Theoretical Morphology of Fossil Cephalopods: Geometry and Hydrostatics of Compressed and Depressed Shells

Cephalopod理论形态学涉及数学 平面螺旋壳几何的表征。 这样的分析， 在促进头足类化石的研究方面发挥了重要作用 适应和演变，特别是在与 活动物的流体静力学特性。 但这 这种方法的局限性在于它只适用于炮弹 具有圆形螺纹横截面。 中描述的研究 这个建议将通过发展方程来消除这个缺点 用于生成曲线面积和其他关键几何参数， 压缩和凹陷的外壳。 此外，这项工作将 纠正了古生物学家使用的方法中的不一致之处， 评估头足类化石的稳定性和方向性。 的 新的程序将用于评估的影响， 壳体几何形状在浮力、方向和 在更宽的壳体形状范围内的流体静力学稳定性， 在过去可以实现。 目标是确定如何 壳体压缩和凹陷影响流体静力学性质 的shell。 这项工作的结果将大大改善 了解头足类化石的生活习性和古生态学，以及 将使流体力学、运动学、 以及其他头足类动物适应和进化的领域。

Cephalopod theoretical morphology involves mathematical characterization of planispiral shell geometry. Such analysis has been instrumental in facilitating research on fossil cephalpood adaptation and evolution, particularly in matters relating to the hydrostatic properties of the living animals. However, this approach is handicapped by its strict applicability only to shells with circular whorl cross sections. The research described in this proposal will remove this shortcoming by developing equations for generating curve area and other key geometric parameters of compressed and depressed shells. In addition, this work will correct inconsistencies in the methods used by paleontologists to evaluate stability and orientation of fossil cephalopods. The new procedures will then be used to evaluate the effects of variation in shell geometry on buoyancy, orientation, and hydrostatic stability over a much wider range of shell form than could be achieved in the past. The objective is to determine how shell compression and depression influence hydrostatic properties of the shell. The results of this work will substantially improve knowledge of fossil cephalopod life habits and paleoecology, and will make possible much needed work in hydrodynamics, locomotion, and other areas of cephalopod adaptation and evolution.