New Set Of Independent Variables Research Articles

Relativistic viscous effects on the primordial gravitational waves spectrum

We study the impact of the viscous effects of the primordial plasma on the evolution of the primordial gravitational waves (pGW) spectrum from Inflation until today, considering a self-consistent interaction that incorporates the back-reaction of the GW into the plasma. We use a relativistic causal hydrodynamic framework with a positive entropy production based on a Second-Order Theory (SOT) in which the viscous properties of the fluid are effectively described by a new set of independent variables. We study how the spin-2 modes typical of SOTs capture the simplest GW-fluid viscous interaction to first order. We consider that all non-ideal properties of the primordial plasma are due to an extra effectively massless self-interacting scalar field whose state becomes a many-particles one after Reheating and for which an effective fluid description is suitable. We numerically solve the evolution equations and explicitly compute the current GW spectrum obtaining two contributions. On the one hand we have the viscous evolution of the pGW: for the collision-dominated regime the GW source becomes negligible while in the collisionless limit there exists an absorption of the pGW energy due to the damping effect produced by the free-streaming spin-2 modes of the fluid and driven by the expansion of the Universe. The latter effect is characterized by a relative amplitude decrease of about 1 to 10 % with respect to the GW free evolution spectrum. On the other hand we get the GW production due to the decay of the initial spin-2 fluctuations of the fluid that is negligible compared with the above-mentioned contribution.This SOT framework captures the same qualitative effects on the evolution of GW coupled to matter reported in previous works in which a kinetic theory approach has been used.

The Major Factors Influencing on the Growth of Solar Energy Usage in India

The purpose of this paper is to explore the major factors that are contributing to and promoting the growth of solar energy usage in India. Four direct relationships are empirically proven to have significant influence on the dependent variable, growth of solar energy usage. Within the scope of the current study, a survey was conducted, secondary sources of data were used to develop a framework and were reviewed. The findings reveal that all four identified independent variables have a positive effect on the growth of the solar energy sector in India. This study aims to identify a new set of independent variables that impact the growth of solar energy usage in India.

Weak well-posedness for a modified two-component Camassa–Holm system

In this paper, we consider the weak well-posedness for a modified two-component Camassa–Holm system with initial data z0=(u0,γ0)∈(H1(R)∩W1,∞(R))×(H1(R)∩W1,∞(R)). At first, by introducing a new set of independent variables, we transform the modified two-component Camassa–Holm system into an ODE system. Then, we prove the local existence and uniqueness of the solution to the ODE system and obtain the unique solution to the original system. Finally, we investigate the weak continuous dependence on initial conditions to the modified two-component Camassa–Holm system.

QUANTIFICATION OF THE CONTRIBUTION OF FILLER CHARACTERISTICS TO NATURAL RUBBER REINFORCEMENT USING PRINCIPAL COMPONENT ANALYSIS

ABSTRACTPractical statistical models were developed to quantify individual contributions from characteristics of conventional and non-conventional fillers and predict resulting mechanical properties of both hevea and guayule natural rubber composites. Carbon black N330 and four different agro-industrial residues, namely, eggshells, carbon fly ash, processing tomato peels, and guayule bagasse, were used in this study. Filler characteristics were used as explanatory variables in multiple linear regression analyses. Principal component analysis was used to evaluate correlations among explanatory variables based on their correlation matrices and to transform them into a new set of independent variables, which were then used to generate reliable regression models. Surface area, dispersive component of surface energy, carbon black, and waste-derived filler loading were found to have almost equal importance in the prediction of composite properties. However, models developed for ultimate elongation poorly explained variability, indicating the dependence of this property on other variables. Agro-industrial residues could potentially serve as more sustainable fillers for polymer composites than conventional fillers. This new modeling approach for polymer composites allows the performance of a wide range of different waste-derived fillers to be predicted with minimum laboratory work, facilitating the optimization of compound recipes to address specific product requirements.

Fully implicit compositional simulator for modeling of asphaltene deposition during natural depletion

This paper describes development of a fully implicit compositional simulator for modeling of asphaltene deposition during natural depletion. In this paper, a new approach for multiphase flash calculation has been developed. This approach provides a more detailed description of the kinetic part of asphaltene deposition which needs to be explained more clearly. Due to a large number of unknowns, there are many ways to solve such a system by choosing different sets of independent variables. A new set of independent variables in a fully implicit model is considered for asphaltene deposition modeling. By incorporating an asphaltene precipitation model into a compositional simulator where the phase equilibrium equations, the volumetric constraint equation, the component transport equations, the multiphase flash equations and the deposition equation are solved simultaneously; a simulator for asphaltene deposition was developed with respect to natural depletion. The pure solid model is used to model asphaltene precipitation. The solid particles are considered to be separated into three parts: precipitated, flocculated and deposited solid. A first-order chemical reaction is used which models forward and reverse rates for the conversion of precipitated asphaltene to flocculated asphaltene. Also, a deposition model including adsorption, pore throat plugging, and re-entrainment was used. The simulator can also predict formation damage including porosity and permeability reduction in each block.

