A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Surface explosive instability for high frequency waves

High frequency three-wave nonlinear 'explosive' interaction of the surface modes of a semi-infinite beam-plasma system under no external field is investigated. The conditions that favour nonlinear instability, keep the plasma linearly stable. The beam runs parallel to the surface. If at least one of the three wave vectors of the surface modes is parallel to the beam, explosive interaction at the surface takes place after it has happened in the plasma bulk, provided the bulk waves propagate almost perpendicular to the surface and are of short wavelength. On the other hand if the bulk modes have long wavelength and propagate almost parallel to the surface, the surface modes can 'explode' first.

Surface explosive instability for high frequency waves

High frequency three-wave nonlinear 'explosive' interaction of the surface modes of a semi-infinite beam-plasma system under no external field is investigated. The conditions that favour nonlinear instability, keep the plasma linearly stable. The beam runs parallel to the surface. If at least one of the three wave vectors of the surface modes is parallel to the beam, explosive interaction at the surface takes place after it has happened in the plasma bulk, provided the bulk waves propagate almost perpendicular to the surface and are of short wavelength. On the other hand if the bulk modes have long wavelength and propagate almost parallel to the surface, the surface modes can 'explode' first.

Remarkable role of positional isomers in the design of sensors for the ratiometric detection of copper and mercury ions in water

Cation sensing properties of the three positional isomers of rhodamine based sensors (1-3) are studied in water. The sensors differ only in the position of pyridine's nitrogen. The chemosensor 1, with pyridine nitrogen at ortho-position, showed a selective colorimetric detection of Cu(II) ions in water, at physiological pH 7.4 and also in medium containing BSA (bovine serum albumin) and blood serum. Notably the compound 2 and 3, with pyridine end located at meta-and para-positions did not show any color change with Cu(II) ions, although both the compounds showed turn-on change both in color and fluorescence with Hg(II) ions specifically. All the probes showed ratiometric changes with the specific metal ions. The changing position of nitrogen also changed the complexation pattern of the sensors with the metal ions. Probe 1 showed 2 : 1 complexation with Cu(II), whereas 2 and 3 showed 1 : 1 complexation with Hg(II) ions. The mechanism investigation showed that the change in color upon addition of metal ions is due to the ring-opening of the spirolactam ring of the probes. Cu(II) interacted with ligand 1 through a three-point interaction mode comprising carbonyl oxygen, amido nitrogen and pyridine nitrogen end. But in case of 2 and 3, Hg2+ only interacted through pyridine nitrogen ends. Quantitative estimation of Cu2+ and Hg2+ in complex biological media such as bovine albumin protein (BSA) and human blood serum were performed using these sensors. Rapid on-site detection as well as discrimination of these toxic ions was demonstrated using easily prepared portable test-strips.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

Localised spin wave modes in a Heisenberg ferromagnet with biquadratic interaction

The presence of biquadratic exchange in a one-dimensional ferromagnetic Heisenberg chain with an impurity spin is shown to change the nature of the impurity modes and its eigenvalues considerably which can be observed experimentally.

Instability of Coupled Longitudinal and Transverse Electromagnetic Modes of Wave‐Propagation in Bounded Streaming Plasmas

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k 2)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<0.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k3)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k2)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.

Multiple support excitations of open-plane frames by a filtered white noise and soil-structure interaction

