scholarly journals Packing Densities of Patterns

10.37236/1833 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Reid W. Barton
Keyword(s):  
Packing Density ◽  
Maximum Proportion ◽  
Packing Densities

The packing density of a permutation $\pi$ of length $n$ is the maximum proportion of subsequences of length $n$ which are order-isomorphic to $\pi$ in arbitrarily long permutations $\sigma$. For the generalization to patterns $\pi$ which may have repeated letters, two notions of packing density have been defined. In this paper, we show that these two definitions are equivalent, and we compute the packing density for new classes of patterns.

scholarly journals Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates

10.37236/774 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Cathleen Battiste Presutti
Keyword(s):  
Lower Bounds ◽  
Packing Density ◽  
Permutation Pattern ◽  
Maximum Proportion ◽  
Limiting Value ◽  
Packing Densities

The packing density of a permutation pattern $\pi$ is the limiting value, ${n}$ $\rightarrow$ $\infty$, of the maximum proportion of subsequences of $\sigma$ $\in$ ${S_{n}}$ that are order-isomorphic to $\pi$. We generalize methods for obtaining lower bounds for the packing density of any pattern and demonstrate the methods' usefulness when patterns are non-layered.

Effect of Adding Stone Sludge as Sand Replacement on Fresh Properties of Mortar

2020 ◽  
Vol 984 ◽  
pp. 213-218
Author(s):  
Yong Xia ◽  
Jia Jian Chen ◽  
An Min Ma ◽  
Zi Hong Li
Keyword(s):  
Film Thickness ◽  
Packing Density ◽  
Fresh Properties ◽  
River Sand ◽  
Average Film Thickness ◽  
Density Results ◽  
Packing Densities

Shortage of river sand and disposal of stone sludge are the problem of the construction and stone product industries, respectively. Utilization of stone sludge in mortar is one of the feasible strategies to solve these two problems. To study the effects of addition of stone sludge on the performance of mortar, 20 mixes of stone sludge powder mortar with various water/cement ratios and various stone sludge powder contents were produced for flowability measurement. To further study the governing mechanism of flowability and the packing densities of the solid proportions of the 20 mortar mixes were measured. Based on the packing density results, the average film thickness (AFT) of the 20 mortar mixes were calculated for flowability indication. Results proved that addition of stone sludge powder as sand replacement would decrease the flowability. The flowability was mainly governed by the AFT.

scholarly journals POLOS PACKING DENSITY AND EFFECT OF RELATIVE BLOCK DENSITY

1978 ◽  
Vol 1 (16) ◽  
pp. 137
Author(s):  
J.A. Zwamborn
Keyword(s):  
Physical Properties ◽  
Packing Density ◽  
Model Tests ◽  
Test Results ◽  
Regular Waves ◽  
Shape Factors ◽  
Flume Tests ◽  
Testing Techniques ◽  
The Mean ◽  
Packing Densities

Accuracy and compatibility of measuring and testing techniques are discussed briefly and a plea is made for standardization to avoid, as far as possible, deviations in test results of different laboratories. One of the main causes of these differences is inconsistency in Dolos packing densities and corresponding layer thicknesses or shape factors. In an attempt to alleviate this problem three placing densities, namely 'light', 'mean' and 'dense' have been defined and their physical properties determined. Flume tests with regular waves, and Dolos armour units at these packing densities, showed very little difference in stability and, considering practical limitations during construction, it is suggested that the 'mean' packing density be used for a 'first design', followed by proper model tests. The results of tests with model Dolosse using three different unit densities were inconclusive and further tests using a wider range of densities are underway.

scholarly journals Drying Shrinkage and Cracking Tendency of Concrete Pavement Mixtures with Variable Packing Densities of Aggregates and Paste Contents

2020 ◽  
Vol 322 ◽  
pp. 01045
Author(s):  
Jan Olek ◽  
Adam Rudy
Keyword(s):  
Packing Density ◽  
Drying Shrinkage ◽  
Concrete Pavement ◽  
Concrete Mixture ◽  
Concrete Pavements ◽  
Saturation Ratio ◽  
Cracking Potential ◽  
Paste Content ◽  
Cracking Tendency ◽  
Packing Densities

