Measuring Transverse Relaxation with a Single-Beam 894 nm VCSEL for Cs-Xe NMR Gyroscope Miniaturization.

The spin-exchange-pumped nuclear magnetic resonance gyroscope (NMRG) is a pivotal tool in quantum navigation. The transverse relaxation of atoms critically impacts the NMRG's performance parameters and is essential for judging normal operation. Conventional methods for measuring transverse relaxation typically use dual beams, which involves complex optical path and frequency stabilization systems, thereby complicating miniaturization and integration. This paper proposes a method to construct a 133Cs parametric resonance magnetometer using a single-beam vertical-cavity surface-emitting laser (VCSEL) to measure the transverse relaxation of 129Xe and 131Xe. Based on this method, the volume of the gyroscope probe is significantly reduced to 50 cm3. Experimental results demonstrate that the constructed Cs-Xe NMRG can achieve a transverse relaxation time (T2) of 8.1 s under static conditions. Within the cell temperature range of 70 °C to 110 °C, T2 decreases with increasing temperature, while the signal amplitude inversely increases. The research lays the foundation for continuous measurement operations of miniaturized NMRGs.

Molecular Biological Effects of Weak Low-Frequency Magnetic Fields: Frequency-Amplitude Efficiency Windows and Possible Mechanisms.

This review covers the phenomenon of resonance-like responses of biological systems to low-frequency magnetic fields (LFMF). The historical development of this branch of magnetobiology, including the most notable biophysical models that explain the resonance-like responses of biological systems to LFMF with a specific frequency and amplitude, is given. Two groups can be distinguished among these models: one considers ion-cofactors of proteins as the primary targets for the LFMF influence, and the other regards the magnetic moments of particles in biomolecules. Attention is paid to the dependence of resonance-like LFMF effects on the cell type. A radical-pair mechanism of the magnetic field's influence on biochemical processes is described with the example of cryptochrome. Conditions for this mechanism's applicability to explain the biological effects of LFMF are given. A model of the influence of LFMF on radical pairs in biochemical oscillators, which can explain the frequency-amplitude efficiency windows of LFMF, is proposed.

Effect of weak alternating magnetic fields on planarian regeneration.

We investigated the effect of weak combined magnetic field (CMF) on stem cell proliferation and regeneration of the planarian Schmidtea mediterranea. CMF parameters were set in accordance with Valery Lednev's theory of magnetic parametric resonance. It was shown that CMF with an amplitude of 74 µT and a frequency of 30 Hz accelerated the growth of the planarian head blastema by 25%. Alterations of the frequency in range from 27 to 33 Hz led to a complete disappearance of the effect. A further decrease in the CMF frequency inhibited regeneration. The maximum inhibition (24%) was observed at a frequency of 16 Hz. A further decrease in the CMF frequency (down to 13 Hz) led to disappearance of the described effect. Regeneration rate changes under the CMF are influenced by alterations in stem cell mitotic activity, which in turn depends on the wound-induced gene expression level. Thus, the CMF, preset in accordance to the Lednev's theory, can specifically influence the expression of regeneration-related genes and regeneration itself, what can find biomedical applications.

All-Optical Parametric-Resonance Magnetometer Based on 4He Atomic Alignment.

Parametric-resonance magnetometer is a high-sensitivity quantum sensor characterized by applying the non-resonant radio-frequency (RF) fields to the atomic ensemble. The RF fields lead to crosstalk in the multi-sensor design, thus disturbing the magnetic-field measurement results. We propose an optically modulated alignment-based 4He parametric-resonance magnetometer. By using the fictitious field generated by the modulated light shift, parametric resonance is realized, and crosstalk caused by the magnetic RF field is prevented. The relative intensity noise of the lasers is suppressed to optimize the sensitivity of the magnetometer. Our magnetometer experimentally demonstrates a magnetic-field noise floor of 130 fT/Hz1/2 in both open- and closed-loop operations and has the potential to reach 70 fT/Hz1/2 when compared with the optimized magnetic RF scheme. It provides near-zero magnetic-field measurements with a 2 kHz bandwidth at room temperature, which is useful for high-bandwidth measurements in biomagnetic applications.

