Faiz Ahmad

Acoustic scattering by transversely isotropic cylinders

We study the scattering of an acoustic wave incident on a transversely isotropic cylinder immersed in a fluid. Scalar potentials are expanded in series of normal modes. This expansion changes in character as the angle of incidence increases. There exist critical angles beyond which the angular pattern of scattering changes dramatically. The transversely isotropic materials are of two types. Materials of the first type have two critical angles of incidence whereas materials of the second type have an additional critical angle. Below the first critical angle the form function is rich in peaks whose number steadily goes down as the angle of incidence increases.

Guided waves in a transversely isotropic cylinder immersed in a fluid

Propagation of flexural guided waves in a fluid-loaded transversely isotropic cylinder is studied. Numerical results are presented for a cobalt cylinder immersed in water. The phase velocities are not significantly affected except for several modes in which the energy leakage occurs into the fluid over certain frequency ranges. Attenuation spectra for the leaking modes are plotted.

Thermoelastic plane waves in a rotating isotropic medium

SummaryWe 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.

Lamb modes with multiple zero-group velocity points in an orthotropic plate.

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.

Theory of radiation reaction and atom self-energies: an operator reaction field

The field generalizes in a natural way the c-number theory of radiation reaction and frequency shifts due to Lorentz. By a trivial extension the operator field can be applied to the more complicated cases of a single multi-level atom and the super-radiant problem of N atoms on the same site where these are coupled either to the vacuum or the vacuum and additional imposed quantized fields. By further extension it also applies to the case of N atoms on different sites. Explicit expressions for positive and negative frequency parts of the total operator field are given in terms of arbitrary dipole operator sources and are apparently valid for times t>> omega s-1>> omega max-1 where omega s is the atomic resonance and omega max a cut-off used systematically throughout the theory.

Theory of the Bloch-Siegert shift

The method recently developed for treating Bloch-Siegert shift of the main resonance in a magnetic resonance experiment is successfully applied to the higher order resonances due to multiquantum transitions. A general analytical expression for the (2n+1)th resonances is given. Results for the main and third order resonance in the low or vanishingly low range of static magnetic fields are also reported.

Effect of rotation on wave propagation in a transversely isotropic medium.

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.

A simple formula for the longitudinal modes in a cylinder

For CT<C<CL, the Pochhammer dispersion relation can be replaced by an approximate equation which can be solved to obtain the dimensionless wave number explicitly as a function of the phase velocity. This equation is similar to the corresponding equation for the Lamb modes in plate. The two types of modes are interlaced, i.e., between every pair of modes of the plate there is a longitudinal mode of cylinder and vice versa.

A simple formula for the Lamb modes in a plate

The dispersion relation for the Rayleigh–Lamb modes in an elastic plate can be replaced by a simpler equation, which admits exact solution. The approximation is valid for almost all modes when the phase velocity is between cT and cL.

Extremal iota energy of bicyclic digraphs

The energy of an n-vertex digraph D is defined by E(D)=k=1n|Re(zk)|, where z1,,zn are eigenvalues of D and Re(zk) is the real part of eigenvalue zk. Very recently, a new type of energy of digraphs has been introduced, which is known as the iota energy of digraphs. The iota energy of the digraph D is defined by Ec(D)=k=1n|Im(zk)|, where z1,,zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk. The unicyclic digraphs with extremal iota energy are known. In this paper, we consider a class Dn of n-vertex bicyclic digraphs with vertex-disjoint directed cycles and find the digraphs in Dn with minimal and maximal iota energy.