Exponential power-law function generator

1970 ◽  
Vol 13 (5) ◽  
pp. 649-653
Author(s):  
M. Ya. Likhttsinder ◽  
O. A. Katsyuba ◽  
P. K. Lange
Keyword(s):  
Power Law ◽  
Function Generator ◽  
Power Law Function ◽  
Exponential Power

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Exact and Slow-Roll Solutions for Exponential Power-Law Inflation Connected with Modified Gravity and Observational Constraints

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 199
Author(s):  
Igor Fomin ◽  
Sergey Chervon
Keyword(s):  
Scalar Field ◽  
Power Law ◽  
Hubble Parameter ◽  
Gravity Models ◽  
Observational Constraints ◽  
Slow Roll ◽  
Correct Model ◽  
Scalar Spectral Index ◽  
Wide Range ◽  
Exponential Power

We investigate the ability of the exponential power-law inflation to be a phenomenologically correct model of the early universe. We study General Relativity (GR) scalar cosmology equations in Ivanov–Salopek–Bond (or Hamilton–Jacobi like) representation where the Hubble parameter H is the function of a scalar field ϕ. Such approach admits calculation of the potential for given H(ϕ) and consequently reconstruction of f(R) gravity in parametric form. By this manner the Starobinsky potential and non-minimal Higgs potential (and consequently the corresponding f(R) gravity) were reconstructed using constraints on the model’s parameters. We also consider methods for generalising the obtained solutions to the case of chiral cosmological models and scalar-tensor gravity. Models based on the quadratic relationship between the Hubble parameter and the function of the non-minimal interaction of the scalar field and curvature are also considered. Comparison to observation (PLANCK 2018) data shows that all models under consideration give correct values for the scalar spectral index and tensor-to-scalar ratio under a wide range of exponential-power-law model’s parameters.

scholarly journals Unveiling the Evolution of Type I AGNs in the IR (15μm) — As Seen by ISO in the ELAIS-S1 Region

2002 ◽  
Vol 184 ◽  
pp. 167-172
Author(s):  
Israel Matute ◽  
Fabio La Franca ◽  
Carlotta Gruppioni ◽  
Francesca Pozzi ◽  
Carlo Lari
Keyword(s):  
Power Law ◽  
Luminosity Function ◽  
Evolution Model ◽  
Cosmological Evolution ◽  
Type I ◽  
Infrared Background ◽  
Power Law Function ◽  
Cosmic Infrared Background ◽  
Luminosity Evolution

AbstractWe present the first estimate of the evolution of type 1 AGNs in the IR (15 μm) obtained from the ELAIS survey in the S1 region. We find that the luminosity function (LF) of Type 1 AGNs at 15μm is fairly well represented by a double power-law function with a bright slope of 2.9 and a faint slope of 1.1. There is evidence for significant cosmological evolution according to a pure luminosity evolution model L15(z)α(l+z)k, with in a (Ωm,ΩΛ)=(1.0,0.0) cosmology. This evolution is similar to what is observed at other wavebands. From the luminosity function and its evolution, we estimate a contribution of ~ 2% from Type 1 AGN to the total Cosmic Infrared Background (CIRB) at 15 μm.

Power Law with Exponential Cut‐off Utility

Metamorphosis ◽  
2014 ◽  
Vol 13 (1) ◽  
pp. 26-32
Author(s):  
Afreen Arif H. ◽  
T.P.M. Pakkala
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Power Law ◽  
Risk Preferences ◽  
Portfolio Allocation ◽  
Utility Functions ◽  
Relative Risk Aversion ◽  
Optimal Solutions ◽  
New Class ◽  
Exponential Power

Most of the utility functions studied earlier concentrated on properties of risk aversion. In this article, the authors have introduced a new class of utility function called the Power Law with Exponential Cut-off (PLEC) utility function, which exhibits all the absolute and relative risk aversion and risk loving preferences of individuals, under various conditions. It generalises and encompasses other systems of utility functions like that of exponential power. Certain properties of this utility function are discussed. Sensitivity analysis exhibits different portfolio allocations for various risk preferences. The analysis also shows that arbitrary risk preferences may lead to biased risk response estimates. Performance of PLEC utility function in portfolio allocation problem is demonstrated through numerical examples. This is evaluated through optimal solutions.

