scholarly journals Reflection and Diffraction of Atomic de Broglie Waves by Evanescent Laser Waves - Bare-state Method

1996 ◽  
Vol 49 (4) ◽  
pp. 765 ◽  
Author(s):  
Xiao-Ping Feng ◽  
NS Witte ◽  
Lloyd CL Hollenberg ◽  
Geoffrey I Opat
Keyword(s):  
Differential Equations ◽  
Laplace Transformation ◽  
The Other ◽  
Bare State ◽  
Coupled Differential Equations ◽  
Born Series ◽  
De Broglie Waves ◽  
Whole Space ◽  
State Method ◽  
Dressed State

We present two results in an investigation of reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both results use the bare-state rather than dressed-state picture. One is based on the Born series, whereas the other is based on the Laplace transformation of the coupled differential equations. The two solutions yield the same theoretical expressions for reflected and diffracted atomic waves in the whole space, including the interaction and the asymptotic regions.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

EQUIVALENCE OF THE TWO METHODS IN CALCULATING THE EQUILIBRIUM SHAPES OF CYLINDRICAL VESICLES

1999 ◽  
Vol 13 (16) ◽  
pp. 547-553
Author(s):  
SHAOGUANG ZHANG ◽  
ZHONGCAN OUYANG ◽  
JIXING LIU
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
The Other ◽  
General Shape ◽  
Calculus Of Variation ◽  
And Topology ◽  
Shape Equation ◽  
Equilibrium Shapes ◽  
Comparison Of The Results ◽  
The Relationship

So far, two methods are often used in solving the equilibrium shapes of vesicles. One method is by starting with the general shape equation and restricting it to the shapes with particular symmetry. The other method is by assuming the symmetry and topology of the vesicle first and treating it with the calculus of variation to get a set of ordinary differential equations. The relationship between these two methods in the case of cylindrical vesicles, and a comparison of the results are given.

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