Structural Diffusion Model Research Articles

Structural Diffusion Model and Urban Green Innovation Efficiency—A Hybrid Study Based on DEA-SBM, NCA, and fsQCA

This research is based on structural theory and innovation diffusion theory, exploring the theoretical foundations and influencing factors of urban green innovation to provide theoretical support for the realization of the world’s sustainable development goals (SDGs). By using the methods of Data Envelopment Analysis with Slacks-Based Measure (DEA) non-expected model, Necessary Condition Analysis of Research Methods (NCA), and Fuzzy Set Qualitative Comparative Analysis (fsQCA) in combination, the research analyzes the variables influencing the capability of urban green innovation. The study finds that the level of urban culture and absorptive capacity are necessary conditions for urban green innovation, with urban absorptive capacity having a high level of influence. The main paths for urban green innovation are a comprehensive cultural innovation path, an open cultural inclusion path, an open participation innovation integration path, and an outcome transformation to drive the innovation path. In addition, the research discovered patterns of cultural influence that go beyond institutional and resource-based structural factors, subject action processes, and transformation models guided by absorption and sustainable participation. The research results have important significance for understanding the driving factors and promotion paths of urban green innovation, providing empirical evidence for the realization of the world’s SDGs.

NON-FICKIAN DIFFUSION IN TIME–SPACE FLUCTUATING DIFFUSIVITY LANDSCAPES: FROM SUPERFAST TO ULTRASLOW

In this study, the local time and space structural derivative diffusion model is introduced to describe non-Fickian diffusion in heterogeneous media from ultraslow to superfast. Its equivalent heterogeneous diffusion process (HDP) model with time and space-dependent diffusion coefficient is also given. The connection and difference between the proposed model and the existing HDP models are compared. Different types of diffusion processes can be captured by selecting proper structural functions in the structural derivative model, which is determined based on the concentration of tracers, mean squared displacement (MSD) and diffusion coefficient of the heterogeneous media. The dynamics of the free cooling granular gases with constant restitution coefficient and velocity-dependent restitution coefficient is investigated to test the proposed model. The results show that the diffusion law of the granular particles is not uniform for the short and long-time scales, but one uniform diffusion law derived from the proposed model can well fit the data in different time scales. The patterns of the time-dependent diffusion coefficient are also simulated to deeply understand the complicated non-Fickian diffusion in complex system.

A Survey of Models of Ultraslow Diffusion in Heterogeneous Materials

Ultraslow diffusion is characterized by a logarithmic growth of the mean squared displacement (MSD) as a function of time. It occurs in complex arrangements of molecules, microbes, and many-body systems. This paper reviews mechanical models for ultraslow diffusion in heterogeneous media from both macroscopic and microscopic perspectives. Macroscopic models are typically formulated in terms of a diffusion equation that employs noninteger order derivatives (distributed order, structural, and comb models (CM)) or employs a diffusion coefficient that is a function of space or time. Microscopic models are usually based on the continuous time random walk (CTRW) theory, but use a weighted logarithmic function as the limiting formula of the waiting time density. The similarities and differences between these models are analyzed and compared with each other. The corresponding MSD in each case is tabulated and discussed from the perspectives of the underlying assumptions and of real-world applications in heterogeneous materials. It is noted that the CMs can be considered as a type of two-dimensional distributed order fractional derivative model (DFDM), and that the structural derivative models (SDMs) generalize the DFDMs. The heterogeneous diffusion process model (HDPM) with time-dependent diffusivity can be rewritten to a local structural derivative diffusion model mathematically. The ergodic properties, aging effect, and velocity autocorrelation for the ultraslow diffusion models are also briefly discussed.

A spatial structural derivative model for the characterization of superfast diffusion/dispersion in porous media

Many theoretical and experimental results show that anomalous diffusion/dispersion occurs in porous media. To exactly solve anomalously fast dispersion, we introduce a structural derivative diffusion model to present superfast diffusion via a logarithmic structural function in space. The fundamental solution of the diffusion model is a form of log-normal distribution, and the corresponding analytical mean squared displacement grows like et/β2, 0<β<1. Compared with the existing models, the proposed model is more effective and accurate in fitting experimental data.

