Position-dependent Frequency Research Articles

Multiscale and local engineering of speckle morphology through disordered media.

In this Letter, we prompt a novel, to the best of our knowledge, method based on transmission matrix decomposition with wavelets to engineer the speckle morphology behind disordered media. By analyzing the speckles in multiscale spaces, we experimentally realized multiscale and localized control on the speckle size, position-dependent spatial frequency, and global morphology by operating on the decomposition coefficients using different masks. Speckles with contrasting features in different parts of the fields can be generated in one step. Our experimental results demonstrate a high degree of flexibility in manipulating light in a customizable manner. This technique has stimulating prospects in correlation control and imaging under scattering conditions.

Two-tone Doppler cooling of radial two-dimensional crystals in a radio-frequency ion trap

We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals of trapped barium ions in a radiofrequency trap. Ions in radial 2D crystals experience micromotion of an amplitude that increases linearly with the distance from the trap center, leading to a position-dependent frequency modulation of laser light in each ion's rest frame. We use two tones of Doppler-cooling laser light separated by approximately 100 MHz to efficiently cool distinct regions in the crystals with differing amplitudes of micromotion. This technique allows us to trap and cool more than 50 ions populating four shells in a radial 2D crystal, where with a single tone of Doppler cooling light we are limited to 30 ions in three shells. We also individually characterize the micromotion of all ions within the crystals and use this information to locate the center of the trap and to determine the Matthieu parameters ${q}_{x}$ and ${q}_{y}$.

Pantograph Arc Location Estimation Using Resonant Frequencies in DC Railway Power Systems

Pantograph arcing in electrified railway systems not only reduces the power collection quality of a locomotive but can also damage pantograph strips and overhead lines (OHLs). Most research detects pantograph-to-OHL arcs based on onboard voltage/current measurements, pantograph cameras, and so on. The use of onboard voltage/current data, though being cost-effective, rarely reflects arc locations along OHLs. This article develops an arc positioning method, which matches the position-dependent resonant frequency (RF) of an OHL with the RF extracted from voltage measurements in a pantograph arc event. A particular 20-km DC railway line supplied by two substations is first modelled in MATLAB/Simulink, with the model effectiveness being assessed based on voltage measurements in an arc event. Then, the OHL-related RFs estimated by the model are validated by the Tableau formula and discussed alongside impacts on RFs based on line models, locomotive locations, and line lengths. These evaluations permit the generation of an RF curve that links OHL-related RFs with arc locations. The arc positioning method is tested based on the pantograph arc events presumed at various positions along the 20-km line, showing errors within 0.2 km at certain locations. The ability to determine arc locations will permit periodic inspections to be performed on the determined line sections.

Application of interpolation methods for the determination of position-dependent frequency response functions for the simulation of 5-axis milling processes

The occurrence of chatter vibrations in 5-axis milling processes is a common problem and can result in part failure, surface defects and increased wear of the cutting tool and the machine tool. In order to prevent process vibrations, machining processes can be optimized by utilizing geometric physically-based simulation systems. Since the modal parameters of the machine tool are dependent on the position of the linear and rotary axes, the dynamic behavior of milling processes can change along the NC path despite constant engagement conditions. In order to model the pose-dependent modal properties at the tool tip, the frequency response functions (FRFs) were measured at different locations of the workspace of the machine tool for various poses of the rotary axis of the spindle. To take the varying compliance within the workspace of a machine tool into account in a geometric physically-based milling process simulation, different interpolation methods for interpolating FRFs or parameter values of oscillator-based compliance models (OPV) were applied. For validation, the resulting models were analyzed and compared to measured data. In OPV interpolation, the individual oscillation modes were interpolated in their respective characteristics based on the oscillator parameters (eigenfrequencies, modal masses and damping values). In FRF interpolation, however, there was no differentiation between the modes, resulting in a wrong interpolation. It can therefore provide good results when only a small shift of the eigenfrequencies is expected, as in case of the analyzed machine tool, with only small movements of the translatory axes.

