Search results for: integrability

Authors: Manisha Kankarej

Abstract:

The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

Procedia PDF Downloads 492

Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

Abstract:

Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

Procedia PDF Downloads 182

Authors: Barnali Laha

Abstract:

In this paper, we would like to establish some of the properties of slant and hemislant submanifolds of an indefinite trans-Sasakian manifold. We have four sections in this paper. The first section is introductory. In Section 2, we recall some necessary details of an indefinite trans-Sasakian manifold. In Section 3, we have obtained some interesting properties on a totally umbilical slant submanifolds of an indefinite trans-Sasakian manifold. Finally, in Section 4, some results on integrability conditions of the distributions of hemislant submanifolds of an indefinite trans-Sasakian manifold have been obtained.

Keywords: slant submanifold, indefinite trans-Sasakian manifold, hemislant submanifold, integrability conditions

Procedia PDF Downloads 457

Authors: Edamana Vasudevan Krishnan

Abstract:

This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

Procedia PDF Downloads 452

Authors: Maba Boniface Matadi

Abstract:

This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

Procedia PDF Downloads 76

Authors: Muhammad Younis

Abstract:

In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

Procedia PDF Downloads 397

Authors: Ahmed Al-Adaileh, Souheil Khaddaj

Abstract:

Outcomes of exhaustion of natural resources started influencing each spirit on this planet. Energy is an essential factor in this aspect. To restore the circumstance to the appropriate track, all attempts must focus on two fundamental branches: producing electricity from clean and renewable reserves and decreasing the overall unnecessary consumption of energy. The focal point of this paper will be on lessening the power consumption in the household's segment. This paper is an attempt to give a clear understanding of a framework called Reduction of Energy Consumption in Household Sector (RECHS) and how it should help householders to reduce their power consumption by substituting their household appliances, turning-off the appliances when stand-by modus is detected, and scheduling their appliances operation periods. Technically, the framework depends on utilizing Z-Wave compatible plug-ins which will be connected to the usual house devices to gauge and control them remotely and semi-automatically. The suggested framework underpins numerous quality characteristics, for example, integrability, scalability, security and adaptability.

Keywords: smart energy management systems, internet of things, wireless mesh networks, microservices, cloud computing, big data

Procedia PDF Downloads 147

Authors: Jesus Kombaya, Nadia Hamani, Lyes Kermad

Abstract:

The preservation of a company’s place on the market in such aggressive competition is becoming a survival challenge for manufacturers. In this context, survivors are only those who succeed to satisfy their customers’ needs as quickly as possible. The production system should be endowed with a certain level of flexibility to eliminate or reduce the rigidity of the production systems in order to facilitate the conversion and/or the change of system’s features to produce different products. Therefore, it is essential to guarantee the quality, the speed and the flexibility to survive in this competition. According to literature, this adaptability is referred to as the notion of "change". Indeed, companies are trying to establish a more flexible and agile manufacturing system through several reconfiguration actions. Reconfiguration contributes to the extension of the manufacturing system life cycle by modifying its physical, organizational and computer characteristics according to the changing market conditions. Reconfigurability is characterized by six key elements that are: modularity, integrability, diagnosability, convertibility, scalability and customization. In order to control the production systems, it is essential for manufacturers to make good use of this capability in order to be sure that the system has an optimal and adapted level of reconfigurability that allows it to produce in accordance with the set requirements. This document develops a measure of customization of reconfigurable production systems. These measures do not only impact the production system but also impact the product design and the process design, which can therefore serve as a guide for the customization of manufactured product. A case study is presented to show the use of the proposed approach.

Keywords: reconfigurable manufacturing systems, customization, measure, flexibility

Procedia PDF Downloads 96

Authors: Peter Burggräf, Matthias Dannapfel, Hanno Voet, Patrick-Benjamin Bök, Jérôme Uelpenich, Julian Hoppe

Abstract:

The increasing digitalization of value chains can help companies to handle rising complexity in their processes and thereby reduce the steadily increasing planning and control effort in order to raise performance limits. Due to technological advances, companies face the challenge of smart value chains for the purpose of improvements in productivity, handling the increasing time and cost pressure and the need of individualized production. Therefore, companies need to ensure quick and flexible decisions to create self-optimizing processes and, consequently, to make their production more efficient. Lean production, as the most commonly used paradigm for complexity reduction, reaches its limits when it comes to variant flexible production and constantly changing market and environmental conditions. To lift performance limits, which are inbuilt in current value chains, new methods and tools must be applied. Digitalization provides the potential to derive these new methods and tools. However, companies lack the experience to harmonize different digital technologies. There is no practicable framework, which instructs the transformation of current value chains into digital pervasive value chains. Current research shows that a connection between lean production and digitalization exists. This link is based on factors such as people, technology and organization. In this paper, the introduced method for the determination of digitally pervasive value chains takes the factors people, technology and organization into account and extends existing approaches by a new dimension. It is the first systematic approach for the digital transformation of lean production and consists of four steps: The first step of ‘target definition’ describes the target situation and defines the depth of the analysis with regards to the inspection area and the level of detail. The second step of ‘analysis of the value chain’ verifies the lean-ability of processes and lies in a special focus on the integration capacity of digital technologies in order to raise the limits of lean production. Furthermore, the ‘digital evaluation process’ ensures the usefulness of digital adaptions regarding their practicability and their integrability into the existing production system. Finally, the method defines actions to be performed based on the evaluation process and in accordance with the target situation. As a result, the validation and optimization of the proposed method in a German company from the electronics industry shows that the digital transformation of current value chains based on lean production achieves a raise of their inbuilt performance limits.

Keywords: digitalization, digital transformation, Industrie 4.0, lean production, value chain

Procedia PDF Downloads 273