Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate.

Changing resonator geometry to boost sound power decouples size and song frequency in a small insect

Despite their small size, some insects, such as crickets, can produce high amplitude mating songs by rubbing their wings together. By exploiting structural resonance for sound radiation, crickets broadcast species-specific songs at a sharply tuned frequency. Such songs enhance the range of signal transmission, contain information about the signaler's quality, and allow mate choice. The production of pure tones requires elaborate structural mechanisms that control and sustain resonance at the species-specific frequency. Tree crickets differ sharply from this scheme. Although they use a resonant system to produce sound, tree crickets can produce high amplitude songs at different frequencies, varying by as much as an octave. Based on an investigation of the driving mechanism and the resonant system, using laser Doppler vibrometry and finite element modeling, we show that it is the distinctive geometry of the crickets' forewings (the resonant system) that is responsible for their capacity to vary frequency. The long, enlarged wings enable the production of high amplitude songs; however, as a mechanical consequence of the high aspect ratio, the resonant structures have multiple resonant modes that are similar in frequency. The drive produced by the singing apparatus cannot, therefore, be locked to a single frequency, and different resonant modes can easily be engaged, allowing individual males to vary the carrier frequency of their songs. Such flexibility in sound production, decoupling body size and song frequency, has important implications for conventional views of mate choice, and offers inspiration for the design of miniature, multifrequency, resonant acoustic radiators.

Transition and acoustic response of recirculation structures in an unconfined co-axial isothermal swirling flow

This paper reports the first observations of transition from a pre-vortex breakdown (Pre-VB) flowreversal to a fully developed central toroidal recirculation zone in a non-reacting, double-concentric swirling jet configuration and its response to longitudinal acoustic excitation. This transition proceeds with the formation of two intermediate, critical flow regimes. First, a partially penetrated vortex breakdown bubble (VBB) is formed that indicates the first occurrence of an enclosed structure as the centre jet penetration is suppressed by the growing outer roll-up eddy; resulting in an opposed flow stagnation region. Second, a metastable transition structure is formed that marks the collapse of inner mixing vortices. In this study, the time-averaged topological changes in the coherent recirculation structures are discussed based on the non-dimensional modified Rossby number (Ro(m)) which appears to describe the spreading of the zone of swirl influence in different flow regimes. Further, the time-mean global acoustic response of pre-VB and VBB is measured as a function of pulsing frequency using the relative aerodynamic blockage factor (i.e., maximum radial width of the inner recirculation zone). It is observed that all flow modes except VBB are structurally unstable as they exhibit severe transverse radial shrinkage (similar to 20%) at the burner Helmholtz resonant modes (100-110 Hz). In contrast, all flow regimes show positional instability as seen by the large-scale, asymmetric spatial shifting of the vortex core centres. Finally, the mixing transfer function M (f) and magnitude squared coherence lambda(2)(f) analysis is presented to determine the natural couplingmodes of the system dynamic parameters (u', p'), i.e., local acoustic response. It is seen that the pre-VB flow mode exhibits a narrow-band, low pass filter behavior with a linear response window of 100-105 Hz. However, in the VBB structure, presence of critical regions such as the opposed flow stagnation region alters the linearity range with the structure showing a response even at higher pulsing frequencies (100-300 Hz). (C) 2013 AIP Publishing LLC.

Resonant absorption of alfvén waves near a neutral point

It is shown that, although the mathematical analysis of the Alfven-wave equation does not show any variation at non-zero or zero singular points, the role of surface waves in the physical mechanism of resonant absorption of Alfven waves is very different at these points. This difference becomes even greater when resistivity is taken into account. At the neutral point the zero-frequency surface waves that are symmetric surface modes of the structured neutral layer couple to the tearing mode instability of the layer. The importance of this study for the energy balance in tearing modes and the association of surface waves with driven magnetic reconnection is also pointed out.

Capturing higher modes of vibration of micromachined resonators

MEMS resonators have potential applications in the areas of RF-MEMS, clock oscillators, ultrasound transducers, etc. The important characteristics of a resonator are its resonant frequency and Q-factor (a measure of damping). Usually large damping in macro structures makes it difficult to excite and measure their higher modes. In contrast, MEMS resonators seem amenable to excitation in higher modes. In this paper, 28 modes of vibration of an electrothermal actuator are experimentally captured–perhaps the highest number of modes experimentally captured so far. We verify these modes with FEM simulations and report that all the measured frequencies are within 5% of theoretically predicted values.

