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Many cities of various types are distributed in the large area of mountainous regions in China. In these cities, there are acute contradictions between man and earth. Considering that the space growth mode of mountainous cities is widely different from that of flatland cities, the fractal method was adopted in the research aimed at demarcating the urban growth boundary of mountainous cities. The fractal features of the investigated mountainous cities in space were figured out via inference from their function, dimension, region, grade, and environment, and the fractal mode and conceptual framework of urban growth boundary of Qin-Ba mountainous region were constructed according to some concepts and methods such as fractal dimension, fractal network, and fractal order. In the research, the traditional urban growth boundary form-was decomposed into scattered points (point form), paths (linear form), and patches (plane form) to form the fractal theory units for the research of urban growth boundary, and the leading idea, procedure, and control method for “fractal demarcation of urban growth boundary” were established to provide strategies for demarcation of urban space growth boundary of Qin-Ba mountainous region.

Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer‐aided design (CAD) and computer‐aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to generate the necessary toolpath information. So this workflow cannot be applied for a fractal object. In this paper, to realize the fabrication of a fractal represented object by the LM technology, a methodology is proposed.

In the proposed methodology, a slab grid is generated in each layer of the object and it consists of a number of pixels. The interior property (corresponding to the fractal object) of each pixel in the slab grid is checked so that slab models of the fractal are created. The boundary of each slab is traced and refined so that the toolpath of the object can be generated from these boundaries.

Applying the proposed methodology, the LM toolpath information can be extracted from the mathematical model of the fractal and the tessellating or slicing processes are not needed to be performed. The problem of representing a fractal in a CAD platform can be eliminated.

The proposed methodology can be applied to iterative function system (IFS) or complex fractal. However, for some fractals constructed from more than one kind of fractal objects, such as multi‐IFS fractals, the methodology must be further developed.

The proposed methodology is a novel development for realizing the fabrication of fractal objects by the LM technology.

In this paper, the influence of fractal interface geometry to the evolution of the friction mechanism is studied. The paper is based on fractal approaches for the modeling of the multiscale self‐affine topography of these interfaces. More specifically, these approaches are based on scale‐independent parameters such as the fractal dimension. Here, friction between rough surfaces is assumed to be the result of the gradual plastification of the fractal interface asperities. In order to study the resulting highly nonlinear problem a variational formulation is used in order to describe contact between the interfaces. The numerical method used here leads to the successive solution of quadratic optimization problems. Finally, structures with different fractal interfaces are analyzed in order to obtain results for the relation between the fractal dimension and the overall response of the structures.

The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.

The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.

The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.

The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.

We live in organizations addicted to problematic narratives. My purpose is to develop intelligent action understandings of how to care for organizations addicted to problematic elevator pitch narratives and one-sided stories by mapping quantum storytelling “Tamara-Land” forces ignored beneath and between them both (Boje, 1995). Tamara-land is the everyday activity of people in organizations chasing stories spatially distributed in different rooms, hallways, buildings that are temporally simultaneous, with materialities that are agential to the telling. For example, in this conference, the immersive theater into Tamara-Land is done in Steel Case open office spaces, as audience decides which actors to follow as they exit each scene. You cannot chase them all, and cannot be everywhere at once in this spacetimemattering. Quantum storytelling does not search for simple word or text messaging tag lines to explain open offices. Quantum storytelling uncovers deep behavior patterns of the spacetimemattering. “Quantum storytelling includes nondiscursive and behavioral aspects embodied in the storyteller’s life, in their living story behavioral-performative agentiality” (Boje, 1995, p. 114) and in nonhuman’s materialism featured in Karen Barad’s (2007) and Anete Strand’s material storytelling work. Quantum storytelling of Tamara-Land mapping at macro scale traces the interplay of people, planet, and profit (aka Triple Bottom Line, 3BL) but does not reduce it to imagined profitability metrics. I will critique 3BL for not proposing any method to measure people and planet first and by default reducing all dimensions to just bottom line profit measures. The consequence is that a runaway, maximizing fractal, known in socioeconomic work as the Taylor–Fayol–Weber rationality or “TFW virus” (Worley, Zardet, Bonnet, & Savall, 2015, pp. 23–24; Savall& Peron, 2015), attains functional structuralism (Alvesson & Spicer, 2012). In quantum storytelling fractal work, it’s “TFW fractal” profiteering that is destroying both planet and people, at an ever-accelerating rate (Boje & Henderson, 2014; Boje, 2015; Henderson & Boje, 2015). My contribution is to propose a different fractal pattern, the Mandelbrot fractal that actually sets limits on runaway fractal appetite. Both the 3BL and the VA techno-digital fractal narrative spiral more and more materials, energy, and people into the risk of an addictive TFW virus pattern, without limit.

The purpose of this paper is to reveal the dynamic contact characteristics of the slip ring. Dynamic contact resistance models considering wear and self-excited were established based on fractal theory.

The effects of tangential velocity, stiffness and damping coefficient on dynamic contact resistance are studied. The relationships between fractal parameters, wear time and contact parameters are revealed.

The results show that the total contact area decreases with the friction coefficient and fractal roughness under the same load. Self-excited vibration occurs at a low speed (less than 0.6 m/s). It transforms from stick-slip motion at 0.4 m/s to pure sliding at 0.5 m/s. A high stiffness makes contact resistance fluctuate violently, while increasing the damping coefficient can suppress the self-excited vibration and reduce the dynamic contact resistance. The fractal contact resistance model considering wear is established based on the fractal parameters models. The validity of the model is verified by the wear tests.

The results have a great significance to study the electrical contact behavior of conductive slip ring.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2023-0300/

The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces considering substrate deformation. Three deformation modes of the asperity of the rough surface are considered, including elastic deformation, elastic–plastic deformation and full plastic deformation.

The influences of contact load, fractal dimension and fractal roughness on the TCC of the rough surface were studied.

The results show that the TCC of the rough surface increases with the increase of contact load. When D > 2.5, the larger the fractal dimension, the higher the increased rate of the TCC of the rough surface with the increase of contact load. The TCC of the rough surface increases with the increase of fractal dimension and decreases with the increase of fractal roughness. The TCC of the rough surface can be achieved by selecting a contact surface with roughness.

A fractal model of TCC of rough surfaces considering substrate deformation was established in this study. The achievements of this study provide some theoretical basis for the investigation of TCC of rough surfaces.

The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

To the best of the authors’ knowledge, first time these results are presented.

The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.