Correlation between frequency and location on the wafer for terahertz quantum-cascade lasers

We have investigated the emission frequency of terahertz (THz) quantum-cascade lasers (QCLs) as a function of the location on the wafer. The frequency varies due to an inhomogeneous growth rate across the wafer. For three wafers based on GaAs/AlAs heterostructures for lasers with target frequencies of 3.36 and 3.92 THz, we observed a blue shift of the emission frequency from the center to the edge of the wafer. This blue shift is attributed to a decrease of the period length of the QCLs, which can be determined with spectroscopic techniques. The location-dependent period length is used to calculate a position-dependent frequency of the gain maximum for the active region. The correlation of the calculated frequencies with the emission frequencies of lasers fabricated from different locations on the wafer allows us to establish an effective method for the fabrication of THz QCLs emitting at a particular target frequency.

Spatial Decomposition of a Broadband Pulse Caused by Strong Frequency Dispersion of Sound in Acoustic Metamaterial Superlattice.

An acoustic metamaterial superlattice is used for the spatial and spectral deconvolution of a broadband acoustic pulse into narrowband signals with different central frequencies. The operating frequency range is located on the second transmission band of the superlattice. The decomposition of the broadband pulse was achieved by the frequency-dependent refraction angle in the superlattice. The refracted angle within the acoustic superlattice was larger at higher operating frequency and verified by numerical calculated and experimental mapped sound fields between the layers. The spatial dispersion and the spectral decomposition of a broadband pulse were studied using lateral position-dependent frequency spectra experimentally with and without the superlattice structure along the direction of the propagating acoustic wave. In the absence of the superlattice, the acoustic propagation was influenced by the usual divergence of the beam, and the frequency spectrum was unaffected. The decomposition of the broadband wave in the superlattice’s presence was measured by two-dimensional spatial mapping of the acoustic spectra along the superlattice’s in-plane direction to characterize the propagation of the beam through the crystal. About 80% of the frequency range of the second transmission band showed exceptional performance on decomposition.

Polaritonic frequency-comb generation and breather propagation in a negative-index metamaterial with a cold four-level atomic medium

We develop a concept for a waveguide that exploits spatial control of nonlinear surface-polaritonic waves. Our scheme includes an optical cavity with four-level $\text{N}$-type atoms in a lossless dielectric placed above a negative-index metamaterial layer. We propose exciting a polaritonic Akhmediev breather at a certain position of the interface between the atomic medium and the metamaterial by modifying laser-field intensities and detunings. Furthermore, we propose generating position-dependent polaritonic frequency combs by engineering widths of the electromagnetically induced transparency window commensurate with the surface-polaritonic modulation instability. Therefore, this waveguide acts as a high-speed polaritonic modulator and position-dependent frequency-comb generator, which can be applied to compact photonic chips.

A single-molecule sequencing assay for the comprehensive profiling of T4 DNA ligase fidelity and bias during DNA end-joining.

DNA ligases are key enzymes in molecular and synthetic biology that catalyze the joining of breaks in duplex DNA and the end-joining of DNA fragments. Ligation fidelity (discrimination against the ligation of substrates containing mismatched base pairs) and bias (preferential ligation of particular sequences over others) have been well-studied in the context of nick ligation. However, almost no data exist for fidelity and bias in end-joining ligation contexts. In this study, we applied Pacific Biosciences Single-Molecule Real-Time sequencing technology to directly sequence the products of a highly multiplexed ligation reaction. This method has been used to profile the ligation of all three-base 5′-overhangs by T4 DNA ligase under typical ligation conditions in a single experiment. We report the relative frequency of all ligation products with or without mismatches, the position-dependent frequency of each mismatch, and the surprising observation that 5′-TNA overhangs ligate extremely inefficiently compared to all other Watson–Crick pairings. The method can easily be extended to profile other ligases, end-types (e.g. blunt ends and overhangs of different lengths), and the effect of adjacent sequence on the ligation results. Further, the method has the potential to provide new insights into the thermodynamics of annealing and the kinetics of end-joining reactions.