A Robust Angular Rate Sensor Utilizing 2:1 Auto-Parametric Resonance Excitation.

This paper presents a single-axis angular rate sensor that is robust to variations in its operating voltage and frequencies. The sensor is developed to overcome the shortcomings of conventional mode-matched Micromachined Vibratory Gyroscopes in open loop operations, namely narrow frequency bandwidths and unstable scale factors. The developed sensor utilizes inherent forcing and inertial nonlinearities from electrostatic forces and fabrication imperfections to auto-parametrically excite the sense mode via 2:1 auto-parametric resonance, which yields a broader bandwidth frequency response for the sensor's sense mode. The experimental results demonstrated −3 dB frequency bandwidth of 500 Hz, a scale factor of 50 µV/°/s, and a dynamic range of ±330°/s.

Numerical investigation of parametric resonance due to hydrodynamic coupling in a realistic wave energy converter.

Representative models of the nonlinear behavior of floating platforms are essential for their successful design, especially in the emerging field of wave energy conversion where nonlinear dynamics can have substantially detrimental effects on the converter efficiency. The spar buoy, commonly used for deep-water drilling, oil and natural gas extraction and storage, as well as offshore wind and wave energy generation, is known to be prone to experience parametric resonance. In the vast majority of cases, parametric resonance is studied by means of simplified analytical models, considering only two degrees of freedom (DoFs) of archetypical geometries, while neglecting collateral complexity of ancillary systems. On the contrary, this paper implements a representative 7-DoF nonlinear hydrodynamic model of the full complexity of a realistic spar buoy wave energy converter, which is used to verify the likelihood of parametric instability, quantify the severity of the parametrically excited response and evaluate its consequences on power conversion efficiency. It is found that the numerical model agrees with expected conditions for parametric instability from simplified analytical models. The model is then used as a design tool to determine the best ballast configuration, limiting detrimental effects of parametric resonance while maximizing power conversion efficiency.

Parametric Resonance of Magnetization Excited by Electric Field.

Manipulation of magnetization by electric field is a central goal of spintronics because it enables energy-efficient operation of spin-based devices. Spin wave devices are promising candidates for low-power information processing, but a method for energy-efficient excitation of short-wavelength spin waves has been lacking. Here we show that spin waves in nanoscale magnetic tunnel junctions can be generated via parametric resonance induced by electric field. Parametric excitation of magnetization is a versatile method of short-wavelength spin wave generation, and thus, our results pave the way toward energy-efficient nanomagnonic devices.

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness.

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation.

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

Dipole and quadrupole resonance excitation in linear quadrupoles.

In the development of commercial quadrupole mass spectrometers, there is an interest in improving the performance characteristics such as transmission, resolution, and mass range. In particular, parametric and dipolar resonance excitation of trapping ions are used for linear quadrupole mass filters. Theoretical methods and numerical simulation of ion trajectories were applied for study of ion-optical properties. The review is devoted to description of different excitation methods to improve QMF performance and consists of three parts. The first part presents the results of a linear ion trap simulation for various operating conditions and excitation methods. The second part considers the effects of dipole excitation (DE) on the performance of the quadrupole mass filter. The last part analyzes the formation of stability islands by different methods of quadrupole excitation. To date conditions of mass separation in quadrupole mass filters with sin wave supply were described for stability islands of the first and third stability regions formed by quadrupole and DE. By complicating the electronics such methods allow to overcome the destructive influence of electric field distortions and obtain a resolving power and ion transmission efficiency comparable with commercial devices. At quadrupole resonance excitation by a two-frequency signal, it is possible to reduce the length of electrodes three times without losses in resolution and transmission, which reduces the cost of rod set production with micrometer accuracy. Dipole resonance excitation allows controlling the shape of the mass peak by changing amplitude and phase of the auxiliary AC signal. The main factors affecting the resolving power of a linear ion trap are described theoretically. The numerical modeling results are confirmed by experiment.

