Reconstruction and normalization of LISA for spatial analysis.

The local indicators of spatial association (LISA) are important measures for spatial autocorrelation analysis. However, there is an inadvertent fault in the mathematical processes of deriving LISA in literature so that the local Moran and Geary indicators do not satisfy the second basic requirement for LISA: the sum of the local indicators is proportional to a global indicator. This paper aims at reconstructing the calculation formulae of the local Moran indexes and Geary coefficients through mathematical derivation and empirical evidence. Two sets of LISAs were clarified by new mathematical reasoning. One set of LISAs is based on non-normalized weights and non-centralized variable (MI1 and GC1), and the other set is based on row normalized weights and standardized variable (MI2 and GC2). The results show that the first set of LISAs satisfy the above-mentioned second requirement, but the second the set cannot. Then, the third set of LISA was proposed and can be treated as canonical forms (MI3 and GC3). This set of LISAs satisfies the second requirement. The observational data of city population and traffic mileage in Beijing-Tianjin-Hebei region of China were employed to verify the theoretical results. This study helps to clarify the misunderstandings about LISAs in the field of geospatial analysis.

Derivation of correlation dimension from spatial autocorrelation functions.

BACKGROUND: Spatial complexity is always associated with spatial autocorrelation. Spatial autocorrelation coefficients including Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation process is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, a scaling exponent such as fractal dimension can be used to compensate for the shortcoming of characteristic length parameters such as Moran's index. METHOD: This paper is devoted to finding an intrinsic relationship between Moran's index and fractal dimension by means of spatial correlation modeling. Using relative step function as spatial contiguity function, we can convert spatial autocorrelation coefficients into spatial autocorrelation functions. RESULT: By decomposition of spatial autocorrelation functions, we can derive the relation between spatial correlation dimension and spatial autocorrelation functions. As results, a series of useful mathematical models are constructed, including the functional relation between Moran's index and fractal parameters. Correlation dimension proved to be a scaling exponent in the spatial correlation equation based on Moran's index. As for empirical analysis, the scaling exponent of spatial autocorrelation of Chinese cities is Dc = 1.3623±0.0358, which is equal to the spatial correlation dimension of the same urban system, D2. The goodness of fit is about R2 = 0.9965. This fractal parameter value suggests weak spatial autocorrelation of Chinese cities. CONCLUSION: A conclusion can be drawn that we can utilize spatial correlation dimension to make deep spatial autocorrelation analysis, and employ spatial autocorrelation functions to make complex spatial autocorrelation analysis. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes. The work may inspire new ideas for spatial modeling and exploration of complex systems such as cities.

Development of novel paper-based supercapacitor electrode material by combining copper-cellulose fibers with polyaniline.

Along with the developing of flexible electronics, there is a strong interest in high performance flexible energy storage materials. As natural carbohydrate polymer, cellulose fibers have potential applications in the area due to their biodegradability and flexibility. However, their conductive and electrochemical properties are impossible to meet the demands of practical applications. In this study, cellulose fibers were combined with polyaniline to develop novel paper-based supercapacitor electrode material. Cellulose fibers were firstly coordinated to Cu(II) and subsequently involved in polymerization of polyaniline. Not only the mass loading of polyaniline was significantly increased, but also an impressive area specific capacitance (2767 mF/cm2 at 1 mA/cm2) was achieved. The developed strategy is efficient, environmentally friendly, and has implications for the development of cellulosic paper-based advanced functional materials.

Innovative modification of cellulose fibers for paper-based electrode materials using metal-organic coordination polymers.

Cellulosic paper-based electrode materials have attracted increasing attention in the field of flexible supercapacitor. As a conductive polymer, polyaniline exhibits high theoretical pseudocapacitive capacitance and has been applied in paper-based electrode materials along with cellulose fibers. However, the stacking of polyaniline usually leads to poor performance of electrodes. In this study, metal-organic coordination polymers of zirconium-alizarin red S and zirconium-phytic acid are applied to modulate the polyaniline layer to obtain high-performance cellulosic paper-based electrode materials. Zirconium hydroxide is firstly loaded on cellulose fibers while alizarin red S and phytic acid are introduced to regulate the morphology of polyaniline through doping and coordination processes. The results show that the introduction of dual coordination polymers is effective to regulate the morphology of polyaniline on cellulose fibers. The performances of the paper-based electrode materials, including electrical conductivity and electrochemistry, are apparently improved. It provides a promising strategy for the potential development of economical and green electrode materials in the conventional paper-making process.

Spatial autocorrelation equation based on Moran's index.

