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Statistics and Probability

Muhammad Usman

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman Mar 2015

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Muhammad Usman

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

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Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang Mar 2015

Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang

Muhammad Usman

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.

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A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman Mar 2015

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Muhammad Usman

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

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A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran Mar 2015

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Muhammad Usman

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

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Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang Mar 2015

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Muhammad Usman

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem uuxuxxx 0 < x < 1, t > 0, (*) It is shown that if the …

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Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman Mar 2015

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Muhammad Usman

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

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