Using impressed current cathodic protection systems of pipelines for electromagnetic exploration

Low-frequency electromagnetic (EM) signals generated by networks of technical infrastructure such as power-lines, pipelines, or railways may provide a cheap and efficient means to perform EM depth sounding of the upper few kilometers of the earth. We attempt to use the signals emitted by an impressed current cathodic protection (ICCP) system of a 35 km long gas pipeline segment in northwestern Germany. The installed ICCP system uses a periodical 12 s on/3 s off current switching scheme, which resembles current waveforms used in controlled-source electromagnetics (CSEM). In contrast to CSEM, where a grounded electrical dipole is used as the source, the current flow in pipelines is not constant along its legs. Our efforts are therefore concentrated toward the determination of the temporal and spatial behavior of the electrical current within the investigated pipeline segment. Although the time dependency of the current can be measured directly at the injection point, the spatial distribution is only accessible through indirect observations. We use fluxgate magnetic field measurements at multiple locations directly above the pipeline to infer the local source current and its frequency-dependency and phase lag. We observe that the current decays roughly exponentially away from the injection point, exhibits a position-dependent frequency dependency, and experiences a phase shift that accumulates to more than 30° at the ends of the segment. These effects can be consistently explained with a transmission line model. Having determined the current distribution, we can represent the pipeline as an EM source superposed of point dipoles. The estimated source model allows us to predict the electric (and magnetic) fields at remote locations. To verify our approach, we deploy an array of telluric recorders in the vicinity of the pipeline, estimate the frequency-domain transfer functions, and invert the data into a 3D electrical conductivity model using smoothness-constrained inversion techniques.

Effect of the screw–nut joint stiffness on the position-dependent dynamics of a vertical ball screw feed system without counterweight

The study on the position-dependent dynamic characteristics of a vertical ball screw feed system without counterweight is an important step in the enhancement of the structural performance of mini-type vertical milling machines. The ball screw is generally driven by a servomotor, which converts a rotary motion into a linear motion through a screw–nut pair. To assess the position-dependent dynamic characteristics of a vertical ball screw feed system subjected to the influence of the screw–nut joint stiffness, a variable-coefficient lumped parameter model of the system is developed. This model is established taking into account the screw–nut joint stiffness under three different strategies: (1) considering the preload and the weight of the spindle system, (2) considering the elastic deformation but ignoring the effect of the weight, and (3) a perfectly rigid model. The differences between the three models in predicting the position-dependent dynamic characteristics of the system are compared, revealing that the stiffness of screw–nut joint greatly affects the vibratory behavior of the spindle system in the transmission direction. A set of conducted experimental results demonstrate that the stiffness model under the preload and the weight of the spindle system is the most accurate model for the prediction of the position-dependent natural frequency and displacement response of the system with the spindle system position. Therefore, it is more suitable for structure design, performance simulation, and evaluation of a vertical ball screw feed system without counterweight.

Cryogenic LED pixel-to-frequency mapper for kinetic inductance detector arrays

We present a cryogenic wafer mapper based on light emitting diodes (LEDs) for spatial mapping of a large microwave kinetic inductance detector (MKID) array. In this scheme, an array of LEDs, addressed by DC wires and collimated through horns onto the detectors, is mounted in front of the detector wafer. By illuminating each LED individually and sweeping the frequency response of all the resonators, we can unambiguously correspond a detector pixel to its measured resonance frequency. We have demonstrated mapping a 76.2 mm 90-pixel MKID array using a mapper containing 126 LEDs with 16 DC bias wires. With the frequency to pixel-position correspondence data obtained by the LED mapper, we have found a radially position-dependent frequency non-uniformity of ≲1.6% over the 76.2 mm wafer. Our LED wafer mapper has no moving parts and is easy to implement. It may find broad applications in superconducting detectors and quantum computing/information experiments.