Moran's index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran's index is chiefly a statistical measurement rather than a mathematical model. This paper is devoted to establishing spatial autocorrelation models by means of linear regression analysis. Using standardized vector as independent variable, and spatial weighted vector as dependent variable, we can obtain a set of normalized linear autocorrelation equations based on quadratic form and vector inner product. The inherent structure of the models' parameters are revealed by mathematical derivation. The slope of the equation gives Moran's index, while the intercept indicates the average value of standardized spatial weight variable. The square of the intercept is negatively correlated with the square of Moran's index, but omitting the intercept does not affect the estimation of the slope value. The datasets of a real urban system are taken as an example to verify the reasoning results. A conclusion can be reached that the inner product equation of spatial autocorrelation based on Moran's index is effective. The models extend the function of spatial analysis, and help to understand the boundary values of Moran's index.

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra.

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

High mass loading paper-based electrode material with cellulose fibers under coordination of zirconium oxyhydroxide nanoparticles and sulfosalicylic acid.

With the rapid expansion of the flexible electronics market, it is critical to develop high-performance flexible energy storage electrode materials. Cellulose fibers, which are sustainable, low cost, and flexible, fully meet the requirements of flexible electrode materials, but they are electrically insulating and cause a decrease in energy density. In this study, high-performance paper-based flexible electrode materials (PANI:SSA/Zr-CFs) were prepared with cellulose fibers and polyaniline. A high mass loading of polyaniline was wrapped on zirconia hydroxide-modified cellulose fibers under metal-organic acid coordination through a facile in situ chemical polymerization process. The increase in mass loading of PANI on cellulose fibers not only improves the electrical conductivity but also enhances the area-specific capacitance of the flexible electrodes. The results of electrochemical tests show that the area specific capacitance of the PANI:SSA/Zr-CFs electrode is 4181 mF/cm2 at 1 mA/cm2, which is more than two times higher than that of the electrode with PANI on pristine CFs. This work provides a new strategy for the design and manufacture of high-performance flexible electronic electrodes based on cellulose fibers.

Exploring Spatial Patterns of Interurban Passenger Flows Using Dual Gravity Models.

Geographical gravity models can be employed to quantitatively describe and predict spatial flows, including migration flows, passenger flows, daily commuting flows, etc. However, how to model spatial flows and reveal the structure of urban traffic networks in the case of missing partial data is still a problem to be solved. This paper is devoted to characterizing the interurban passenger flows in the Beijing-Tianjin-Hebei region of China using dual gravity models and Tencent location big data. The method of parameter estimation is the least squares regression. The main results are as follows. First, both the railway and highway passenger flows can be effectively described by dual gravity models. A small part of missing spatial data can be compensated for by predicted values. Second, the fractal properties of traffic flows can be revealed. The railway passenger flows follow the gravity scaling law better than the highway passenger flows. Third, the prediction residuals indicate the changing trend of interurban connections in the study area in recent years. The center of gravity of the spatial dynamics has shifted from the Beijing-Tianjin-Tangshan triangle to the Beijing-Baoding-Shijiazhuang axis. A conclusion can be reached that the dual gravity model is an effective tool for analyzing spatial structures and dynamics of traffic networks and flows. Moreover, the model provides a new approach to estimating the fractal dimensions of traffic networks and spatial flow patterns.

Gravitational scaling analysis on spatial diffusion of COVID-19 in Hubei Province, China.

The spatial diffusion of epidemic disease follows distance decay law in geography and social physics, but the mathematical models of distance decay depend on concrete spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province, China. The modeling approach is to integrate analytical method and experimental method. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and least squares calculation. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observational data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial lockdown and isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of urban gravity (size and distance) should be taken into account to prevent and control epidemic disease.

An analytical process of spatial autocorrelation functions based on Moran's index.

A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary's coefficient and Getis' index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

Utilization of NaP zeolite synthesized with different silicon species and NaAlO2 from coal fly ash for the adsorption of Rhodamine B.

