Faiz Ahmad | National University of Sciences & Technology (NUST) (original) (raw)

Papers by Faiz Ahmad

Electronic Journal of Differential Equations, 2007

Abstract. The Navier-Stokes equations for the boundary layer are trans-formed, by a similarity tr... more Abstract. The Navier-Stokes equations for the boundary layer are trans-formed, by a similarity transformation, into the ordinary Blasius differential equation which, together with appropriate boundary conditions constitutes the Blasius problem, f (η) + 1 2 f(η)f (η)=0, f(0) = 0, f (0) = ...

The Journal of the Acoustical Society of America, 2012

In this paper the spectrum of Lamb modes in an orthotropic plate is studied. Infinitely many mode... more In this paper the spectrum of Lamb modes in an orthotropic plate is studied. Infinitely many modes are found which undergo a change of sign in their slopes twice, thus leading to two zero-group velocity points. A few modes possessing three such points also exist.

The Quarterly Journal of Mechanics and …, 2009

The number of linear invariants under SO (3) as well as SO (2) of a Cartesian tensor of an arbitr... more The number of linear invariants under SO (3) as well as SO (2) of a Cartesian tensor of an arbitrary rank is studied. A linear form is defined in terms of elements of a tensor. It is established that the number of linear invariants of a tensor of rank n under SO (3) equals ...

Journal of Physics A: Mathematical, Nuclear and General

The semi-classical laser equations are analysed outside the rotating-wave approximation and a new... more The semi-classical laser equations are analysed outside the rotating-wave approximation and a new exact steady-state solution for stationary but inhomogeneously broadened atoms is obtained. Results applicable to any solid-state laser are derived and these are also relevant to a gas laser working near threshold or at very high intensities. The resonance frequency exhibits a Bloch-Siegert shift. New results in the

The Journal of the Acoustical Society of America, 2015

The transient response of an elastic cylinder to a laser impact is studied. When the laser source... more The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by laser interferometry below 8 MHz. Most of these resonances correspond to Zero-Group Velocity guided modes while a few others can be ascribed to thickness modes. We observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifest as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured one, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.

International Journal of the Physical Sciences, 2012

Simple proofs are obtained for the Cowin-Mehrabadi theorem for the identification of a plane of s... more Simple proofs are obtained for the Cowin-Mehrabadi theorem for the identification of a plane of symmetry or an axis of symmetry in an elastic material. The treatment is generalized to a cartesian tensor of arbitrary rank. Necessary and sufficient conditions are found for the existence of a plane of symmetry or an axis of symmetry for a piezoelectric material. Conditions are obtained for the identification of an n-fold axis of symmetry with 3  n .

Physical Review A, 1975

We analyze the problem of a spin-½ system coupled to a longitudinal field B 0 and a transverse fi... more We analyze the problem of a spin-½ system coupled to a longitudinal field B 0 and a transverse field 2Bcosωt. We show that the magnetization is not periodic in general. Time-averaged population inversion is non-negative for the case ω=-γB 0 . We discuss the significance of this result ...

The Quarterly Journal of Mechanics and Applied Mathematics, 2002

We study invariants of the anisotropic elasticity tensor. The invariants are obtained by defining... more We study invariants of the anisotropic elasticity tensor. The invariants are obtained by defining certain tensors of order two associated with the elasticity tensor. We find four second-order invariants with respect to arbitrary orthogonal transformations. This increases by two the number of already known such invariants. When the transformation is confined to rotations about the x 3-axis, the number of second-order invariants becomes seventeen, again an increase by two in the already known number. We describe a method for ascertaining linear independence of these invariants. We also recover structural invariants of Ting and find a few new structural invariants.

Mathematical Problems in Engineering, 2001

Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry... more Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry is studied. For propagation at high frequencies, effects of rotation are negligible but for a frequency which is much smaller than the frequency of rotation, there is a fast wave and two very slow waves. When the two frequencies are equal, the speed of a wave becomes unbounded.

The Journal of the Acoustical Society of America, 1998

International Journal of Theoretical Physics, 2011

A general theory for finding the invariants of an arbitrary tensor is described. Group theoretic ... more A general theory for finding the invariants of an arbitrary tensor is described. Group theoretic methods produce formulas which precisely determine the number of invariants for a Cartesian tensor of arbitrary rank defined over a space of dimension 2, 3 or 4. Explicit expressions are obtained for simple cases.

