Mechanical Principles of a Self-Similar Hierarchical Structure

2009 ◽  
Vol 1188 ◽  
Author(s):  
Huajian Gao
Keyword(s):  
Aspect Ratio ◽  
Hierarchical Structure ◽  
Hierarchical Model ◽  
Characteristic Length ◽  
Hierarchical Structures ◽  
Hierarchical Level ◽  
Multi Scale ◽  
Flaw Tolerance ◽  
Email Address ◽  
Self Similar

AbstractNatural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures. Here we summarize some recent studies on an idealized self-similar hierarchical model of bone and bone-like materials, and discuss mechanical principles of self-similar hierarchy, in particular to show how the characteristic length, aspect ratio and density at each hierarchical level can be selected to achieve flaw tolerance and superior stiffness and toughness across scale. Tel.: (401) 863-2626; Email address:

Multiscale Analysis of Trabecular Bone

2000 ◽  
Author(s):  
Frederic Bouyge ◽  
Iwona Jasiuk
Keyword(s):  
Trabecular Bone ◽  
Elastic Properties ◽  
Hierarchical Structure ◽  
Hierarchical Model ◽  
Multiscale Analysis ◽  
Random Network ◽  
Theoretical Models ◽  
Collagen Fibrils ◽  
Laminated Structure ◽  
Multi Scale

Abstract Bone has a complex hierarchical structure. We study trabecular bone as a multi-scale material. In particular, we distinguish the following scales: nanostructural (collagen fibrils and apatite crystals), microscale (single laminae and laminated structure), mesoscale (random network of struts), and macroscale. We first present experimental observations and an overview of existing theoretical models of bone. Then, we construct a hierarchical model to predict elastic properties of trabecular bone.

Relationships between hierarchical structure and properties in macromolecular systems

1987 ◽  
Vol 45 ◽  
pp. 440-443
Author(s):  
E. Baer
Keyword(s):  
Uniaxial Tension ◽  
Hierarchical Structure ◽  
Inorganic Material ◽  
Hierarchical Structures ◽  
Bone Collagen ◽  
Structure And Properties ◽  
Connective Tissues ◽  
Scale Level ◽  
Fibrous Protein ◽  
Macromolecular Systems

The most advanced macromolecular materials are found in plants and animals, and certainly the connective tissues in mammals are amongst the most advanced macromolecular composites known to mankind. The efficient use of collagen, a fibrous protein, in the design of both soft and hard connective tissues is worthy of comment. Very crudely, in bone collagen serves as a highly efficient binder for the inorganic hydroxyappatite which stiffens the structure. The interactions between the organic fiber of collagen and the inorganic material seem to occur at the nano (scale) level of organization. Epitatic crystallization of the inorganic phase on the fibers has been reported to give a highly anisotropic, stress responsive, structure. Soft connective tissues also have sophisticated oriented hierarchical structures. The collagen fibers are “glued” together by a highly hydrated gel-like proteoglycan matrix. One of the simplest structures of this type is tendon which functions primarily in uniaxial tension as a reinforced elastomeric cable between muscle and bone.

Hierarchical composition in complex object drawing

2019 ◽  
Author(s):  
Michiru Makuuchi
Keyword(s):  
Hierarchical Structure ◽  
Homo Sapiens ◽  
Hierarchical Structures ◽  
Target Object ◽  
Point Of View ◽  
Complex Object ◽  
Complex Objects ◽  
Cognitive Domains ◽  
Adult Participants ◽  
Symbolic Cognition

Symbolic behaviours such as language, music, drawing, dance, etc. are unique to humans and are found universally in every culture on earth1. These behaviours operate in different cognitive domains, but they are commonly characterised as linear sequences of symbols2,3. One of the most prominent features of language is hierarchical structure4, which is also found in music5,6 and mathematics7. Current research attempts to address whether hierarchical structure exists in drawing. When we draw complex objects, such as a face, we draw part by part in a hierarchical manner guided by visual semantic knowledge8. More specifically, we predicted how hierarchical structure emerges in drawing as follows. Although the drawing order of the constituent parts composing the target object is different amongst individuals, some parts will be drawn in succession consistently, thereby forming chunks. These chunks of parts would then be further integrated with other chunks into superordinate chunks, while showing differential affinity amongst chunks. The integration of chunks to an even higher chunk level repeats until finally reaching the full object. We analysed the order of drawing strokes of twenty-two complex objects by twenty-five young healthy adult participants with a cluster analysis9 and demonstrated reasonable hierarchical structures. The results suggest that drawing involves a linear production of symbols with a hierarchical structure. From an evolutionary point of view, we argue that ancient engravings and paintings manifest Homo sapiens’ capability for hierarchical symbolic cognition.

