Nonlinear effects in the rheology of dilute suspensions

1967 ◽  
Vol 28 (4) ◽  
pp. 657-673 ◽  
Author(s):  
J. D. Goddard ◽  
Chester Miller
Keyword(s):  
Rheological Behaviour ◽  
Nonlinear Effects ◽  
Inertial Effects ◽  
Particle Deformation ◽  
Rheological Equation ◽  
Non Linear ◽  
Rheological Relation ◽  
Monodisperse Suspension ◽  
Dilute Suspensions ◽  
Special Case

An analysis is presented of the deformation of a solid-like, viscoelastic sphere suspended in the infinite Stokesian flow field of a Newtonian fluid undergoing an arbitrary time-dependent homogeneous deformation far from the particle. The results of the analysis are then used to deduce the macroscopic rheological behaviour of a dilute monodisperse suspension of slightly deformable spheres.Even though inertial effects and second-order terms in the particle deformation are neglected, it is found that non-linear rheological effects can arise, because of the interaction between the deformed particle and the flow. As a consequence, the rheological relation obtained here differs from those presented earlier by Fröhlich & Sack (1946) and by Oldroyd (1955) through the appearance of certain terms which are non-linear in the deformation rate.When the suspended particles are purely elastic in their behaviour the rheological equation presented here reduces for certain flows to a special case of Oldroyd's (1958) phenomenological model, with material constants which can be directly related to suspension properties.

ON TAYLOR'S SCRAPING PROBLEM AND FLOW OF A SISKO FLUID

2009 ◽  
Vol 14 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Ali R. Ansari ◽  
Ahmed Ahmad ◽  
N. Ahmad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Normal Stress ◽  
Partial Differential ◽  
Sisko Fluid ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Special Case

The aim of the present investigation is to study the properties of a Sisko fluid flowing between two intersecting planes. The problem is similar to Taylor's scraping problem for a viscous fluid. We determine the solution of the complicated set of non‐linear partial differential equations describing the flow analytically. The analysis is carried out in detail reflecting the effects of varying the angle of the scraper on the flow. In addition, the tangential and normal stress are also computed. We also show the well known Taylor scraper problem as a special case.

scholarly journals Estimating the nonlinear effects of female directors on financial performance

2016 ◽  
Vol 31 (2) ◽  
pp. 97-113 ◽  
Author(s):  
Chen Ming ◽  
Lim Hock Eam
Keyword(s):  
Financial Performance ◽  
Linear Relationship ◽  
Initial Public Offerings ◽  
Gender Diversity ◽  
Nonlinear Effects ◽  
Board Members ◽  
Women Directors ◽  
Content Type ◽  
Return On Equity ◽  
Non Linear

Purpose The purpose of this paper is to identify the non-linear effects of the presence of women directors on the board on the financial performances of Malaysian companies which undertakes initial public offerings (IPOs). This paper also analyzes the impacts of non-executive directors and independent directors on their company performances. Design/methodology/approach This paper traces the effects of gender diversity on the board on the financial performance of a sample of 123 Malaysian companies from the list of 230 companies which have made IPOs and are listed during the period 2005-2012. The multiple regressions (with linear and non-linear specification) are used to estimate the effects of women directors on companies’ performance. Findings The results show that presence of women directors on the board do not purport to have any significant linear or non-linear impact on the financial performance of the companies under reference, except for the companies in the top 80th percentile of return on equity. Similarly, strong evidence is also found when the number of women as board members is more than 15 per cent. Research limitations/implications The findings of this paper suggest that presence of women directors provides a beneficial impact on the return on equity of companies in Malaysia. Therefore, it is suggested that there should be greater participation of women as board members in the country. Originality/value Prior studies tried to estimate linear relationship between the presence of woman directors on company performance. Present study assessed it from three different angles: the sample consists of companies in Malaysia issuing IPOs; possible non-linear relationship is also assessed; and apart from multiple regression, quantile regression technique was also used.

scholarly journals NeAT: a Nonlinear Analysis Toolbox for Neuroimaging

2020 ◽  
Vol 18 (4) ◽  
pp. 517-530
Author(s):  
Adrià Casamitjana ◽  
◽  
Verónica Vilaplana ◽  
Santi Puch ◽  
Asier Aduriz ◽  
...  
Keyword(s):  
Linear Models ◽  
Brain Aging ◽  
Nonlinear Effects ◽  
Brain Morphology ◽  
Model Estimation ◽  
Wide Range ◽  
Non Linear ◽  
Linear Effects ◽  
Interaction With Age ◽  
User Friendly

