N. Mikhail

On the validity and stability of the method of lines for the solution of partial differential equations

The method of lines (MOL) for the numerical solution of partial differential equations is presented. Its application to equations of the elliptic type is examined with a view to showing that the instability usually blamed on MOL has its origin in the original equation. The MOL system of ordinary differential equations is shown to be a valid representation of the partial differential equation. The effect of increasing the number of lines used is discussed. It is shown that as the number of lines is increased, the accuracy of the MOL representation of the original system increases.

Swarm Congestion & Power Aware Routing Protocol for MANETs

The evolution of wireless devices along with the increase in user mobility have created new challenges such as the need to make efficient use of power resources. Nodes in an ad hoc network have limited power resources as well as limited processing power. When routing, a sharp degradation in the network service may result if the routing algorithm does not account for the limited resources, eventually decreasing the network lifetime. The objective of our work is to extend the life time of ad hoc networks through implementing a multi-path congestion and power aware routing protocol. The protocol developed is a swarm-based routing protocol that incorporated both power awareness and load balancing techniques. PowerAnt extended network lifetime by 33% on average; besides, it provided a cheaper energy routing strategy per byte by 23% compared with AODV.

The acoustic boundary layers: a detailed analysis

Abstract The viscosity of the medium plays an important role in defining the characteristics of sound wave propagation in ducts. This effect, due to the difficulty of analysis, has been either completely neglected in the literature or considered only approximately. In this study, a mathematical model is constructed to describe the physical problem in its general form without imposing assumptions a priori. The physical quantities have been conveniently expressed in only two nondimensional quantities, a frequency or wave number bK and a Reynolds number Re. The set of equations describing the model is solved in two-dimensional ducts in the case of no mean flow. Closed-form, exact solutions for the acoustic parameters are obtained. The effect of both Re and bK are computed and presented graphically. The results confirm the existence of a small region, the acoustic boundary layer, inside which the acoustic parameters vary very rapidly. For the first time, the vaues of u, v and p are computed inside the acoustic boundary layer. The profiles of these parameters are presented across the duct width. The widely used assumption that the viscous effect is confined to the boundary layers, and the rest of the field is essentially inviscid is not supported by the current results.

Effect of the medium viscosity on sound propagation and attenuation in ducts

Abstract The viscosity of the medium plays an important role in defining the characteristics of sound wave propagation in ducts. This effect, due to the difficulty of analysis, has been either completely neglected in the literature or considered only approximately. One common assumption has been that viscosity would affect the inviscid acoustic wave indirectly through its effect on the mean flow. In this study, a mathematical model is constructed to describe the physical problem in its general form without imposing assumptions a priori. The set of equations describing the model are solved in a two-dimensional duct. The losses due to thermal conductivity of the medium are neglected in order to focus on that due to viscosity. The physical quantities have been conveniently expressed in only two nondimentional quantities, a frequency or wave number bK and a Reynolds number Re. The effect of these two parameters on the propagation and attenuation constants was studied in detail for a wide range of bK and Re. Results were obtained for the zeroth- and higher-order modes. The huge amount of numerical results obtained led to rather interesting conclusions.

Universal Mobility with Global Identity (UMGI) Architecture

The resultant escalation of cyber attacks and the emerging needs of operators to increase their coverage with a blended service offering, that enhances user mobility, have raised a need for an architecture that can find global digital identities and link them back to users’ activities in the mobility universe. In this paper, our focus is to provide an architecture that associates mobile users’ credentials as IP,hostname, and network equipment identifiers (ex. network cards or mobile sets) with their (U)SIM (Universal subscriber identity module) cards to create a global identity.Then the architecture makes use of this global identity to extend the user mobility to universal mobility. The architecture proposes the Universal mobility concept by adopting a new mobile IP (MIP) architecture to enables users to maintain their connection to their corporate or to an internet service when moving between different access networks without impacting their existing sessions and with minimum handover time. The main advantages of the new mobile IP concept is; its independence of the access media or the user’s equipment. Being independent of the users equipment is a goal as loading equipments with complex application will decrease its performance and increase the power consumption thus destroying the concept of mobility.The second advantage is enhancing the new MIP concept with a strong security mechanism that protects against identity spoofing. This mechanism adopts a secure hierarchal method for message passing, authentication and addresses the security limitation of standard internet protocols like DHCP, ARP, and DNS …etc.

Automatic grid generation for finite element models using the finite element package

A method for the generation of the grid for finite element solution of Engineering problems is suggested. The method is applied to generate the grid for two different geometries and the results are discussed. Using this method for grid generation, it is possible to use the same finite element for generating the grid as well as for analysis which might be stress, thermal, on fluid mechanics. This certainly is an advantage. the method is promising as far as complete automatic mesh generation is concerned.

Enhanced Mobile IP Protocol

One of the most recent Internet challenges is to support transparent movement of people along with their computers, data and most of all applications. Therefore, Mobile IP has been developed to provide Internet mobility services. This paper aims at enhancing the IETF Mobile IP standard. The model developed in this paper suggests a new caching mechanism, which is based on the Mobile Information Server (MIS). Actually, the MIS is designed to be part of the border router of any network that supports mobility services. Moreover, the paper suggests a peering technique by which information about mobiles hosts could be shared among different MISs. All the design issues including model components as well as mechanisms for caching and peering are described in details. The simulation results show that the proposed design provides improved performance and better bandwidth utilization. The suggested architecture provides other qualitative advantages such as scalability and transparency.

Measuring network performance of swarm power aware routing protocol for MANETs

The huge growth in wireless communication and increase in user mobility have introduced new challenges, such as the need to make efficient use of power resources besides preserving good network characteristics. Power resources as well as processing power are constrained in an ad hoc network. Overlooking the limitation of resources in an Ad hoc network might result in a sharp degradation in the network services. The objective of our work is to observe the effect of incorporating power awareness and load balancing techniques on network performance parameters: throughput, packet delivery ratio and routing overhead. The protocol developed is a swarm-based routing protocol that incorporated both power awareness and load balancing techniques. PowerAnt provided more throughput by 11% on average; besides, it provided better packet delivery ratio by 15% compared with AODV.

A super-element approach for the solution of problems of the boundary value type

In this paper, an algorithm for the solution of the general boundary value problem is presented together with an example of its application to fluid flow problem in two independent variables. Indications are that the method posses advantages over other techniques from both of economy of computation and ease of applications points of view. The accuracy obtained in the test case is extremely high. The computation inside each elment is completely independent of computation inside other elements. This simply means that course grain parallel processing is possible that would result in great improvement of computational speed. The same technique is applicable to nonlinear as well as linear problems and is easily extendable to problems of three and four dimensions.