Finite Element Approximation of a Rigid Punch Indenting a Membrane

Optimal order H¹ and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, _c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R², given ,g R⁺ and an obstacle defined over E we consider the minimization of |v|²_1,+gµover (v, µ) H¹₀() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (_c,^h_c)Ch ln 1/h, where ^h_c is the finite element approximation to_c. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm.     

Reflection at a Discontinuity in a Transmission Line

An exact expression is obtained for the reflection coefficientwhen a TEM wave, propagating along a co-axial line in a regionwhere both conductors are perfectly conducting, is incidenton a region where the inner conductor consists of dielectriccoated with a resistive film whilst the outer conductor remainsperfectly conducting.     

Magnetic response of split ring resonator metamaterials: From effective medium dispersion to photonic band gaps

On systematically investigating the electromagnetic response of periodic split-ring resonator (SRR) metamaterials as a function of the size-to-wavelength (a/λ) ratio, we find that the stop bands due to the geometric resonances of the SRR weaken with increasing (a/λ) ratio, and are eventually replaced by stop bands due to Bragg scattering. Our study traces the behaviour of SRR-based metamaterials as the resonance frequency increases and the wavelength of the radiation finally becomes comparable to the size of the unit cell of the metamaterial. In the intermediate stages, the dispersion of the SRR metamaterial can still be described as due to a localized magnetic resonances while Bragg scattering finally becomes the dominant phenomenon as a/λ∼1/2.     

Evaluation of certain improper integrals arising in potential problems

The use of Schwarz‐Christoffel transform of the complex variable theory is shown to be well‐suited for the evaluation of certain improper integrals arising in potential problems, in closed form.     

Structure and melting of Morse solids

Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of the Morse pair potential. The structural properties of the liquid and solid phases vary significantly with the range. The longer range, softer potentials are associated with increased densities and cohesive energies in both the solid and liquid phases. The extent of local disorder associated with lattice sites in the solid phase, as measured by the Lindemann and bond orientational order parameters, increases with increasing range of the pair potential.     

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem forLaplace's equation which is a generalization of the one occurringin the course of solution of the problem of diffraction of surfacewater waves by a nearly vertical submerged barrier. The methodof solution involves the use of complex function theory, theSchwarz reflection principle, and reduction to a system of twouncoupled Riemann-Hilbert problems. Known results, representingthe reflection and transmission coefficients of the water waveproblem involving a nearly vertical barrier, are derived interms of the shape function.     

Drift wave in pair-ion plasma

The conditions for the existence of low-frequency electrostatic drift wave in pair-ion plasma are discussed. It is shown that the temperature and/or mass difference of both species could produce drift wave in a pair-ion plasma. The results are discussed in the context of the fullerene pair-ion plasma experiment.     

A Note on a Singular Integral Equation

A direct method is presented for solving a singular integralequation which is a generalization of one occurring in wave-guidetheory and in the theory of dislocations. The present methodavoids elaborate application of the complex variable methodsnormally associated with such singular integral equations.