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag–Leffler function as the structural function, in which the MSD is a function of inverse Mittag–Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag–Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

Sorption kinetics of eight gases on a carbon molecular sieve at elevated pressure

The sorption kinetics of eight different molecules (O 2, N 2, Ar, CO, CO 2, SO 2, CH 4 and H 2) on a carbon molecular sieve was studied over a wide range of pressures up to 15 atm by using a volumetric method. The acentric factor was suggested as a potential factor to estimate the relative sorption rate. Since the apparent time constants of all the components showed much stronger dependence of pressure than those expected by the traditional Darken relation and the structural diffusion model, new models with the diffusion relation at the supercritical condition was proposed to predict the kinetic behaviors in the micropores. The proposed model successfully predicted the apparent time constant up to high pressure. In addition, the semi-empirical model that combined acentric factor with the proposed model was able to predict the strong pressure dependence accurately. However, since the strong adsorbates, CO 2 and SO 2, showed two-stage kinetic behavior with pressure, which was different from that of the other adsorbates. The kinetic behaviors of these molecules could be predicted by using two different sorption models.

Modelling the structure factors and pair distribution functions of amorphous germanium, silicon and carbon

We present the results of calculations of the static structure factor S( k) and the pair distribution function g( r) of the tetrahedral amorphous semiconductors germanium, silicon and carbon using the structural diffusion model (SDM). The results obtained with the SDM for S( k) and g( r) are of comparable quality with those obtained by the unconstrained Reverse Monte Carlo simulations and existing ab initio molecular dynamics simulations for these systems. We have found that g( r) exhibits a small peak, or shoulder, a weak remnant of the prominent third neighbour peak present in the crystalline phase of these systems. This feature has been experimentally found to be present in recently reported high energy X-ray experiments of amorphous silicon (Phys. Rev. B 60 (1999) 13520), as well as in the previous X-ray diffraction of as-evaporated amorphous germanium (Phys. Rev. B 50 (1994) 539).

Consistent and accurate scattering functions for liquids. Comment on calculations based on lattice structure models

The diffuse lattice model for liquid structure, due to Prins, produces certain lattice expansion representations of the scattering function S( k). These are compared with modified expansions derived from consideration of more general spatial random processes, in particular structural diffusion. The latter expansions are free from limitations of accuracy and inconsistency inherent in the former. Numerical results from the structural diffusion model are compared with recent calculations based on the Prins model.

Atomic ordering in liquid Si and Ge by structural diffusion model calculations

A semi-empirical model for the atomic-scale structure of liquid Si and Ge has been constructed on the basis of atomic arrangements with the structure of the normal and high-pressure phases of solid Si and Ge. It has been found that liquid Si and Ge have quite similar atomic orderings, exhibiting the local tetrahedral features of the considered solid phases of Si and Ge where the features of the high-pressure phase predominate over those of the normal phase. The present model picture has been found to account well for the peculiar character of the solid-liquid phase transition in Si and Ge.

Atomic pair correlations in Lennard-Jones fluids: Analysis in terms of structural diffusion models

We present an analysis of pair correlation data of a Lennard-Jones fluid (argon), covering a wide range of thermodynamic states, in terms of structural diffusion (SD) models. These are based on the notion of a locally observed ordered structure and of spatial disorder as an outcome of a random spatial process. A general recipe is developed for analysing structural data by such models. First, we analyse fluid argon in terms of the simple SD model (SDM1). Nine lattices are chosen for the description of the local order in the fluid. It is found that close packed lattices are better suited for describing the high density fluid structure while open lattices are better suited for the description of the low density fluid. The SDM parameters obtained by constrained optimization describe the dependence of the pair correlation on density and temperature, and constitute a structural map of the fluid in the (ρ, T) plane. Two possible ways are presented for improving the fitting of g(r) data: (1) distortion of a chosen symmetric lattice (FCC in our case) by varying the basic cell angles and optimizing within the SDM1. It is found that the higher symmetry lattices, BCC and FCC, give the best fitting to the experimental g(r); (2) use of an extended version of the model (SDM2) that enables us to obtain a refined fitting through a built-in contraction function, f(r). A simple choice for f(r) in the model expression of g(r), applied to the four most dense lattices, gives an improved fit for high densities. The best results are obtained with the hcp lattice.