… -PAKISTAN ACADEMY OF …, 2007

Abstract: We use Wang's transfo~ illation of the Blasius problem to find a numerical sequenc... more Abstract: We use Wang's transfo~ illation of the Blasius problem to find a numerical sequence Tcrr the approximate values of the second derivative at the origin. An application of thc Pade'approximation produces improved values up to a certain point and the method ...

Communications in Nonlinear Science and Numerical Simulation, 2009

We solve the governing equations for the flow of a third grade fluid in a porous half space. We f... more We solve the governing equations for the flow of a third grade fluid in a porous half space. We find a simple expression which describes the solution accurately over the whole domain [0,∞). The rate of exponential decay of the flow is independent of the parameters which ...

Communications in Nonlinear Science and Numerical Simulation, 2009

The [4/3] Pade approximant for the derivative is modified so that the resulting expression has th... more The [4/3] Pade approximant for the derivative is modified so that the resulting expression has the required asymptotic behavior. This gives an analytical result which represents the solution of the classical Blasius problem on the whole domain.

Electronic Journal of Differential equations, 2003

Electronic Journal of Differential Equations, Vol. 2003(2003), No. 92, pp. 1–6. ISSN: 1072-6691. ... more Electronic Journal of Differential Equations, Vol. 2003(2003), No. 92, pp. 1–6. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) ... LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A ...

Applied Mathematics and Mechanics, 1998

Abstract The diagnonal Pade'approximates for exp (x), tanx and tanhx are obtained in a simpl... more Abstract The diagnonal Pade'approximates for exp (x), tanx and tanhx are obtained in a simple manner by using the property of Legendre polynomials that on [− 1, 1] P n (x) is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used to ...

Acta Mechanica, 1999

Summary We discuss the theory of thermoelastic wave propagation in a rotating isotropic material.... more Summary We discuss the theory of thermoelastic wave propagation in a rotating isotropic material. In any given direction there are four waves. In general, all of these waves are attenuated, and none of them is purely dilatational or transverse. Some earlier published results are found to be false.

Advances in Acoustics and Vibration, 2014

Electronic Journal of Differential Equations, 2007

Abstract. The Navier-Stokes equations for the boundary layer are trans-formed, by a similarity tr... more Abstract. The Navier-Stokes equations for the boundary layer are trans-formed, by a similarity transformation, into the ordinary Blasius differential equation which, together with appropriate boundary conditions constitutes the Blasius problem, f (η) + 1 2 f(η)f (η)=0, f(0) = 0, f (0) = ...

The Journal of the Acoustical Society of America, 2012

In this paper the spectrum of Lamb modes in an orthotropic plate is studied. Infinitely many mode... more In this paper the spectrum of Lamb modes in an orthotropic plate is studied. Infinitely many modes are found which undergo a change of sign in their slopes twice, thus leading to two zero-group velocity points. A few modes possessing three such points also exist.

The Quarterly Journal of Mechanics and …, 2009

The number of linear invariants under SO (3) as well as SO (2) of a Cartesian tensor of an arbitr... more The number of linear invariants under SO (3) as well as SO (2) of a Cartesian tensor of an arbitrary rank is studied. A linear form is defined in terms of elements of a tensor. It is established that the number of linear invariants of a tensor of rank n under SO (3) equals ...

Journal of Physics A: Mathematical, Nuclear and General

The semi-classical laser equations are analysed outside the rotating-wave approximation and a new... more The semi-classical laser equations are analysed outside the rotating-wave approximation and a new exact steady-state solution for stationary but inhomogeneously broadened atoms is obtained. Results applicable to any solid-state laser are derived and these are also relevant to a gas laser working near threshold or at very high intensities. The resonance frequency exhibits a Bloch-Siegert shift. New results in the

The Journal of the Acoustical Society of America, 2015

The transient response of an elastic cylinder to a laser impact is studied. When the laser source... more The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by laser interferometry below 8 MHz. Most of these resonances correspond to Zero-Group Velocity guided modes while a few others can be ascribed to thickness modes. We observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifest as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured one, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.