scholarly journals Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

2014 ◽  
Vol 24 (4) ◽  
pp. 043135 ◽  
Author(s):  
Bapun K. Giri ◽  
Chiranjit Mitra ◽  
Prasanta K. Panigrahi ◽  
A. N. Sekar Iyengar
Keyword(s):  
Glow Discharge ◽  
Discharge Plasma ◽  
Glow Discharge Plasma ◽  
Multi Scale ◽  
Self Similar

Numerical Simulation of Flow and Heat Transfer in Rectangular Channel With Different Aspect Ratios

2016 ◽  
Author(s):  
Liu Wenhua ◽  
Mo Yang ◽  
Li Ling ◽  
Qiao Liang ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Characteristic Length ◽  
Rectangular Channel ◽  
Equivalent Diameter ◽  
Correction Coefficient ◽  
Corner Region ◽  
Flow And Heat Transfer ◽  
Aspect Ratios

Turbulent flow and heat transfer in rectangular channel has an important significance in engineering. Conventional approach to caculate Nusselt number of rectangular channel approximately is to take the equivalent diameter as the characteristic length and use the classic circular channel turbulent heat transfer coefficient correlations. However, under these conditions, the caculation error of Nusselt number can reach to 14% and thus this approach can not substantially describe the variation of Nusselt number of rectangular cross-sections with different aspect ratios. Therefore, caculation by using equivalent diameter as the characteristic length in classic experiment formula needs to be corrected. Seven groups of rectangular channel models with different aspect ratios have been studied numerically in this paper. By using standard turbulence model, the flow and heat transfer law of air with varing properties has been studied in 4 different sets of conditions in Reynolds number. The simulation and experimental results are in good agreement. The simulation results show that with the increase of aspect ratio, the cross-sectional average Nusselt number increased, Nusselt number of circumferential wall distributed more evenly and the difference between the infinite plate channel and square channel went up to 25%. The effects of corner region and long\short sides on heat transfer have also been investigated in this paper. Results show that in rectangular channel, heat transfer in corner region is significantly weaker than it in other region. With the increase of aspect ratio, effect on the long side of heat transfer of the short side is gradually reduced, and then eventually eliminates completely in the infinite flat place. Based on the studies above, correction coefficient for rectangular channels with different aspect ratios has been proposed in this paper and the accuracy of the correction coefficient has been varified by numerical simulations. This can reflect the variation of Nusselt number under different aspect ratios more effectively and thus has current significance for project to calculate Nusselt number of heat transfer in rectangular channel.

Perceiving Hierarchical Structures in Nonrepresentational Paintings

1998 ◽  
Vol 16 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Tsion Avital ◽  
Gerald C. Cupchik
Keyword(s):  
Factor Analysis ◽  
Multidimensional Scaling ◽  
Hierarchical Structure ◽  
Hierarchical Structures ◽  
Exploratory Activity ◽  
Affective Responses ◽  
Hierarchical Complexity ◽  
The Hierarchical Structure ◽  
Relative Separation ◽  
Dimension 2

A series of four experiments were conducted to examine viewer perceptions of three sets of five nonrepresentational paintings. Increased complexity was embedded in the hierarchical structure of each set by carefully selecting colors and ordering them in each successive painting according to certain rules of transformation which created hierarchies. Experiment 1 supported the hypothesis that subjects would discern the hierarchical complexity underlying the sets of paintings. In Experiment 2 viewers rated the paintings on collative (complexity, disorder) and affective (pleasing, interesting, tension, and power) scales, and a factor analysis revealed that affective ratings were tied to complexity (Factor 1) but not to disorder (Factor 2). In Experiment 3, a measure of exploratory activity (free looking time) was correlated with complexity (Factor 1) but not with disorder (Factor 2). Multidimensional scaling was used in Experiment 4 to examine perceptions of the paintings seen in pairs. Dimension 1 contrasted Soft with Hard-Edged paintings, while Dimension 2 reflected the relative separation of figure from ground in these paintings. Together these results show that untrained viewers can discern hierarchical complexity in paintings and that this quality stimulates affective responses and exploratory activity.