Unique Conservative Solutions to a Variational Wave Equation

Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation $u_{tt}-c(u) (c(u)u_x)_x=0$. Given a solution $u(t,x)$, even if the wave speed $c(u)$ is only H\"older continuous in the $t$-$x$ plane, one can still define forward and backward characteristics in a unique way. Using a new set of independent variables $X,Y$, constant along characteristics, we prove that $t,x,u$, together with other variables, satisfy a semilinear system with smooth coefficients. From the uniqueness of the solution to this semilinear system, one obtains the uniqueness of conservative solutions to the Cauchy problem for the wave equation with general initial data $u(0,\cdot)\in H^1(\mathbb{R})$, $u_t(0,\cdot)\in L^2(\mathbb{R})$.

Phase stability analysis using a reduction method

Phase stability testing is an important sub-problem in phase equilibrium calculations, which require the most important computational effort in reservoir compositional simulations and some process simulators. In this work, a new reduction method for phase stability analysis is proposed. Based on the multi-linear expression of the logarithm of fugacity coefficients as functions of some component properties (elements of the reduction matrix) and of the coefficients depending only on the reduction parameters, a new set of independent variables (which are unbounded, unlike reduction parameters) and the related set of error equations are proposed. Second order Newton iterations are directly used, without the need of switching from successive substitution iterations. It is shown that the proposed method has the same convergence path as the conventional method (in the compositional space) using the logarithm of formal mole numbers as independent variables. Besides, the proposed primary variables are Lagrange multipliers corresponding to a constrained minimization of the modified tangent plane distance function with respect to a specific set of variables and constraints. The robustness and the efficiency of the proposed method are tested for several synthetic and reservoir mixtures, and it compares favorably to conventional and previous reduction methods. Several interesting features are discussed, and a link between conventional and reduction methods is presented.

Global dissipative solutions of a modified two-component Camassa–Holm shallow water system

By introducing a new set of independent variables, we first transform a modified two-component Camassa–Holm shallow water system into a semilinear system. To obtain a dissipative solution, we modify the corresponding system into a discontinuous system. Then we map the solution of system to the dissipative solution of original equation. Moreover we prove that these global dissipative solutions construct a semigroup.

A new reduction method for phase equilibrium calculations

Phase equilibrium calculations require the most important computational effort in many process simulators and in reservoir compositional simulations. In this work, a new reduction method for phase equilibrium calculations is proposed. A new set of independent variables (and the related set of error equations) is introduced, based on the observation that, under certain conditions, the equilibrium ratios can be related only to some component properties (elements of the reduction matrix) and to equation of state parameters. The new formulation leads to simpler expressions of the elements of the Jacobian matrix. Some important features are presented, and an interesting and useful link with classical flash calculation methods is revealed. The reliability and efficiency of the proposed method are tested on several synthetic and reservoir hydrocarbon mixtures. The proposed method proves to be robust and it performs in all cases better than previous reduction methods. Finally, it is discussed how the new set of independent variables can be used for a variety of phase equilibrium calculations.

Predicting ready biodegradability in the Japanese ministry of international trade and industry test

AbstractTwo new predictive models for assessing a chemical's biodegradability in the Japanese Ministry of International Trade and Industry (MITI) ready biodegradation test have been developed. The new methods use an approach similar to that in the existing BIOWIN© program, in which the probability of rapid biodegradation is estimated by means of multiple linear or nonlinear regression against counts of 36 chemical substructures (molecular fragments) plus molecular weight (mol wt). The data set used to develop the new models consisted of results (pass/no pass) from the MITI test for 884 discrete organic chemicals. This data set was first divided into randomly selected training and validation sets, and new coefficients were derived for the training set using the BIOWIN fragment library and mol wt as independent variables. Based on these results, the fragment library was then modified by deleting some fragments and adding or refining others, and the new set of independent variables (42 substructures and mol wt) was fit to the MITI data. The resulting linear and nonlinear regression models accurately classified 81% of the chemicals in an independent validation set. Like the established BIOWIN models, the MITI models are intended for use in chemical screening and in setting priorities for further review.

The triple layer model revised

The triple layer model (TLM) and the procedures for searching out its parameters, i.e. statistical optimization and the double extrapolation, have been critically reviewed and modified. The Gouy-Chapman equation and the assumption of constant values for the capacitances have been demonstrated to be inconsistent with the rest of the model. However, the constant capacitance model physically resembles the TLM near the point of zero charge (PZC). A new set of independent variables and functions has been employed. The dependence of these functions on the electrolyte activity and adsorption density at the PZC has been shown to have a very simple analytical form. A new statistical optimization procedure has been developed. It needs no approximations, two adjustable parameters, and an independent knowledge of two or three quantities among surface charge, surface potential, inner layer capacitance, total surface site density and inert electrolyte adsorption density. Only the data around the PZC may be employed to estimate the system constants.

A QUASI-NEWTON ALGORITHM FOR SOLVING MULTIPHASE EQUILIBRIUM FLASH PROBLEMS

Abstract A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem. The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem. Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables. The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction. Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model. These parameters become the problem independent variables. The Quasi-Newton method of Broyden is employed to promote convergence of these variables. The algorithm first obtains a solution for the vapor-liquid equilibrium flash. By examining the liquid phase, a heuristic al...