The application of topological geometry to the architectural concept design process in the flow of digitalization

PurposeThe paper aims to research the applications of topological geometry to the architectural concept design process and their combination with the modern digital technology to find novel architectural spaces and forms which are dynamic, easily adaptable to the context and surroundings.Design/methodology/approachThe article uses the method of studying the existing literature on topological geometry and architectural design theory including design thinking, architectural design methods and architectural compositions to analyze and compare them with architectural practices and suggest new topological design tools and methods. Moreover, the paper tests the proposals with a number of preliminary design research experiments. In addition, graphic design software, parametric design, building information modeling (BIM) and digital development trends in architecture were explored and experienced to reveal the application potential of topological design thinking and methods in the trend of architectural digitization.FindingsThe paper has analyzed, synthesized and systematized the basic theories of topological geometry in order to clarify their applications in the architectural concept design process. On that basis, the paper proposes a novel topological design thinking and method for finding rich diversified architectural ideas and forms based on original invariant design constraints. Finally, the paper clarifies the combination as well as the mutual, motivating relationship between topological geometry and modern digital technologies when applied to architectural design.Originality/valueThe research contributes a novel design thinking and method based on topological geometry combined with modern digital technology to the architectural design theory. It will be a valuable tool capable of suggesting architects how to think and innovate in architecture in the era of industrial revolution 4.0.

Topologically protected optical signal processing using parity–time-symmetric oscillation quenching

The concept of topology is universally observed in various physical objects when the objects can be described by geometric structures. Although a representative example is the knotted geometry of wavefunctions in reciprocal space for quantum Hall family and topological insulators, topological states have also been defined for other physical quantities, such as topologically distinct Fermi surfaces and enhanced lattice degrees of freedom in hyperbolic geometry. Here, we investigate a different class of topological states – topological geometry of dynamical state trajectories – in non-Hermitian and nonlinear optical dynamics, revealing topologically protected oscillation quenching mechanisms determined by parity–time (PT) symmetry. For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death. We then show that these PT-symmetric quenching mechanisms lead to immunity against temporal perturbations, enabling the applications of topologically protected laser modulation and rectification. The observed connection between the topological geometry of dynamical states, oscillation quenching phenomena in dynamical systems theory, and PT symmetry provides a powerful toolkit for noise-immune signal processing.

Comparison of the Interface-Capturing Behavior between LSM and MCLS

Numerical simulation of the moving interface is widely investigated in the fields of two-phase flow, crystal growth, molten metal casting and so on. To simulate accurately and quickly motion state of the moving interface, two types of interface-capturing method, LSM (level set method) and MCLS (mass-conserving LSM coupled with VOF (volume of fluid)), were comparatively analysed and studied. Two kinds of moving interface, rotation motion of Zaleska slotted disk interface and shearing deformation of the circle interface, were simulated. The level set advection equation was solved with IATVD (the characteristic integral-averaging finite volume method), RK-WENO (the third order Runge-Kutta method with WENO (weighted essentially non-oscillatory)), or the low order method, respectively. The level set function was re-initialized with modified Godunov method. Computation was implemented in different size mesh. When it is independent with mesh size, results show that the high order method, IATVD and RK-WENO, can get higher computing accuracy in LSM without topological geometry change. But computing time cost of RK-WENO is much greater than that of IATVD. For the low order method, LSM captures the moving interface in bad, however, MCLS’s numerical result is very good. But computing time cost of MCLS is much and much greater than that of LSM. For interface-capturing with topological geometry change, these two high order methods all can not capture the moving interface in good in LSM. Nevertheless, the resulting interfaces all are same as original interface in MCLS. These indicate that an appropriate numerical method and interface-capturing method can be chosen to accurately and quickly capture the related moving interface.

Station Deployment of Workspace Measuring and Positioning System Based on Multi-Objective Genetic Algorithm

Workspace measuring and positioning system (wMPS) is a kind of large-scale and multi-station intersection system, of which the station layout optimization is a common but important problem. Station optimal topological geometry based on genetic algorithm was proposed in this paper. Firstly, the positioning error, coverage area and cost were taken as objectives to establish the multi-objective optimization function. Secondly, genetic algorithm optimization process was established according to multi-objective function. Thirdly, simulation analysis for layout optimization algorithm of 2-4 stations was performed. The results show that the proposed method is able to quickly converge to optimal solutions, have good adaptability and improve wMPS measuring performance as well.

Influence and Application of Topological Geometry in Architectural Design

Topology geometry was established in the nineteenth century. It has long been widely used in architectural design. This article makes a brief introduction of topology geometry, discusses the main research objectives and the spatial characteristics in topology, and takes some good cases in architectural design.

Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition

SUMMARYThis paper introduces the mathematical logical proposition into kinematics and presents a novel method for topological design and representation of mechanisms. The six-value non-classical logical matrix in three orders is proposed to represent spatial basic motions, relations, and selection of moving reference frame. The combinatorial logical sets of mechanisms are built and axiomatized to analyze serial–parallel hybrid mechanisms. In accordance to the logical relations, the mapping between topological arrangement and topological geometry is developed, and algorithm of decomposition synthesis is presented. Furthermore, the higher dimensional topological arrangement of multi-loop hybrid mechanism can be obtained by mapping of higher dimensional geometry. At last, four typical examples are developed to illustrate application of method of logical proposition in topological design of mechanisms. The method is helpful for topological design and analysis of multi-loop hybrid mechanisms.