NEUTRINO OSCILLATION IN DENSE MEDIUMS

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3483-3492 ◽  
Author(s):  
Z. Y. LAW ◽  
A. H. CHAN ◽  
C. H. OH
Keyword(s):  
Neutrino Oscillation ◽  
Standard Treatment ◽  
Neutral Current ◽  
Matter Density ◽  
Order Equation ◽  
Second Order ◽  
Dense Medium ◽  
First Order ◽  
Probability Current ◽  
Current Interaction

It is found that a term normally discarded in the standard treatment of the MSW effect might be relevant in the case of non-adiabatic varying matter density, leading to a second order field equation, instead of the usual first order "Schrodinger equation". This leads to dispersion relation that gives rise to the possibility of neutrino trapping in a dense medium as well as the coupling of neutrino oscillation to neutral current interaction. This is found to be in agreement with previous results1. The corresponding conserved probability current is derived for this second order equation, and applied to the case of 2-flavor neutrino oscillation in a dense medium. The results in this work might be applicable to the oscillation of neutrinos in dense astrophysical medium.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Kinetics of Glyphosate Adsorption on Composite Resin from Aqueous Solution

2013 ◽  
Vol 803 ◽  
pp. 157-160
Author(s):  
Zhen Zhen Kong ◽  
Dong Mei Jia ◽  
Su Wen Cui
Keyword(s):  
Experimental Data ◽  
Aqueous Solution ◽  
Composite Resin ◽  
Order Equation ◽  
Second Order ◽  
First Order ◽  
Basic Resin ◽  
Pseudo Second Order ◽  
Kinetics Of ◽  
Best Fit

The composite weakly basic resin (D301Fe) was prepared and examined using scanning electron microscopy and Fourier transform infrared spectroscopy. The adsorption kinetics of glyphosate from aqueous solution onto composite weakly basic resin (D301Fe) were investigated under different conditions. The experimental data was analyzed using various adsorption kinetic models like pseudo-first order, the pseudo-second order, the Elovich and the parabolic diffusion models to determine the best-fit equation for the adsorption of glyphosate onto D301Fe. The results show that the pseudo-second order equation fitted the experimental data well and its adsorption was chemisorption-controlled.

A Comparative Study on the Removal of 2,2',4,4'-Tetrabrominated Diphenyl Ether (BDE-47) by Four Different Methods

2014 ◽  
Vol 700 ◽  
pp. 211-215
Author(s):  
Yi Miao Lin ◽  
Ling Yun Li ◽  
Ji Wei Hu ◽  
Ming Yi Fan ◽  
Chao Zhou ◽  
...  
Keyword(s):  
Exchange Resin ◽  
Diphenyl Ether ◽  
Ion Exchange Resin ◽  
Order Equation ◽  
Second Order ◽  
Order Kinetic ◽  
First Order ◽  
Atomic Force ◽  
Phase Reduction ◽  
Pseudo Second Order

The zero-valent iron (ZVI) particles were synthesized by the aqueous phase reduction, and the tapping mode image of atomic force microscope (AFM) showed that the diameter of the ZVI particles was in the range of 90 nm - 400 nm. By comparison of the debromination of BDE-47 by sunlight, ZVI, ZVI impregnated activated carbon (ZVI/AC) and ZVI impregnated ion exchange resin (ZVI/IER), the debromination effect was found to descend in the following order: ZVI/IER > ZVI/AC > ZVI > sunlight. Second order and first order kinetic models were used for the fitting of the debromination data of BDE-47. Results show that the debromination data of BDE-47 by the sunlight, ZVI, ZVI/AC and ZVI/IER in the current study are generally best described by the pseudo first order equation. Meanwhile, the debromination data of BDE-47 by the ZVI and ZVI/IER can also be described by the pseudo second order equation.

Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

2020 ◽  
Author(s):  
Farid P. Bakti ◽  
Moo-Hyun Kim
Keyword(s):  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Computational Time ◽  
Forward Speed ◽  
Frequency Wave ◽  
Order Difference ◽  
First Order ◽  
Current Interaction ◽  
Current Loading

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.

scholarly journals On wave matrices, and some properties of the wave equation

1936 ◽  
Vol 157 (890) ◽  
pp. 1-27 ◽  
Keyword(s):  
Wave Equation ◽  
Wave Theory ◽  
Order Equation ◽  
Second Order ◽  
Order Operator ◽  
First Order ◽  
Second Order Wave Equation

1—Wave matrices became important in wave theory as the result of the use of them made by Dirac to express the operator of the second order wave equation as the square of a linear one, and hence obtain a first order equation. Thus, p 2 representing the second order operator, the equation p 2 Ψ = 0, may be factorized, and written (∑ E α p α ) (∑ E α p α ) Ψ = 0, (α = 1, 2, . . . , n ), giving the first order equation ∑ E α p α Ψ = 0, (1) if the p α commute with themselves and with the E α , and if the E α are matrix roots of +1 or of —1, which satisfy E α E β = — E β E a (β ≠ α). (2)

On the Calculation of Scalar Mesons in Functional Nonlinear Spinor Theory

1974 ◽  
Vol 29 (10) ◽  
pp. 1394-1406
Author(s):  
W. Bauhoff
Keyword(s):  
Integral Equation ◽  
Angular Momentum ◽  
Scalar Meson ◽  
Functional Space ◽  
Order Equation ◽  
Second Order ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons

Abstract The formulation of nonlinear spinor theory in functional space is used for the calculation of scalar meson masses. The second order equation used, requires an explicit angular momentum reduction. For illustration, this method is also applied to the first order equation. In second order, we get an integral equation of the Bethe-Salpeter type which is solved in Fredholm approximation.

Adsorption of Aniline from Aqueous Solution by KSF Montmorillonite

2011 ◽  
Vol 356-360 ◽  
pp. 208-216
Author(s):  
Jiang Ying Zhang ◽  
Jian Xu ◽  
Yuan Zhang ◽  
Lei Li ◽  
Ying Zhang ◽  
...  
Keyword(s):  
Aqueous Solution ◽  
Adsorption Process ◽  
Intraparticle Diffusion ◽  
Order Equation ◽  
Second Order ◽  
First Order ◽  
Ph Values ◽  
Whole Process ◽  
Pseudo Second Order ◽  
Pseudo First Order

In the present paper, the adsorption characteristics of aniline onto KSF montmorillonite from aqueous solution were investigated. Experiments were conducted at various pH values, temperatures, ionic strength and surfactant concentrations. Pseudo-first-order, pseudo-second-order and intraparticle diffusion models were adopted to investigate the rate parameters, and the pseudo-second-order equation was proved to be able to successfully predict whole process. Optimal adsorption pH was determined at 3.6. Among the selected models (linear, Langmuir, Freundlich, DR (Dubinin–Radusckevich) models), linear and DR models were found to be better fit the experimental data, which revealed the physisorption nature of the adsorption process. Meanwhile, with the increase of reaction temperatures, the adsorption capacity decreased. The results of the calculated thermodynamic parameters demonstrated that the adsorption was an exothermic, spontaneous and unfavorable process.

OCTONIC FIRST-ORDER EQUATIONS OF RELATIVISTIC QUANTUM MECHANICS

2009 ◽  
Vol 24 (22) ◽  
pp. 4157-4167 ◽  
Author(s):  
VICTOR L. MIRONOV ◽  
SERGEY V. MIRONOV
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Maxwell Equations ◽  
Relativistic Quantum ◽  
Order Equation ◽  
Second Order ◽  
Relativistic Quantum Mechanics ◽  
Quantum Fields ◽  
First Order ◽  
Spatial Operators

We demonstrate a generalization of relativistic quantum mechanics using eight-component octonic wave function and octonic spatial operators. It is shown that the second-order equation for octonic wave function describing particles with spin 1/2 can be reformulated in the form of a system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special types of wave functions the second-order equation can be reduced to the single first-order equation analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not have quantum fields.

An Expansion Theorem for a Pair of Singular First Order Equations

1954 ◽  
Vol 6 ◽  
pp. 554-560 ◽  
Author(s):  
S. D. Conte ◽  
W. C. Sangren
Keyword(s):  
Classical Method ◽  
Complex Variables ◽  
Order Equation ◽  
Second Order ◽  
Expansion Theorem ◽  
First Order ◽  
Image Position

Titchmarsh (4) has shown how the classical method of complex variables can be used to obtain expansion theorems for the singular cases of the second order equation(1) .The purpose of this paper is to indicate how these results can be generalized to the singular cases of the pair of first order equations,

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