Spatial Chaos Research Articles

Can spatial planning in the Polish Carpathians be enforced? How spatial chaos indicators depict a gap between scientific knowledge and practice

Despite their strategic hydrological importance for neighbouring areas, the Polish Carpathians are experiencing spatial chaos, which may weaken their adaptability to the progressive climate change. The article attempts to answer the question of whether spatial planning, which is supposed to guarantee spatial order, fulfils its role and whether the knowledge of the natural conditions of spatial development is respected in the spatial planning process. Using GIS techniques, up to 238 communes were analysed in terms of their spatial coverage, the degree of scattered settlement, and the violation of natural barriers by location of buildings in areas that are threatened with mass movements or floods; by settlement on excessively inclined slopes and in areas with adverse climatic conditions. Spearman non-parametric rank correlation analysis and the multidimensional Principal Component Analysis (PCA) technique were performed to investigate relations between spatial chaos indicators and the planning situation. The analysis of the data has revealed that spatial planning does not fulfil its role. Serious errors in location of buildings have been noted even though the communes are covered by local spatial development plans. Scientific knowledge is not sufficiently transferred into planning documents, and bottom-up initiatives cannot replace systemic solutions. There is a need for strengthening the role of environmental studies documents in the spatial planning system. This would facilitate the transfer of scientific knowledge into the planning process and help to protect mountain areas. The development of a special spatial strategy for the Polish Carpathians in compliance with the Carpathian Convention is also recommended.

Spatio-temporal breather dynamics in microcomb soliton crystals

Solitons, the distinct balance between nonlinearity and dispersion, provide a route toward ultrafast electromagnetic pulse shaping, high-harmonic generation, real-time image processing, and RF photonic communications. Here we uniquely explore and observe the spatio-temporal breather dynamics of optical soliton crystals in frequency microcombs, examining spatial breathers, chaos transitions, and dynamical deterministic switching – in nonlinear measurements and theory. To understand the breather solitons, we describe their dynamical routes and two example transitional maps of the ensemble spatial breathers, with and without chaos initiation. We elucidate the physical mechanisms of the breather dynamics in the soliton crystal microcombs, in the interaction plane limit cycles and in the domain-wall understanding with parity symmetry breaking from third-order dispersion. We present maps of the accessible nonlinear regions, the breather frequency dependences on third-order dispersion and avoided-mode crossing strengths, and the transition between the collective breather spatio-temporal states. Our range of measurements matches well with our first-principles theory and nonlinear modeling. To image these soliton ensembles and their breathers, we further constructed panoramic temporal imaging for simultaneous fast- and slow-axis two-dimensional mapping of the breathers. In the phase-differential sampling, we present two-dimensional evolution maps of soliton crystal breathers, including with defects, in both stable breathers and breathers with drift. Our fundamental studies contribute to the understanding of nonlinear dynamics in soliton crystal complexes, their spatio-temporal dependences, and their stability-existence zones.

How Does the Fractional Derivative Change the Complexity of the Caputo Standard Fractional Map

The impact of power-law memory on the dynamics of the Caputo standard fractional map is investigated in this paper. The definition of a complexity measure for the Caputo standard fractional map is introduced. This measure evaluates both the average algebraic complexity of a trajectory and the distribution of the trajectories of different types in the phase space of the system. The interplay between the small-scale spatial chaos and the large-scale spatial behavior is observed and measured during the transition of the Caputo standard fractional map from the circle map to the classical standard map. It is demonstrated that the impact of the fractional derivative on the complexity of the fractional system is not straightforward and is predetermined by the physical properties governing the dynamics of that system.

Suburbanisation uncontrolled? The role of legal framework in limiting the dispersion of built-up areas in Poland

The article aims to determine the legal rationale for the dispersion of built-up areas in Poland and draws some polemical conclusions. The current legislative system of spatial planning and construction is the main cause behind the aggravation of spatial chaos. Built-up areas have been exhibiting dispersed patterns that often contravene natural, technical, infrastructural, economic, social or even legislative imperatives. The authors prove that suburbanisation in the strict sense is not existent in Poland, and that, quite the contrary, the decisions for new investment sites tend to be taken deliberately by landowners, investors and representatives of public administration. The authors review the causes and effects as well as legislative reasons for the dispersion of built-up areas. The text ends with recommendations for legislative changes aimed at counteracting the dispersion processes.

