote regional economic growth and inhibit haze pollution, and the spatial s...

The sustainable development has been seriously challenged by global climate change due to carbon emissions. As a developing country, China promised to reduce 40%-45% below the level of the year 2005 on its carbon intensity by 2020. The realization of this target depends on not only the substantive transition of society and economy at the national scale, but also the action and share of energy saving and emissions reduction at the provincial scale. Based on the method provided by the IPCC, this paper examines the spatiotemporal dynamics and dominating factors of China's carbon intensity from energy consumption in 1997-2010. The aim is to provide scientific basis for policy making on energy conservation and carbon emission reduction in China. The results are shown as follows. Firstly, China's carbon emissions increased from 4.16 Gt to 11.29 Gt from 1997 to 2010, with an annual growth rate of 7.15%, which was much lower than that of GDP (11.72%). Secondly, the trend of Moran's I indicated that China's carbon intensity has a growing spatial agglomeration at the provincial scale. The provinces with either high or low values appeared to be path-dependent or space-locked to some extent. Third, according to spatial panel econometric model, energy intensity, energy structure, industrial structure and urbanization rate were the dominating factors shaping the spatiotemporal patterns of China's carbon intensity from energy consumption. Therefore, in order to realize the targets of energy conservation and emission reduction, China should improve the efficiency of energy utilization, optimize energy and industrial structure, choose the low-carbon urbanization approach and implement regional cooperation strategy of energy conservation and emissions reduction.

We propose a reaction-diffusion model of spatial pattern formation whose solutions can exhibit scaleinvariance over any desired range for suitable choices of parameters in the model. The model does not invoke preset polarity or any other adboc distinction between cells and provides a solution to the French flag probleit without sources at the boundary. Furthermore, patterns other than the polar pattern that usually arises first in a growing one-dimensional syst6m described by Turing's model can be obtained. Evidence is given that suggests that the model may apply in the slug stage of Dictyostelium discoideum.

The evolution of spatiotemporal patterns of water footprint economic benefits (WFEB) in the 32 counties (cities and districts) of the Poyang Lake City Group in Jiangxi Province was evaluated based on panel data. Whereafter, the spatial spillover effects of the regional WFEB in the Poyang Lake City Group were investigated using the spatial Durbin model (SDM). The results showed a rising trend in the total water footprint (WF) and WFEB of the Poyang Lake City Group from 2010 to 2013, and the number of cities at the levels of high efficiency in the Poyang Lake City Group increased steadily. Clear local spatial autocorrelations were found in WFEB, the degree of spatial clustering of WFEB gradually strengthened during 2010–2013, and the spatial agglomeration of WFEB in the Poyang Lake City Group mainly showed Low-High and Low-Low types of trends, which accounted for 9.4% and 12.5%, respectively, of the four types of trends. Our SDM analysis further confirmed significant spatial dependence of WFEB in the Poyang Lake City Group in Jiangxi Province.

Keywords: water footprint economic benefits; spatiotemporal pattern; spillover effects; Poyang Lake City Group

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Poyang Lake Eco-economic Zone is an eco-economic demonstration area in harmony between mankind and nature. It is an imperative to develop a green urbanization road with coordination and harmony between ecological civilization construction and economic and social development in a bid to effectively protect local ecological environment. By beginning with the basic connotations of green development, the evolution trend of green urbanization spatial pattern is revealed and the influences of ecological environment on evolution of spatial pattern in the research. By building comprehensive evaluation index of green urbanization development level, the green urbanization development level of 9 representative prefecture-level cities at Poyang Lake Eco-economic Zone from 2008 to 2014 is measured through entropy evaluation method. Besides, the in-depth analysis on evolution process of spatial pattern is carried out. Meanwhile, spatial autocorrelation test is carried out with Moran'sI index. From four perspectives such as economy, society, environment and social security, the influence factor variables are selected and analyzed by virtue of influences factors of spatial econometric model on spatial pattern evolution. According to the research, it manifests that green urbanization of Poyang Lake Eco-economic Zone shows high level aggregated distribution and high level area has the trend of spreading to the low level area. In addition, the area with good ecological environment also has high regional development level because of the great influence of ecological environment on spatial pattern.

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.

We have explored the growth of patterns in chlorine dioxide-iodine-malonic acid reaction-diffusion system when the injection rate of the activator and inhibitor is varied over a range. The transition from spot to stripe and their mixture and finally the target wave which appears at the Hopf bifurcation boundary are observed. Our numerical simulations have been corroborated by theoretical analysis of amplitude equation for targets.

It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction−diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells. The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose−response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction−diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

Abstract. This article reviews the development of the concept of reactiondiffusion leading to pattern formation in living organisms. The article commences with an historical background and then describes biological development, and ideas of the formation of patterns using dynamic activator inhibitor systems. In addition to this, different models to represent such systems and their computer simulations are discussed.