Abstract NeAT is a modular, flexible and user-friendly neuroimaging analysis toolbox for modeling linear and nonlinear effects overcoming the limitations of the standard neuroimaging methods which are solely based on linear models. NeAT provides a wide range of statistical and machine learning non-linear methods for model estimation, several metrics based on curve fitting and complexity for model inference and a graphical user interface (GUI) for visualization of results. We illustrate its usefulness on two study cases where non-linear effects have been previously established. Firstly, we study the nonlinear effects of Alzheimer’s disease on brain morphology (volume and cortical thickness). Secondly, we analyze the effect of the apolipoprotein APOE-ε4 genotype on brain aging and its interaction with age. NeAT is fully documented and publicly distributed at https://imatge-upc.github.io/neat-tool/.

A New Simple Non Linear Modelling of the Quasi Statics of Granular Media: predictions, comparisons with experiments

2000 ◽  
Vol 627 ◽  
Author(s):  
Pierre Evesque
Keyword(s):  
Granular Material ◽  
Granular Media ◽  
Stress Ratio ◽  
Rheological Behaviour ◽  
Stress Strain ◽  
Linear Modelling ◽  
Non Linear ◽  
Strain Paths ◽  
Contact Distribution

ABSTRACTFirst, a non linear incremental modelling is proposed to describe rheological behaviour of granular material under different simple (i.e. triaxial-, oedometric-, undrained-) stress-strain paths. Validity of isotropic-response assumption is demonstrated whatever the stress ratio as far as deformation range remains small (ε1<5%). This contradicts some recent hypothesis made on the evolution of contact distribution during anisotropic loading.

Relativistic formulation for non-linear waves in a non-uniform plasma

1968 ◽  
Vol 2 (2) ◽  
pp. 257-281 ◽  
Author(s):  
D. S. Butler ◽  
R. J. Gribben
Keyword(s):  
Mathematical Formulation ◽  
Collisionless Plasma ◽  
Debye Length ◽  
Type Equation ◽  
Distribution Functions ◽  
Small Scale ◽  
Relativistic Limit ◽  
Background Distribution ◽  
Non Linear ◽  
Special Case

The mathematical formulation for the problem of non-linear oscillations in a self-consistent, non-uniform, collisionless plasma is considered. The fully nonlinear treatment illuminates the effect of the wave on the background distribution of the plasma through which it is passing. It is assumed that, although the overall non-uniformity may be large, significant changes occur only over time or length scales which are large compared with the plasma period or Debye length respectively. Exclusion of secular terms from the solution leads to a Liouvile type equation, which must be satisfied by the background distribution, and to propagation laws for the waves.The theory is restricted to almost one-dimensional electrostatic waves and a general presentation is given from a relativistically-invariant point of view. Then the equations are derived in terms of physical variables for the special case in which: (i) the distribution functions and electrostatic potential depend on one space co-ordinate (that of propagation of the wave) and the former on the corresponding particle velocity component only, (ii) the wave is slowly-varying only with respect to this co-ordinate and time, and (iii) the magnetic field is zero. Finally, the non-relativistic limit of this case is considered in more detail. The boundary conditions satisfied by the distribution functions are discussed and this leads to the conclusion that in some circumstances thin sheets of probability fluid are formed in phase space and the background distribution cannot be strictly defined. This motivates a reformulation and subsequent re-solution of the problem (for this non-relativistic special case) in terms of weak functions, corresponding to the physical assumption of the presence of a small-scale mixing mechanism, which is excited by and smears the sheeted distribution but is otherwise dormant.The results of the investigation are given as a system of differentio-integral equations which must be solved if necessary conditions for the absence of nonsecular solutions (of the Vlasov and Maxwell equations) are to be satisfied. No solution of this system is attempted here.

On the general bilinear time series model

1988 ◽  
Vol 25 (3) ◽  
pp. 553-564 ◽  
Author(s):  
Jian Liu ◽  
Peter J. Brockwell
Keyword(s):  
Time Series ◽  
Stationary Solution ◽  
Time Series Model ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Special Cases ◽  
Non Linear ◽  
Necessary And Sufficient ◽  
Special Case

A sufficient condition is derived for the existence of a strictly stationary solution of the general bilinear time series equations. The condition is shown to reduce to the conditions of Pham and Tran (1981) and Bhaskara Rao et al. (1983) in the special cases which they consider. Under the condition specified, a solution is constructed which is shown to be causal, stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non-linear terms, our condition reduces to the well-known necessary and sufficient condition for existence of a causal stationary solution.

