Spatial interference of normal waves in oceanic waveguides

Expressions are derived for the frequency shifts of interference maxima that occur at separate observation points because of a two-dimensional anisotropic random perturbation of the oceanic medium. A relation between the frequency shifts of the field maxima at the observation points and the variations in the phase differences between interfering normal waves is revealed. The use of the frequency shifts in solving direct problems of wave propagation is discussed.     

Variability of the vertical interference structure of the sound field in a shallow sea

Dynamics of the spectral intensity oscillations that occur in the vertical plane because of the time variability of the medium along the propagation path is described. The errors arising in measuring the frequency shifts of the interference structure are considered. For low-frequency broadband signals received on a stationary propagation path, experimental data on the shifts of their frequency spectra due to the variation of the reception depth are presented. The number of interfering modes and their arrival directions in the vertical plane are estimated from the measured frequency shifts of the spectral intensity oscillation.     

Frequency shifts of sound field maxima in oceanic waveguides

The frequency shifts of sound field maxima that are caused by the variability of the medium in an oceanic waveguide are described. The condition under which the time spectrum of the frequency shifts of interference maxima is proportional to the time spectrum of fluctuations in the dispersion characteristic of the waveguide is determined.     

The possibility of reconstruction of two-dimensional random inhomogeneities in a shallow sea by frequency shifts of the spatial interference structure of the sound field

Fluctuations of frequency shifts of the spatial interference structure of the sound field in the oceanic waveguide, caused by a two-dimensional field of a random perturbation, are described. Various schemes of observation point spacing are considered. The possibility is shown to reconstruct the spatial spectrum of waveguide perturbations by measuring the spatial spectrum of the frequency shift of the interference pattern. The results of the theoretical treatment are illustrated by the examples of background internal waves and bottom roughness. The sensitivity of monitoring based on measurements of frequency shifts of the interference structure of the sound field is estimated. For medium perturbations by background internal waves, the fluctuations of liquid layer vibrations, sound speed, and temperature, which are minimum detectable by frequency shifts of the interference pattern, were estimated.     

Electron tuning of frequency in gyrotrons

Formulas for shifts of gyrotron autooscillation frequency due to change of electron beam parameters are presented. The frequency shifts can be commensurable with the frequency band of the beam-unloaded cavity. The autooscillation frequency is most sensitive to the change of the magnetic field, less to the change of the anode voltage and least to the the change of the beam voltage. Experiments presented are in satisfactory agreement with the theory.The authors wish to thank M.I. Petelin for his interest to the present work.     

Automatic correction for phase shifts, frequency shifts, and lineshape distortions across a series of single resonance lines in large spectral data sets

A new model-free method is presented that automatically corrects for phase shifts, frequency shifts, and additional lineshape distortions of one single resonance peak across a series of in vivo NMR spectra. All separate phase and frequency variations are quickly and directly derived from the common lineshape in the data set using principal component analysis and linear regression. First, the new approach is evaluated on simulated data in order to quantitatively assess the phase and frequency shifts which can be removed by the proposed correction procedure. Subsequently, the value of the method is demonstrated on in vivo (31)P NMR spectra from skeletal muscle of the hind leg of the mouse focusing on the phosphocreatine resonance which is distorted by the experimental procedure. Phase shifts, frequency shifts, and lineshape distortions with respect to the common lineshape in the spectral data set could successfully be removed.     

Frequency shifts of sound field maxima under the effect of intense internal waves

Numerical simulation is carried out to study frequency shifts of a low-frequency sound field maxima under the effect of solitary internal waves (solitons) propagating along an acoustic track in the presence of mode coupling. The frequency shifts are measured by the correlation method. Simulation data obtained with allowance for mode coupling and data obtained in the adiabatic approximation are compared and analyzed.     

Atomic-based stabilization for laser-pumped atomic clocks

We describe a novel technique for stabilizing frequency shifts in laser-interrogated vapor-cell atomic clocks. The method suppresses frequency shifts due to changes in the laser frequency, intensity, and modulation index as well as atomic vapor density. The clock operating parameters are monitored by using the atoms themselves, rather than by using conventional schemes for laser frequency and cell temperature control. The experiment is realized using a chip-scale atomic clock. The novel atomic-based stabilization approach results in a simpler setup and improved long-term performance.     

Acoustic monitoring of frontal zone

A new method for detecting frequency shifts of acoustic field interference maxima is proposed. The method is based on the cross-correlation processing of frequency-swept signals. Perturbations of medium are modeled as variations in the frontal zone width. The potential of this method is analyzed in comparison with the known methods for measuring frequency shifts of interference maxima. A model reconstruction of the frontal zone variability is performed.     

Resonance shifts in ABMR due to inhomogeneities of the magnetic and rf-fields

On the basis of the non-relativistic time dependent Schrödinger theory shifts of the resonance frequency due to an arbitrary inhomogeneity of the rf-field with respect to amplitude, direction and phase, and shifts due to small inhomogeneities of the magnetic field are considered. A general relation is derived by which one can find the appropriate experimental methods to determine the shifts without a detailed knowledge of the actual line shapes. Usually small effects as shifts due to non-constant field direction or due to neighbouring states are included in the formalism. The results have been used successfully in precision experiments in which frequency shifts of about 10^?2 of the resonance width were eliminated up to a few 10^?5.     

Frequency shifts in parametrically enhanced low-field MR detection

A high-amplitude, high-frequency readout field has previously been proposed for use with low-field MR. Because the resulting modulation sidebands are at higher frequencies than the low-field steady precession, improved detection sensitivity results. However, if the ac readout field is inhomogeneous, it will necessarily have transverse components resulting in frequency shifts and broadening of the MR signal. Numerical solutions of Bloch's equations are compared to the Bloch-Siegert result to assess the size of the frequency shifts. A formula is derived by the average Hamiltonian method and provides an excellent fit to the numerically obtained shifts.     

