The effect of electric field maximum on the Rabi flopping and generated higher frequency spectra

We investigate the effect of the electric field maximum on the Rabi flopping and the generated higher frequency spectra properties by solving Maxwell-Bloch equations without invoking any standard approximations. It is found that the maximum of the electric field will lead to carrier-wave Rabi flopping (CWRF) through reversion dynamics which will be more evident when the applied field enters the sub-one-cycle regime. Therefore, under the interaction of sub-one-cycle pulses, the Rabi flopping follows the transient electric field tightly through the oscillation and reversion dynamics, which is in contrast to the conventional envelope Rabi flopping. Complete or incomplete population inversion can be realized through the control of the carrier-envelope phase (CEP). Furthermore, the generated higher frequency spectra will be changed from distinct to continuous or irregular with the variation of the CEP. Our results demonstrate that due to the evident maximum behavior of the electric field, pulses with different CEP give rise to different CWRFs, and then different degree of interferences lead to different higher frequency spectral features.

Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

The Finometer can function as a standalone instrument in blood pressure variability studies and does not require support equipment to determine breathing frequency

Objective: The Finometer (FMS, Finapres Measurement Systems, Amsterdam) records the beat-to-beat finger pulse contour and has been recommended for research studies assessing shortterm changes of blood pressure and its variability. Variability measured in the frequency domain using spectral analysis requires that the impact of breathing be restricted to high frequency spectra (> 0.15 Hz) so data from participants needs to be excluded when the breathing impact occurs in the low frequency spectra (0.04 - 0.15 Hz). This study tested whether breathing frequency can be estimated from standard Finometer recordings using either stroke volume oscillation frequency or spectral stroke volume variability maximum scores. Methods: 22 healthy volunteers were tested for 270s in the supine and upright positions. Finometer recorded the finger pulse contour and a respiratory transducer recorded breathing. Stoke volume oscillation frequency was calculated manually while the stroke volume spectral maximums were obtained using the software Cardiovascular Parameter Analysis (Nevrokard Kiauta, Izola, Slovenia). These estimates were compared to the breathing frequency using the Bland-Altman procedures. Results: Stroke volume oscillation frequency estimated breathing frequency to <±10% 95% levels of agreement in both supine (-7.7 to 7.0%) and upright (-6.7 to 5.4%) postures. Stroke volume variability maximum scores did not accurately estimate breathing frequency. Conclusions: Breathing frequency can be accurately derived from standard Finometer recordings using stroke volume oscillations for healthy individuals in both supine and upright postures. The Finometer can function as a standalone instrument in blood pressure variability studies and does not require support equipment to determine breathing frequency.

The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

Voltage and current spectra for matrix power converters

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120◦ out of phase one from another, and the output is to be delivered as a similar three-phase supply. The matrix converter switches rapidly, to connect each output line in sequence to each of the input lines in an attempt to synthesize the prescribed output voltages. The switching is carried out at high frequency and it is of practical importance to know the frequency spectra of the output voltages and of the input and output currents. We determine in this paper these spectra using a new method, which has significant advantages over the prior default method (a multiple Fourier series technique), leading to a considerably more direct calculation. In particular, the determination of the input current spectrum is feasible here, whereas it would be a significantly more daunting procedure using the prior method instead.

Experimental Verification of the Lateral Periodicity of Axially Periodic Incoherent Fields Using the Lau Effect

General' objects, which are specially prepared to possess restricted spatial frequency spectra, have been used in the conventional Lau experiment to obtain experimental proof for the existence of lateral periodicity arising from axial periodicity, for a subclass of axially periodic wavefields in an incoherent situation.

Spectral response of a droplet in pulsating external flow field

A droplet introduced in an external convective flow field exhibits significant multimodal shape oscillations depending upon the intensity of the aerodynamic forcing. In this paper, a theoretical model describing the temporal evolution of normal modes of the droplet shape is developed. The fluid is assumed to be weakly viscous and Newtonian. The convective flow velocity, which is assumed to be incompressible and inviscid, is incorporated in the model through the normal stress condition at the droplet surface and the equation of motion governing the dynamics of each mode is derived. The coupling between the external flow and the droplet is approximated to be a one-way process, i.e., the external flow perturbations effect the droplet shape oscillations and the droplet oscillation itself does not influence the external flow characteristics. The shape oscillations of the droplet with different fluid properties under different unsteady flow fields were simulated. For a pulsatile external flow, the frequency spectra of the normal modes of the droplet revealed a dominant response at the resonant frequency, in addition to the driving frequency and the corresponding harmonics. At driving frequencies sufficiently different from the resonant frequency of the prolate-oblate oscillation mode of the droplet, the oscillations are stable. But at resonance the oscillation amplitude grows in time leading to breakup depending upon the fluid viscosity. A line vortex advecting past the droplet, simulated as an isotropic jump in the far field velocity, leads to the resonant excitation of the droplet shape modes if and only if the time taken by the vortex to cross the droplet is less than the resonant period of the P-2 mode of the droplet. A train of two vortices interacting with the droplet is also analysed. It shows clearly that the time instant of introduction of the second vortex with respect to the droplet shape oscillation cycle is crucial in determining the amplitude of oscillation. (C) 2014 AIP Publishing LLC.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

Spectral analysis and control to obtain sub-5 fs pulses by femtosecond filamentation

A spectral-filter method is numerically demonstrated to obtain sub-5 fs pulses by using femtosecond filamentation in fused silica. Instead of employing spectral phase compensation, by properly employing a high-pass filter to select the broadened high-frequency spectra that are located almost in phase in the tailing edge of the self-compressed pulses owing to self-steepening, as short as single-cycle pulses can be obtained. For instance, for an input pulse with a duration of 50 fs and energy 2.2 mu J, the minimum pulse duration can reach to similar to 4 fs (about 1.5 cycles) by applying a proper spectral filter. (C) 2008 Optical Society of America

Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d (0)=3.00 mm and the aspect ratio A=l/d (0)=0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378].

Ocean wave imaging mechanism by imaging radar

Analytical representations of the high frequency spectra of ocean wave and its variation due to the variation of ocean surface current are derived from the wave-number spectrum balance equation. The ocean surface imaging formulation of real aperture radar (RAR) is given using electromagnetic wave backscattering theory of ocean surface and the modulations of ocean surface winds, currents and their variations to RAR are described. A general representation of the phase modulation induced by the ocean surface motion is derived according to standard synthetic aperture radar (SAR) imaging theory. The detectability of ocean current and sea bottom topography by imaging radar is discussed. The results constitute the theoretical basis for detecting ocean wave fields, ocean surface winds, ocean surface current fields, sea bottom topography, internal wave and so on.

Modelling electromagnetically levitated liquid droplet oscillations

This work comprises accurate computational analysis of levitated liquid droplet oscillations in AC and DC magnetic fields. The AC magnetic field interacting with the induced electric current within the liquid metal droplet generates intense fluid flow and the coupled free surface oscillations. The pseudo-spectral technique is used to solve the turbulent fluid flow equations for the continuously dynamically transformed axisymmetric fluid volume. The volume electromagnetic force distribution is updated with the shape and position change. We start with the ideal fluid test case for undamped Rayleigh frequency oscillations in the absence of gravity, and then add the viscous and the DC magnetic field damping. The oscillation frequency spectra are further analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. In the extreme case electrically poorly conducting, diamagnetic droplet (water) levitation dynamics are simulated. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions.