Detection of a periodic structure hidden in random background: the role of signal amplitude in the matched filter detection method

The matched filter method for detecting a periodic structure on a surface hidden behind randomness is known to detect up to (r(0)/Lambda) gt;= 0.11, where r(0) is the coherence length of light on scattering from the rough part and 3 is the wavelength of the periodic part of the surface-the above limit being much lower than what is allowed by conventional detection methods. The primary goal of this technique is the detection and characterization of the periodic structure hidden behind randomness without the use of any complicated experimental or computational procedures. This paper examines this detection procedure for various values of the amplitude a of the periodic part beginning from a = 0 to small finite values of a. We thus address the importance of the following quantities: `(a)lambda) `, which scales the amplitude of the periodic part with the wavelength of light, and (r(0))Lambda),in determining the detectability of the intensity peaks.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

On the theory of the indentation test for the measurement of tensile strength of brittle materials

A theoretical solution has been obtained for the state of stress in a rectangular plate under a pair of symmetrically placed rigid indenters. The stress distributions along the two central axes have been calculated for a square plate assuming the pressure distribution under the indenters as uniform, parabolic and one resulting from 'constant displacement' on a semiinfinite boundary, for different ratios of indenter-width to side of square. The results are compared with those of photoelastic analysis of Berenbaum and Brodie and the validity of the solution is discussed. The solution has been extended to orthotropic materials and numerical results for one type of coal are given.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.

Phenomenological theory of the kinetics of ultrasonic emulsification

A working model is given for the rate of ultrasonic emulsification, considering the dispersion at the interface (area A) and the coagulations in the volume V of the emulsion. A bimolecular coagulation leads to the equation c=c∞tanh bt;c∞=(Aα/Vβ)1/2;b=(Aαβ/V)1/2 while a monomolecular coagulation gives c=c∞{1-exp (-at)};c∞=Aα/Vβ;a=β. The experiments on the dependence of c∞, a and b upon A and V favour the bimolecular coagulation. The results are satisfactorily explained on general theoretical grounds.

Comparison of elasticity and shell-theory solutions for finite circular cylindrical shells

A finite circular cylindrical shell subjected to a band of uniform pressure on its outer rim was investigated, using three-dimensional elasticity theory and the classical shell theories of Timoshenko (or Donnell) and Flügge. Detailed comparison of the resulting stresses and displacements was carried out for shells with ratios of inner to outer shell radii equal to 0.80, 0.85, 0.90 and 0.93 and for ratios of outer shell diameter to length of the shell equal to 0.5, 1 and 2. The ratio of band width to length of the shell was 0.2 and Poisson's ratio used was equal to 0.3. An Elliot 803 digital computer was used for numerical computations.

Experimental evidence of the cavity theory of sorption-desorption hysteresis by a study of the effect of electric discharge on entrapped water in silica gel

With the use of the quartz fiber spring balance, sorptions and desorptions of water on silica gel at 30°C were studied and the permanent and reproducible hysteresis loop was obtained. At different points on the desorption curve forming the loop, the gel was subjected to high tension glow electric discharge. As a result of the electric discharge, the gel at any point on the desorption curve shifts to a corresponding point on the sorption curve. This is due to the release from the cavities of gel of the entrapped water held in a metastable state. The electric discharge has no effect on the gel at different points on portions of the desorption curve which coincide with the sorption curve and also on the sorption curve itself, indicating the absence of entrapped water in the gel in these regions. The results afford direct experimental evidence of the reality of the cavity theory of sorption-desorption hysteresis.