scholarly journals Global and local contributions to corneal surface curvature: a simple model

2008 ◽  
Vol 67 (1) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Mathematical Model ◽  
Simple Model ◽  
Tear Film ◽  
Surface Curvature ◽  
Simple Mathematical Model ◽  
Corneal Surface ◽  
Local Effects ◽  
Numerical Example ◽  
Global And Local ◽  
Insight Into

Variations in corneal surface powers reflect variations in the geometry of the cornea.  In particular one can regard corneal surface curvature as a combination of local and global effects.  A simple mathematical model of the cornea is presented which makes use of measurements of the curvature of the anterior and posterior surfaces to decompose the curvature into global and local contributions.  The model gives insight into the source of variations in keratometric measurements, lids and eye turn, perhaps, for global effects and the tear film, perhaps, for local effects.  The model also takes account of the thickness of the cornea.  A numerical example is presented.

Insight into the basis of root growth in Arabidopsis thaliana provided by a simple mathematical model

2006 ◽  
Vol 119 (2) ◽  
pp. 85-93 ◽  
Author(s):  
Akitoshi Iwamoto ◽  
Daisuke Satoh ◽  
Masahiko Furutani ◽  
Shinichiro Maruyama ◽  
Hideaki Ohba ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Arabidopsis Thaliana ◽  
Root Growth ◽  
Simple Mathematical Model ◽  
Insight Into

scholarly journals Mechanosensitive remodeling of the bacterial flagellar motor is independent of direction of rotation

2021 ◽  
Vol 118 (15) ◽  
pp. e2024608118
Author(s):  
Navish Wadhwa ◽  
Yuhai Tu ◽  
Howard C. Berg
Keyword(s):  
Escherichia Coli ◽  
Mathematical Model ◽  
Steady State ◽  
Bacterial Motility ◽  
Flagellar Motor ◽  
Simple Mathematical Model ◽  
Output Torque ◽  
Chemical Stimuli ◽  
Bacterial Flagellar Motor ◽  
Insight Into

Motility is important for the survival and dispersal of many bacteria, and it often plays a role during infections. Regulation of bacterial motility by chemical stimuli is well studied, but recent work has added a new dimension to the problem of motility control. The bidirectional flagellar motor of the bacterium Escherichia coli recruits or releases torque-generating units (stator units) in response to changes in load. Here, we show that this mechanosensitive remodeling of the flagellar motor is independent of direction of rotation. Remodeling rate constants in clockwise rotating motors and in counterclockwise rotating motors, measured previously, fall on the same curve if plotted against torque. Increased torque decreases the off rate of stator units from the motor, thereby increasing the number of active stator units at steady state. A simple mathematical model based on observed dynamics provides quantitative insight into the underlying molecular interactions. The torque-dependent remodeling mechanism represents a robust strategy to quickly regulate output (torque) in response to changes in demand (load).

scholarly journals Guided graph spectral embedding: Application to the C. elegans connectome

2019 ◽  
Vol 3 (3) ◽  
pp. 807-826 ◽  
Author(s):  
Miljan Petrovic ◽  
Thomas A. W. Bolton ◽  
Maria Giulia Preti ◽  
Raphaël Liégeois ◽  
Dimitri Van De Ville
Keyword(s):  
Optimization Criterion ◽  
Energy Concentration ◽  
Nodal Domain ◽  
Local Effects ◽  
Order Processing ◽  
C Elegans ◽  
Importance Weighting ◽  
Spectral Embedding ◽  
Global And Local ◽  
Insight Into

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions—for example, based on wavelets and Slepians—that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows us to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode’s neural network in terms of functionality and importance of cells. Compared with Laplacian embedding, the guided approach, focused on a certain class of cells (sensory neurons, interneurons, or motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low- or high-order processing functions.

scholarly journals Variability of the mechanical properties of bone, and its evolutionary consequences

2006 ◽  
Vol 4 (12) ◽  
pp. 127-135 ◽  
Author(s):  
John D Currey ◽  
Jonathan W Pitchford ◽  
Paul D Baxter
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Mineral Content ◽  
Optimal Allocation ◽  
Compact Bone ◽  
Simple Mathematical Model ◽  
Trade Off ◽  
Evolutionary Consequences ◽  
Insight Into ◽  
Mechanical Phenomena

The relative variabilities (coefficient of variation (CV)) of 10 different mechanical properties of compact bone were determined from 2166 measurements. All measures of variability were made on a minimum of four specimens from any bone. Three pre-yield properties had a CV of about 12%. Six post-yield properties had CVs varying from 24 to 46%. Pre-yield properties increase as a function of mineral content, whereas post-yield properties decrease. These differences give insight into mechanical phenomena occurring at different stages during loading. Furthermore, the fact that some properties are more tightly determined than others has implications for the optimum values set by natural selection. This assertion is made more rigorous using a simple mathematical model for the evolutionarily optimal allocation in a trade-off where one property is imprecisely determined. It is argued that in general the optimum will be biased in favour of the more tightly determined properties than would be the case if all properties had the same CV.