ELF magnetic fields tuned to ion parametric resonance conditions do not affect TEA-sensitive voltage-dependent outward K(+) currents in a human neural cell line.

Despite the experimental evidence of significant biological effects of extremely low frequency (ELF) magnetic fields (MFs), the underlying mechanisms are still unclear. Among the few mechanisms proposed, of particular interest is the so called "ion parametric resonance (IPR)" hypothesis, frequently referred to as theoretical support for medical applications. We studied the effect of different combinations of static (DC) and alternating (AC) ELF MFs tuned on resonance conditions for potassium (K(+)) on TEA-sensitive voltage-dependent outward K(+) currents in the human neuroblastoma BE(2)C cell line. Currents through the cell membrane were measured by whole-cell patch clamp before, during, and after exposure to MF. No significant changes in K(+) current density were found. This study does not confirm the IPR hypothesis at the level of TEA-sensitive voltage-dependent outward K(+) currents in our experimental conditions. However, this is not a direct disprove of the hypothesis, which should be investigated on other ion channels and at single channel levels also.

Dynamic Stability of Tensegrity Structures-Part II: The Periodic External Load.

The paper contains a parametric analysis of tensegrity structures subjected to periodic loads. The analysis focuses on determining the main region of dynamic instability. When load parameters fall within this region, the resulting vibration amplitudes increase, posing a risk to the durability of structures. The study considers structures built using commonly used modules. The influence of the initial prestress on the distribution of the instability regions is examined. Additional prestress can significantly reduce the extent of instability regions, potentially narrowing them by up to 99%. A nondimensional parameter is introduced to accurately assess changes in the extent of the instability region. A geometrically non-linear model is employed to evaluate the behavior of the analyzed structures.

Analysis of Parametric and Subharmonic Excitation in Push-Pull Driven Disk Resonator Gyroscopes.

For micro-electromechanical system (MEMS) resonators, once the devices are fabricated and packaged, their intrinsic quality factors (Q) will be fixed and cannot be changed, which seriously limits the further improvement of the resonator's performance. In this paper, parametric excitation is applied in a push-pull driven disk resonator gyroscope (DRG) to improve its sensitivity by an electrical pump, causing an arbitrary increase of the "effective Q". However, due to the differential characteristics of the push-pull driving method, the traditional parametric excitation method is not applicable. As a result, two novel methods are proposed and experimentally carried out to achieve parametric excitation in the push-pull driven DRGs, resulting in a maximum "effective Q" of 2.24 × 106 in the experiment, about a 7.6 times improvement over the intrinsic Q. Besides, subharmonic excitation is also theoretically analyzed and experimentally characterized. The stability boundary of parametric excitation, defined by a threshold voltage, is theoretically predicted and verified by related experiments. It is demonstrated that, when keeping the gyroscope's vibration at a constant amplitude, the fundamental frequency driving voltage will decrease with the increasing of the parametric voltage and will drop to zero at its threshold value. In this case, the gyroscope operates in a generalized parametric resonance condition, which is called subharmonic excitation. The novel parametric and subharmonic excitation theories displayed in this paper are proven to be efficient and tunable dynamical methods with great potential for adjusting the quality factor flexibly, which can be used to further enhance the resonator's performance.

Development of an Electrostatic Comb-Driven MEMS Scanning Mirror for Two-Dimensional Raster Scanning.

Microelectromechanical System (MEMS)-based scanning mirrors are important optical devices that have been employed in many fields as a low-cost and miniaturized solution. In recent years, the rapid development of Light Detection and Ranging (LiDAR) has led to opportunities and challenges for MEMS scanners. In this work, we propose a 2D electrostatically actuated micro raster scanner with relatively large aperture. The 2D scanner combines a resonant scanning axis driven by an in-plane comb and a quasistatic scanning axis driven by a vertical comb, which is achieved by raising the moving comb finger above the fixed comb finger through the residual stress gradient. The analytic formula for the resonant axis frequency, based on the mechanical coupling of two oscillation modes, is derived and compared with finite element simulation. A prototype is designed, fabricated, and tested, and an overall optical Field-of-View (FoV) of about 60° × 4° is achieved. Finally, some possibilities for further improvement or optimization are discussed.