NaP zeolite was successfully synthesized by using various commercial silicon sources and NaAlO2 extracted from coal fly ash as raw materials. Multiple characterization methods were employed to investigate the effect of silicon sources on NaP zeolite. Adsorption performance and mechanism of NaP zeolite for Rhodamine B were surveyed. The product synthesized by fumed SiO2 at n(Na2O)/n(SiO2) = 0.70 presented single spherical morphology with the average grain size of 3.22 µm. The shearing of NaOH resulted in the formation of silicates with different polymerization degrees and silicates occurring in the forms of monomeric, dimeric, trimeric, long-chain, and cyclic oligomers, initiating an improvement in pore structure and morphology. The introduction of dynamic crystallization mode (with the rotating speed of 150 r/min) not only reduced grain size (from 3.22 µm to 1.78 µm) but also shortened crystallization time (from 12 h to 10 h) of NaP-fumed SiO2. NaP zeolite had excellent adsorption performance for Rhodamine B with the removal rate of 98.26%. Adsorption behavior fitted well with pseudo-second-order kinetics and Langmuir isotherm adsorption equations. Adsorption process was endothermic and feasible. NaP zeolite had good regeneration and alkali resistance capacities. Adsorption manners mainly contained pore filling, electrostatic attraction, and hydrogen bonding, focused on physisorption.

Periodic Analysis of Surface Acoustic Wave Resonator with Dimensionally Reduced PDE Model Using COMSOL Code.

Radio-frequency (RF) surface acoustic wave (SAW) resonators used as filters and duplexers are mass-produced and widely used in current mobile phones. With the numerous emergences of the diverse device structure, a universal method used for the accurate and fast simulation of the SAW resonator calls for urgent demand. However, there are too many instances where the behavior of the entire acoustic resonator cannot be characterized rapidly and efficiently due to limitations in the current computer memory and speed. This is especially true for SAW resonators configured with long arrays of inter-digital transducers (IDTs), and we have to resort to a periodic analysis. In this paper, the previously reported generalized partial differential equations (PDE) based on the two-dimensional finite element method (2D-FEM) model is extended to analysis for the periodic structure of the SAW resonator. We present model order reduction (MOR) techniques based on FEM and periodic boundary conditions to achieve a dimensionally reduced PDE model without decreasing the accuracy of computations. Examples of different SAW devices, including the regular SAW, IHP-SAW and TC-SAW resonators, are provided which shows the results of the periodic analysis compared with the experimental results of the actual resonators. The investigation results demonstrate the properties of the proposed methodology and prove its effectiveness and accuracy.

Multifractal scaling analyses of urban street network structure: The cases of twelve megacities in China.

Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory.

Fractal Modeling and Fractal Dimension Description of Urban Morphology.

The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.

New framework of Getis-Ord's indexes associating spatial autocorrelation with interaction.

Spatial autocorrelation and spatial interaction are two important analytical processes for geographical analyses. However, the internal relations between the two types of models have not been brought to light. This paper is devoted to integrating spatial autocorrelation analysis and spatial interaction analysis into a logic framework by means of Getis-Ord's indexes. Based on mathematical derivation and transform, the spatial autocorrelation measurements of Getis-Ord's indexes are reconstructed in a new and simple form. A finding is that the local Getis-Ord's indexes of spatial autocorrelation are equivalent to the rescaled potential energy indexes of spatial interaction theory based on power-law distance decay. The normalized scatterplot is introduced into the spatial analysis based on Getis-Ord's indexes, and the potential energy indexes are proposed as a complementary measurement. The global Getis-Ord's index proved to be the weighted sum of the potential energy indexes and the direct sum of total potential energy. The empirical analysis of the system of Chinese cities are taken as an example to illustrate the effect of the improved methods and measurements. The mathematical framework newly derived from Getis-Ord's work is helpful for further developing the methodology of geographical spatial modeling and quantitative analysis.

Ultrasonic-assisted preparation of highly active Co3O4/MCM-41 adsorbent and its desulfurization performance for low H2S concentration gas.

Co3O4/MCM-41 adsorbents were successfully prepared by ultrasonic assisted impregnation (UAI) and traditional mechanical stirring impregnation (TMI) technologies and characterized by X-ray diffraction (XRD), N2 adsorption desorption, Fourier transform infrared spectra (FT-IR), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and thermogravimetry-differential thermal analysis (TG-DTA). The H2S removal performances for a simulated low H2S concentration gas were investigated in a fixed-bed. The effect of preparation and adsorption conditions on the H2S removal over Co3O4/MCM-41 were systematically examined. The results showed that UAI promotes more and well defined highly dispersed active Co3O4 phase on MCM-41. As compared to the Co3O4/MCM-41-T prepared via TMI, the saturated H2S capacity of Co3O4/MCM-41-U prepared via UAI improved by 33.2%. The desulfurization performance of adsorbents decreased in the order of Co3O4/MCM-41-U > Co3O4/MCM-41-T > MCM-41. The Co3O4/MCM-41-U prepared using Co(NO3)2 concentration of 10%, ultrasonic time of 2 h, calcination temperature of 550 °C and calcination time of 3 h exhibited the best H2S removal efficiency. At adsorption temperature of 25 °C with model gas flowrate of 20 mL min-1, the breakthrough time of Co3O4/MCM-41-U was 10 min, and the saturated H2S capacity and H2S removal rate was 52.6 mg g-1 and 47.8%, respectively.