Excessive drying shrinkage, and associated cracking, can lead to serious durability problem in concrete pavements and bridges. In the course of this study, the magnitude of drying shrinkage and cracking potential was evaluated for several concrete pavement mixtures as a function of packing density of the aggregate and paste contents. The results indicated that both, the shrinkage and the cracking potential depend on the volume of voids between aggregate particles (packing density), paste content of concrete mixture, and the paste-aggregate void saturation ratio.

scholarly journals Effect of packing density on selected tissue biochemical parameters of hatchery produced fingerlings of orange spotted grouper Epinephelus coioides (Hamilton, 1822) during transportaion

2018 ◽  
Vol 65 ◽  
Author(s):  
Biji Xavier ◽  
Sekar Megarajan ◽  
Ritesh Ranjan ◽  
Ponnaganti Shiva ◽  
Biswajit Dash ◽  
...  
Keyword(s):  
Water Quality ◽  
Packing Density ◽  
Biochemical Parameters ◽  
Ammonia Nitrogen ◽  
Quality Parameters ◽  
Water Quality Parameters ◽  
Epinephelus Coioides ◽  
Tissue Samples ◽  
Total Ammonia ◽  
Packing Densities

<p>Effect of different packing densities on water quality parameters, survival and selected tissue biochemical parameters during transportation of hatchery produced fingerlings of orange spotted grouper <em>Epinephelus coioides</em> (Hamilton, 1822) was investigated. Fingerlings (weight 3.0±0.2 g and length 6.0±0.2 cm) were packed in sealed double layered oxygen packed polythene bags (water and oxygen ratio 1:3) at different packing densities of 20, 30, 40 and 50 no. l-1. The packed fishes were transported for 6 h. After transportation, water samples and tissue samples from fishes were collected for further analyses. Levels of tissue glucose and selected metabolic enzymes (lactate dehydrogenase, LDH; aspartate amino transferase, AST and alanine amino transferase, ALT) significantly (p&lt;0.05) increased with increased packing density. Water quality parameters <em>viz.,</em> pH, dissolved oxygen, CO2, alkalinity, total ammonia nitrogen (TAN) and nitrite nitrogen (NO2-N) were also significantly different at higher packing densities (p&lt;0.05). However, levels of all the tissue biochemical parameters tested were in tolerable range and no mortality of fingerlings was recorded at any of the packing densities. Though the tissue enzyme levels were significantly higher and water quality was significantly deteriorated at the highest packing density of 50 no. l-1, it did not lead to mortality of fish. Therefore, it is inferred that this density can be used for short distance transportation of fingerlings of orange spotted grouper.</p>

scholarly journals Handling and Curing Characteristics of Cut-Strip Tobacco. Part 1: Effect of Strip-Size, Packing Density and Mode of Orientation

2002 ◽  
Vol 20 (1) ◽  
pp. 7-13
Author(s):  
WH Johnson ◽  
JH Young ◽  
GH Ellington ◽  
WW Weeks ◽  
JC Tutor
Keyword(s):  
Packing Density ◽  
Energy Use ◽  
Energy Savings ◽  
Reducing Sugars ◽  
Leaf Chemistry ◽  
Vertical Orientation ◽  
Leaf Quality ◽  
Horizontal Orientation ◽  
Total Alkaloids ◽  
Packing Densities

AbstractPrevious work has demonstrated potential handling and curing efficiencies in the use of cut-strip tobacco. The present work considers further the effect of cut-strip size, packing density and mode of orientation on cured leaf chemistry (starch, reducing sugars, and total alkaloids) and leaf quality. Results showed that cured leaf chemistry of 15.2 × 22.9 cm cut-strip more closely matched properties of whole leaf than pieces 15.2 × 15.2 cm or smaller. Starch contents were significantly higher for the smaller cut-strip sizes, perhaps due to edge drying effects, while alkaloids were significantly lower. Within the range of 194 to 292 kg/m, packing density had little effect on leaf chemistry, with the exception that reducing sugars were slightly lower for the higher packing densities. This could be due to a longer time for the drying front to move through the more tightly packed tobacco, and hence more respiratory loss of sugars. Government grades and average market prices of cured strips were essentially unaffected over the range of strip sizes or packing densities tested. Based on airflow resistance measurements and observed drying characteristics, vertical orientation of strips was far superior to horizontal orientation, both with vertical airflow through the tobacco. The higher packing density reduced specific energy use (kWh/kg green tobacco) by as much as 22%, indicating potential energy savings for cut-strip over whole leaf curing.