Augmented reality as a technology that supports the spatial development process

Motives: The solutions for designing spatial development methods in planning documents are presented as 2D graphics with supplementary descriptions. Due to the lack of specialist knowledge and insufficient spatial imagination, some readers may be unable to understand the graphic and descriptive content of such documents. The above can lead to the construction of objects that disrupt spatial order without violating the law. This problem can be solved by applying augmented reality (AR) in spatial planning. This paper presents the capabilities of a method for visualizing different spatial development variants on the example of buildings. A model of a building plot and the surrounding area, covered by a local spatial development plan, was developed.Aim: The aim of this study was to determine the applicability of the AR technology for identifying low-precision areas in the plan and its potential impact on the method of land development, with a resulting deterioration in spatial order.Results: The use of the AR technology enables analyses and assessments of planned development in the context of spatial order and its integration with the existing elements. Visualizations presented with the AR technology show that different interpretations of the local zoning plan generate spatial chaos. The utility of 3D visualization for an average reader was also presented. The AR technology can be used at the stage of preparing planning documents (community participation, adopting the plan), adopting by-laws (councilors), and enforcing these regulations (investors’ decisions).

Hamming distance as a measure of spatial chaos in evolutionary games.

From a context of evolutionary dynamics, social games can be studied as complex systems that may converge to a Nash equilibrium. Nonetheless, they can behave in an unpredictable manner when looking at the spatial patterns formed by the agents' strategies. This is known in the literature as spatial chaos. In this paper we analyze the problem for a deterministic prisoner's dilemma and a public goods game and calculate the Hamming distance that separates two solutions that start at very similar initial conditions for both cases. The rapid growth of this distance indicates the high sensitivity to initial conditions, which is a well-known indicator of chaotic dynamics.

Chimera patterns with spatial random swings between periodic attractors in a network of FitzHugh-Nagumo oscillators.

For the study of symmetry-breaking phenomena in neuronal networks, simplified versions of the FitzHugh-Nagumo model are widely used. In this paper, these phenomena are investigated in a network of FitzHugh-Nagumo oscillators taken in the form of the original model and it is found that it exhibits diverse partial synchronization patterns that are unobserved in the networks with simplified models. Apart from the classical chimera, we report a new type of chimera pattern whose incoherent clusters are characterized by spatial random swings among a few fixed periodic attractors. Another peculiar hybrid state is found that combines the features of this chimera state and a solitary state such that the main coherent cluster is interspersed with some nodes with identical solitary dynamics. In addition, oscillation death including chimera death emerges in this network. A reduced model of the network is derived to study oscillation death, which helps explaining the transition from spatial chaos to oscillation death via the chimera state with a solitary state. This study deepens our understanding of chimera patterns in neuronal networks.

Less important space? Spatial planning in small towns in Poland

The aim of this paper is to present the condition of spatial planning in small towns in the Kujawsko-Pomorskie Voivodeship in Poland (urban municipalities up to 20,000 inhabitants) taking into account the analytical background in the form of a set of small towns (urban municipalities) in Poland. The authors posed the following research questions: (Q1) How up-to-date is the strategic planning document Study of conditions and directions of spatial development (SCDSDs) in small towns? (Q2) What is the coverage of small towns with local spatial development plans (LSDPs) and is it sufficient, and to what degree are decisions on development conditions (DCs) used in spatial planning in small towns? (Q3) What is the opinion of the inhabitants of a small town (Lipno) about spatial planning and public participation in the planning process conducted in the city in which they live? To achieve the aim of the study, the authors conducted a three-stage study consisting of a qualitative and a quantitative part. In the qualitative part, an assessment was conducted of the topicality of the Studies of Conditions and Directions of Spatial Development (SCDSDs) of small towns in the Kujawsko-Pomorskie Voivodeship. In the quantitative part, we analysed and evaluated statistical data from the Local Data Bank of Statistics Poland concerning local spatial development plans (LSDPs) and decisions on development conditions (DCs) in small towns in the Kujawsko-Pomorskie Voivodeship. At this stage, a questionnaire was also carried out using the Paper and Pencil Interview + Computer Assisted Web Interview (PAPI+CAWI) method, addressed to the community of the town of Lipno. The research shows that the problems in small towns are: low topicality of SCDSDs, and in the vast majority of the small towns analysed – very low LSDP coverage. These municipalities also issue the largest number of DCs, which exacerbates the spatial chaos. The questionnaire survey shows that residents are interested in issues related to the shaping of urban space, but indicate a lack of adequate knowledge on spatial planning, which lowers their participation in the process. They also recognise the great importance of spatial planning in socio-economic development, which translates into quality of life.

