Formulation and solution of the classical seashell problem

Summary Despite an extensive scholarly literature dating back to classical times, seashell geometries have hitherto resisted rigorous theoretical analysis, leaving applied scientists to adopt a directionless empirical approach toward classification. The voluminousness of recent palaeontological literature demonstrates the importance of this problem to applied scientists, but in no way reflects corresponding conceptual or theoretical advances beyond the XIX century thinking which was so ably summarized by Sir D’Arcy Wentworh Thompson in 1917. However, in this foundation paper for the newly emerging science of theoretical conchology, unifying theoretical considerations for the first time, permits a rigorous formulation and a complete solution of the problem of biological shell geometries. Shell coilingabout the axis of symmetry can be deduced from first principles using energy considerations associated with incremental growth. The present paper shows that those shell apertures which are incurved (?cowrielike?), outflared (?stromblike?) or even backturned (?Opisthostomoidal?) are merely special cases of a much broader spectrum of ?allowable? energy-efficient growth trajectories (tensile elastic clockspring spirals), many of which were widely used by Cretaceous ammonites. Energy considerations also dictate shell growthalong the axis of symmetry, thus seashell spires can be understood in terms of certain special figures of revolution (M?bius elastic conoids), the better-known coeloconoidal and cyrtoconoidal shell spires being only two special cases arising from a whole class of topologically possible, energy efficient and biologically observed geometries. The ?wires? and ?conoids? of the present paper are instructive conceptual simplifications sufficient for present purposes. A second paper will later deal with generalized tubular surfaces in three dimensions.

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Riassunto Malgrado un’ampia e dotta letteratura che risale ai tempi classici, la geometria delle conchiglie ha resistito fino ad ora ad analisi teoriche rigorose, quindi gli scienziati che si cimentano in questo campo hanno adottato un metodo empirico senza direttiva per quanto riguarda la classificazione. L’abbondanza della recente letteratura paleontologica dimostra l’importanza di questo problema per gli scienziati di questo campo, ma non riflette in alcun modo i corrispondenti progressi concettuali o teorici rispetto al pensiero del diciannovesimo secolo che venne cosí abilmente riassunto da Sir D’Arcy Wentworth Thompson nel 1917. Tuttavia, in questo lavoro fondamentale per la nuova scienza emergente di conchigliologia teorica, l’unificazione delle considerazioni teoriche permette una rigorosa formulazione e una completa soluzione del problema della geometria biologica delle conchiglie. L’avvolgimento delle conchiglieintorno all’asse di simmetria si deduce dai primi princípi usando considerazioni sull’energia associata alla crescita per aumento di dimensioni. Questo lavoro mostra che le aperture delle conchiglie che sono incurvate (di tipo ?cowrie?), allargate verso l’esterno (di tipo ?strombe?) o anche rivoltate all’indietro (di tipo ?opistostomoideo?) sono solamente casi speciali di uno spettro piú ampio di traiettorie di crescita efficienti d’energia ?permesse? (spirali tensili, elastiche a molla d’orologio), molte delle quali vennero estesamente usate dagli ammoniti del Cretaceo. Considerazioni d’energia dettano anche la crescita della conchiglialungo l’asse di simmetria, cosí le spirali delle conchiglie marine possono essere comprese nei termini di certe speciali figure di rivoluzione (conoidi elastici di M?bius), essendo i gusci meglio conosciuti delle conchiglie coeloconoidali e cyrtoconoidali soltanto due casi speciali che derivano da una intera classe di geometria topologicamente possibili, efficienti di energia e biologicamente osservate. I ?fili? e i ?conoidi? di questo lavoro sono istruttive semplificazioni concettuali sufficienti a questo scopo. Un secondo lavoro tratterà successivamente superfici tubolari generalizzate in tre dimensioni.

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Резюме Несмотря на большое количество литературы, до настоящего времени отсутствует строгий теоретический анализ геометрией морских раковин. Многотомность существующей палеонтологической литературы демонстрирует важность этой проблемы для прикладных ученых ине отражает соответствующих концептуальных и теоретических достижений после XIX века, которые были систематизированы Томсоном в 1917 г. Однако в этой фундаментальной работе по теоретической конхиологии были объединены теоретические рассмотрения, которые впервые позволили сформулировать и полностью решить проблему биологических геометрий морских раковин. Свертывание раковин спиралью вокруг оси симметрии можно получить из первых принципов, используя энергетические рассуждения, связанные с дифференциальным ростом. В настоящей статье показывается, что те отверстия раковин, которые являются искривленными, в форме раструба, или даже повернутыми назад, представляют просто частные случаи более широкого спектра ?разрешенных? траекторий роста. Энергетические рассуждения ткаже диктуют рост раковин вдоль оси симметрии, тонкое острие морских раковин можно понять в терминах некоторых специальных фигур вращения. ?Провода? и ?коноиды? настоящей статьи представляют поучительные концептуальные упрощения, достаточные для наших целей. Вторая статья будет посвящена трубчатым поверхностям в трех измерениях.

