Precise Estimation of Mobility of PFPE Lubricants Combining the Experimental Method and Numerical Method

2002 ◽  
Author(s):  
Mineo Oka ◽  
Shinichi Nakazawa
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Solutions ◽  
Thickness Distribution ◽  
Initial Distribution ◽  
Step Function ◽  
Similar Solution ◽  
Pfpe Lubricant ◽  
Inclined Slope ◽  
Measured Distribution ◽  
Pfpe Lubricants

The diffusion coefficient has been used to estimate the mobility of PFPE lubricant on hard disk media. In former researches, initial lubricant thickness distribution is assumed to be step function. And similar solution was used to estimate the diffusion coefficient. But based on our experimentally measured data, initial distribution is not step function but has inclined slope. It leads the over estimation of the diffusion coefficient especially for low mobility lubricants. In this paper, instead of assuming initial distribution is step function and using similar solution, the diffusion coefficient is estimated by the method combining the experimentally measured results and the numerical solutions. The estimated diffusion coefficient is much lower for the low mobility lubricants. Calculated thickness distribution agrees well with the experimentally measured distribution. The mobility and spreading characteristics of PFPE lubricants can be estimated precisely using this method.

scholarly journals Modelling the Molecular Transportation of Subcutaneously Injected Salubrinal

2011 ◽  
Vol 3 ◽  
pp. BECB.S7050
Author(s):  
Andy Chen ◽  
Ping Zhang ◽  
Zhiyao Duan ◽  
Guofeng Wang ◽  
Hiroki Yokota
Keyword(s):  
Diffusion Coefficient ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Subcutaneous Tissue ◽  
Subcutaneous Administration ◽  
Cellular Damage ◽  
Whole Body ◽  
Chemical Agent ◽  
Permeability Factor

For the subcutaneous administration of a chemical agent (salubrinal), we constructed a mathematical model of molecule transportation and subsequently evaluated the kinetics of diffusion, convection, and molecular turnover. Salubrinal is a potential therapeutic agent that can reduce cellular damage and death. The understanding of its temporal profiles in local tissue as well as in a whole body is important to develop a proper strategy for its administration. Here, the diffusion and convection kinetics was formulated using partial and ordinary differential equations in one- and three-dimensional (semi-spherical) coordinates. Several key parameters including an injection velocity, a diffusion coefficient, thickness of subcutaneous tissue, and a permeability factor at the tissue-blood boundary were estimated from experimental data in rats. With reference to analytical solutions in a simplified model without convection, numerical solutions revealed that the diffusion coefficient and thickness of subcutaneous tissue determined the timing of the peak concentration in the plasma, and its magnitude was dictated by the permeability factor. Furthermore, the initial velocity, induced by needle injection, elevated an immediate transport of salubrinal at t < 1h. The described analysis with a combination of partial and ordinary differential equations contributes to the prediction of local and systemic effects and the understanding of the transportation mechanism of salubrinal and other agents.

Boundary Element Analysis of Accelerated Chloride Diffusion in High Performance Concrete

2013 ◽  
Vol 842 ◽  
pp. 151-155
Author(s):  
Yi Wang ◽  
Wo Cheng Hang ◽  
Lu Feng Yang ◽  
Zheng Chen
Keyword(s):  
Diffusion Coefficient ◽  
Boundary Element ◽  
High Performance ◽  
Numerical Solutions ◽  
High Performance Concrete ◽  
Chloride Concentration ◽  
Mineral Admixture ◽  
Mineral Admixtures ◽  
Chloride Diffusion ◽  
Chloride Permeability

This paper aims to analyze accelerated chloride diffusion in high performance concrete (HPC) blended with mineral admixture by using boundary element method (BEM). Rapid chloride permeability test (RCPT) was employed and executed. The experiment proves that the highest resistance to chloride permeability can be acquired in the quaternary-blended concretes (ordinary portland cement + fly ash + blast furnace slag + silica fume). A chloride diffusion BEM model was established according to the diffusion coefficient calculated from the charge passed. The numerical solutions agree with experiments well. It can be inferred that the acceleration degree of RCPT is not the same in different mix proportion. Besides, the results also suggest that the low chloride permeability of the concretes with mineral admixtures may be attributed to the lower diffusion coefficient and the lower surface chloride concentration.

Approximate travelling waves for generalized KPP equations and classical mechanics

1994 ◽  
Vol 446 (1928) ◽  
pp. 529-554 ◽  
Keyword(s):  
Travelling Waves ◽  
Classical Mechanics ◽  
Initial Distribution ◽  
Travelling Wave ◽  
Step Function ◽  
Initial Position ◽  
Classical Path ◽  
Huygens Principle ◽  
Kpp Equations ◽  
Complete Riemannian Manifolds

We consider the existence of approximate travelling waves of generalized KPP equations in which the initial distribution can depend on a small parameter μ which in the limit μ → 0 is the sum of some δ -functions or a step function. Using the method of Elworthy & Truman (1982) we construct a classical path which is the backward flow of a classical newtonian mechanics with given initial position and velocity before the time at which the caustic appears. By the Feynman–Kac formula and the Maruyama–Girsanov–Cameron–Martin transformation we obtain an identity from which, with a late caustic assumption, we see the propagation of the global wave front and the shape of the trough. Our theory shows clearly how the initial distribution contributes to the propagation of the travelling wave. Finally, we prove a Huygens principle for KPP equations on complete riemannian manifolds without cut locus, with some bounds on their volume element, in particular Cartan–Hadamard manifolds.