scholarly journals Numerical Investigation of Coil Configurations That Provide Ultrahigh Packing Density of Saccular Aneurysms

2009 ◽  
Vol 3 (4) ◽  
Author(s):  
Chander Sadasivan ◽  
Baruch B. Lieber
Keyword(s):  
Packing Density ◽  
Circular Cross Section ◽  
Cerebral Aneurysms ◽  
Endovascular Coiling ◽  
Stable Configuration ◽  
Term Outcome ◽  
Long Term Outcome ◽  
Coefficients Of Variation ◽  
Packing Densities

The long-term outcome of endovascular coiling of cerebral aneurysms is directly related to the packing density at the time of treatment. In general, the highest packing density achievable is only about 45% due to the quasirandom distribution of currently available coils within aneurysms. We investigated whether packing densities could be maximized via more ordered coil configurations. Three different coil configurations—circular loops, planar spirals, and spherical helices—were investigated. The packing densities achievable in maximally filling the volume of an exemplar human basilar aneurysm with each coil configuration were calculated numerically. Coil packing simulations were also carried out for aneurysms idealized as spheres over diameters ranging from 2 mm to 30 mm. The packing densities with the loop, spiral, and spherical helix configurations were 82%, 60%, and 73%, respectively, for the human aneurysm model; the numbers of coils required were 693, 34, and 13, respectively. Simulations within idealized aneurysms suggest that aneurysms cannot be packed to more than 91% with coils of constant circular cross section. The spherical helix configuration provides a constant packing density (coefficient of variation of 0.4%) over the range of aneurysm diameters studied as compared to the two other configurations (coefficients of variation of 9% and 8%). Coil configurations that allow for ordered filling of cerebral aneurysms can potentially provide packing densities that are twice those currently achieved. The spherical helix configuration seems to be the most technically feasible and stable configuration of the three coil types investigated.

Abstract WP76: Investigation of the Influence of Coil Configuration on Cerebral Aneurysm Fluid Dynamics Using a Novel Finite Element Approach

Stroke ◽  
2013 ◽  
Vol 44 (suppl_1) ◽  
Author(s):  
Haithem Babiker ◽  
L. Fernando Gonzalez ◽  
Brian Chong ◽  
David H Frakes
Keyword(s):  
Fluid Dynamics ◽  
Finite Element ◽  
Cerebral Aneurysm ◽  
Packing Density ◽  
Coil Design ◽  
Flow Measurements ◽  
Finite Element Approach ◽  
Element Approach ◽  
Packing Densities

INTRODUCTION: Despite more than a decade of endovascular coil treatment, the effects of coils on cerebral aneurysm (CA) hemodynamics are still poorly understood. Coils present several challenges to in vivo and in vitro flow measurement techniques and previous in silico methods have suffered from large assumptions on coil geometry. Here we present the first fluid dynamic simulations of coiled CAs that consider the structure and deployment mechanics of embolic coils. We also investigate the influence of coil packing density, design, and configuration on CA fluid dynamics. Methods: Coil deployment was modeled using a novel finite element approach that realistically simulates coil dynamics during deployment. Two coil designs were investigated: helical and 3D. Coil design and material properties were matched to manufacturer specifications. Five deployment sequences of each coil design, at different microcatheter placements, were simulated in two idealized CA models with variable neck sizes. Blood flow was simulated using computational fluid dynamics. Simulated deployments and fluid dynamics were then compared to deployments of actual coils in identical physical CA models and in vitro particle image velocimetry flow measurements. Results: Simulated results closely matched in vitro data. Reductions in aneurysmal velocity magnitudes were largest for 3D coils and in a narrow-neck model. In that model, 3D coil deployments reduced average aneurysmal velocity magnitudes by a 51% - 69% range at packing densities less than 20% and by a 74% - 84% range at packing densities greater than 30%. Linear regression results showed reductions were strongly dependent on the spacing between coil loops within the aneurysm and packing density, with correlations of 0.6 and 0.7 respectively. Conclusion: Coil design and packing density may play equally important roles in determining CA hemodynamics. Results in an anatomical model will also be presented. The proposed virtual coiling approach represents a novel and effective method for realistically simulating coiled CAs, and is an important step towards clinical preoperative planning of coil treatment.