Mass filter with phase modulation of radio frequency voltage.

In this work, the parametric quadrupole resonance caused by the phase modulation of waveform potential is studied. Based on analytical and numerical description of the ion motion in the quadrupole mass filter with the phase modulation, a stability island is found with good ion optical properties such as high ion transmission efficiency (16%), high mass resolution (peak width measured at 10% of peak height, R0.1 = 6000), the required separation time (100-150 radio frequency [RF] cycles), and good peak shape of trapezoid form. Furthermore, the analysis of the frequency spectrum of the applied potential and the quadrupole mass filter (QMF) acceptance are also presented; a resonance frequency is found from this spectrum. Finally, a suitable stability X-islands with relative modulation frequency, ν = 2 ± ß , ß = 1 P , 10 ≤ P ≤ 40 , is established and studied in detail. Here, ß is the imaginary part of the characteristic exponent of stable solutions to the Mathieu equation.

Transverse motion instability of a submerged moored buoy.

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

2D Au-Coated Resonant MEMS Scanner for NIR Fluorescence Intraoperative Confocal Microscope.

The electrostatic MEMS scanner plays an important role in the miniaturization of the microscopic imaging system. We have developed a new two-dimensional (2D) parametrically-resonant MEMS scanner with patterned Au coating (>90% reflectivity at an NIR 785-nm wavelength), for a near-infrared (NIR) fluorescence intraoperative confocal microscopic imaging system with a compact form factor. A silicon-on-insulator (SOI)-wafer based dicing-free microfabrication process has been developed for mass-production with high yield. Based on an in-plane comb-drive configuration, the resonant MEMS scanner performs 2D Lissajous pattern scanning with a large mechanical scanning angle (MSA, ±4°) on each axis at low driving voltage (36 V). A large field-of-view (FOV) has been achieved by using a post-objective scanning architecture of the confocal microscope. We have integrated the new MEMS scanner into a custom-made NIR fluorescence intraoperative confocal microscope with an outer diameter of 5.5 mm at its distal-end. Axial scanning has been achieved by using a piezoelectric actuator-based driving mechanism. We have successfully demonstrated ex vivo 2D imaging on human tissue specimens with up to five frames/s. The 2D resonant MEMS scanner can potentially be utilized for many applications, including multiphoton microendoscopy and wide-field endoscopy.

A Study on Parametric Amplification in a Piezoelectric MEMS Device.

In various applications, damping from the surrounding fluid severely degrades the performance of micro-electro-mechanical systems (MEMS). In this paper, mechanical amplification through parametric resonance was investigated in a piezoelectrically actuated MEMS to overcome the effects of damping. The device was fabricated using the PiezoMUMPS process, which is based on a Silicon-on-Insulator (SOI) process with an additional aluminum nitride (AlN) layer. Here, a double-clamped cantilever beam with a concentrated mass at the center was excited at its first resonance mode (out-of-plane motion) in air and at atmospheric conditions. A parametric signal modulating the stiffness of the beam was added at twice the frequency of the excitation signal, which was swept through the resonance frequency of the mode. The displacement at the center of the device was detected optically. A four-fold increase in the quality-factor, Q, of the resonator was obtained at the highest values in amplitude used for the parametric excitation. The spring modulation constant was obtained from the effective quality-factor, Q e f f , versus parametric excitation voltage curve. This study demonstrates that through these methods, significant improvements in performance of MEMS in fluids can be obtained, even for devices fabricated using standard commercial processes.

Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback.

The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS), which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.

An electromechanical Ising Hamiltonian.

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.