scholarly journals Light of Planck-2015 on Noncanonical Inflation

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Kh. Saaidi ◽  
A. Mohammadi ◽  
T. Golanbari
Keyword(s):  
Scalar Field ◽  
Observational Data ◽  
Power Law ◽  
Hubble Parameter ◽  
Field Model ◽  
Kinetic Term ◽  
Inflationary Scenario ◽  
Slow Roll ◽  
Power Law Function ◽  
Free Parameters

Slow-roll inflationary scenario is considered in noncanonical scalar field model supposing a power-law function for kinetic term and using two formalisms. In the first approach, the potential is picked out as a power-law function, that is, the most common approach in studying inflation. Hamilton-Jacobi approach is selected as the second formalism, so that the Hubble parameter is introduced as a function of scalar field instead of the potential. Employing the last observational data, the free parameters of the model are constrained, and the predicted form of the potential and attractor behavior of the model are studied in detail.

Taylor’s power law and fixed-precision sampling: application to abundance of fish sampled by gillnets in an African lake

2017 ◽  
Vol 74 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Meng Xu ◽  
Jeppe Kolding ◽  
Joel E. Cohen
Keyword(s):  
Power Law ◽  
Fish Assemblage ◽  
Mesh Size ◽  
Stock Management ◽  
Taylor’S Power Law ◽  
Scaling Relationship ◽  
Temporal Variance ◽  
Taylor's Power Law ◽  
Power Law Function ◽  
The Mean

Taylor’s power law (TPL) describes the variance of population abundance as a power-law function of the mean abundance for a single or a group of species. Using consistently sampled long-term (1958–2001) multimesh capture data of Lake Kariba in Africa, we showed that TPL robustly described the relationship between the temporal mean and the temporal variance of the captured fish assemblage abundance (regardless of species), separately when abundance was measured by numbers of individuals and by aggregate weight. The strong correlation between the mean of abundance and the variance of abundance was not altered after adding other abiotic or biotic variables into the TPL model. We analytically connected the parameters of TPL when abundance was measured separately by the aggregate weight and by the aggregate number, using a weight–number scaling relationship. We utilized TPL to find the number of samples required for fixed-precision sampling and compared the number of samples when sampling was performed with a single gillnet mesh size and with multiple mesh sizes. These results facilitate optimizing the sampling design to estimate fish assemblage abundance with specified precision, as needed in stock management and conservation.

A note on static and dynamic calibration of constant-temperature hot-wire probes

1976 ◽  
Vol 76 (1) ◽  
pp. 145-156 ◽  
Author(s):  
H. H. Bruun
Keyword(s):  
Constant Temperature ◽  
Power Law ◽  
Comparative Investigation ◽  
Dynamic Calibration ◽  
Calibration Data ◽  
Hot Wire ◽  
Velocity Range ◽  
Static Calibration ◽  
Large Velocity ◽  
Power Law Function

This note describes a comparative investigation of static and dynamic calibration procedures for standard hot-wire probes. It is demonstrated that nearly the same sensitivity dE/dV can be obtained by both procedures. The discrepancy reported by Perry & Morrison (1971) is shown to be due mainly to a poor approximation of static calibration data over a large velocity range by a constant-exponent power-law function.

scholarly journals Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

2014 ◽  
Vol 112 (6) ◽  
pp. 1791-1796 ◽  
Author(s):  
Clément Lagrue ◽  
Robert Poulin ◽  
Joel E. Cohen
Keyword(s):  
Population Density ◽  
Body Mass ◽  
Power Law ◽  
Power Laws ◽  
Spatial Variance ◽  
Free Living ◽  
Power Law Function ◽  
Taylor’S Law ◽  
Animal Community ◽  
Parameter Values

How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor’s law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution.

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