A variety of fractional soliton solutions for three important coupled models arising in mathematical physics

2021 ◽  
Author(s):  
Saima Arshed ◽  
Riaz Ur Rahman ◽  
Nauman Raza ◽  
Ahmad Kamal Khan ◽  
Mustafa Inc
Keyword(s):  
Water Waves ◽  
Graphical Representation ◽  
Soliton Solutions ◽  
Coupled Models ◽  
Analytical Methodology ◽  
Fractional Models ◽  
Definition Of ◽  
Beneficial Approach ◽  
Expansion Scheme ◽  
Comprehensive Study

This paper deals with the optical solitons of fractional coupled Boussinesq, Burgers-type and mKdV equations by the hypothesis of traveling wave and [Formula: see text]-expansion scheme. These equations are important in different fields such as propagation of long water waves, fluid dynamics, and shallow water wave propagation. In comparison to other analytical procedures, the analytical methodology [Formula: see text] is an incredibly beneficial approach. This technique can also be used with other nonlinear fractional models. The suggested method generates three distinct solutions such as trigonometric, hyperbolic, and rational. Moreover, graphical representation has been used to portray the physical significance of the constructed solutions. Finally, a comprehensive study is made by using a definition of Beta fractional derivative and obtained solutions are represented graphically to understand considered models.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

The Influence Of The Led Luminaires Electrical Parameters On Their Correlated Colour Temperature During Operation Mode

2020 ◽  
pp. 89-96
Author(s):  
Sergei S. Kapitonov ◽  
Alexei S. Vinokurov ◽  
Sergei V. Prytkov ◽  
Sergei Yu. Grigorovich ◽  
Anastasia V. Kapitonova ◽  
...  
Keyword(s):  
Operation Mode ◽  
Light Sources ◽  
Electrical Parameters ◽  
Colour Temperature ◽  
Radiation Spectra ◽  
Service Period ◽  
Close Proximity ◽  
Definition Of ◽  
Comprehensive Study

The article describes the results of comprehensive study aiming at increase of quality of LED luminaires and definition of the nature of changes in their correlated colour temperature (CCT) in the course of operation. Dependences of CCT of LED luminaires with remote and close location of phosphor for 10 thousand hours of operation in different electric modes were obtained; the results of comparison between the initial and final radiation spectra of the luminaires are presented; using mathematical statistics methods, variation of luminaire CCT over the service period claimed by the manufacturer is forecast; the least favourable electric operation modes with the highest CCT variation observed are defined. The obtained results have confirmed availability of the problem of variation of CCT of LED luminaires during their operation. Possible way of its resolution is application of more qualitative and therefore expensive LEDs with close proximity of phosphor or LEDs with remote phosphor. The article may be interesting both for manufacturers and consumers of LED light sources and lighting devices using them.

Missing Data - Better "Not to Have Them", but What If You Do? (Part 1)

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 21-32
Author(s):  
Dirk Temme ◽  
Sarah Jensen
Keyword(s):  
Missing Data ◽  
Statistical Power ◽  
Missing Values ◽  
Graphical Representation ◽  
Marketing Research ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Full Information Maximum Likelihood ◽  
Definition Of ◽  
Traditional Approaches

Missing values are ubiquitous in empirical marketing research. If missing data are not dealt with properly, this can lead to a loss of statistical power and distorted parameter estimates. While traditional approaches for handling missing data (e.g., listwise deletion) are still widely used, researchers can nowadays choose among various advanced techniques such as multiple imputation analysis or full-information maximum likelihood estimation. Due to the available software, using these modern missing data methods does not pose a major obstacle. Still, their application requires a sound understanding of the prerequisites and limitations of these methods as well as a deeper understanding of the processes that have led to missing values in an empirical study. This article is Part 1 and first introduces Rubin’s classical definition of missing data mechanisms and an alternative, variable-based taxonomy, which provides a graphical representation. Secondly, a selection of visualization tools available in different R packages for the description and exploration of missing data structures is presented.

