具身形态学:基于身体行为的计算性几何

文章从建筑形式的具身性本质出发,分析了多重身体维度下行为规律与建筑空间几何的关联性。文章进一步聚焦计算性几何的范畴,通过对基于数字化技术的行为研究进行综述,对行为规律的“几何化”路径进行了分析。在此基础上,文章通过一系列研究和实践案例,总结出从行为规律逆向推导建筑空间几何的计算性设计方法,并讨论了基于“行为几何”的设计应用场景,拓展了基于建筑与身体关系的形态认知和操作边界。

A framework for quantifying properties of 3-dimensional movement-based signals

Understanding how signal properties are optimized for the reliable transmission of information requires accurate de- scription of the signal in time and space. For movement-based signals where movement is restricted to a single plane, measure- ments from a single viewpoint can be used to consider a range of viewing positions based on simple geometric calculations. However, considerations of signal properties from a range of viewing positions for movements extending into three-dimensions （3D） are more problematic. We present here a new framework that overcomes this limitation, and enables us to quantify the extent to which movement-based signals are view-specific. To illustrate its application, a Jacky lizard tail flick signal was filmed with synchronized cameras and the position of the tail tip digitized for both recordings. Camera aligmnent enabled tl^e construction of a 3D display action pattern profile. We analyzed the profile directly and used it to create a detailed 3D animation. In the virtual environment, we were able to film the same signal from multiple viewing positions and using a computational motion analysis algorithm （gradient detector model） to measure local image velocity in order to predict view dependent differences in signal properties. This approach will enable consideration of a range of questions concerning movement-based signal design and evolu- tion that were previously out of reach [Current Zoology 56 （3）： 327-336, 2010].

A Comparative Study of the Performance of Symmetric and Asymmetric Mixed-conducting Membranes

According to the configuration,mixed-conducting membranes are classified as symmetric membranes and asymmetric membranes consisting of a thin dense layer and a porous support.In this study,these two kinds of SrCo0.4Fe0.5Zr0.1O3-δ oxide-based membranes were systematically compared in terms of oxygen permeability and chemical stability,and their differences were elucidated by means of the theoretical calculation.For the oxygen permeability,the asymmetric membrane was greater than the symmetric membrane due to the significant decrease of bulk diffusion resistance in the thin dense layer of the asymmetric membrane.In regard to the chemical stability,the increase of oxygen partial pressure on the asymmetric membrane surface at CH4 side produced the stable time of over 1032h in partial oxidation of methane at 1123K,while the symmetric membrane was only of 528h.This study demonstrated that the asymmetric membrane was a promising geometrical configuration for the practical application.

Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space

For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.

From a projective invariant to some new properties of algebraic hypersurfaces

Projective invariants are not only important objects in mathematics especially in geometry,but also widely used in many practical applications such as in computer vision and object recognition. In this work,we show a projective invariant named as characteristic number,from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property,two high-dimensional generalizations of Pascal's theorem are given,one establishing the connection of hypersurfaces of distinct degrees,and the other concerned with the intersections of a hypersurface and a simplex.

Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry

In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.

Parameter identification through mode isolation for reaction-diffusion systems on arbitrary geometries

We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many nat- ural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally, we show that in some cases the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally,we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.