Dynamic optimization method with applications for machine tools based on approximation model

Natural frequencies and modal shapes of machine tools have position-dependent characteristics owing to their dynamic behaviors changing with the positions of moving parts. It is time-consuming and difficult to evaluate the dynamic behaviors of machine tools and their machining accuracy at different positions. In this paper, a Kriging approximation model coupled with finite element method is proposed to substitute the dynamic equations for obtaining the position-dependent natural frequencies of a machine tool, as well as relative positions between the tool and the workpiece during the machining process. Based on the proposed method, dynamic performance optimization design of the machine tool is conducted under the condition of minimum relative positions. Three case studies are illustrated to demonstrate the implementation of the proposed method.

DNA Sequence can Pin the Position of DNA Supercoils

While DNA obviously functions as the carrier of genetic information, it may also encode the three-dimensional spatial structure of DNA in cells. Here we study the relationship between structure and sequence in supercoiled DNA, which involves a reorganization of the DNA configuration via the formation of so-called plectonemes - coiled loop structures that locally form to minimize the torsional stress within the DNA. We use a novel high-throughput single-molecule assay called ISD (‘Intercalation-induced Supercoiling of DNA’, see Ganji et al, Nano Lett. 16, 4699, 2016), where we induce supercoiling of surface-attached DNA molecules by adding an intercalating dye. This assay allows us to visualize individual plectonemes and characterize their position-dependent frequency as well as dynamics such as nucleation, termination, and diffusion. From profiles of the average plectoneme density as a function of the position along the DNA molecule, we can study whether plectonemes exhibit any preference for certain DNA sequences. We indeed find that particular local DNA sequences pin plectonemes. Specifically, we identify DNA stretches with exclusively A or T bases (which we name ‘TorA tracts’) that strongly pin plectonemes. Interestingly, TorA tracts pin plectonemes just as well as poly-A tracts. This suggests that it is not a local intrinsic bending of the DNA (such as predicted for polyA tracts) that underlies the plectoneme pinning. Instead, we propose that local melting may lead to the formation of a kink at the tip of a plectoneme that provides a pinning site. Indeed we observed strong pinning at DNA mutation sites where 1 to 10 neighboring nucleotides are mispaired such that a ssDNA bubble is formed. Our data show that the DNA sequence does not merely encode for genetic information but also for structural information that governs the three-dimensional organization of supercoiled DNA.

Anharmonic resonance absorption of short laser pulses in clusters: A molecular dynamics simulation study

Linear resonance (LR) absorption of an intense 800 nm laser light in a nano-cluster requires a long laser pulse >100 fs when Mie-plasma frequency (ωM) of electrons in the expanding cluster matches the laser frequency (ω). For a short duration of the pulse, the condition for LR is not satisfied. In this case, it was shown by a model and particle-in-cell (PIC) simulations [Phys. Rev. Lett. 96, 123401 (2006)] that electrons absorb laser energy by anharmonic resonance (AHR) when the position-dependent frequency Ω[r(t)] of an electron in the self-consistent anharmonic potential of the cluster satisfies Ω[r(t)]=ω. However, AHR remains to be a debate and still obscure in multi-particle plasma simulations. Here, we identify AHR mechanism in a laser driven cluster using molecular dynamics (MD) simulations. By analyzing the trajectory of each MD electron and extracting its Ω[r(t)] in the self-generated anharmonic plasma potential, it is found that electron is outer ionized only when AHR is met. An anharmonic oscillator model, introduced here, brings out most of the features of MD electrons while passing the AHR. Thus, we not only bridge the gap between PIC simulations, analytical models, and MD calculations for the first time but also unequivocally prove that AHR process is a universal dominant collisionless mechanism of absorption in the short pulse regime or in the early time of longer pulses in clusters.

Position-dependent hearing in three species of bushcrickets (Tettigoniidae, Orthoptera).

