Mathematical Problems in Engineering

https://www.hindawi.com/journals/mpe/

List of Papers (Total 7,730)

A stochastic formulation of the Bass model of new-product diffusion

For a large variety of new products, the Bass Model (BM) describes the empirical cumulative-adoptions curve extremely well. The BM postulates that the trajectory of cumulative adoptions of a new product follows a deterministic function whose instantaneous growth rate depends on two parameters, one of which captures an individual's intrinsic tendency to purchase, independent of...

Systems approach to modeling the Token Bucket algorithm in computer networks

In this paper, we construct a new dynamic model for the Token Bucket (TB) algorithm used in computer networks and use systems approach for its analysis. This model is then augmented by adding a dynamic model for a multiplexor at an access node where the TB exercises a policing function. In the model, traffic policing, multiplexing and network utilization are formally defined...

An LQG approach to systems with saturating actuators and anti-windup implementation

This paper extends the LQG design methodology to systems with saturating actuators and shows that resulting linear controllers do not require an anti-windup implementation.

Sliding mode control on electro-mechanical systems

The first sliding mode control application may be found in the papers back in the 1930s in Russia. With its versatile yet simple design procedure the methodology is proven to be one of the most powerful solutions for many practical control designs. For the sake of demonstration this paper is oriented towards application aspects of sliding mode control methodology. First the...

On the numerical solution of the diffusion equation with a nonlocal boundary condition

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The...

Analytical investigations of the Sumudu transform and applications to integral production equations

The Sumudu transform, whose fundamental properties are presented in this paper, is little known and not widely used. However, being the theoretical dual to the Laplace transform, the Sumudu transform rivals it in problem solving. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. Here, we...

Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are...

Thermomechanical constraints and constitutive formulations in thermoelasticity

We investigate three classes of constraints in a thermoelastic body: (i) a deformation-temperature constraint, (ii) a deformation-entropy constraint, and (iii) a deformation-energy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii) and (iii) are equivalent. By using a limiting procedure, we show that for...

Sliding mode observers and observability singularity in chaotic synchronization

We present a new secured data transmission based on a chaotic synchronization and observability singularity. For this, we adopt an approach based on an inclusion of the message in the system structure and we use a sliding mode observer for system with unknown input in order to recover the information. We end the paper with an example of chaotic system with an observability...

Reliability for Laplace distributions

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R=Pr(X2<X1) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R=Pr(X2<X1) has been worked out for the majority of the well-known distributions in the standard forms. However, there are...

Volterra equations with fractional stochastic integrals

Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black-Scholes is considered.

On the coefficients of variation of uptime and downtime in manufacturing equipment

It was reported in the literature that the coefficients of variation of uptime and downtime of manufacturing equipment are often less than 1. This technical paper is intended to provide an analytical explanation of this phenomenon. Specifically, it shows that the distributions of uptime and downtime have the coefficients of variation less than 1 if the breakdown and repair rates...

Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally...

On the reliability of a renewable multiple cold standby system

We present a general reliability analysis of a renewable multiple cold standby system attended by a single repairman. Our analysis is based on a refined methodology of queuing theory. The particular case of deterministic failures provides an explicit exact result for the survival function of the duplex system.

On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer

Luikov's theory of heat and mass transfer provides a framework to model drying porous materials. Coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the physical...

Suboptimal feedback control of TCP flows in computer network using random early discard (RED) mechanism

We consider a dynamic model that simulates the interaction of TCP sources with active queue management system (AQM). We propose a modified version of an earlier dynamic model called RED. This is governed by a system of stochastic differential equations driven by a doubly stochastic point process with intensity as the control. The feedback control law proposed observes the router...

Heat transfer analysis on rotating flow of a second-grade fluid past a porous plate with variable suction

We deal with the study of momentum and heat transfer characteristics in a second-grade rotating flow past a porous plate. The analysis is performed when the suction velocity normal to the plate, as well as the external flow velocity, varies periodically with time. The plate is assumed at a higher temperature than the fluid. Analytic solutions for velocity, skin friction, and...

Three-dimensional wave polynomials

We demonstrate a specific power series expansion technique to solve the three-dimensional homogeneous and inhomogeneous wave equations. As solving functions, so-called wave polynomials are used. The presented method is useful for a finite body of certain shape. Recurrent formulas to improve efficiency are obtained for the wave polynomials and their derivatives in a Cartesian...

Characterization of the speed of a two-phase interface in a porous medium

A typical situation of oil reservoir simulation is considered in a porous medium where the resident oil is displaced by water injection. An explicit expression of the speed of the oil-water interface is given in a pseudo-2D case via the resolution of an auxiliary Riemann problem. The explicit 2D solution is then corroborated with numerical simulations by solving the transport...

Study on the Rock Mass Caving and Surface Subsidence Mechanism Based on an In Situ Geological Investigation and Numerical Analysis

To deeply understand the mechanism of the rock mass caving and associated surface subsidence during sublevel caving mining, the Xiaowanggou iron mine was selected as an engineering project case study. The study area was analyzed by means of an in situ geological investigation and numerical simulation. First, a borehole television (BHTV) system and a GPS monitoring system were...

Heronian Mean Operator of Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Methods

Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian...

Prediction Model of Failure Zone in Roadway Sidewall considering the Lithologic Effect of Rock Formation

Coal seam damage area and its stress distribution law in roadway with medium thickness or extrathick coal seam are important issues for understanding the instability mechanism of roadway surrounding rock in weakly cemented soft rock strata in western China. Firstly, a variable parameter microelement analysis model is established based on the assumption of a plane stress...

A Family of Heuristic-Based Inequalities for Maximizing Overall Safety Margins in Aircraft Parking Stands Arrangement Problems

We consider the problem of arranging a set of aircraft in a maintenance hangar operated by an independent aircraft service provider. The overall safety margins of the parking layout need to be maximized within the limited available space, measured by the weighted sum of the individual discrete safety margins of each aircraft. A mixed-integer linear programming model is developed...

Key Characteristics of a Floating Slab Track Based on Longitudinal Interaction Analysis

The passage of railway vehicles produces mechanical vibrations across an extensive range of frequencies. A floating slab track (FST) has recently been proposed and constructed in Korea to reduce the vibrations and noise that result from typical railway operation. The main objective of this study is to investigate the behavior of an FST by means of an interaction analysis of a...

System Sizing with a Model-Based Approach: Application to the Optimization of a Power Transmission System

We test the relevance of a model-based approach for sizing and optimizing complex systems. Classically a model-based approach is characterized by a clear partition between the problem description and the solving process. In the case of a design problem, we show that the sizing task could be systematically characterized and therefore could lead to a declarative model combining...