scholarly journals Fractal structures in freezing brine

2017 ◽  
Vol 826 ◽  
pp. 975-995
Author(s):  
Sergey Alyaev ◽  
Eirik Keilegavlen ◽  
Jan Martin Nordbotten ◽  
Iuliu Sorin Pop
Keyword(s):  
Characteristic Length ◽  
Complex Problem ◽  
Rate Of Change ◽  
Critical Threshold ◽  
Fractal Structures ◽  
Primary Interest ◽  
External Temperature ◽  
Self Similar ◽  
Salt Diffusion ◽  
Heuristic Analysis

The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary emphasis is on the interaction between ice growth and salt diffusion, subject to external forcing provided by temperature. Within this setting two freezing regimes are identified, depending on the rate of change of the temperature: a slow freezing regime where a continuous ice domain is formed; and a fast freezing regime where recurrent nucleation appears within the fluid domain. The second regime is of primary interest, as it leads to fractal-like ice structures. We analyse the critical threshold between the slow and fast regimes by identifying the explicit rates of external temperature control that lead to self-similar salt-concentration profiles in the fluid domains. Subsequent heuristic analysis provides estimates of the characteristic length scales of the fluid domains depending on the time-variation of the temperature. The analysis is confirmed by numerical simulations.

Hierarchical Structure Enhances and Tunes the Damping Behavior of Load-Bearing Biological Materials

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Mahan Qwamizadeh ◽  
Pan Liu ◽  
Zuoqi Zhang ◽  
Kun Zhou ◽  
Yong Wei Zhang
Keyword(s):  
Aspect Ratio ◽  
Biological Materials ◽  
Damping Capacity ◽  
Geometrical Parameters ◽  
Loading Frequency ◽  
Load Bearing ◽  
Damage And Fracture ◽  
Damping Behavior ◽  
Specific Loading ◽  
Self Similar

One of the most crucial functionalities of load-bearing biological materials such as shell and bone is to protect their interior organs from damage and fracture arising from external dynamic impacts. However, how this class of materials effectively damp stress waves traveling through their structure is still largely unknown. With a self-similar hierarchical model, a theoretical approach was established to investigate the damping properties of load-bearing biological materials in relation to the biopolymer viscous characteristics, the loading frequency, the geometrical parameters of reinforcements, as well as the hierarchy number. It was found that the damping behavior originates from the viscous characteristics of the organic (biopolymer) constituents and is greatly tuned and enhanced by the staggered and hierarchical organization of the organic and inorganic constituents. For verification purpose, numerical experiments via finite-element method (FEM) have also been conducted and shown results consistent with the theoretical predictions. Furthermore, the results suggest that for the self-similar hierarchical design, there is an optimal aspect ratio of reinforcements for a specific loading frequency and a peak loading frequency for a specific aspect ratio of reinforcements, at which the damping capacity of the composite is maximized. Our findings not only add valuable insights into the stress wave damping mechanisms of load-bearing biological materials, but also provide useful guidelines for designing bioinspired synthetic composites for protective applications.

scholarly journals Urchin-like CoO–C micro/nano hierarchical structures as high performance anode materials for Li-ion batteries

RSC Advances ◽  
2017 ◽  
Vol 7 (5) ◽  
pp. 2637-2643 ◽  
Author(s):  
Lili Liu ◽  
Lihui Mou ◽  
Jia Yu ◽  
Shimou Chen
Keyword(s):  
Hierarchical Structure ◽  
Anode Materials ◽  
High Performance ◽  
Hierarchical Structures ◽  
Li Ion Batteries ◽  
Carbon Coated ◽  
Li Ion ◽  
Li Storage

Urchin-like microspheres consisting of radial carbon-coated cobalt monoxide nanowires are designed, to fabricate a micro/nano hierarchical structure for efficient Li-storage.

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