A Further Study on the Analytical Model for the Permeability in Flip-Chip Packaging

2018 ◽  
Vol 140 (1) ◽  
Author(s):  
X. J. Yao ◽  
J. J. Fang ◽  
Wenjun Zhang
Keyword(s):  
Porous Medium ◽  
Analytical Model ◽  
Flip Chip ◽  
Flow Behavior ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Proposed Model ◽  
Flip Chip Packaging ◽  
Pore Permeability

The notion of permeability is very important in understanding and modeling the flow behavior of fluids in a special type of porous medium (i.e., the underfill flow in flip-chip packaging). This paper presents a new concept regarding permeability in a porous medium, namely two types of permeability: superficial permeability (with consideration of both the pore cross-sectional area and the solid matrix cross-sectional area) and pore permeability (with consideration of the pore cross-sectional area only). Subsequently, the paper proposes an analytical model (i.e., equation) for the pore permeability and superficial permeability of an underfill porous medium in a flip-chip packaging, respectively. The proposed model along with several similar models in literature is compared with a reliable numerical model developed with the computational fluid dynamics (CFD) technique, and the result of the comparison shows that the proposed model for permeability is the most accurate one among all the analytical models in literature. The main contributions of the paper are as follows: (1) the provision of a more accurate analytical model for the permeability of an underfill porous medium in flip-chip packaging, (2) the finding of two types of permeability depending on how the cross-sectional area is taken, and (3) the correction of an error in the others' model in literature.

Crosstalk Induced Delay Analysis of Randomly Distributed Mixed CNT Bundle Interconnect

2015 ◽  
Vol 24 (10) ◽  
pp. 1550145 ◽  
Author(s):  
Manoj Kumar Majumder ◽  
Pankaj Kumar Das ◽  
Vobulapuram Ramesh Kumar ◽  
Brajesh Kumar Kaushik
Keyword(s):  
Carbon Nanotube ◽  
Analytical Model ◽  
Cross Sectional Area ◽  
Analytical Models ◽  
Delay Analysis ◽  
Sectional Area ◽  
Cross Sectional ◽  
Placement Algorithm ◽  
Swcnts And Mwcnts ◽  
Different Diameters

In this paper, a more realistic analytical model for randomly distributed mixed carbon nanotube (CNT) bundle (MCB) is presented for the analysis of crosstalk induced delay. Several researchers have proposed analytical models for interconnects based on single-walled CNT (SWCNT), multi-walled CNT (MWCNT) bundle and most interestingly, spatially arranged mixed CNTs. Although, bundled SWCNTs and MWCNTs are easily realizable, but, practically it is almost impossible to fabricate a MCB with precise arrangements of SWCNTs and MWCNTs. Motivated by these facts, this paper presents a corner placement algorithm for randomly distributed SWCNTs and MWCNTs of different diameters in a MCB. The performance of MCB is compared with that of conventional bundled SWCNT and bundled MWCNT at different coupled interconnect lengths and spacing. Encouragingly, for a fixed cross-sectional area, the overall crosstalk induced delay of MCB reduces by 65.03% and 23.54% in comparison to the bundles having either SWCNTs or MWCNTs with smaller diameters, respectively. However, in contradiction to most of the previously reported results, bundled MWCNTs with larger diameters outperform the randomly distributed MCBs in terms of crosstalk performance.

Pelvic Canal Narrowing Caused by Triple Pelvic Osteotomy in the Dog

1994 ◽  
Vol 07 (03) ◽  
pp. 110-113 ◽  
Author(s):  
D. L. Holmberg ◽  
M. B. Hurtig ◽  
H. R. Sukhiani
Keyword(s):  
Postoperative Complications ◽  
Pelvic Osteotomy ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Canal Width ◽  
Operative Complications ◽  
Post Operative Complications

SummaryDuring a triple pelvic osteotomy, rotation of the free acetabular segment causes the pubic remnant on the acetabulum to rotate into the pelvic canal. The resulting narrowing may cause complications by impingement on the organs within the pelvic canal. Triple pelvic osteotomies were performed on ten cadaver pelves with pubic remnants equal to 0, 25, and 50% of the hemi-pubic length and angles of acetabular rotation of 20, 30, and 40 degrees. All combinations of pubic remnant lengths and angles of acetabular rotation caused a significant reduction in pelvic canal-width and cross-sectional area, when compared to the inact pelvis. Zero, 25, and 50% pubic remnants result in 15, 35, and 50% reductions in pelvic canal width respectively. Overrotation of the acetabulum should be avoided and the pubic remnant on the acetabular segment should be minimized to reduce postoperative complications due to pelvic canal narrowing.When performing triple pelvic osteotomies, the length of the pubic remnant on the acetabular segment and the angle of acetabular rotation both significantly narrow the pelvic canal. To reduce post-operative complications, due to narrowing of the pelvic canal, overrotation of the acetabulum should be avoided and the length of the pubic remnant should be minimized.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Changes in the parameters of nasal breathing and parameters of the upper respiratory tract during orthognathic operations in patients with II and III skeletal class of jaw anomalies

