scholarly journals Degeneracies and scaling relations in general power-law models for gravitational lenses

2002 ◽  
Vol 332 (4) ◽  
pp. 951-961 ◽  
Author(s):  
O. Wucknitz
Keyword(s):  
Power Law ◽  
Scaling Relations ◽  
Gravitational Lenses ◽  
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.

scholarly journals Evidence of a general 2/3-power law of scaling leaf nitrogen to phosphorus among major plant groups and biomes

2009 ◽  
Vol 277 (1683) ◽  
pp. 877-883 ◽  
Author(s):  
Peter B. Reich ◽  
Jacek Oleksyn ◽  
Ian J. Wright ◽  
Karl J. Niklas ◽  
Lars Hedin ◽  
...  
Keyword(s):  
Power Law ◽  
Plant Traits ◽  
High Growth ◽  
Terrestrial Ecosystems ◽  
Leaf Nitrogen ◽  
Scaling Relations ◽  
Nitrogen And Phosphorus ◽  
Form And Function ◽  
General Relations ◽  
And Function

Scaling relations among plant traits are both cause and consequence of processes at organ-to-ecosystem scales. The relationship between leaf nitrogen and phosphorus is of particular interest, as both elements are essential for plant metabolism; their limited availabilities often constrain plant growth, and general relations between the two have been documented. Herein, we use a comprehensive dataset of more than 9300 observations of approximately 2500 species from 70 countries to examine the scaling of leaf nitrogen to phosphorus within and across taxonomical groups and biomes. Power law exponents derived from log–log scaling relations were near 2/3 for all observations pooled, for angiosperms and gymnosperms globally, and for angiosperms grouped by biomes, major functional groups, orders or families. The uniform 2/3 scaling of leaf nitrogen to leaf phosphorus exists along a parallel continuum of rising nitrogen, phosphorus, specific leaf area, photosynthesis and growth, as predicted by stoichiometric theory which posits that plants with high growth rates require both high allocation of phosphorus-rich RNA and a high metabolic rate to support the energy demands of macromolecular synthesis. The generality of this finding supports the view that this stoichiometric scaling relationship and the mechanisms that underpin it are foundational components of the living world. Additionally, although abundant variance exists within broad constraints, these results also support the idea that surprisingly simple rules regulate leaf form and function in terrestrial ecosystems.

scholarly journals Galaxy mass profiles from strong lensing I: the circular power-law model

2019 ◽  
Vol 487 (4) ◽  
pp. 5143-5154
Author(s):  
C M O’Riordan ◽  
S J Warren ◽  
D J Mortlock
Keyword(s):  
Power Law ◽  
Signal To Noise Ratio ◽  
Theoretical Estimate ◽  
Flux Ratio ◽  
Positional Information ◽  
Position Angle ◽  
Gravitational Lenses ◽  
The Galaxy ◽  
Image Position ◽  
Mass Profiles

Abstract In this series of papers, we develop a formalism for constraining mass profiles in strong gravitational lenses with extended images, using fluxes in addition to positional information. We start in this paper with a circular power-law profile and show that the slope γ is uniquely determined by only two observables: the flux ratio f1/f2 and the image position ratio θ1/θ2 of the two images. We derive an analytic expression relating these two observables to the slope, a result that does not depend on the Einstein angle or the structure or brightness of the source. We then find an expression for the uncertainty on the slope σγ that depends only on the position ratio θ1/θ2 and the total signal-to-noise ratio (S/N) in the images. For example, in a system with position ratio θ1/θ2 = 0.5, S/N = 100, and γ = 2 we find that γ is constrained to a precision of ±0.03. We then test these results against a series of mock observations. We invert the images and fit an 11-parameter model, including ellipticity and position angle for both lens and source and measure the uncertainty on γ. We find agreement with the theoretical estimate for all mock observations. In future papers, we will examine the radial range of the galaxy over which the constraint on the slope applies, and extend the analysis to elliptical lenses.

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.

scholarly journals Inverting the dynamical evolution of globular clusters: clues to their origin

2015 ◽  
Vol 12 (S316) ◽  
pp. 214-221
Author(s):  
Mark Gieles ◽  
Poul Alexander
Keyword(s):  
Power Law ◽  
Globular Clusters ◽  
Milky Way ◽  
Dynamical Evolution ◽  
Mass Function ◽  
Initial Mass Function ◽  
Scaling Relations ◽  
Galactocentric Distance ◽  
Cluster Density ◽  
Bivariate Dependence

AbstractScaling relations for globular clusters (GC) differ from the scaling relations for pressure supported (elliptical) galaxies. In this contribution we discuss the relative importance of nature and nurture in the establishment of the scaling between cluster density (or radius), mass and Galactocentric distance for the Milky Way GCs. We show that energy diffusion by stellar encounters (i.e. two-body relaxation) is the dominant mechanism in shaping the bivariate dependence of density on mass and Galactocentric distance for GCs with masses ≲ 106M⊙, and it can not be excluded that GCs formed with similar scaling relations as the more massive ultra-compact dwarf galaxies (UCDs). To explore the initial properties that give rise to the distributions of these quantities, we developed a fast cluster evolution model (Evolve Me A Cluster of StarS, emacss) and use it in a hierarchical Bayesian framework to fit a parameterised model for the initial properties of Milky Way GCs to the observed present-day properties. The best-fit cluster initial mass function is substantially flatter (power-law with index − 0.6 ± 0.2) than what is observed for young massive clusters (YMCs) forming in the nearby Universe (power-law with index − 2). This result is driven by the metal-poor GCs, a slightly steeper CIMF is allowed when considering the metal-rich GCs separately (α ≃ −1.2 ± 0.4). If stellar mass loss and two-body relaxation in the Milky Way tidal field are the dominant disruption mechanisms, then GCs formed differently from YMCs.

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.

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