scholarly journals Clayton Copula as an Alternative Perspective of Multi-Reaction Model

2018 ◽  
Vol 22 (1) ◽  
pp. 83-106 ◽  
Author(s):  
Alok Dhaundiyal ◽  
Suraj B. Singh ◽  
Muammel M. Hanon ◽  
Norbert Schrempf
Keyword(s):  
Activation Energy ◽  
Distribution Function ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Initial Distribution ◽  
Reaction Model ◽  
Bivariate Distribution ◽  
Clayton Copula ◽  
Scale Parameters ◽  
Temperature Ramp

Abstract This study proposes to assess the effect of some relevant parameters of biomass pyrolysis on the numerical solutions of nthorder distributed activation energy model (DAEM) or multi reaction model (MRM). The two-step process mechanisms of pyrolysis is described by replacing the initial distribution function of f (E) with the Clayton copula. The upper limit (E∞) of ‘dE’ integral, activation energy (A), heating rate (m), and the shape and scale parameters of bivariate distribution function. Temperature ramp rate is assumed to vary linearly with time. Thermo-analytical data is obtained with the help of thermogravimetric (TG) analysis. Asymptotic technique is adopted to approximate double exponential and bivariate distribution function f (E1, E2), where E1and E2are the activation energies for bivariate scheme.

scholarly journals Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

2014 ◽  
Vol 747 ◽  
pp. 218-246 ◽  
Author(s):  
Zhong Zheng ◽  
Ivan C. Christov ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Gravity Currents ◽  
Similar Solution ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Self Similar Solution ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Similar Solutions

AbstractWe report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.

scholarly journals Parameter Estimation in Convection-Diffusion Model

2021 ◽  
Vol 19 ◽  
pp. 619-623
Author(s):  
Xiaoyang Zheng ◽  
Shu Chen ◽  
Jiangping He ◽  
Liqiong Qiu ◽  
Ye Yan ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Solutions ◽  
Difference Schemes ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Special Equation ◽  
Approximation Errors ◽  
Difference Methods ◽  
The Difference

This paper describes a special one-dimensional convection-diffusion equation and analyzes two types of difference schemes. Numerical solutions of the two difference methods for this equation are implemented to estimate the parameters of the velocity component of the fluid and the diffusion coefficient. Good results of parameters estimated are not achieved because of the larger approximation errors by the difference schemes. Then multiple linear regression is applied to estimating the corresponding parameters by using the analytical solution of this special equation. By this means, the better estimated values of the parameters are obtained.

scholarly journals Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Nauman Raza ◽  
Asma Rashid Butt
Keyword(s):  
Finite Element ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Three Dimensions ◽  
Reaction Diffusion Equation ◽  
Sobolev Gradients ◽  
Sobolev Gradient

Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

Analytical and Numerical Study on a Parametric Pendulum with the Step-Wave Modulation of Length and Forcing

2019 ◽  
Vol 19 (05) ◽  
pp. 1941006
Author(s):  
Paweł Olejnik ◽  
Michal Fečkan ◽  
Jan Awrejcewicz
Keyword(s):  
Numerical Modeling ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Time History ◽  
Step Function ◽  
Stable Limit ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Parametric Pendulum ◽  
Stable Limit Cycles

A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator subject to both an almost periodic step elongation and forcing synchronizes with the forcing, tending to almost periodic motions like stable limit cycles. Conditions for that synchronization as well as trajectories of numerical solutions on time history plots and phase planes are shown to confirm correctness of the analytical derivations and dedicated numerical modeling.

Application of full and simplified acoustic analogies to an elementary problem

2007 ◽  
Vol 578 ◽  
pp. 113-118 ◽  
Author(s):  
PHILIPPE R. SPALART
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Initial Distribution ◽  
Acoustic Analogy ◽  
Sound Levels ◽  
Elementary Problem ◽  
History Of ◽  
Radiated Sound ◽  
High Sound ◽  
Euler Solution

The axisymmetric impulse-heating case used by Tam in a critique of Lighthill's acoustic analogy is revisited. Linear and nonlinear sound levels are considered, as are three versions of the acoustic analogy: full; linearized; and one with the quadrupoles frozen at their initial distribution. Numerical solutions confirm that the full version reproduces the Euler solution and, in our analysis but contrary to Tam's, correctly identifies both the source of sound and nonlinear steepening. The linearized version is somewhat inaccurate at high sound levels, near 175 dB. The frozen version is almost as accurate as the linearized version at these levels, and identical at linear levels. In this admittedly artificial problem, it provides the radiated sound from the initial conditions only, i.e. without using the Euler solution. This is in contrast with the full acoustic analogy, which can be viewed as ‘circular’ in the sense of taking the history of all the Euler variables and returning the density.

scholarly journals Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling

2006 ◽  
Vol 364 (1842) ◽  
pp. 1313-1327 ◽  
Author(s):  
Alan P Benson ◽  
Richard H Clayton ◽  
Arun V Holden ◽  
Sanjay Kharche ◽  
Wing C Tong
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Solutions ◽  
Late Pregnancy ◽  
Surrounding Tissue ◽  
Oscillatory Activity ◽  
Gravid Uterus ◽  
Tissue Cell ◽  
Cell Coupling ◽  
Cell Dynamics ◽  
Cell Cell

Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region. We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell–cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region. However, real tissues are heterogeneous with spatial changes in cell–cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell–cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient.

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