Terms Of Geometric Constraints Research Articles

A study on the dynamic structural behavior of Olympic sabres

Sabres used in Olympic fencing are subject to severe elastic deformations during matches and training sessions. Even though strict rules for their manufacturing are prescribed by the international fencing federation, with requirements in terms of geometrical constraints and material (steel) properties, nonetheless frequent unexpected ruptures are observed. These may cause injuries to the fencers, and involve the replacement of the blade. In this study an experimental-numerical approach is adopted to investigate the underlying failure mechanisms. To this purpose, several attacks, “bouts” in fencing, were live filmed during actual practice with digital cameras and a trajectory tracking analysis was performed on the most critical of them, taking advantage of markers fixed on the blades at different positions. The post-processed data were subsequently used as boundary conditions of a 3D finite element model of the blade. Running a non-linear transient analysis, global and local quantities such as maximum stored elastic energy, stress and strain states, strain rates and possible permanent plastic strains were evaluated. A validation of the FE model with experiments was also carried out. From the critical analysis of experimental and numerical results it was possible to speculate about the influence of materials and dynamic related effects on the structural behavior of the blade. Eventually, hypotheses on fracture mechanisms were formulated.

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.

Geometric characteristics of planar quintic Pythagorean-hodograph curves

This study examines necessary and sufficient conditions for a planar quintic Bézier curve to be a Pythagorean-hodograph (PH) curve. Quintic PH curves can be categorized into two classes according to the representation of their derivatives. While the first class has been studied by Farouki (1994) to be a family of regular curves already, a more succinct proof by introducing auxiliary control points is provided in this paper. Geometric characteristics of the second class of quintic PH curves are also studied. The key technique to simplify the discussion is to represent a planar Bézier curve with a complex polynomial in Bernstein form. Benefiting from such complex expression, algebraic characteristics of quintic PH curves can be described by nonlinear complex systems with respect to control points. By treating these systems with geometric methods, conditions for a quintic planar curve to be a PH curve can be described in terms of geometric constraints on its control polygon. Furthermore, we provide methods for the construction of the second class of quintic PH curves. In particular, parameter values of cusps can be explicitly determined in advance for irregular curves.

Active contours textural and inhomogeneous object extraction

A new selective segmentation active contour model is proposed in this paper that embeds an enhanced image information. By utilizing the average image of channels (AIC), which handles texture and noise, our model is capable to selectively segment and capture objects with nonuniform features. Moreover, the AIC is fitted with linear functions which are updated regularly to accurately guide the level set function to handle nonconstant intensities. Furthermore, we employ prior information in terms of geometrical constraints which work in alliance with image information to capture objects with intensity inhomogeneity. Experiments show that the proposed method achieves better results than the latest selective segmentation models. In addition, our approach maintains the performance on some hard real and synthetic color images.

Seismic Image Restoration Using Nonlinear Least Squares Shape Optimization

In this article we present a new method for seismic image restoration. When observed, a seismic image is the result of an initial deposit system that has been transformed by a set of successive geological deformations (flexures, fault slip, etc) that occurred over a large period of time. The goal of seismic restoration consists in inverting the deformations to provide a resulting image that depicts the geological deposit system as it was in a previous state. Providing a tool that quickly generates restored images helps the geophysicists to recognize geological features that may be too strongly altered in the observed image.The proposed approach is based on a minimization process that expresses geological deformations in terms of geometrical constraints. We use a quickly converging Gauss-Newton approach to solve the system.We provide results to illustrate the seismic image restoration process on real data and present how the restored version can be used in a geological interpretation framework.

Curvature Effect on the Structure of Phospholipid Bilayers

High-resolution small-angle X-ray scattering (SAXS), complemented by small-angle neutron scattering (SANS) and dynamic light scattering (DLS) experiments, was used to study the effect of curvature on the bilayer structure of dioleoyl-phosphatidylcholine (DOPC) and dioleoyl-phosphatidylserine (DOPS) unilamellar vesicles (ULVs). Bilayer curvature, as a result of finite vesicle size, was varied as a function of vesicle radius and determined by DLS and SANS measurements. Unilamellarity of large DOPC ULVs was achieved by the addition of small amounts (up to 4 mol %) of the charged lipid, DOPS. A comparison of SANS data over the range of 0.02 < q <0.2 A-1 indicated no change in the overall bilayer thickness as a function of ULV diameter (620 to 1840 A). SANS data were corroborated by high-resolution (0.06 < q <0.6 A-1) SAXS data for the same diameter ULVs and data obtained from planar samples of aligned bilayers. Both the inner and outer leaflets of the bilayer were found to be indistinguishable. This observation agrees well with simple geometric models describing the effect of vesicle curvature. However, 1220-A-diameter pure DOPS ULVs form asymmetric bilayers whose structure can most likely be rationalized in terms of geometrical constraints coupled with electrostatic interactions, rather than curvature alone.

Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases

Bi-stable chemical systems are the basic building blocks for intracellular memory and cell fate decision circuits. These circuits are built from molecules, which are present at low copy numbers and are slowly diffusing in complex intracellular geometries. The stochastic reaction-diffusion kinetics of a double-negative feedback system and a MAPK phosphorylation-dephosphorylation system is analysed with Monte-Carlo simulations of the reaction-diffusion master equation. The results show the geometry of intracellular reaction compartments to be important both for the duration and the locality of biochemical memory. Rules for when the systems lose global hysteresis by spontaneous separation into spatial domains in opposite phases are formulated in terms of geometrical constraints, diffusion rates and attractor escape times. The analysis is facilitated by a new efficient algorithm for exact sampling of the Markov process corresponding to the reaction-diffusion master equation.

Understanding solubilisation using principles of surfactant self-assembly as geometrical constraints

Abstract Our aim is to give a short introduction of the use of phase diagrams in order to rationalise general principles of surfactant self-assembly. These can be rationalised in terms of geometrical constraints: volume, surface and curvature. Binary (two components: surfactant and water) and ternary systems (surfactants, water, oil) are considered separately. Models for solubilisation, to be understood within the general principles and not as tabulated data, are presented. Finally, some examples of application of solubilisation in formulation are given. To cite this article: F. Testard, T. Zemb, C. R. Geoscience 334 (2002) 649–663.

Geometric control of redox level in tetranuclear manganese and cobalt systems

A tetranucleating macrocyclic ligand derived from [2+2] Schiff-base condensation of 2,6-diformyl-4-methylphenol and 1,5-diaminopentan-3-ol was used to prepare a series of localised mixed-valence cobalt and manganese complexes. X-ray crystallographic structure analyses of one Co(II) 4 complex, two Mn(II) 2Mn(III) 2 and two Co(II)Co(III) 3 complexes are presented. The observed redox levels are accounted for in terms of geometric constraints transmitted from one metal ion to the next through the ligand framework, providing a basis for cooperative control of redox processes.

Proof Nets and the Complexity of Processing Center Embedded Constructions

This paper shows how proof nets can be used to formalize the notion of ’’incomplete dependency‘‘ used in psycholinguistic theories of the unacceptability of center embedded constructions. Such theories of human language processing can usually be restated in terms of geometrical constraints on proof nets. The paper ends with a discussion of the relationship between these constraints and incremental semantic interpretation.

Constituent units and framework conformations in zeolite networks

The building units of known zeolite networks have been reinvestigated and related to the framework density. Only a relatively small number of four-connected nets, which can be generated readily from observed constituent units, are “permissible” zeolite networks. Criteria for gauging the “permissibility” of zeolite-type networks in terms of geometrical constraints caused by conformational requirements have been investigated.