DIELECTRIC RESPONSE OF ANISOTROPIC GRADED CYLINDRICAL COMPOSITES WITH A GENERAL POWER-LAW PROFILE

2008 ◽  
Vol 22 (05) ◽  
pp. 507-515 ◽  
Author(s):  
EN-BO WEI ◽  
G. Q. GU ◽  
K. W. YU
Keyword(s):  
Power Law ◽  
Dielectric Response ◽  
Tangential Direction ◽  
Dipole Approximation ◽  
Effective Response ◽  
Geometric Function ◽  
Electric Potentials ◽  
General Power ◽  
Cylindrical Inclusions ◽  
Dilute Limit

The effective dielectric response of composites containing anisotropic graded cylindrical inclusions whose graded profile along the radial direction is different from that along the tangential direction in cylindrical coordinates, has been investigated. As an example, we have studied composites of anisotropic graded cylindrical inclusions with general power-law profiles, [Formula: see text] and [Formula: see text], where r is the distance of a point in the cylindrical inclusion from the origin. Analytical solutions of the local electric potentials are derived in terms of the hyper-geometric function and the formulas for calculating the effective response of anisotropic graded composites are given in the dilute limit. Furthermore, we have validated the anisotropic differential effective dipole approximation (ADEDA) by comparing with our exact results, and obtained excellent agreement.

Time scale of dynamic heterogeneity in model ionic liquids and its relation to static length scale and charge distribution

2015 ◽  
Vol 17 (43) ◽  
pp. 29281-29292 ◽  
Author(s):  
Sang-Won Park ◽  
Soree Kim ◽  
YounJoon Jung
Keyword(s):  
Ionic Liquid ◽  
Ionic Liquids ◽  
Charge Distribution ◽  
Power Law ◽  
Structural Relaxation ◽  
Time Scale ◽  
Length Scale ◽  
Dynamic Heterogeneity ◽  
General Power

We find a general power-law behavior: , where ζdh ≈ 1.2 for all the ionic liquid models, regardless of charges and the length scale of structural relaxation.

Implementing General Power Law to Interconvert Linear Viscoelastic Functions of Modified Asphalt Binders

2018 ◽  
Vol 144 (2) ◽  
pp. 04018010 ◽  
Author(s):  
Pouria Hajikarimi ◽  
Fereidoon Moghadas Nejad ◽  
Mohammad Mohammadi Aghdam
Keyword(s):  
Power Law ◽  
Asphalt Binders ◽  
Modified Asphalt ◽  
Linear Viscoelastic ◽  
General Power

scholarly journals Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
R. Naz ◽  
F. M. Mahomed
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Power Law ◽  
Fourth Order ◽  
Applied Load ◽  
Mass Density ◽  
Load Case ◽  
Order Ordinary Differential Equation ◽  
General Power

We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass densityg(x), and the applied load denoted byf(u), a function of transverse displacementu(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass densityg(x)and applied loadf(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms ofg(x). For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature wheng(x)is constant with variable applied loadf(u). For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.

Local Electric Field Distribution of Graded Cylindrical Composites

2012 ◽  
Vol 476-478 ◽  
pp. 751-754
Author(s):  
Xia Ding ◽  
Guang Hai Guo ◽  
Wei Guo Niu
Keyword(s):  
External Field ◽  
Electric Field ◽  
Field Distribution ◽  
Power Law ◽  
Electric Field Distribution ◽  
Local Electric Field ◽  
Finite Frequency ◽  
Electrical Field ◽  
Inclusion Region ◽  
Dilute Limit

For a sinusoidal alternating current (AC) external field of finite frequency ω , the local electric field distribution at all harmonics has been investigated by graded cylindrical composites with power-law gradient inclusions. In the dilute limit, the obtained results show that the local electrical field distribution in the cylindrical inclusion region is controllable and the electric field peak’s position inside the cylindrical composites can be confined at its centre by varying the parameters of the graded dielectric profiles.

Dielectric Response of a Chain of Disordered Polarizable Spheres: Numerical Simulation and Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
Pedro VillaseiÑor-Gonzalez ◽  
Cecilia Noguez ◽  
Ruben G. Barrera
Keyword(s):  
Numerical Simulation ◽  
Dielectric Response ◽  
Linear Equations ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Effective Response ◽  
Static Approximation ◽  
One Dimensional ◽  
Induced Dipole ◽  
A Chain

ABSTRACTWe applied to a one-dimensional system (1D) a recently developed diagrammatic formalism, in order to calculate the effective dielectric response of a chain of polarizable spheres embeded in an homogeneous host. The effective response is calculated within the dipolar, quasi-static approximation, through the summation of selected classes of diagrams. We compared our results with a numerical simulation, where the position of each sphere was generated at random and the induced dipole moment of each sphere was calculated by solving a set of linear equations through matrix inversion and using periodic boundary conditions.

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