Temporal and spatial chaos of RN-AdS black holes immersed in Perfect Fluid Dark Matter

Temporal and spatial chaos of RN-AdS black holes immersed in Perfect Fluid Dark Matter

Precession Dynamics of the Uniaxial Nanoparticle Magnetization in the Ferromagnetic Resonance Region

The influence of the shape parameter (oblateness) of a uniaxial ellipsoidal nanoparticle on the dynamics of its magnetic moment upon magnetization along the symmetry axis and excitation by a weak transverse high-frequency field in the region of parameters where the equilibrium magnetic moment of the nanoparticle and the external static field is noncollinear has been studied. It is shown that as the oblateness increases, the irregularity of the oscillations increases, which at first affects only their amplitude, but then also the time dependence. The intervals of the shape parameter (or frequency), where various nonlinear modes of precession are realized --- dynamic bistability, complex spatial attractors and chaos, were revealed using bifurcation diagrams. Keywords: ellipsoidal nanoparticle, "easy" axis, effective anisotropy, ferromagnetic resonance, high frequency field, bistability, regular and chaotic precession.

Прецессионная динамика намагниченности одноосной наночастицы в области ферромагнитного резонанса

The influence of the shape parameter (oblateness) of a uniaxial ellipsoidal nanoparticle on the dynamics of its magnetic moment upon magnetization along the symmetry axis and excitation by a weak transverse high-frequency field in the region of parameters where the equilibrium magnetic moment of the nanoparticle and the external static field is noncollinear has been studied. It is shown that as the oblateness increases, the irregularity of the oscillations increases, which at first affects only their amplitude, but then also the time dependence. The intervals of the shape parameter (or frequency), where various nonlinear modes of precession are realized - dynamic bistability, complex spatial attractors and chaos, were revealed using bifurcation diagrams.

Guest Editorial. Cities, Suburbs and Peripheries in Theory and Empirical Research

"In recent years, spatial planning has been subject of debate for researchers who focused on good practices and providing suitable solutions for various issues at the local or regional scale, but also on the poor quality practices, which particularly generate spatial chaos and other negative consequences. The identification and assessment of endogenous dependencies of the implemented spatial management policies require in-depth studies aimed at understanding their nature and consequences. Moreover, the integrated order and spatial development in the urban core area and the suburbs are to be considered when analysing these conditions and dependencies. If we also consider spillover effects and spatial externalities, we must tackle the intensification of problems in spatial management. Therefore, the various aspects of urban development and planning should be approached especially in relation to the economic and social aspects of urban, suburban and rural areas. "

Spatial Chaos in the Airport-Proximate Areas - Case Study of Gdansk Lech Walesa Airport

Abstract The airport may be an opportunity for the development of airport-proximate areas, as well as a source of conflicts and nuisances for stakeholders. From the perspective of spatial order and sustainable development, it is necessary to create a coherent vision of the development and operationalize it via spatial management. This article aims to analyze spatial management in areas proximate to Gdansk Airport in the context of spatial chaos. The analyses are based on 232 local spatial development plans for the period 1996-2020, for 11 selected areas in the vicinity of the Gdansk Lech Walesa Airport, documents obtained from the local government, and open-source data. The research concentrates on the analysis of the functions of areas, spatial chaos, and the threat of potential conflicts. The results demonstrate the spatial chaos in proximate areas of Gdansk Airport. This implies that the decisions made by the authorities responsible for spatial management do not respect spatial order and sustainable development and contribute to spatial chaos.

Correction: Musiaka et al. Spatial Chaos as a Result of War Damage and Post-War Transformations. Example of the Small Town of Węgorzewo. Land 2021, 10, 541

In the original publication [...]

Building blocks that govern spontaneous and programmed pattern formation in pre-compressed bilayers

Surface wrinkling in stiff-film/soft-substrate bilayers is a common phenomenon in biological systems and is increasingly being exploited in thin-film technology. While the onset of surface wrinkling in end-compressed bilayers is well understood, questions remain with regards to the evolution of the wrinkling pattern in the intermediate and deep post-wrinkling regimes, especially when the substrate is strongly pre-compressed. Here, we explore the bifurcation landscape of end-compressed bilayers with strongly pre-compressed substrates, using hyperelastic, plane strain finite-elements and generalized path-following algorithms. After bifurcating from a flat into a sinusoidally wrinkled state, bilayers undergo further n -tupling bifurcations into stable wrinkling patterns of longer wavelength whose periodicity n = { 4 , … , 8 } is a function of overall bilayer length. These five n -tupling wrinkling patterns are shown to be independent localizations of the deformation mode and are accordingly identified as stable ‘building blocks’ that govern the intermediate post-wrinkling regime. Additional end-shortening into the deep post-wrinkling regime then leads to further period doubling and coalescence of the building blocks. Beyond a certain length threshold, a bilayer can form a combinatorial side-by-side arrangement of the five building blocks. In the limit of an infinitely long bilayer, this leads to the phenomenon known as spatial chaos with the emergence of an infinite set of possible wrinkling patterns. In reality, though, the precise side-by-side arrangement of the building blocks is governed by the initial conditions. We show that the morphological evolution of the wrinkling pattern can be programmed by a judicial placement of manufactured dents in the thin film, creating new manufacturing capabilities for textured bilayers.