Evidence of photoreceptor migration during early foveal development: A quantitative analysis of human fetal retinae

1992 ◽  
Vol 8 (6) ◽  
pp. 505-514 ◽  
Author(s):  
Claudia Diaz Araya ◽  
Jan M. Provis
Keyword(s):  
Packing Density ◽  
Cresyl Violet ◽  
Cone Mosaic ◽  
Rods And Cones ◽  
Individual Variations ◽  
Mitotic Figures ◽  
Conventional Manner ◽  
Age Range ◽  
Cone Density ◽  
Packing Densities

AbstractWe have analyzed aspects of photoreceptor topography in wholemounts of human fetal retinae in the age range 13–24 weeks of gestation. Fetal retinae were stained with cresyl violet and the sizes and packing densities of rods and cones analyzed in the conventional manner.Cones and rods were present within a differentiating region, free of mitotic figures and approximately centered on the putative fovea, represented by the foveal cone mosaic. At 13 weeks of gestation the foveal cone mosaic was clearly differentiated, cone nuclei reaching a packing density of 14,200 per mm; a small number of rods were present in the immediately adjacent region. The packing densities of both rods and cones in these regions gradually increased and the area of the foveal cone mosaic gradually decreased throughout the age range sampled, although individual variations were evident. By 24 weeks of gestation, cone density was approximately 38,000 per mm in the foveal cone mosaic. The maximum rod density observed was 59,200 per mm in the region surrounding the foveal cone mosaic in a specimen of 20–21 weeks of gestation. In all specimens, maximum cone density occurred within the foveal cone mosaic and gradually declined towards the periphery of the differentiating region; a pronounced inverse relationship between cone soma diameter and packing density was also observed. The evidence strongly suggests that both rods and cones migrate centripetally, that is towards the center of the developing fovea, from early in development, possibly from the time that they first differentiate. The implications of these findings for fovealdevelopment are discussed.

Low-Dielectric-Constant Materials for ULSI Interlayer-Dielectric Applications

MRS Bulletin ◽  
1997 ◽  
Vol 22 (10) ◽  
pp. 19-27 ◽  
Author(s):  
Wei William Lee ◽  
Paul S. Ho
Keyword(s):  
Packing Density ◽  
Propagation Delay ◽  
Single Chip ◽  
Crosstalk Noise ◽  
Metal Line ◽  
Total Delay ◽  
Interlayer Dielectric ◽  
Low Dielectric ◽  
Interconnect Delay ◽  
Interconnect Technology

Continuing improvement of microprocessor performance historically involves a decrease in the device size. This allows greater device speed, an increase in device packing density, and an increase in the number of functions that can reside on a single chip. However higher packing density requires a much larger increase in the number of interconnects. This has led to an increase in the number of wiring levels and a reduction in the wiring pitch (sum of the metal line width and the spacing between the metal lines) to increase the wiring density. The problem with this approach is that—as device dimensions shrink to less than 0.25 μm (transistor gate length)—propagation delay, crosstalk noise, and power dissipation due to resistance-capacitance (RC) coupling become significant due to increased wiring capacitance, especially interline capacitance between the metal lines on the same metal level. The smaller line dimensions increase the resistivity (R) of the metal lines, and the narrower interline spacing increases the capacitance (C) between the lines. Thus although the speed of the device will increase as the feature size decreases, the interconnect delay becomes the major fraction of the total delay and limits improvement in device performance.To address these problems, new materials for use as metal lines and interlayer dielectrics (ILD) as well as alternative architectures have been proposed to replace the current Al(Cu) and SiO2 interconnect technology.

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