Mathematical Problems in Engineering

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

List of Papers (Total 7,717)

Identification of hysteretic control influence operators representing smart actuators part I: Formulation

A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase...

On the structure of a distinguished-limit quasi-isothermal deflagration for the generalized reaction-rate model

The structure of the quasi-isothermal deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis–Semenov number unity, in the limit of the activation-temperature ratio, β=Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of: (1) the heat-addition-temperature ratio, α=(Tb−Tu)/Tu, of order β−1/2...

Erratum

A model of frontal polymerization including the gel effect

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. This new approach to polymer production requires both theoretical and experimental study. Agreement between the existing theoretical and experimental work done on this subject has generally been fairly good. However, experimental results tend...

A dynamic model for crime control and policy evaluation

The paper is concerned with the development of a rigorous mathematical model describing the dynamics of criminal population subject to sentencing policies of any penal (legal) system. The model enables evaluation of the impact of preventive measures used in the society and correctional measures used by the penitentiaries. A performance index reflecting the effectiveness of such...

A problem related to the hall effect in a semiconductor with an electrode of an arbitrary shape

A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the...

Optimal control for a BMAP/G/1 queue with two service modes

Queueing models with controllable service rate play an important role in telecommunication systems. This paper deals with a single-server model with a batch Markovian arrival process (BMAP) and two service modes, where switch-over times are involved when changing the service mode. The embedded stationary queue length distribution and the explicit dependence of operation criteria...

Similarity transformations of MAPs

We introduce the notion of similar Markovian Arrival Processes (MAPs) and show that the event stationary point processes related to two similar MAPs are stochastically equivalent. This holds true for the time stationary point processes too. We show that several well known stochastical equivalences as e.g. that between the H2 renewal process and the Interrupted Poisson Process...

The queue-length in GI/G/s queues

The distribution of the queue-length in the stationary symmetrical GI/G/s queue is given with an application to the M/G/s queue, particularly in the case of the combination of several packet traffics, with various constant service times, to dimension the buffer capacity.

Robust high-gain observer for nonlinear closed-loop stochastic systems

In this paper, the problem of robust state observation is tackled. A high-gain observer is employed to carry out the state estimation of a continuous time uncertain nonlinear system subject to external perturbations of stochastic nature. Unmodelled dynamics is assumed to be deterministic and belonging to an a priori known class of uncertainties.The control input is constructed...

Burgers

We consider the viscous Burgers

Improvability of assembly systems II: Improvability indicators and case study

Based on the performance analysis technique developed in Part I, this paper presents improvability indicators for assembly lines with unreliable machines. In particular, it shows that assembly lines are unimprovable with respect to workforce re-distribution if each buffer is, on the average, close to being half full. These lines are unimprovable with respect to buffer capacity re...

Vertical flow of a multiphase mixture in a channel

The flow of a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied. The theory of interacting continua or mixture theory is used. Constitutive relations for the stress tensor of the granular materials and the interaction force are presented and discussed. The flow of interest is an ideal one where we assume the flow to be...

Modelling the electromagnetic behaviour of sife alloys using the Preisach theory and the principle of loss seperation

In this paper we present 2 simplified methods for the evaluation of magnetisation loops in laminated SiFe alloys, using the Preisach theory and the statistical loss theory. These methods are investigated in detail as a practical alternative for a very accurate, but much involved numerical approach, viz a combined lamination model – dynamic Preisach model earlier developed by the...

New schemes for a two-dimensional inverse problem with temperature overspecification

Two different finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the (3,3...

A hybrid domain analysis for systems with delays in state and control

The solution of time-delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block-pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of...

Absolute stability of nonlinear systems with time delays and applications to neural networks

In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications...

c-Bottlenecks in serial production lines: Identification and application

The bottleneck of a production line is a machine that impedes the system performance in the strongest manner. In production lines with the so-called Markovian model of machine reliability, bottlenecks with respect to the downtime, uptime, and the cycle time of the machines can be introduced. The two former have been addressed in recent publications [1] and [2]. The latter is...

Modified guidance laws to escape microbursts with turbulence

This paper introduces Modified Altitude- and Dive-Guidance laws for escaping a microburst with turbulence. The goal is to develop a procedure to estimate the highest altitude at which an aircraft can fly through a microburst without running into stall. First, a new metric is constructed that quantifies the aircraft upward force capability in a microburst encounter. In the absence...

Determination of an unknown parameter in a semi-linear parabolic equation

Some finite difference approximations are developed for an inverse problem of determining an unknown parameter p(t) which is a coefficient of the solution u in a semi-linear parabolic partial differential equation subject to a boundary integral overspecification. The accuracy and efficiency of the procedures are discussed. Some computational results using the newly proposed...

Linear discrete-time systems with Markovian jumps and mode dependent time-delay: Stability and stabilizability

This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI) techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A...

An upper and lower solution approach for a generalized Thomas–Fermi theory of neutral atoms

This paper presents an upper and lower solution theory for boundary value problems modelled from the Thomas–Fermi equation subject to a boundary condition corresponding to the neutral atom with Bohr radius.

On potential energies and constraints in the dynamics of rigid bodies and particles

A new treatment of kinematical constraints and potential energies arising in the dynamics of systems of rigid bodies and particles is presented which is suited to Newtonian and Lagrangian formulations. Its novel feature is the imposing of invariance requirements on the constraint functions and potential energy functions. These requirements are extensively used in continuum...

A new formulation of the equivalent thermal in optimization of hydrothermal systems

In this paper, we revise the classical formulation of the problem depriving it of the concepts that are superfluous from the mathematical point of view. We observe that a number of power stations can be substituted by a single one that behaves equivalently to the entire set. Proceeding in this way, we obtain a variational formulation in its purest sense (without restrictions...

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...