Dynamics of magnetization of a uniaxial nanoparticle in the region of noncollinear ferromagnetic resonance

Resonance dynamics of the magnetic moment of a uniaxial ellipsoidal nanoparticle under its magnetic biasing along the symmetry axis and excitation by a transverse high-frequency field is studied with the parameters (frequency, magnetic bias field and shape parameter), corresponding to the noncollinear orientation of equilibrium magnetization and the external static field. We revealed the frequency regions where precession becomes nonlinear at a weak alternating field and dynamic bistability, as well as complex spatial attractors and chaos are implemented. Keywords: ellipsoidal nanoparticle, ferromagnetic resonance, static and high-frequency field, nonlinearity, effective anisotropy, bistability, regular and chaotic precession.

Between Architecture and Planning: Urban Design Education in Poland against a Background of Contemporary World Trends

Urban design, as an academic discipline, was born in the 20th century in response to challenges related to the planning, design, and renewal of urbanized areas. Since then, there has been an ongoing debate about the scope, scientific basis, and teaching formula of the discipline. The aim of this article was to assess the formula for teaching urban design at an academic level in Poland, considering global trends in this field. The theoretical framework involved a review of contemporary scientific concepts, which provided the basis for extracting the most popular and well-recognized domains, definitions, and dimensions of urban design. The research results confirm that urban design has permanently taken its place between architecture and urban planning. In Poland, but not only, the elements of both the theory and practice of urban design are dispersed among various master’s degree courses. This is not conducive to strengthening the position of urban design as such, and in Poland, it may be one of the reasons for deepening spatial chaos.

Objective and Subjective Determinants of Neighborhood Satisfaction in the Context of Retrofitting Suburbs

A strong preference for suburban living has led to extensively developed suburbs that need retrofitting by improving their compactness. However, an attempt to make suburban areas more sustainable only by shaping their spatial form, without considering individual demands and preferences, is usually ineffective. The aim of this research is to better understand the factors that are important for suburban neighborhood satisfaction and to determine the relationship between neighborhood satisfaction and both the objective spatial attributes reflecting different levels of spatial chaos and satisfaction with particular neighborhood characteristics. The factor analysis and a linear multiple regression model have revealed that there are four significant subjective factors explaining neighborhood satisfaction, namely: assessed suburban assets, assessed accessibility, assessed walkability, and assessed mental and social attitude towards the neighborhood. Among these, the assessed accessibility is the most important predictor of the neighborhood satisfaction and synthetic indicator of spatial chaos the least significant one. Although the research proved that subjective measures are more important determinants of neighborhood satisfaction, fighting urban sprawl should be based on the interference in both subjective evaluations and objective spatial attributes, since two of the four subjective factors are likely to be strongly influenced by improving accessibility in the process of retrofitting suburbs.

Spatial Chaos as a Result of War Damage and Post-War Transformations. Example of the Small Town of Węgorzewo

World War II’s military activities and the post-war devastation period destroyed many European cities and towns. One of the areas that was struck the most was former East Prussia, currently located in Poland and the Kaliningrad Region (the Russian Federation). In addition to the destruction of cities, which are strategically and economically important, small towns have also suffered. An example of such a town is Węgorzewo, where the scale of destruction of the pre-war urban tissue exceeded 80%, and the old town’s built-up area practically ceased to exist. This town magnifies most of the processes and spatial problems characteristic of Central and Eastern Europe’s towns of the “metamorphic” type. Post-war zoning during the Polish People’s Republic period, in the spirit of constructing a socialist town and bypassing the original spatial arrangement, brought about irreversible changes in the urban tissue. This was reflected in the break with the town’s original layout and the creation of modernist buildings. The changes were solidified or even deepened during the economic and political transition of the 1990s in Poland. Today, decades after the end of World War II, despite taking corrective measures, the town is still facing the problem of spatial chaos. Its morphological and physiognomic manifestations in the lack of a central public space, the loss of its historic character, the disharmonization of the urban landscape, and the dispersed development are the main subjects of this article’s analysis. This study uses a diverse methodological apparatus consisting of an analysis of the town’s morphological transformations, an analysis of the physiognomy of the urban landscape and architecture, in situ studies, and an analysis of municipal documents and expert interviews. In the discussion, the study results are embedded in the context of the cases of other European cities and towns. The conclusions indicate the risks to the formation of spatial order in Węgorzewo and possible paths of action.

Appearance of Temporal and Spatial Chaos in an Ecological System: A Mathematical Modeling Study.

The ecological theory of species interactions rests largely on the competition, interference, and predator–prey models. In this paper, we propose and investigate a three-species predator–prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington–DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.