Effect of mobility conditions on the throughput of the Wireless Body Area Network

2020 ◽  
Vol 10 ◽  
Author(s):  
Shilpa Shinde ◽  
Santosh Sonavane
Keyword(s):  
Mathematical Model ◽  
Wireless Body Area Network ◽  
Data Rate ◽  
Hand Movements ◽  
Body Area Network ◽  
Area Network ◽  
Mobility Patterns ◽  
Body Area ◽  
Insight Into ◽  
Leg Movements

Background and objective: In the Wireless Body Area Network (WBAN) sensors are placed on the human body; which has various mobility patterns like seating, walking, standing and running. This mobility typically assisted with hand and leg movements on which most of the sensors are mounted. Previous studies were largely focused on simulations of WBAN mobility without focusing much on hand and leg movements. Thus for realistic studies on performance of the WBAN, it is important to consider hand and leg movements. Thus, an objective of this paper is to investigate an effect of the mobility patterns with hand movements on the throughput of the WBAN. Method: The IEEE 802.15.6 requirements are considered for WBAN design. The WBAN with star topology is used to connect three sensors and a hub. Three types of mobility viz. standing, walking and running with backward and forward hand movements is designed for simulation purpose. The throughput analysis is carried out with the three sets of simulations with standing, walking and running conditions with the speed of 0 m/s, 0.5 m/s and 3 m/s respectively. The data rate was increased from 250 Kb to 10000 Kb with AODV protocol. It is intended to investigate the effect of the hand movements and the mobility conditions on the throughput. Simulation results are analyzed with the aid of descriptive statistics. A comparative analysis between the simulated model and a mathematical model is also introduced to get more insight into the data. Results: Simulation studies showed that as the data rate is increased, throughput is also increased for all mobility conditions however, this increasing trend was discontinuous. In the standing (static) position, the throughput is found to be higher than mobility (dynamic) condition. It is found that, the throughput is better in the running condition than the walking condition. Average values of the throughput in case of the standing condition were more than that of the dynamic conditions. To validate these results, a mathematical model is created. In the mathematical model, a same trend is observed. Conclusion: Overall, it is concluded that the throughput is decreased due to mobility of the WBAN. It is understood that mathematical models have given more insight into the simulation data and confirmed the negative effect of the mobility conditions on throughput. In the future, it is proposed to investigate effect of interference on the designed network and compare the results.

scholarly journals Modelling time efficiency of cobot-supported kit preparation

2019 ◽  
Vol 106 (5-6) ◽  
pp. 2227-2241 ◽  
Author(s):  
Patrik Fager ◽  
Martina Calzavara ◽  
Fabio Sgarbossa
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cycle Time ◽  
Laboratory Experiments ◽  
Spare Parts ◽  
Batch Preparation ◽  
Assembly Quality ◽  
Numerical Example ◽  
Business To Business ◽  
Support Time

AbstractKitting – meaning to supply assembly with components in presorted kits – is widely seen as beneficial for assembly quality and efficiency when there is a multitude of component variants. However, the process by which kits are prepared – the kit preparation – is labour-intensive, and kit errors are problematic at assembly processes. The use of robotics to support kit preparation has received some attention by researchers, but literature is lacking with respect to how collaborative robots – cobots – can support kit preparation activities. The purpose of this paper is to identify the potential of a cobot to support time-efficient batch preparation of kits. To address the purpose, the paper presents a mathematical model for estimation of the cycle time associated with cobot-supported kit preparation. The model is applied in a numerical example with experimental data from laboratory experiments, and cobot-supported kit preparation is compared with manual kit preparation. The findings suggest that cobot-supported kit preparation is beneficial with diverse kits and smaller components quantities per SKU (Stock Keeping Unit) and provides less variability of the outcome, when compared to manual kit preparation. The paper reveals several insights about cobot-supported kit preparation that can be valuable for both academics and practitioners. The model developed can be used by practitioners to assess the potential of cobots to support kit-batch preparation in association with assembly, spare parts, repair and maintenance, or business to business industry.

Development of the Tip-Leakage Flow Downstream of a Planar Cascade of Turbine Blades: Vorticity Field

1989 ◽  
Author(s):  
M. Yaras ◽  
S. A. Sjolander
Keyword(s):  
Simple Model ◽  
Turbine Blades ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Vorticity Field ◽  
Trailing Edge ◽  
Tip Leakage ◽  
Blade Row ◽  
Axisymmetric Structure ◽  
Insight Into

The paper presents detailed measurements of the tip-leakage flow emerging from a planar cascade of turbine blades. Four clearances of from 1.5 to 5.5 percent of the blade chord are considered. Measurements were made at the trailing edge plane, and at two main planes 1.0 and 1.56 axial chord lengths downstream of the cascade. The results give insight into several aspects of the leakage flow including: the size and strength of the leakage vortex in relation to the size of the tip gap and the bound circulation of the blade; and the evolution of the components of vorticity as the vortex diffuses laterally downstream of the blade row. The vortex was found to have largely completed its roll-up into a nearly axisymmetric structure even at the trailing edge of the cascade. As a result, it was found that the vortex could be modelled surprisingly well with a simple model based on the diffusion of a line vortex.

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