High sensitive determination of laser-induced frequency shifts of ultracold cesium molecules

We experimentally present a technique for sensitively determining the laser-induced frequency shifts of the long-range molecular vibrational and rotational levels. The scheme relies on an optical frequency shifter, leading to two laser beams with a precise and adjustable frequency interval. A series of photoassociation spectra are recorded with both beams inducing molecular lines, whose peak separation provides an accurate frequency ruler to measure the frequency shifts of cesium molecular levels, which have not yet been observed in previous reports. The data are compared to theoretical predictions and show a good agreement.     

Method of acoustic sweep monitoring of oceanic inhomogeneities (Review)

Theoretical grounds of the new method of monitoring of the temporal variability of oceanic inhomogeneities, which uses the data on frequency shifts of interference maxima of the sound field, were described. The method is free of limitations on both the resolution of signals coming in individual modes (rays) and the adiabatic approximation underlying the conventional methods of inhomogeneity reconstruction. The monitoring sensitivity was estimated, which allows us to estimate minimum detectable changes in the speed of sound by measurement data on frequency shifts of local maxima. Experimental data on shifts of the frequency spectrum of a broadband low-frequency signal on a stationary path in a shallow sea were presented. On their basis, the possibility of applying this method to diagnose tidal variations was shown. Within a numerical simulation, model reconstruction of the frequency spectrum of background internal waves was considered on the basis of the data on measurements of the spectrum of frequency shifts of the interference maximum. The results of the spectrum reconstruction with and without focusing of the conjugate wave field are presented. The problems of monitoring stability and efficiency with respect to the interference pattern formed by various groups of modes were discussed.     

Frequency moments and energy shifts for dilute Mössbauer impurities in metallic solids

Theoretical evaluations of frequency moments and second order Doppler shifts have been made for dilute⁵⁷Fe impurities in the high temperature limit for a harmonic solid. The resonant energy shifts have been calculated from the Green’s function of the impure crystal containing both mass disordering and force constant change terms in the crystal Hamiltonian. High temperature frequency moments for the impurity in different metallic solids are obtained from Mc-Millan ratios using standard Mössbauerf-values at room temperature. The effect of mass disordering predominates over the force constant change term in the evaluations of second order Doppler shifts and hence the frequency moments for dilute⁵⁷Fe impurities. The variation of frequency moments for the impurity with mass modified Debye-temperature of the hosts is shown for a number of metallic solids.     

Chemical shift referencing in MAS solid state NMR

Solid state 13C magic angle spinning (MAS) NMR spectra are typically referenced externally using a probe which does not incorporate a field frequency lock. Solution NMR shifts on the other hand are more often determined with respect to an internal reference and using a deuterium based field frequency lock. Further differences arise in solution NMR of proteins and nucleic acids where both 13C and 1H shifts are referenced by recording the frequency of the 1H resonance of DSS (sodium salt of 2,2-dimethyl-2-silapentane-5-sulphonic acid) instead of TMS (tetramethylsilane). In this note we investigate the difficulties in relating shifts measured relative to TMS and DSS by these various approaches in solution and solids NMR, and calibrate adamantane as an external 13C standard for solids NMR. We find that external chemical shift referencing of magic angle spinning spectra is typically quite reproducible and accurate, with better than +/-0.03 ppm accuracy being straight forward to achieve. Solid state and liquid phase NMR shifts obtained by magic angle spinning with external referencing agree with those measured using typical solution NMR hardware with the sample tube aligned with the applied field as long as magnetic susceptibility corrections and solvent shifts are taken into account. The DSS and TMS reference scales for 13C and 1H are related accurately using MAS NMR. Large solvent shifts for the 13C resonance in TMS in either deuterochloroform or methanol are observed, being +0.71 ppm and -0.74 ppm from external TMS, respectively. The ratio of the 13C resonance frequencies for the two carbons in solid adamantane to the 1H resonance of TMS is reported.     

Cold collision frequency shifts in a 87Rb atomic fountain

We present measurements of cavity frequency pulling and collisional frequency shifts in a 87Rb fountain with a frequency resolution of 3x10(-16). Agreement with theory is found for the cavity pulling and the measured collisional shifts. The clock shift is found at least 50 times smaller than in 133Cs.     

Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads

The potential applications of piezoelectric nanofilms (PNFs) and double-piezoelectric-nanofilm (DPNF) systems as nanoelectromechanical mass sensors are examined. The PNFs carrying multiple nanoparticles at arbitrary locations are modeled as rectangular nonlocal plates with attached concentrated masses. Using the nonlocal elasticity theory and Hamilton’s principle, the differential equations of motion are derived for both PNF-based and DPNF-based nanosensors. The influences of small scale, initial stress and temperature change on the frequency shifts of the nanoelectromechanical sensors are taken into consideration. Explicit expressions are derived for the resonance frequencies of the nanosensors by employing the Galerkin method. The present results show that when the value of nonlocal parameter decreases, the frequency shifts of piezoelectric nanosensors increase. Further, the frequency shifts of DPNF-based mass sensors are always greater than those of PNF-based mass sensors. The present work would be helpful in the design of nanoelectromechanical mass sensors using PNFs.     

Dispersion management for wavelength-division-multiplexed soliton transmission

Residual frequency shifts that are due to two-soliton collisions in stepwise exponentially dispersion-tapered fiber are calculated. Two-step dispersion profiles to minimize the frequency shifts and associated timing jitter are specifically identified. These profiles will improve the performance of wavelength-division-multiplexed soliton systems and permit operation with longer amplifier spans over an increased bandwidth.