scholarly journals General power-law temporal scaling for unequal-size microbubble coalescence

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Rou Chen ◽  
Huidan (Whitney) Yu ◽  
Jianhuan Zeng ◽  
Likun Zhu
Keyword(s):  
Power Law ◽  
Temporal Scaling ◽  
Unequal Size ◽  
General Power

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.

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.

EXACT, E=0, QUANTUM SOLUTIONS FOR GENERAL POWER-LAW POTENTIALS

1996 ◽  
Vol 11 (20) ◽  
pp. 3801-3817 ◽  
Author(s):  
JAMIL DABOUL ◽  
MICHAEL MARTIN NIETO
Keyword(s):  
Partial Wave ◽  
Power Law ◽  
Schrodinger Equation ◽  
Bessel Functions ◽  
Classical Solutions ◽  
Zero Energy ◽  
Centrifugal Barrier ◽  
Exact Quantum ◽  
Repulsive Potentials ◽  
General Power

For zero energy, E=0, we derive exact, quantum solutions for all power-law potentials, V(r)=−γ/rν, with γ>0 and −∞<ν<∞. The solutions are, in general, Bessel functions of powers of r. For ν>2 and l≥1 the solutions are normalizable. Surprisingly, the solutions for ν<−2, which correspond to highly repulsive potentials, are also normalizable, for all l≥0. For these |ν|>2 the partial-wave Hamiltonians, Hl, have overcomplete sets of normalizable eigensolutions. We discuss how to obtain self-adjoint extensions of Hl such that the above E=0 solutions become included in their domains. When 2>ν≥−2 the E=0 solutions are not square-integrable. The ν=2 solutions are also unnormalizable, but are exceptional solutions. We also find that, by increasing the dimension of the Schrödinger equation beyond 4, an effective centrifugal barrier is created which is sufficient to cause binding when E=0 and ν>2, even for l=0. We discuss the physics of the above solutions and compare them to the corresponding classical solutions, which are derived elsewhere.

scholarly journals Wind Speed Influences on Marine Aerosol Optical Depth

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Colin O'Dowd ◽  
Claire Scannell ◽  
Jane Mulcahy ◽  
S. Gerard Jennings
Keyword(s):  
Wind Speed ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Power Law ◽  
Anthropogenic Pollution ◽  
Open Ocean ◽  
Marine Aerosol ◽  
Wind Speeds ◽  
General Power ◽  
Relationship Of

The Mulcahy (Mulcahy et al., 2008) power-law parameterization, derived at the coastal Atlantic station Mace Head, between clean marine aerosol optical depth (AOD) and wind speed is compared to open ocean MODIS-derived AOD versus wind speed. The reported AOD versus wind speed (U) was a function of ∼U2. The open ocean MODIS-derived AOD at 550 nm and 860 nm wavelengths, while in good agreement with the general magnitude of the Mulcahy parameterization, follows a power-law with the exponent ranging from 0.72 to 2.47 for a wind speed range of 2–18 m s−1. For the four cases examined, some MODIS cases underestimated AOD while other cases overestimated AOD relative to the Mulcahy scheme. Overall, the results from MODIS support the general power-law relationship of Mulcahy, although some linear cases were also encountered in the MODIS dataset. Deviations also arise between MODIS and Mulcahy at higher wind speeds (>15 m s−1), where MODIS-derived AOD returns lower values as compared to Mulcahy. The results also support the suggestion than wind generated sea spray, under moderately high winds, can rival anthropogenic pollution plumes advecting out into marine environments with wind driven AOD contributing to AOD values approaching 0.3.

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