Showing papers in "Mathematical Problems in Engineering in 2003"
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TL;DR: In this article, the Sumudu transform was used to solve an integral production-depreciation problem, where the Laplace transform was applied to solve the problem without resorting to a new frequency domain.
Abstract: 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 use it to solve an integral
production-depreciation problem
311 citations
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TL;DR: In this paper, the authors studied the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength.
Abstract: This paper is devoted to the
study of the two-dimensional flow of a Johnson-Segalman fluid in
a planar channel having walls that are transversely displaced by
an infinite, harmonic travelling wave of large wavelength. Both
analytical and numerical solutions are presented. The analysis
for the analytical solution is carried
out for small Weissenberg
numbers. (A Weissenberg number is the ratio of the relaxation
time of the fluid to a characteristic time associated with the
flow.) Analytical solutions have been obtained for the stream
function from which the relations of the velocity and
the longitudinal pressure gradient have been derived. The
expression of the pressure rise over a wavelength has
also been determined. Numerical computations are performed and
compared to the perturbation analysis. Several limiting
situations with their implications can be examined from the
presented analysis.
104 citations
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TL;DR: In this paper, the concept of exponential dissipativity has been extended to nonlinear systems, and a generalization of the strict positive real lemma and the strict bounded real (strict positive real) lemma to non-linear systems has been proposed.
Abstract: We extend the notion of dissipative dynamical systems to
formalize the concept of the nonlinear analog of strict positive
realness and strict bounded realness. In particular, using
exponentially weighted system storage functions with appropriate
exponentially weighted supply rates, we introduce the concept of
exponential dissipativity. The proposed results provide a
generalization of the strict positive real lemma and the strict
bounded real lemma to nonlinear systems. We also provide a nonlinear
analog to the classical passivity and small gain stability
theorems for state space nonlinear feedback systems. These
results are used to construct globally stabilizing static and
dynamic output feedback controllers for nonlinear passive systems
that minimize a nonlinear nonquadratic performance criterion.
53 citations
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TL;DR: In this paper, the authors prove the existence of mild and strong solutions of integral differential equations with nonlocal conditions in Banach spaces, using the Schauder fixed-point theorem.
Abstract: We prove the existence of mild and strong solutions of
integrodifferential equations with nonlocal conditions in Banach
spaces. Further sufficient conditions for the controllability of
integrodifferential systems are established. The results are
obtained by using the Schauder fixed-point theorem. Examples are
provided to illustrate the theory.
41 citations
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TL;DR: In this article, 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 local boundary conditions.
Abstract: 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 method of lines (MOL) semidiscretization
approach is used to transform the model partial differential
equation into a system of first-order linear ordinary differential
equations (ODEs). The partial derivative with respect to the space
variable is approximated by a second-order finite-difference
approximation. The solution of the resulting system of first-order
ODEs satisfies a recurrence relation which involves a matrix
exponential function. Numerical techniques are developed by
approximating the exponential matrix function in this recurrence
relation. We use a partial fraction expansion to compute the
matrix exponential function via Pade approximations, which is
particularly useful in parallel processing. The algorithm is
tested on a model problem from the literature.
39 citations
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TL;DR: In this paper, the relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation, and the integral equation has been solved numerically for those processes of surface heating whose time scale is of the order of picoseconds.
Abstract: The relationship between the local temperature and the local heat
flux has been established for the homogeneous hyperbolic heat
equation. This relationship has been written in the form of a
convolution integral involving the modified Bessel functions. The
scale analysis of the hyperbolic energy equation has been
performed and the dimensionless criterion for the mode of energy
transport, similar to the Reynolds criterion for the flow
regimes, has been proposed. Finally, the integral equation,
relating the local temperature and the local heat flux, has been
solved numerically for those processes of surface heating whose
time scale is of the order of picoseconds.
20 citations
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TL;DR: In this paper, the steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied and the nonlinear ordinary differential equations resulting from the balance of momentum and mass are discretised by a finite-difference method and numerically solved by means of an iteration method in which, by a coordinate transformation, the semi-infinite physical domain is converted to a finite calculation domain.