Structural diffusion model calculations of the pair distribution function and structure factor of BCC-like amorphous systems

The Structural Diffusion Model (SDM) has been used to calculate the pair distribution, function, g(r), and the structure factor, S(k), of three amorphous systems whose parent crystallographic structure is bcc, namely Na, Rb and Cr. With the choice of local lattice structure made in this work, the agreement between the calculated and the simulated g(r) (Na, Rb) and experimental S(k) (Cr) are reasonably good. It is very interesting to point out that the distorted bcc lattice, chosen for these calculations, is the same as the distorted fcc lattice used in previous work for SDM calculations of amorphous systems whose parent crystallographic structure is fcc.

Structural diffusion model calculations of the pair distribution function of aluminium: From the liquid to the amorphous phase

We present the results of calculations - within the structural diffusion model - of the pair distribution function of aluminium at six different temperatures spanning both the liquid and amorphous phases. We find that the temperature dependence of the logarithm of the structural diffusion coefficient is linear.

Structural diffusion model calculations of the pair distribution function and structure factors for a class of amorphous systems

We have used the Structural Diffusion Model (SDM) to calculate the pair distribution function, g( r), and the structure factor, S( k), of three amorphous systems whose parent crystallographic structure is fcc, namely Fe, Co, and Ni. With the choice of local lattice structure made in this work, the agreement between the calculated and experimental g( r), and S( k), is reasonably good. We suggest that the most promising procedure to choose the local lattice for SDM calculation of the amorphous solids studied in this work is to start with the fcc crystallographic unit cell, which is then distorted by keeping bond lengths and two of the internal angles fixed. The value of the third internal angle leading to the local lattice structure used in our calculations is β = 5π 13 .

Constraints imposed by S (k)-g (r) relationship on general models of condensed matter structure

The positivity of the structure factor implies that the pair distribution function can be represented as an infinite sum of characteristic functions of probability distributions. The structural diffusion model is an example of such a representation. The empirically determined parameters specifying the radial distribution function characterize it in terms of two partial structures, a large and a small scale structure of the medium.

The Radial Distribution Function of Supercooled Liquids and Amorphous Solids in the Structural Diffusion Model*

The Radial Distribution Function of Supercooled Liquids and Amorphous Solids in the Structural Diffusion Model*

Quasicrystalline structural diffusion in amorphous systems

The representation of aperiodic, globally ordered, structures by means of hyperlattices is utilized in a general theory of random spatial processes to obtain an extended structural diffusion model of disordered systems. Two characteristic parameters of the model, determining the spatial rate of decay of coherence between local structures, lead to a distinction between two extreme types of disordered systems: (1) normal liquids and glasses and (2) disordered quasicrystals whose bond orientations and lengths are preserved over macroscopic distances. A continuous range of disordered phases exists between the two extremes. With a proper choice of the local structure, the model offers a concise description of pair distributions and structure factors of condensed disordered phases.

Mean Square Deviations of Interatomic Distances in Liquid Carbon Tetrachloride

Abstract In simulating the X-ray scattering intensity of liquid carbon tetrachloride, the structural diffusion model for the bcc local structure has been refined by formulating the mean square deviations of interatomic distances by dividing them into two parts, namely, translational and rotational contributions. By this treatment, the simulation has not been improved in comparison with the modified Prins relation, but the description of the motion of carbon tetrachloride molecules in the liquid becomes clear. The degree of depolarization of the ν1 Raman line is well accounted for by the use of the translational mean square deviations determined.

A model for structural recombination in tellurite glasses

The results of a neutron diffraction study on the short-range order in the TeO2-Li2O glassy system are presented. On the basis of the obtained atomic radial distribution function a model for structural recombination in TeO4 tetrahedra for tellurite glasses is proposed. This model takes into account the influence of the modifier and the free-electron pair of the Te atom in TeO4 polyhedra. The limits of applicability to this system of the modified structural diffusion model and the model proposed are established.