A primary task of auditory systems is the localization of sound sources in space. Sound source localization in azimuth is usually based on temporal or intensity differences of sounds between the bilaterally arranged ears. In mammals, localization in elevation is possible by transfer functions at the ear, especially the pinnae. Although insects are able to locate sound sources, little attention is given to the mechanisms of acoustic orientation to elevated positions. Here we comparatively analyse the peripheral hearing thresholds of three species of bushcrickets in respect to sound source positions in space. The hearing thresholds across frequencies depend on the location of a sound source in the three-dimensional hearing space in front of the animal. Thresholds differ for different azimuthal positions and for different positions in elevation. This position-dependent frequency tuning is species specific. Largest differences in thresholds between positions are found in Ancylecha fenestrata. Correspondingly, A. fenestrata has a rather complex ear morphology including cuticular folds covering the anterior tympanal membrane. The position-dependent tuning might contribute to sound source localization in the habitats. Acoustic orientation might be a selective factor for the evolution of morphological structures at the bushcricket ear and, speculatively, even for frequency fractioning in the ear.

Cover Picture: Macromol. Theory Simul. 7∕2014

Cover: A novel hybrid simulation approach combines the deterministic and stochastic modeling of complex polymerization networks, for all types of polymerization reactions in ideal and non-ideal reactors. The fast deterministic simulation solves the heat and pressure balances and generates position-dependent event frequency profiles. The detailed stochastic simulation offers insight into the polymeric microstructure of each macromolecule. Further details can be found in the article by E. Neuhaus, T. Herrmann, I. Vittorias, D. Lilge, G. Mannebach, A. Gonioukh, and M. Busch* on page 415.

Low-Voltage Electrostatic Actuation With Inherent Position Feedback

Electrostatic actuation in microelectromechanical systems (MEMS) often requires generation and control of high-voltage drive signals for sufficient force. Voltages in excess of a few volts require specialized circuit technologies and often cannot be implemented monolithically with other functions, such as precision sense amplifiers. This paper presents a circuit for enabling high-voltage actuation with low-voltage electronics by utilizing passive amplification provided by the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> factor of an electrical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> resonator. The resonator is formed with the capacitive MEMS actuator connected in series to an inductor. Experimental results demonstrating voltage amplification by over an order of magnitude are presented. As a further benefit, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuit provides continuous position feedback in the form of position-dependent resonance frequency which is detected electronically. Inverse position dependence of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> factor also extends stable range of parallel-plate actuators over that achieved with constant-voltage drive.

Single-atom localization via resonance-fluorescence photon statistics

We present a scheme for subwavelength single-atom localization that is based on the photon statistics measurement of the resonance fluorescence from the two-level atomic system. The photon number distribution of the resonance fluorescence depends on the position of the atom inside the standing-wave driving field via the position-dependent Rabi frequency. We show that this position-dependent Rabi frequency can be used to localize the atom within the subwavelength region.

A cross-language acoustic study of initial and final allophones of /l/

Formant frequency data for /l/ in 23 languages/dialects where the consonant may be typically clear or dark show that the two varieties of /l/ are set in contrast mostly in the context of /i/ but also next to /a/, and that a few languages/dialects may exhibit intermediate degrees of darkness in the consonant. F2 for /l/ is higher utterance initially than utterance finally, more so if the lateral is clear than if it is dark; moreover, the initial and final allophones may be characterized as intrinsic (in most languages/dialects) or extrinsic (in several English dialects, Czech and Dutch) depending on whether the position-dependent frequency difference in question is below or above 200/300 Hz. The paper also reports a larger degree of vowel coarticulation for clear /l/ than for dark /l/ and in initial than in final position. These results are interpreted in terms of the production mechanisms involved in the realization of the two /l/ varieties in the different positional and vowel context conditions subjected to investigation.

Diffusion equations for a Markovian jumping process

We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency. For small steps, we derive the Fokker-Planck equation and show the presence of the normal diffusion, subdiffusion, and superdiffusion. For the Lévy distribution of the step size, we construct a fractional equation, which possesses a variable coefficient, and solve it in the diffusion limit. Then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance. We also solve the master equation numerically and demonstrate that there are deviations from the Lévy stable distribution for large wave numbers.