Field and potential around local scatterers in thin metal films studied by scanning tunneling potentiometry

We report the direct observation of electrochemical potential and local transport field variations near scatterers like grain boundaries, triple points, and voids in thin platinum films studied by scanning tunneling potentiometry. The field is highest at a void, followed by a triple point and a grain boundary. The local transport field near a void can even be four orders of magnitude higher than the macroscopic field, indicating that the void is the most likely place for an electromigration induced failure. The field build up for a particular type of scatterer depends on the grain connectivity. We estimate an average grain boundary reflection coefficient for the film from the temperature dependence of its resistivity.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Measurement of the acoustical impedance of a black box at low frequencies using a shorter impedance tube

For the experimental evaluation of the acoustical impedance of a termination by the impedance-tube method at low frequencies, the length of the impedance tube is a problem. In the present paper, the method of exact analysis of standing waves developed by the authors for the stationary medium as well as for mean flow, has been extended for measurement of the acoustical impedance of a termination at low frequencies. The values of the tube attenuation factor and the wave number at the low frequency of interest are established from the experiment conducted, with the given impedance tube, at a higher frequency. Then, exciting the tube at the desired low frequency it is sufficient to measure sound pressure at three differenct locations (not necessarily the minima) in order to evaluate reflection coefficient and hence the impedance of the termination at that frequency.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

Localization of light in coherently amplifying random media

We derive and analyze the statistics of reflection coefficient of light backscattered coherently from an amplifying and disordered optical medium modeled by a spatially random refractive index having a uniform imaginary part in one dimension. We find enhancement of reflected intensity owing to a synergy between wave confinement by Anderson localization and coherent amplification by the active medium. This is not the same as that due to enhanced optical path lengths expected from photon diffusion in the random active medium. Our study is relevant to the physical realizability of a mirrorless laser by photon confinement due to Anderson localization.

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Analytical Study of Low-Field Diffusive Transport in Highly Asymmetric Bilayer Graphene Nanoribbon

We present a simplified theory of carrier backscattering coefficient in a twofold degenerate asymmetric bilayer graphene nanoribbon (BGN) under the application of a low static electric field. We show that for a highly asymmetric BGN(Delta = gamma), the density of states in the lower subband increases more that of the upper, in which Delta and gamma are the gap and the interlayer coupling constant, respectively. We also demonstrate that under the acoustic phonon scattering regime, the formation of two distinct sets of energy subbands signatures a quantized transmission coefficient as a function of ribbon width and provides an extremely low carrier reflection coefficient for a better Landauer conductance even at room temperature. The well-known result for the ballistic condition has been obtained as a special case of the present analysis under certain limiting conditions which forms an indirect validation of our theoretical formalism.

A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.

Determination of coefficient of consolidation from early stage of log t plot

The standard curve-fitting methods, Casagrande's log t method and Taylor's root t method, for the determination of the coefficient of consolidation use the later part of the consolidation curve and are influenced by secondary compression effects. Literature shows that secondary compression is concurrent with primary consolidation and that its effect is to decrease the value of the coefficient of consolidation. If the early part of the time-compression data is used, the values obtained will be less influenced by secondary compression effects. A method that uses the early part of the log t plot is proposed in this technical note. As the influence of secondary compression is reduced, the value obtained by this method is greater than that yielded by both the standard methods. The permeability values computed from C-v (obtained from the proposed method) rue more in agreement with the measured values than the standard methods showing that the effects of secondary compression are minimized. Time-compression data for a shorter duration is sufficient for the determination of C-v if the coefficient of secondary compression is not required.

Evaluation Of Diffusion-Coefficient And Ionic Mobility In (Nh4)4fe(Cn)6.1.5 H2o

The diffusion coefficient, D, and the ionic mobility, μ, in the protonic conductor ammonium ferrocyanide hydrate have been determined by the isothermal transient ionic current method. D is also determined from the time dependence of the build up of potential across the samples and theretical expressions describing this build up in terms of double exponential dependence on time are obtained. The values obtained are D=3.875×10−11m2s−1 and μ=1.65×10−9 m2V−1s−1.

Experimental study of the damping coefficient variations in zinc crystal

Much work has been done on obtaining empirical stress-velocity relations and evaluating the temperature dependence and activation energy of plastic deformation /1, 2/. Another prevalent concept is that of the drag coefficient and its variation with degree of crystal imperfection /3/. Significant differences and discrepancies exist in the reported values /2, 4/. Although it is recognised that the yield point is caused by point interstitials and aggregates, little has been done on the evaluation of specific crystal-solute combinations and interaction parameters. Some of the first efforts, in this direction were performed by Wain and Cottrell /5/.

Ratio of Diffusion Coefficient to Mobility for Electrons in SF6-Air and Freon-Nitrogen Mixtures

The ratio of diffusion coefficient to mobility (D/¿) for electrons has been measured in SF6-air and freon-nitrogen mixtures for various concentrations of SF6 and freon in the mixtures over the range 140¿ E/p¿ 220 V.cm-1 - torr-1. In SF6-air mixtures, the values of D/¿ were always observed to lie intermediate between the values for the pure gases. However, in freon-nitrogen mixtures, with a small concentration (10 percent) of freon in the mixture, the values of D/¿ are found to lie above the boundaries determined by the pure gases. In this mixture, over the lower E/p range (140 to 190) the electrons appear to lose a large fraction of their energy by the excitation of the complex freon molecules, while at higher E/p values (200 to 240), the excitation and consequent deexcitation of nitrogen molecules and its metastables seem to cause an increased rate of ionization of freon molecules.

Dispersion of the stress-optic coefficient in glasses

The stress-optic coefficient (n3/2)(q11-q12) has been determined for a series of 18 optical glasses of different compositions in the wavelength range 5700-3200 Å. The coefficients are negative for all the glasses except for a high-lead-content glass of density 6·7 and refractive index 1·89. The numerical value of the coefficient decreases as one proceeds to the ultraviolet. This behaviour is just the opposite of what is observed in fused silica. By applying Mueller's theory, the strain polarizability constant and its dispersion have been evaluated.

Comments on "Diffuse sound reflection by maximum length sequences"

Some improvements are suggested to Schroeder's scheme [J. Acoust. Soc. Am. 57, 149–150 (1975)] of achieving diffuse sound reflection in concert halls.Subject Classification