Spatial dependence of moving three-level atoms interacting with a three-laser beam

2013 ◽  
Vol 91 (12) ◽  
pp. 1068-1073 ◽  
Author(s):  
M. Abdel-Aty ◽  
D. Abo-Kahla ◽  
A.-S.F. Obada
Keyword(s):  
Spatial Dependence ◽  
Laser Field ◽  
Homotopy Perturbation Method ◽  
Dynamical Behavior ◽  
Resonant Interaction ◽  
Time Dependent ◽  
Homotopy Perturbation ◽  
Sensitive Dependence ◽  
Dephasing Rate

We investigate the dynamical behavior of a three-level moving atom interacting with a laser field. We show that the sensitivity of atomic dynamics can be considerably improved by exploiting the spatial dependence of moving atoms within the framework of the homotopy perturbation method. The dynamics of the system is analyzed as well as the effect of various parameters including detuning and dephasing rate. The spatial dependence approach has the same properties as the time-dependent approach, but it is preferable when the time-scale is very small. The very sensitive dependence and the role of the off-resonant interaction are highlighted.

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

THE FRACTIONAL COMPLEX TRANSFORM: A NOVEL APPROACH TO THE TIME-FRACTIONAL SCHRÖDINGER EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050141
Author(s):  
QURA TUL AIN ◽  
JI-HUAN HE ◽  
NAVEED ANJUM ◽  
MUHAMMAD ALI
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Nonlinear Part ◽  
Fractional Complex Transform ◽  
Homotopy Perturbation ◽  
Novel Approach ◽  
Time Fractional Derivative

This paper presents a thorough study of a time-dependent nonlinear Schrödinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to convert the problem into its differential partner, and its nonlinear part is then discretized using He’s polynomials so that the homotopy perturbation method (HPM) can be applied powerfully. The two-scale concept is used to explain the substantial meaning of the fractional time complex transform and the solution.

scholarly journals Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method

2020 ◽  
Vol 51 (4) ◽  
pp. 333-347
Author(s):  
Devipriya Ganeshan ◽  
Kavitha TS
Keyword(s):  
Infectious Disease ◽  
Wireless Sensor Networks ◽  
Homotopy Perturbation Method ◽  
Dynamical Behavior ◽  
Wireless Sensor ◽  
Worm Propagation ◽  
Homotopy Perturbation ◽  
Military Applications ◽  
Wireless Computing ◽  
Computing Infrastructure

Wireless sensor networks (WSNs) have received wide-ranging considerationdue to their boundless potential in civil and military applications. Maliciousself-replicating codes, known as malware, pose substantial threat to the wireless computing infrastructure. The attacks of the malicious signals in the WSNare epidemic in nature. Biological epidemic models will be helpful to understand the dynamical behavior of the malware attack in WSN. In this paper,A (SEIRS-V) Susceptible - Exposed - Infected - Recovered - Susceptible witha Vaccination compartment, describing the undercurrents of worm propagation with respect to time in wireless sensor network (WSN) is considered. Theanalytical solution of WSN is obtained by Homotopy Perturbation Method.Numerical results are obtained and are graphically interpreted using Maple.The results assures that the dynamics of worm propagation in WSN by theproposed model exhibits rich dynamics.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

Sign in / Sign up

Export Citation Format

Share Document