     

肝组织工程支架的仿生设计与有限元分析

为了解决细胞在细胞支架复合培养中难以植入的问题,提出了一种卷裹型支架.将平面多孔支架采用卷裹的方式成型,使细胞在整个支架内部形成螺旋状三维分布,支架表面的管道结构可使培养液在支架内部渗透,从而提高物质交换效率.提出了一种具有仿生参数的流道设计方案,从肝脏血管铸型中提取血管的形状数据,作为仿生学依据进行流道设计,具体为树状多层分支结构.用此流道结构仿生了动脉、静脉的血液循环功能,并利用多孔材料仿生了毛细血管的渗透功能.建立了不同形状参数的流场分析模型,进行流体与多孔材料的渗流分析.结果表明,仿生设计方案的流场分布最为均匀,且平均流速较高,间接表明营养物质的输送效率最高.该支架能够使细胞呈三维分布,并扩大培养液在支架内的有效分布范围,更好地维持细胞的存活、增殖和迁移,为向组织化方向发展奠定了一定的基础.     

形状记忆合金丝驱动的仿生转动关节臂

提出了动物关节臂的力学模型,讨论了形状记忆合金（ＳＭＡ）和动物骨骼肌生物力学行为的相似性和力学性能的差异．基于仿生学的原理,研究了用ＳＭＡ丝驱动仿生转动关节的技术．研制了能实现ＳＭＡ感知功能的控制电路和ＳＭＡ丝驱动的仿生转动关节驱动器,并用该关节驱动器开发了一个两自由度的微型关节臂,该微型关节臂可用于微型步行机器人和人工假肢．     

柔性翼微型飞行器的稳定特性

为提高微型飞行器(M AV)的抗风扰动飞行稳定性,需要遵循仿生学原理,效仿自然界中的鸟类和昆虫,探讨抗风飞行的新方法。提出了柔性仿生机翼的概念,阐述了其设计思想与工作原理,并导出了大气扰动下柔性机翼气动力的解析表达。为验证柔性仿生机翼的实际性能,设计和制作了柔性仿生机翼M AV原理样机,并在风中进行了飞行试验。试验结果表明:采用柔性机翼能够显著改善有风条件下M AV的飞行品质,突风过载可降低40%左右,大大减弱了大气扰动对飞行的影响,有效提高了M AV的飞行稳定性。     

Isotopic dimension in biology—A counterpart for quantum indeterminism?

Summary We suggest that the random distribution of stable isotopes may act as a contributing factor towards unpredictability and irreproducibility in living systems. In this respect isotopic randomness could act as a counterpart or competitor of the ?standard? quantum-mech cal indeterminism.     

壁虎的动态吸附与壁虎纳米材料仿生学

以壁虎为代表的一类脚底板具有超细绒毛结构的动物具备极强的吸附和脱附能力。这种独特的能力引起科学家的极大关注并逐渐成为研究的热点。与一般的粘附材料（比如胶水）产生的吸附力不同的是,这种吸附力可以在需要时产生或消失（动态吸附）。模拟这种结构的纳米材料具有极高的实用价值。本文以壁虎为例,从化学、物理学、生物学、机械工程学及材料学的角度全方位系统地介绍了壁虎动态吸附理论和基于这种理论在仿生方面研究的最新进展,最终提出本领域研究工作的展望。     

仿生水下机器人的增强学习姿态镇定

针对一类双波动鳍仿生水下机器人的姿态镇定问题,提出一种基于增强学习的自适应PID控制方法.对增强学习自适应PID控制器进行了具体设计,包括PD控制律和基于增强学习的参数自适应方法.基于实际模型参数对偏航角镇定问题进行了仿真试验.结果表明,经过较小次数的学习控制后,仿生水下机器人的偏航角镇定性能得到明显改善,而且能够在短时间内对一般性扰动进行抑制,表现出了较好的适应性.     

A lattice gas model for enzyme kinetics (a correlated walks' theory and variational procedures)

Summary We have shown that, by using a correlated walks' theory or variational procedures, for the lattice gas model we can find for enzyme kinetics some new equations, which in the limit of no interactions between sites reduce to the classical Michaelis-Henri equation. These new equations can be useful for the experimental investigation.     

On the formation of dissipative spatial patterns of charge carriers in biosystems

Summary It is shown that in systems like large aggregates of biological molecules, population inversion of charge carriers, for example as produced by photoexcitation processes, may have competitive advantage beyond critical levels of excitation to produce ordered spatial structures (morphological transitions). In our analysis electromagnetic radiation transfers electrons from bonding states into a continuum of itinerant antibonding states in ap-type doped sample. In this system, in which energy is pumped continuously by an external source, the interplay of collective and dissipative processes can be responsible for the condensation of a self-organized spatially ordered structure. The study we present here is carried out resorting to the powerful nonequilibrium statistical operator method, thus showing that it can be provide a mechano-statistical formalism at the microscopic level for the treatment of Prigogine's synergetic dissipative structures. The authors of this paper have agreed to not receive the proofs for correction     

Modulated Weiner process

Summary We define and develop a novel process, related to stochastic resonance, in which a particle experiences three forces: a constant drift, a zero-mean white noise, and a time-periodic modulation. Upon reaching a threshold, the particle immediately returns to the starting point. The resulting process exhibits multiple maxima in the output power at the modulation frequency as a function of the white-noise variance, multimodal first-passage-time densities, and evidence of phase locking. Our model is an extension of the Gerstein-Mandelbrot model of neuron firing to the case of periodic stimuli, and therefore has applications in neural modeling. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.