An Exactly Solvable Ogston Model of Gel Electrophoresis. 7. Diffusion and Mobility of Hard Spherical Particles in Three-Dimensional Gels

2001 ◽  
Vol 34 (10) ◽  
pp. 3437-3445 ◽  
Author(s):  
Jean-François Mercier ◽  
Gary W. Slater
Keyword(s):  
Gel Electrophoresis ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Exactly Solvable

scholarly journals Development of a highly sensitive three-dimensional gel electrophoresis method for characterization of monoclonal protein heterogeneity

2013 ◽  
Vol 438 (2) ◽  
pp. 117-123 ◽  
Author(s):  
Keiichi Nakano ◽  
Shogo Tamura ◽  
Kohei Otuka ◽  
Noriyasu Niizeki ◽  
Masahiko Shigemura ◽  
...  
Keyword(s):  
Gel Electrophoresis ◽  
Three Dimensional ◽  
Monoclonal Protein ◽  
Highly Sensitive ◽  
Electrophoresis Method

Effective Stiffness of a Debonded Particle in Particulate Composites

2007 ◽  
Vol 334-335 ◽  
pp. 33-36 ◽  
Author(s):  
Akihiro Wada ◽  
Yusuke Nagata ◽  
Shi Nya Motogi
Keyword(s):  
Three Dimensional ◽  
Particulate Composite ◽  
Spherical Particles ◽  
Particulate Composites ◽  
Particle Volume ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Load Carrying ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In this study, partially debonded spherical particles in a particulate composite are analyzed by three-dimensional finite element method to investigate their load carrying capacities, and the way to replace a debonded particle with an equivalent inclusion is examined. The variation in Young’s modulus and Poisson’s ratio of a composite with the debonded angle was evaluated for different particle arrangements and particle volume fractions, which in turn compared with the results derived from the equivalent inclusion method. Consequently, it was found that by replacing a debonded particle with an equivalent orthotropic one, the macroscopic behavior of the damaged composite could be reproduced so long as the interaction between neighboring particles is negligible.

Darcy-Forchheimer porous medium effect on rotating hybrid nanofluid on a linear shrinking/stretching sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Medium Effect ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow

Purpose The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced ϕ2 in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value Dual branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors’ knowledge, this research is novel and there is no previously published work relevant to the present study.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals Clusters Formed by Dumbbell-like One-Patch Particles Confined in Thin Systems

2021 ◽  
Author(s):  
Masahide Sato
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
The Other ◽  
Spherical Particles ◽  
Dimensionless Distance ◽  
Large Island ◽  
Cluster Shape

Abstract Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model. The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between them. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when q < 1. With increasing q, the clusters become chain-like. When q increases further, elongated clusters and regular polygonal clusters are created. In hte simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

scholarly journals Numerical Study of Branched Turboprop Inlet Ducts Using a Multiple Block Grid Procedure

1991 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Mark E. Braaten
Keyword(s):  
Numerical Solutions ◽  
Numerical Study ◽  
Three Dimensional ◽  
Separated Flow ◽  
Experimental Tests ◽  
Spherical Particles ◽  
Branch Duct ◽  
Pressure Losses ◽  
Overlapping Grids ◽  
Inlet Duct

An important requirement in the design of an inlet duct of a turboprop engine is the ability to provide foreign object damage protection. A possible method for providing this protection is to include a bypass branch duct as an integral part of the main inlet duct. This arrangement would divert ingested debris away from the engine through the bypass. However, such an arrangement could raise the possibility of separated flow in the inlet, which in turn can increase pressure losses if not properly accounted for during the design. A fully elliptic three-dimensional body-fitted computational fluid dynamics (CFD) code based on pressure correction techniques has been developed that has the capability of performing multiple block grid calculations compatible with present day turboshaft and turboprop branched inlet ducts. Calculations are iteratively performed between sets of overlapping grids with one grid representing the main duct and a second grid representing the branch duct. Both the grid generator and the flow solver have been suitably developed to achieve this capability. The code can handle multiple branches in the flow. Using the converged flow field from this code, another program was written to perform a particle trajectory analysis. Numerical solutions were obtained on a supercomputer for a typical branched duct for which experimental flow and pressure measurements were also made. The flow separation zones predicted by the calculations were found to be in good agreement with those observed in the experimental tests. The total pressure recovery factors measured in the experiments were also compared with those obtained numerically. Within the limits of the grid resolution and the turbulence model, the agreement was found to be fairly good. In order to simulate the path of debris entering the duct, the trajectories of spherical particles of different sizes introduced at the inlet were determined.

scholarly journals Construction of potential functions associated with a given energy spectrum — An inverse problem

2020 ◽  
Vol 35 (20) ◽  
pp. 2050104
Author(s):  
A. D. Alhaidari
Keyword(s):  
Energy Spectrum ◽  
Three Dimensional ◽  
Logarithmic Potential ◽  
Potential Functions ◽  
Physical Parameters ◽  
Linear Potential ◽  
Hahn Polynomial ◽  
Exactly Solvable ◽  
The One ◽  
Solvable Problems

Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy spectrum. In this work, we study the class of problems associated with the continuous dual Hahn polynomial. These include the one-dimensional logarithmic potential and the three-dimensional Coulomb plus linear potential.

scholarly journals Clusters formed by dumbbell-like one-patch particles confined in thin systems

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Masahide Sato
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
The Other ◽  
Spherical Particles ◽  
Dimensionless Distance ◽  
Large Island ◽  
Cluster Shape

AbstractPerforming isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model . The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when $$q<1$$ q < 1 . With increasing q, the clusters become chain-like . When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

scholarly journals A statistical analysis for pattern recognition of small cloud particles sampled with a PMS-2DC probe

1997 ◽  
Vol 15 (6) ◽  
pp. 840-846 ◽  
Author(s):  
A. Fouilloux ◽  
J. Iaquinta ◽  
C. Duroure ◽  
F. Albers
Keyword(s):  
Pattern Recognition ◽  
Statistical Analysis ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Spherical Particles ◽  
Data Sets ◽  
Ice Water Content ◽  
Dimensional Shape ◽  
Exact Shape ◽  
Ice Water

Abstract. Although small particles (size between 25 µm and 200 µm) are frequently observed within ice and water clouds, they are not generally used properly for the calculation of structural, optical and microphysical quantities. Actually neither the exact shape nor the phase (ice or water) of these particles is well defined since the existing pattern recognition algorithms are only efficient for larger particle sizes. The present study describes a statistical analysis concerning small hexagonal columns and spherical particles sampled with a PMS-2DC probe, and the corresponding images are classified according to the occurrence probability of various pixels arrangements. This approach was first applied to synthetic data generated with a numerical model, including the effects of diffraction at a short distance, and then validated against actual data sets obtained from in-cloud flights during the pre-ICE'89 campaign. Our method allows us to differentiate small hexagonal columns from spherical particles, thus making possible the characterization of the three dimensional shape (and consequently evaluation of the volume) of the particles, and finally to compute e.g., the liquid or the ice water content.

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