Seismic structural design is essentially the estimation of structural response to a forced motion, which may be deterministic or stochastic, imposed on the ground. The assumption that the same ground motion acts at every point of the base of the structure (or at every support) is not always justifiable; particularly in case of very large structures when considerable spatial variability in ground motion can exist over significant distances example long span bridges. This variability is partly due to the delay in arrival of the excitation at different supports (which is called the wave passage effect) and due to heterogeneity in the ground medium which results in incoherency and local effects. The current study examines the influence of the wave passage effect (in terms of delay in arrival of horizontal ground excitation at different supports and neglecting transmission through the structure) on the response of a few open-plane frame building structures with soil-structure interaction. The ground acceleration has been modeled by a suitably filtered white noise. As a special case, the ground excitation at different supports has also been treated as statistically independent to model the extreme case of incoherence due to local effects and due to modifications to the ground motion resulting from wave reflections and refractions in heterogeneous soil media. The results indicate that, even for relatively short spanned building frames, wave passage effect can be significant. In the absence of soil-structure interaction, it can significantly increase the root mean square (rms) value of the shear in extreme end columns for the stiffer frames but has negligible effect on the flexible frames when total displacements are considered. It is seen that pseudo-static displacements increasingly contribute to the rms value of column shear as the time delay increases both for the stiffer and for the more flexible frames. When soil-structure interaction is considered, wave passage effect (in terms of total displacements) is significant only for low soil shear modulus, G. values (where soil-structure interaction significantly lowers the fundamental frequency) and for stiff frames. The contribution of pseudo-static displacement to these rms values is found to decrease with increase in G. In general, wave passage effect for most interactive frames is insignificant compared to the attenuating effect a decrease in G, has on the response of the interactive structure to uniform support excitation. When the excitations at different supports are statistically independent, it is seen that for both the stiff and flexible frames, the rms value of the column shear in extreme end columns is several times larger (more for the stiffer frames) than the value corresponding to uniform base excitation with the pseudo-static displacements contributing over 99% of the rms value of column shear. Soil-structure interaction has an attenuating effect on the rms value of the column shear, the effect decreasing with increase in G,. Here too, the pseudo-static displacements contribute very largely to the column shear. The influence of the wave passage effect on the response of three 2-bay frames with and without soil-structure interaction to a recorded horizontal accelerogram is also examined. (C) 2010 Elsevier Ltd. All rights reserved.

Aerodynamic noise from wave-turbulence interaction

Abstract. In order to estimate the acoustic energy scattered when a unit volume of free turbulence, such as in free jets, interacts with a plane steady sound wave, theoretical expressions are derived for two simple models of turbulence: eddy model and isotropic model. The effect of convection by mean motion of the energy-bearing eddies on the incident sound wave and on the sound generated from wave-turbulence interaction is taken into account. Finally, by means of a representative calculation,the directionality pattern and Mach number dependence of the noise so generated is discussed.

Surface acoustic wave distribution and acousto-optic interaction in proton exchanged LiNbO3 waveguides

The efficiency of acoustooptic (AO) interaction in YZ-cut proton exchanged (PE) LiNbO3 waveguides is theoretically analysed by determining the overlap between the optical and acoustic field distributions. The present analysis takes into account the perturbed SAW field distribution due to the presence of the PE layer on the LiNbO3 substrate determined by the rigorous layered medium approach. The overlap is found to be significant upto very high acoustic frequencies of the order of 5 GHz, whereas in the earlier analysis by vonHelmolt and Schaffer [6] for diffused waveguides, it was shown that the overlap integral rolls down to nearly zero at this high frequency range.

Repulsive fermions in optical lattices: Phase separation versus coexistence of antiferromagnetism and d-wave superfluidity

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond d-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole e(hole)(x) has a minimum at doping x = x(c) that signals phase separation between the antiferromagnetic and d-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Equivalent Circuit Analysis of Serpentine Folded-waveguide Slow-wave Structures for Millimeter-wave Traveling-wave Tubes

A simple equivalent circuit model for the analysis of dispersion and interaction impedance characteristics of serpentine folded-waveguide slow-wave structure was developed by considering the straight and curved portions of structure supporting the dominant TE10-mode of the rectangular waveguide. Expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam-hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was simple yet accurate in predicting the dispersion and interaction impedance behaviour at millimeter-wave frequencies. The analysis was benchmarked against measurement as well as with 3D electromagnetic modeling using MAFIA for two typical slow-wave structures (one at the Ka-band and the other at the W-band) and close agreement observed.

Analysis of Rectangular Folded-Waveguide Millimeter-Wave Slow-wave Structures using Conformal Transformations

An analysis of rectangular folded-waveguide slow-wave structure was developed using conformal mapping technique through Schwarz's polygon transformation and closed form expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures, one operating in Ka-band and the other operating in Q-band, against measurement and 3D electromagnetic modeling using MAFIA.