Correlations between Structure of Elastomers and the Mechanism of their Degradation by Ozone

1968 ◽  
Vol 41 (3) ◽  
pp. 643-652 ◽  
Author(s):  
G. Salomon ◽  
F. van Bloois
Keyword(s):  
Surface Layer ◽  
Stress Corrosion ◽  
Elastic Energy ◽  
Critical Stress ◽  
Rheological Behaviour ◽  
Stress And Strain ◽  
Crack Geometry ◽  
Structural Relationships ◽  
Special Case ◽  
Stored Elastic Energy

Abstract Ozone cracking is treated as a special case of stress corrosion. The correlation between delayed fracturing, stress and strain is explained in terms of changing crack geometry. Structural relationships have been studied in the region of minimum, critical stress. Two groups of ozone sensitive polymers can be distinguished: in highly ozone sensitive materials cracks are initiated at very low values of stored elastic energy, while initiation in the more resistant butyl rubbers and EPT rubbers occurs only at much higher values of stored elastic energy. The rate of cracking in neoprene is shown to be much less stress sensitive than the corresponding rate in other polydiene rubbers. It is conjectured that this favorable property of neoprene depends on the rheological behaviour of the ozonized surface layer.

Rheological behaviour of dilute suspensions of platelet particles

1999 ◽  
Vol 38 (5) ◽  
pp. 437-442 ◽  
Author(s):  
André Luciani ◽  
Yves Leterrier ◽  
Jan-Anders E. Månson
Keyword(s):  
Rheological Behaviour ◽  
Dilute Suspensions

scholarly journals Enantiodivergent Non-Linear Effects in Asymmetric Catalysis

2020 ◽  
Author(s):  
Yannick Geiger ◽  
thierry achard ◽  
aline maisse-françois ◽  
Stephane Bellemin-Laponnaz
Keyword(s):  
Metal Complexes ◽  
Asymmetric Catalysis ◽  
Catalytic System ◽  
Catalyst Concentration ◽  
Enantiomeric Excess ◽  
Product Formation ◽  
Experimental Results ◽  
Non Linear ◽  
Linear Effects ◽  
Special Case

In this paper, we theoretically discuss the enantiodivergent product formation in asymmetric catalysis, a process in which the sign of the overall product enantiomer switches upon a change of catalyst concentration. The presented model is based on a catalytic system that consists of both discrete and dimeric aggregated metal complexes, in competition and in equilibrium. These concepts were then expanded to a non-enantiopure catalyst, giving rise to enantiodivergent non-linear effects – a special case of a hyperpositive non-linear effects where the product enantiomer’s sign switches upon a change of the catalyst enantiomeric excess. Different cases are considered allowing a discussion of the influence of the parameters governing both models. Finally, we present experimental results that support the enantiodivergence while varying the concentration of enantiopure catalyst or while varying the enantiomeric excess of the catalyst, using chiral N-methylephedrine as a ligand for the enantioselective addition of dimethylzinc to benzaldehyde.

A differential equation for undamped forced non-linear oscillations. I

1955 ◽  
Vol 51 (2) ◽  
pp. 297-312 ◽  
Author(s):  
G. R. Morris
Keyword(s):  
Differential Equation ◽  
Damping Force ◽  
Restoring Force ◽  
All Solutions ◽  
Non Linear ◽  
Variable Damping ◽  
Existence Of Periodic Solutions ◽  
Dynamical Description ◽  
Image Position ◽  
Special Case

In this paper and its sequels I consider the differential equationin which e(t) is an even periodic function of t and dots denote differentiation with respect to t. We can regard (1·1) as a special case of the equation(the ‘differential equation of non-linear oscillations’), which describes the motion on the x–axis of a particle of unit mass subject to a restoring force g(x), a variable damping force f(x, ẋ)ẋ and an external force p(t); the dynamical description used in the title appeals to this interpretation. The most interesting problems on (1·2) and its specializations concern the behaviour of solutions as t → ∞ for example, we may seek conditions on f, g and p which allow us to assert that some or all solutions are bounded or, having assumed that p(t) is periodic, seek conditions on f and g which allow us to assert the existence of periodic solutions.

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