Ultrahigh-flux (>190,000 L·m-2h-1) separation of oil and water by a robust and durable Cu(OH)2 nanoneedles mesh with inverse wettability.

Single-stage oil/water separation membranes usually suffer from weak chemical stability, susceptible mechanical damage and relatively low permeating flux, and the sophisticated preparation processes also limit their massive utilization. In this work, Cu(OH)2 nanoneedles coated copper mesh (CM) is prepared by simple and eco-friendly anodic oxidation at a current density of 4 mA/cm2 for 6 min, which is the most efficient route reported so far. The mesh exhibits outstanding superhydrophilicity and underwater superoleophobicity towards various oils with contact angles up to 164.9°, achieving superior oil/water separation efficiency of above 99.5% and ultrahigh permeating flux of 191 160 L·m-2h-1 solely driven by gravity. Impressively, the Cu(OH)2/CM demonstrates excellent chemical stability and anti-fouling performance when exposed to acidic and strongly alkaline solutions, saturated NaCl solution and various organic solvents. High durability to withstand mechanical challenges, e.g. high-power sonication and sand abrasion, is experimentally confirmed owing to strong cohesional strength of Cu(OH)2 nanoneedles on CM surface. Importantly, the Cu(OH)2/CM exhibits favorable long-term recyclability with stable microstructure morphologies even after 50 cycles. These distinct advantages endow the Cu(OH)2/CM to be an ideal candidate to efficiently separate oil pollutants from water. The oil/water separation mechanisms are proposed based on the concept of intrusion pressure.

Green Ferrate(VI) for Multiple Treatments of Fracturing Wastewater: Demulsification, Visbreaking, and Chemical Oxygen Demand Removal.

Fracturing wastewater is often highly emulsified, viscous, and has a high chemical oxygen demand (COD), which makes it difficult to treat and recycle. Ferrate(VI) is a green oxidant that has a high redox potential and has been adopted for the efficient oxidation of fracturing wastewater to achieve triple effects: demulsification, visbreaking, and COD removal. Firstly, optimal conditions were identified to build a model for fast and efficient treatment. Secondly, wastewater treatment using ferrate oxidation was investigated via demulsification, visbreaking, and COD removal. Finally, a mechanism for ferrate oxidation was proposed for the three effects using Fourier-transform infrared (FT-IR) spectroscopy and scanning electron microscopy (SEM). The theoretical and experimental data demonstrated that the ferrate oxidation achieved the three desired effects. When ferrate was added, the demulsification efficiency increased from 56.2% to 91.8%, the total viscosity dropped from 1.45 cp to 1.10 cp, and the total removal rate of COD significantly increased to 74.2%. A mechanistic analysis showed that the strongly-oxidizing ferrate easily and efficiently oxidized the O/W interfacial film materials, viscous polymers, and compounds responsible for the COD, which was a promising result for the triple effects.

The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation.

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.

Optimization of crystal growth of sub-micron ZSM-5 zeolite prepared by using Al(OH)3 extracted from fly ash as an aluminum source.

A novel approach was proposed to prepare ZSM-5 zeolite via hydrothermal synthesis by using Al(OH)3, which was extracted from fly ash by a staged treatment, as an aluminum source. The synthesis parameters and crystal growth of ZSM-5 were optimized. The optimization of crystal growth for ZSM-5 was investigated under the effect of organic steric-hindrance agents. The crystal phase and morphology of the ZSM-5 were characterized by X-ray diffractometry and scanning electron microscopy, and the particle size distribution was measured by laser particle-size analyzer. The crystal growth of ZSM-5 under different hydrothermal conditions obeyed the "S" regulation. According to the analysis, the formation of ZSM-5 crystal occurred via four steps: (1) the formation of amorphous aluminosilicate by the condensation of silicate ions and aluminate ions; (2) the particle growth and aggregation of the amorphous aluminosilicate; (3) crystallization and crystal growth of ZSM-5; (4) Gentle growth after the zeolite crystal reaches a certain size. The addition of organic steric hindrance agents resulted in a decrease in grain size and crystal-particle formation with a narrow size distribution. Single-grain dispersion resulted and the micropore volume, mesopore volume, and specific surface areas were improved by the presence of organic steric agents.