International Journal of the Physical Sciences, 2012

Simple proofs are obtained for the Cowin-Mehrabadi theorem for the identification of a plane of s... more Simple proofs are obtained for the Cowin-Mehrabadi theorem for the identification of a plane of symmetry or an axis of symmetry in an elastic material. The treatment is generalized to a cartesian tensor of arbitrary rank. Necessary and sufficient conditions are found for the existence of a plane of symmetry or an axis of symmetry for a piezoelectric material. Conditions are obtained for the identification of an n-fold axis of symmetry with 3  n .

Physical Review A, 1975

We analyze the problem of a spin-½ system coupled to a longitudinal field B 0 and a transverse fi... more We analyze the problem of a spin-½ system coupled to a longitudinal field B 0 and a transverse field 2Bcosωt. We show that the magnetization is not periodic in general. Time-averaged population inversion is non-negative for the case ω=-γB 0 . We discuss the significance of this result ...

The Quarterly Journal of Mechanics and Applied Mathematics, 2002

We study invariants of the anisotropic elasticity tensor. The invariants are obtained by defining... more We study invariants of the anisotropic elasticity tensor. The invariants are obtained by defining certain tensors of order two associated with the elasticity tensor. We find four second-order invariants with respect to arbitrary orthogonal transformations. This increases by two the number of already known such invariants. When the transformation is confined to rotations about the x 3-axis, the number of second-order invariants becomes seventeen, again an increase by two in the already known number. We describe a method for ascertaining linear independence of these invariants. We also recover structural invariants of Ting and find a few new structural invariants.

Mathematical Problems in Engineering, 2001

Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry... more Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry is studied. For propagation at high frequencies, effects of rotation are negligible but for a frequency which is much smaller than the frequency of rotation, there is a fast wave and two very slow waves. When the two frequencies are equal, the speed of a wave becomes unbounded.

The Journal of the Acoustical Society of America, 1998

International Journal of Theoretical Physics, 2011

A general theory for finding the invariants of an arbitrary tensor is described. Group theoretic ... more A general theory for finding the invariants of an arbitrary tensor is described. Group theoretic methods produce formulas which precisely determine the number of invariants for a Cartesian tensor of arbitrary rank defined over a space of dimension 2, 3 or 4. Explicit expressions are obtained for simple cases.

… -PAKISTAN ACADEMY OF …, 2007

Abstract: We use Wang's transfo~ illation of the Blasius problem to find a numerical sequenc... more Abstract: We use Wang's transfo~ illation of the Blasius problem to find a numerical sequence Tcrr the approximate values of the second derivative at the origin. An application of thc Pade'approximation produces improved values up to a certain point and the method ...

Communications in Nonlinear Science and Numerical Simulation, 2009

We solve the governing equations for the flow of a third grade fluid in a porous half space. We f... more We solve the governing equations for the flow of a third grade fluid in a porous half space. We find a simple expression which describes the solution accurately over the whole domain [0,∞). The rate of exponential decay of the flow is independent of the parameters which ...

Communications in Nonlinear Science and Numerical Simulation, 2009

The [4/3] Pade approximant for the derivative is modified so that the resulting expression has th... more The [4/3] Pade approximant for the derivative is modified so that the resulting expression has the required asymptotic behavior. This gives an analytical result which represents the solution of the classical Blasius problem on the whole domain.

Electronic Journal of Differential equations, 2003

Electronic Journal of Differential Equations, Vol. 2003(2003), No. 92, pp. 1–6. ISSN: 1072-6691. ... more Electronic Journal of Differential Equations, Vol. 2003(2003), No. 92, pp. 1–6. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) ... LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A ...

Applied Mathematics and Mechanics, 1998

Abstract The diagnonal Pade'approximates for exp (x), tanx and tanhx are obtained in a simpl... more Abstract The diagnonal Pade'approximates for exp (x), tanx and tanhx are obtained in a simple manner by using the property of Legendre polynomials that on [− 1, 1] P n (x) is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used to ...

Acta Mechanica, 1999

Summary We discuss the theory of thermoelastic wave propagation in a rotating isotropic material.... more Summary We discuss the theory of thermoelastic wave propagation in a rotating isotropic material. In any given direction there are four waves. In general, all of these waves are attenuated, and none of them is purely dilatational or transverse. Some earlier published results are found to be false.

Advances in Acoustics and Vibration, 2014