Sensitivity of polyvinylidene fluoride films to mechanical vibration modes and impact after optimizing stretching conditions

The β-phase of polyvinylidene fluoride (PVDF) is well known for its piezoelectric properties. PVDF films have been developed using solvent cast method. The films thus produced are in α-phase. The α-phase is transformed to piezoelectric β-phase when the film is hot-stretched with various different stretching factors at various different temperatures. The films are then characterized in terms of their mechanical properties and surface morphological changes during the transformation from α- to β-phases by using X-ray diffraction, differential scanning calorimeter, Raman spectra, Infrared spectra, tensile testing, and scanning electron microscopy. The films showed increased crystallinity with stretching at temperature up to 80°C. The optimum conditions to achieve β-phase have been discussed in detail. The fabricated PVDF sensors have been tested for free vibration and impact on plate structure, and its response is compared with conventional piezoelectric wafer type sensor. The resonant and antiresonant peaks in the frequency response of PVDF sensor match well with that of lead zirconate titanate wafer sensors. Effective piezoelectric properties and the variations in the frequency response spectra due to free vibration and impact loading conditions are reported. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers.

Layer-dependent resonant Raman scattering of a few layer MoS2

We report resonant Raman scattering of MoS2 layers comprising of single, bi, four and seven layers, showing a strong dependence on the layer thickness. Indirect band gap MoS2 in bulk becomes a direct band gap semiconductor in the monolayer form. New Raman modes are seen in the spectra of single- and few-layer MoS2 samples which are absent in the bulk. The Raman mode at similar to 230 cm(-1) appears for two, four and seven layers. This mode has been attributed to the longitudinal acoustic phonon branch at the M point (LA(M)) of the Brillouin zone. The mode at similar to 179 cm(-1) shows asymmetric character for a few-layer sample. The asymmetry is explained by the dispersion of the LA(M) branch along the G-M direction. The most intense spectral region near 455 cm(-1) shows a layer-dependent variation of peak positions and relative intensities. The high energy region between 510 and 645 cm(-1) is marked by the appearance of prominent new Raman bands, varying in intensity with layer numbers. Resonant Raman spectroscopy thus serves as a promising non invasive technique to accurately estimate the thickness of MoS2 layers down to a few atoms thick. Copyright (C) 2012 John Wiley & Sons, Ltd.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Studies on elastic coupling parameters of fracture modes in orthotropic materials

The characterisation of cracks is usually done using the well known three basic fracture modes, namely opening, shearing and tearing modes. In isotropic materials these modes are uncoupled and provide a convenient way to define the fracture parameters. It is well known that these fracture modes are coupled in anisotropic materials. In the case of orthotropic materials also, coupling exists between the fracture modes, unless the crack plane coincides with one of the axes of orthotropy. The strength of coupling depends upon the orientation of the axes of orthotropy with respect to the crack plane and so the energy release rate components associated with each of the modes vary with crack orientation. The variation, of these energy release rate components with the crack orientation with respect to orthotropic axes, is analyzed in this paper. Results indicate that in addition to the orthotropic planes there exists other planes with reference to which fracture modes are uncoupled.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Probing the Neutral Edge Modes in Transport across a Point Contact via Thermal Effects in the Read-Rezayi Non-Abelian Quantum Hall States

Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.

Theoretical-Studies on the Modes of Binding of Some of the Beta-Glycosidically Linked Glucobioses to Concanavalin-A

The probable modes of binding for methyl-α-d-sophoroside, methyl-β-d-sophoroside, laminariboise and cellobiose to concanavalin A have been determined using theoretical methods. Methyl-d-sophorosides can bind to concanavalin A in two modes, i.e. by placing their reducing as well as non-reducing sugar units in the carbohydrate specific binding site, whereas laminaribiose and cellobiose can reach the binding site only with their non-reducing glucose units. However, the probability for methyl-α-d-sophoroside to bind to concanavalin A with its reducing sugar residue as the occupant of the binding site is much higher than it is with its non-reducing sugar residue as the occupant of the sugar binding site. A few of the probable conformers of methyl-β-d-sophoroside can bind to concanavalin A with either the reducing or non-reducing glucose unit. Higher energy conformers of cellobiose or laminaribiose can reach the binding site with their non-reducing residues alone. The relative differences in the binding affinities of these disaccharides are mainly due to the differences in the availability of proper conformers which can reach the binding site and to non-covalent interactions between the sugar and the protein. This study also suggests that though the sugar binding site of concanavalin A accommodates a single sugar residue, the residue outwards from the binding site also interacts with concanavalin A, indicating the existence of extended concanavalin A carbohydrate interactions.

Algebraic characterization of decentralized fixed modes

An input-output, frequency-domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula.

Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.