Optical Differentiation Phase Measurement Using the Bias Shifting Method

A new optical phase measurement method using a differentiation filter is proposed. The new method uses two images obtained by shifting the filter. This method has an advantage in that non-uniformity of the wavefront intensity does not produce errors. We present herein the theory of the newly proposed method and verify the theory by computer simulation. The effects of non-uniformity of the wavefront intensity, noise, and bias shifting length for errors are discussed. The system has been demonstrated for a plane wave and a spherical wave. For the proposed method, although the number of errors due to noise increases, the number of errors due to non-uniformity decreases. Therefore, the proposed method is useful for the phase measurement of a wavefront for which the intensity is not uniform. In addition, it improves the accuracy of the phase measurement system using a differentiation filter.     

An experimental study of the discharge coefficient of pipe perforations

Experiments were conducted to study the variation of the pressure loss coefficient of pipe perforations with geometrical parameters of the perforations and a Reynolds number based on the hydraulic diameter of an orifice representing the perforations. The experimental data are used to develop an empirical relationship between the head loss across the perforations and the geometrical and hydraulic parameters related to the perforations which was seen to give better predictions when the perforations are not very closely spaced. The experimental results reported herein correspond to the pipes of small perforated length, with downstream end of the pipe closed.List of symbols a area of the orifice - A total area of perforations - A ₁ inner area of pipe - A ₂ outlet area - C _r factor for static pressure regain - D diameter of the orifice - D _h hydraulic diameter - D _p internal diameter of the pipe - f_o friction factor for orifice surface - f_p friction factor for perforated pipe - g acceleration due to gravity - H water head inside the perforated pipe - H ₀ head outside the perforated pipe - H(A) experimental water head difference - H1 water head difference between inside and outside of perforations when A ₂ is outlet area and A ₁ is inside perforated surface area of pipe - H2 water head difference between inside and outside of perforations when A ₂ is outlet area and A ₁ is cross-sectional area of pipe - H3 water head difference between inside and outside of perforations when A ₂ is infinity and A ₁ is inside perforated surface area of pipe - H4 water head difference between inside and outside of perforations when A ₂ is infinity and A ₁ is cross-sectional area of pipe - H _t total head at the inlet of the perforated pipe - H₀ head loss across the orifice - H_f head loss due to surface friction - H_m head loss due to momentum reduction - K _f pressure loss coefficient for frictional losses - L _p perforated length of the pipe - n total number of orifices in a perforated pipe - N number of orifice rows - p pitch of perforations - P _a perimeter of the flow passage - P ₀ porosity of the perforated pipe - q flow rate through orifice - Q flow rate through perforations - Re ₀ Reynolds number based on orifice diameter - Re _p Reynolds number based on pipe diameter - T wall thickness of the pipe - v velocity of flow through the orifice Greek symbols V ₁ velocity of flow upstream of the orifice - V ₂ velocity of flow downstream of the orifice - (tou) coefficient depending on T/D ratio of the orifice - (zeeta) loss coefficient of fluid flow through perforated pipe - coefficient depending on the shape of the inlet edge of the orifice     

Normal co-ordinate analysis of 1, 8-dibromooctane

The organic compound 1,8-dibromooctane (1,8-DBO) exists in liquid phase at ambient temperatures and has versatile synthetic applications. In its liquid phase 1,8-DBO has been expected to exist in four most probable conformations, with all its carbon atoms in the same plane, having symmetries C _2h , C _i , C ₂ and C ₁ . In the present study a detailed vibrational analysis in terms of assignment of Fourier transform infrared (FT-IR) and Raman bands of this molecule using normal co-ordinate calculations has been done. A systematic set of symmetry co-ordinates has been constructed for this molecule and normal co-ordinate analysis is carried out using the computer program MOLVIB. The force-field transferred from already studied lower chain bromo-alkanes is subjected to refinement so as to fit the observed infrared and Raman frequencies with those of calculated ones. The potential energy distribution (PED) has also been calculated for each mode of vibration of the molecule for the assumed conformations.     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.     

Elucidation of 3D-to-2D transformation by magnetization studies for Hc in Bi2Sr2CaCu2O8

New magnetization results (for Hc) on a single crystal of Bi2212 elucidating the transition from a one-component to a two- component response across the 3D-to-2D transformation are reported. The two-component response is identified to emanate from the 2D planes and interplanar links. The magnetization response above the transformation temperature T_s and very close to T_c is found to be irreversible in contrast to the reversible behavior so far believed in. A new phase diagram for the mixed state of layered superconductors near T_c is proposed.     

Comparison of nuclear Bragg scattering with Mössbauer spectroscopy for the measurement of hyperfine interactions

Fourier analysis of the time evolution of the nuclear Bragg scattering from the (7, 7, 7) reflection in α-hematite (⁵⁷Fe) excited by synchrotron radiation was used to extract values of Zeeman splitting of the ground and 14.413-keV states of⁵⁷Fe in the crystal magnetic field. The results so obtained apparently do not agree with the corresponding values obtained from Mössbauer spectroscopy on α-hematite. Possible reasons for the discrepancy are discussed.     

Thermomagnetic history effects in niobium and its implication for H c1 in highT c superconductors

The existence of a remanent magnetization (M _rem) on switching off the field of a field cooled (FC) sample of a highT _c superconductor is often reported. It has recently been argued thatM _rem should equal the difference in FC and zero field cooled (ZFC) magnetizations (M _FC —M _ZFC) in hard superconductors and this has been demonstrated to hold in single crystals of YBCO at 4.2K over a limited range ofH values. We report the detailed magnetization measurements under various thermomagnetic histories (of whichM _rem is one special case) on two specimens of Nb, which show different extents of flux trapping. We find that there are in general three regions inH, T space, corresponding toM _rem+M _ZFC−M _FC=0,M _rem<(M _FC−M _ZFC) andM _rem>(M _FC−M _ZFC). At anyT, the equality holds forH<H _c1(T), and forH→H _c2 (M _FC−M _ZFC) asymptotically vanishes and thereM _rem>(M _FC−M _ZFC). We show that there exists an intermediate region in all hard superconductors, whereM _rem<(M _FC−M _ZFC). The range over which this situation persists, however, depends on the degree of irreversibility in a sample. We can explain qualitatively all the history dependent magnetization data in terms of the critical state model. We point out an inconsistency in an earlier analysis to determineH _c1(T) from such data in YBCO. We also propose a new criterion for putting limits onH _c1(T) in hard superconductors.     

Cross-flow induced vibrations in a tube bank—Turbulent buffeting and fluid elastic instability

Experimental results are reported for a wind tunnel study of cross-flow induced vibrations in a tube bank. The rotated triangular array had a pitch ratio of 1·375 and consisted of 19 flexibly mounted tubes surrounded by 116 rigid, removable tubes. The natural frequency and damping of the flexibly mounted tubes could be carefully controlled. Details of the experimental facility and the vortex shedding behaviour of the tube bank were reported in the first of these two companion papers. The turbulent buffeting and fluid elastic response are treated in this second paper. The effects on the fluid elastic threshold of the motion of surrounding tubes, damping and number of upstream rows of tubes are discussed.