Chemical Transport Facilitated by Multiphase Flow Systems1

1985 ◽  
Vol 17 (9) ◽  
pp. 1-12 ◽  
Author(s):  
Carl G. Enfield
Keyword(s):  
Organic Carbon ◽  
Boundary Conditions ◽  
Transport Equation ◽  
Fluid Phase ◽  
Chemical Transport ◽  
Facilitated Transport ◽  
Organic Fraction ◽  
Dispersive Transport ◽  
Transformation Of Variables ◽  
The Impact

Relatively immobile chemicals have been observed moving significantly faster than anticipated from hydrophobic theory. A theory is developed considering transport in three mobile fluid phases which can be used to describe this facilitated transport. The convective dispersive transport equation is solved utilizing a transformation of variables which permits utilizing existing solutions covering a wide variety of boundary conditions. The impact of the facilitated transport is demonstrated for one case where the soils organic carbon is 10%. If 2% of the fluid phase is an organic fraction, the theory developed projects that hydrophobic theory may underestimate mobility by more than 100 times. At concentrations of dissolved organic carbon normally observed in nature (5 - 10 mg/l), a measurable increased mobility is anticipated for the very immobile compounds like dioxins.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

scholarly journals Stability analysis of an interacting holographic dark energy model

2019 ◽  
Vol 34 (19) ◽  
pp. 1950147
Author(s):  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dark Energy ◽  
System Analysis ◽  
Holographic Dark Energy ◽  
Equilibrium Points ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lyapunov Function Method ◽  
Transformation Of Variables ◽  
The Stability ◽  
Manifold Theory

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

Optimum Design of Straight-Walled Diffusers

1959 ◽  
Vol 81 (3) ◽  
pp. 321-329 ◽  
Author(s):  
S. J. Kline ◽  
D. E. Abbott ◽  
R. W. Fox
Keyword(s):  
Flow Regimes ◽  
Literature Survey ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Constant Ratio ◽  
Straight Line ◽  
Throat Width ◽  
Transformation Of Variables ◽  
Optimum Recovery ◽  
Future Reference

The four common optimum problems in diffuser design are defined. These optima are located in relation to the over-all flow regimes in terms of geometrical parameters for straight-walled units. Using an empirically derived transformation of variables between the conical and two-dimensional geometries, all available data for optimum recovery at constant ratio of wall length to throat width are correlated by a single straight line. This line lies slightly above and parallel to the line of onset of large transitory stall on the chart of over-all flow regimes. The correlated results are based on a literature survey. The range of conditions for each investigation is tabulated for convenient future reference.

Objective Inference for Climate Parameters: Bayesian, Transformation-of-Variables, and Profile Likelihood Approaches

2014 ◽  
Vol 27 (19) ◽  
pp. 7270-7284 ◽  
Author(s):  
Nicholas Lewis
Keyword(s):  
Climate Sensitivity ◽  
Bayesian Methods ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Likelihood Method ◽  
Jeffreys Prior ◽  
Bayesian Approaches ◽  
Noninformative Priors ◽  
Likelihood Functions ◽  
Transformation Of Variables

Abstract Insight is provided into the use of objective-Bayesian methods for estimating climate sensitivity by considering their relationship to transformations of variables in the context of a simple case considered in a previous study, and some misunderstandings about Bayesian inference are discussed. A simple model in which climate sensitivity (S) and effective ocean heat diffusivity (Kυ) are the only parameters varied is used, with twentieth-century warming attributable to greenhouse gases (AW) and effective ocean heat capacity (HC) being the only data-based observables. Probability density functions (PDFs) for AW and HC are readily derived that represent valid independent objective-Bayesian posterior PDFs, provided the error distribution assumptions involved in their construction are justified. Using them, a standard transformation of variables provides an objective joint posterior PDF for S and Kυ; integrating out Kυ gives a marginal PDF for S. Close parametric approximations to the PDFs for AW and HC are obtained, enabling derivation of likelihood functions and related noninformative priors that give rise to the objective posterior PDFs that were computed initially. Bayes’s theorem is applied to the derived AW and HC likelihood functions, demonstrating the effect of differing prior distributions on PDFs for S. Use of the noninformative Jeffreys prior produces an identical PDF to that derived using the transformation-of-variables approach. It is shown that similar inference for S to that based on these two alternative objective-Bayesian approaches is obtained using a profile likelihood method on the derived joint likelihood function for AW and HC.

Calculation of Direct Exchange Areas for Non-Uniform Zones

2003 ◽  
Author(s):  
Weixue Tian ◽  
Wilson K. S. Chiu
Keyword(s):  
Heat Flux ◽  
Computational Time ◽  
Thermal Gradients ◽  
Reasonable Accuracy ◽  
Radiation Heat ◽  
Radiation Heat Flux ◽  
Double Integral ◽  
Zonal Method ◽  
Direct Exchange ◽  
Transformation Of Variables

This paper presents a special transformation of variables to reduce a double integral into three single integrals and its use for calculating Direct Exchange Areas (DEA) in Zonal method. This technique was originally presented for calculation of DEA using a uniform zone system in a cylindrical enclosure. However, non-uniform zones are needed for applications with large thermal gradients. Thus we extended this technique to calculate the DEA for non-uniform zones in an axisymmetrical cylinder system. At least six times of saving in computational time was observed in calculating DEA compared with cases without transforming of variables. It is shown that accuracy and efficiency of estimation of radiation heat flux is improved when using a non-uniform zone system. Reasonable accuracy of all DEA are calculated without resorting to the conservative equations. Results compared well with analytical solutions and numerical results of previous researchers. A brief discussion of its application in calculating DEA in a 3-D rectangular enclosure is also provided.

Invariants of the Markov process by the transformation of variables

1977 ◽  
Vol 8 (12) ◽  
pp. 1327-1336
Author(s):  
NAOHIRO ISHII ◽  
NOBUO SUZUMURA ◽  
SHINIGHI NISHINO
Keyword(s):  
Markov Process ◽  
Transformation Of Variables
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