2020 ◽  
pp. 22-27
Author(s):  
S.Sh. Gammadaeva ◽  
M.I. Misirkhanova ◽  
A.Yu. Drobyshev
Keyword(s):  
Respiratory Tract ◽  
Nasal Cavity ◽  
Nasal Septum ◽  
Cross Sectional Area ◽  
Upper Respiratory Tract ◽  
Sectional Area ◽  
Nasal Breathing ◽  
Cross Sectional ◽  
Skeletal Class ◽  
Upper Respiratory

The study analyzed the functional parameters of nasal breathing, linear parameters of the nasal aperture, nasal cavity and nasopharynx, volumetric parameters of the upper airways in patients with II and III skeletal class of jaw anomalies before and after orthognathic surgery. The respiratory function of the nose was assessed using a rhinomanometric complex. According to rhinoresistometry data, nasal resistance and hydraulic diameter were assessed. According to the data of acoustic rhinometry, the minimum cross-sectional area along the internal valve, the minimum cross-sectional area on the head of the inferior turbinate and nasal septum and related parameters were estimated. According to the CBCT data, the state of the nasal septum, the inferior turbinates, the nasal aperture, the state of the nasal cavity, and the linear values of the upper respiratory tract (nasopharynx) were analyzed. The patients were divided into 4 groups according to the classification of the patency of the nasal passages by

Unequal Probability Scheme for Fruit Count in a Guava Tree

2016 ◽  
Vol 3 (4) ◽  
Author(s):  
R. C. BHARATI
Keyword(s):  
Cross Sectional Area ◽  
Equal Probability ◽  
Sampling Scheme ◽  
Research Station ◽  
Sectional Area ◽  
Cross Sectional ◽  
Unequal Probability ◽  
Selection Probabilities ◽  
Horticultural Research ◽  
Number Of Branches

Data on fruit count corresponding to primary, secondary and tertiary branches of a randomly selected guava CV. Allahabad Safeda were recorded from the guava orchard of Horticultural Research Station, Birauli. The proposed sampling scheme in which the selection probabilities are based on length of braches between two forking points was compared with equal probability(PE), probability proportional to the number of branches(PPN), probability proportional to the cross sectional area (PPA) and probability proportional to volume (PPV) method of sampling and found to be more efficient.

Effect of Early Low-Intensity Exercise on Rat Hind-Limb Muscles Following Acute Ischemic Stroke

2006 ◽  
Vol 7 (3) ◽  
pp. 163-174 ◽  
Author(s):  
Myoung-Ae Choe ◽  
Gyeong Ju An ◽  
Yoon-Kyong Lee ◽  
Ji Hye Im ◽  
Smi Choi-Kwon ◽  
...  
Keyword(s):  
Hind Limb ◽  
Gastrocnemius Muscle ◽  
Exercise Group ◽  
Cross Sectional Area ◽  
Type I ◽  
Sectional Area ◽  
Muscle Type ◽  
Cross Sectional ◽  
Low Intensity ◽  
Low Intensity Exercise

This study examined the effects of daily low-intensity exercise following acute stroke on mass, Type I and II fiber cross-sectional area, and myofibrillar protein content of hind-limb muscles in a rat model. Adult male Sprague-Dawley rats were randomly assigned to 1 of 4 groups (n = 7-9 per group): stroke (occlusion of the right middle cerebral artery [RMCA]), control (sham RMCA procedure), exercise, and stroke-exercise. Beginning 48 hours post-stroke induction/sham operation, rats in the exercise group had 6 sessions of exercise in which they ran on a treadmill at grade 10 for 20 min/day at 10 m/min. At 8 days poststroke, all rats were anesthetized and soleus, plantaris, and gastrocnemius muscles were dissected from both the affected and unaffected sides. After 6 sessions of exercise following acute ischemic stroke, the stroke-exercise group showed the following significant (p < .05) increases compared to the stroke-only group: body weight and dietary intake, muscle weight of affected soleus and both affected and unaffected gastrocnemius muscle, Type I fiber cross-sectional area of affected soleus and both affected and unaffected gastrocnemius muscle, Type II fiber cross-sectional area of the unaffected soleus, both affected and unaffected plantaris and gastrocnemius muscle, Type II fiber distribution of affected gastrocnemius muscle, and myofibrillar protein content of both affected and unaffected soleus muscle. Daily low-intensity exercise following acute stroke attenuates hind-limb muscle atrophy in both affected and unaffected sides. The effects of exercise are more pronounced in the soleus and gastrocnemius as compared to the plantaris muscle.

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