Dissociation and Subsidence of Hydrated Sediment: Coupled Models

2009 ◽  
Vol 27 (2) ◽  
pp. 105-131 ◽  
Author(s):  
Mohamed Iqbal Pallipurath
Keyword(s):  
Thermal Dissociation ◽  
Hydrate Formation ◽  
Coupled Models ◽  
Two Phase ◽  
Strength Deterioration ◽  
Intrinsic Kinetics ◽  
Radial Heat Flow ◽  
Radial Heat ◽  
Definition Of ◽  
Pressure Changes

Thermal dissociation of hydrated sediment by a pumped hot fluid is modeled. A radial heat flow from the hot pipe is assumed. The coordinate system is cylindrical. Three components (hydrate, methane and water) and three phases (hydrate, gas, and aqueous-phase) are considered in the simulator. The intrinsic kinetics of hydrate formation or dissociation is considered using the Kim-Bishnoi model. Mass transport, including two-phase flow, molecular diffusions and heat transfer involved in formation or dissociation of hydrates are included in the governing equations, which are discretized with finite volume difference method and are solved in an explicit manner. The strength deterioration of the hydrate bed as a result of dissociation is investigated with a geo-mechanical model. The way in which dissociation affects the bed strength is determined by plugging in the porosity and saturation change as a result of dissociation into the sediment collapse equations. A mechanism to measure the pore pressure changes occurring due to dissociation is developed. The rate of collapse as dissociation proceeds is determined and the model thus enables the definition of a safety envelope for gas hydrate drilling.

Chirped and chirp-free optical solitons for Heisenberg ferromagnetic spin chains model

2021 ◽  
pp. 2150139
Author(s):  
Syed Tahir Raza Rizvi ◽  
Aly R. Seadawy ◽  
Ishrat Bibi ◽  
Muhammad Younis
Keyword(s):  
Graphical Representation ◽  
Spin Dynamics ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Optical Solitons ◽  
Spin Chains ◽  
Solitary Wave Solutions ◽  
Rational Solutions ◽  
Wave Solutions ◽  
Ode Method

In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions.

The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

2021 ◽  
Vol 24 (4) ◽  
pp. 1003-1014
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Restitution Coefficient ◽  
Classical Physics ◽  
Bouncing Ball ◽  
Mechanical Experiment ◽  
Fractional Models ◽  
Definition Of

Abstract This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

scholarly journals The Polish Experience in the Development of Smart Cities

2021 ◽  
Vol 11 (2) ◽  
pp. 48-64
Author(s):  
Magdalena Kisała
Keyword(s):  
Smart City ◽  
Smart Cities ◽  
Urban Spaces ◽  
Polish Experience ◽  
The Subject ◽  
Universal Definition ◽  
Definition Of ◽  
Urban Population Growth ◽  
Changes Over Time ◽  
Beneficial Approach

Abstract In recent years, Poland has seen an increased migration of people to cities, which translates into significant urban population growth. This, in turn, raises new challenges in the performance of cities’ tasks and responsibilities. Additionally, climate changes and the depletion of natural resources necessitate the modification of existing urban practices. Polish cities seek solutions which would enable social, economic and environmental demands to be reconciled so that urban spaces become friendly for the city’s inhabitants and investors. Some Polish cities have applied the smart city concept to solve their problems. Despite the fact that the concept has been the subject of scientific research for many years, no universal definition of the smart city has been agreed upon. Analyzed assumptions of the smart city concept as well as the Polish experiences in the implementation indicate that the concept is dynamic and changes over time. It should be considered as a perpetual process unrestricted by a specific timeframe. This impedes the formulation of uniform, generally accepted assumptions of the concept since its existence is inscribed in the change related to urban development. This article claims that this would be a beneficial approach for formulating the general characteristics of the smart city that could be applicable to any city, and that could be employed regardless of the present challenges cities may face.

scholarly journals Modern social policy of the Russian Federation in relation to low-income citizens and families

2021 ◽  
Vol 7 (3B) ◽  
pp. 604-620
Author(s):  
Dina Viktorovna Alontseva ◽  
Irina Aleksandrovna Zaitseva ◽  
Alexander Yevgenyevich Krikunov ◽  
Olga Anatolyevna Lavrishcheva ◽  
Sergey Sergeevich Fomenko
Keyword(s):  
Social Policy ◽  
Russian Federation ◽  
Low Income ◽  
Living Alone ◽  
Standard Of Living ◽  
The Russian Federation ◽  
Low Income Families ◽  
Definition Of ◽  
Objective Indicators ◽  
Comprehensive Study

In this article, the authors conducted a comprehensive study of the main directions of the modern social policy of the Russian Federation in relation to low-income citizens living alone and low-income families. Namely, based on the analysis of doctrinal sources, the provisions of international acts and the norms of the current Russian legislation: we formulated the definition of the concept of "poor"; justified the opinion that it is necessary to use a set of objective indicators and indicators to determine a decent standard of living. The identified problems and the proposed system of scientific views significantly expand the previously obtained theoretical teachings on the types and forms of state social support and protection of low-income families and low-income citizens living alone, considering the realities of modern politics and trends in the development of the Russian Federation.

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