Abstract: The governing equations for the unsteady flow of a uniformly conducting incompressible fourth-grade fluid due to noncoaxial rotations of a porous disk and the fluid at infinity are constructed. The steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied. The nonlinear ordinary differential equations resulting from the balance of momentum and mass are discretised by a finite-difference method and numerically solved by means of an iteration method in which, by a coordinate transformation, the semi-infinite physical domain is converted to a finite calculation domain. In order to solve the fourth-order nonlinear differential equations, asymptotic boundary conditions at infinity are augmented. The manner in which various material parameters affect the structure of the boundary layer is delineated. It is found that the suction through the disk and the magnetic field tend to thin the boundary layer near the disk for both the Newtonian fluid and the fourth-grade fluid, while the blowing causes a thickening of the boundary layer with the exception of the fourth-grade fluid under strong blowing. With the increase of the higher-order viscosities, the boundary layer has the tendency of thickening.
15 citations
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TL;DR: In this paper, a method for finding the solution of time-varying singular nonlinear systems by using single-term Walsh series is proposed, where the properties of Walsh series are given and used to find the solution.
Abstract: A method for finding the solution of time-varying singular
nonlinear systems by using single-term Walsh series is proposed.
The properties of single-term Walsh series are given and are
utilized to find the solution of time-varying singular nonlinear
systems.
15 citations
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TL;DR: In this paper, the robust dissipativity with respect to the quadratic supply rate for uncertain impulsive dynamical systems is discussed. And the Hamilton-Jacobi inequality approach is employed to obtain sufficient conditions for robust dissipative properties of such systems.
Abstract: We discuss the robust dissipativity with respect to the quadratic
supply rate for uncertain impulsive dynamical systems. By
employing the Hamilton-Jacobi inequality approach, some sufficient
conditions of robust dissipativity for this kind of system are
established. Finally, we specialize the obtained results to the
case of uncertain linear impulsive dynamical systems.
8 citations
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TL;DR: In this paper, a simple algorithm is developed for unbiased parameter identification of autoregressive (AR) signals subject to white measurement noise, which can produce better AR parameter estimates whenever a reasonable guess of the noise variance ratio is available.
Abstract: A simple algorithm is developed for unbiased parameter
identification of autoregressive (AR) signals subject to white
measurement noise. It is shown that the corrupting noise
variance, which determines the bias in the standard least-squares
(LS) parameter estimator, can be estimated by simply using the
expected LS errors when the ratio between the driving noise
variance and the corrupting noise variance is known or obtainable
in some way. Then an LS-based algorithm is established via the
principle of bias compensation. Compared with the other LS-based
algorithms recently developed, the introduced algorithm requires
fewer computations and has a simpler algorithmic structure.
Moreover, it can produce better AR parameter estimates whenever a
reasonable guess of the noise variance ratio is available.
8 citations
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TL;DR: In this paper, the authors investigate three classes of constraints in a thermoelastic body: (i) a deformation-temperature constraint, (ii) a degrading-entropy constraint, and (iii) a degradation-energy constraint.
Abstract: 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 the constraint (i), the entropy plays
the role of a Lagrange multiplier while for (ii) and (iii), the
absolute temperature plays the role of Lagrange multiplier. We
further demonstrate that the governing equations for materials
subject to constraint (i) are identical to those
of an unconstrained material whose internal energy is an affine
function of the entropy, while those for materials subject to
constraints (ii) and (iii) are identical to those of an
unstrained material whose Helmholtz potential is affine in the
absolute temperature. Finally, we model the thermoelastic
response of a peroxide-cured vulcanizate of natural
rubber and show that imposing the constraint in which the
volume change depends only on the internal energy leads to very
good predictions (compared to experimental results) of the stress
and temperature response under isothermal and isentropic
conditions.
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TL;DR: In this paper, the stability and stabilizability of uncertain systems with multiple time delays were investigated and their robustness was also studied when the norm-bounded uncertainties were considered.
Abstract: 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
established to check if a system of this class is stable and/or
is stabilizable. Some numerical examples are provided to show the
usefulness of
the proposed results.