Frequency Dependence Research Articles

Dichotomous dynamics of magnetic monopole fluids

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure [Formula: see text], the time dependence of magnetic flux threading the sample when a net monopole current [Formula: see text] is generated by applying an external magnetic field [Formula: see text] These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~[Formula: see text] from monopole current initiation. Application of sinusoidal magnetic fields [Formula: see text] generates oscillating monopole currents whose loss angle [Formula: see text] exhibits a characteristic transition at frequency [Formula: see text] over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~[Formula: see text]. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry.

Cognitive representations of intracranial self-stimulation of midbrain dopamine neurons depend on stimulation frequency.

Dopamine neurons in the ventral tegmental area support intracranial self-stimulation (ICSS), yet the cognitive representations underlying this phenomenon remain unclear. Here, 20-Hz stimulation of dopamine neurons, which approximates a physiologically relevant prediction error, was not sufficient to support ICSS beyond a continuously reinforced schedule and did not endow cues with a general or specific value. However, 50-Hz stimulation of dopamine neurons was sufficient to drive robust ICSS and was represented as a specific reward to motivate behavior. The frequency dependence of this effect is due to the rate (not the number) of action potentials produced by dopamine neurons, which differently modulates dopamine release downstream.

Controlling the residual charge to alleviate the frequency dependence of ternary direct current triboelectric nanogenerators

Recently, the ternary direct current triboelectric nanogenerators (T-DC-TENGs), especially those working in rotation mode, have received much attentions due to their high DC output and superior durability. However, the frequency dependence of T-DC-TENG was largely ignored, which greatly hinders the miniaturization of the device. Because the electron-donating capacity of positive tribo-layer is unequal to the electron-gaining capacity of negative tribo-layer, the number of residual charges on the intermediate triboelectric layer due to not instant dissipation depends on the rotation frequency of T-DC-TENGs. At higher frequency, the more undissipated residual charges will exemplify their effect on the triboelectrification process and limit the output of T-DC-TENGs. Herein, we disclose these residual charges first and then their frequency dependent effect on triboelectrification in T-DC-TENGs. In this study, a charge collecting electrode (CCE) is introduced to construct an electrostatic breakdown T-DC-TENG (EBT-DC-TENG) with greatly reduced frequency dependence. By efficiently reducing the residual charges, the charge density output of EBT-DC-TENG is increased by 51.75% at 90 rpm (from 145.7 to 221.1 μC m−2 r−1) compared with T-DC-TENG without CCE. Furthermore, with the help of its soft property, the less residual charges accumulated polyester fur enables EBT-DC-TENG to maintain 100% output without wear after 10,000 cycles. This EBT-DC-TENG with a better crest factor of 1.028 can continuously power 1200 LEDs in series connection, showing unique advantages in harvesting environmental energy steadily and efficiently. This work also provides a theoretical and practical path for the miniaturization of the rotating mode T-DC-TENG.

LAMA improve tissue oxygenation more than LABA in patients with COPD

Background The effect of bronchodilators is mainly assessed with forced expiratory volume in 1s (FEV1) in COPD. Their impact on oxygenation and lung periphery is less known. Objectives To compare the action of long-acting ß2-agonists (LABA-olodaterol) and muscarinic antagonists (LAMA-tiotropium) on tissue oxygenation in COPD, considering their impact on proximal and peripheral ventilation as well as lung perfusion. Methods FEV1, Helium slope (SHe) from a single-breath washout test (SHe decrease reflecting a peripheral ventilation improvement), frequency dependence of resistance (R5-R19), area under reactance (AX), lung capillary blood volume (Vc) from double diffusion (DLNO/DLCO) and transcutaneous oxygenation (TcO2) were measured before and 2 hours post-LABA (day 1) and LAMA (day 3) in 30 COPD patients (FEV1 54±18% pred; GOLD A 31%/B 48%/E 21%) after 5-7 days of washout, respectively. Results TcO2 increased more (p=0.03) after LAMA (11±12%from baseline, p<0001) compared to LABA (4±11%, p=0.06) despite a lower FEV1 increase (p=0.03) and similar SHe (p=0.98), AX (p=0.63) and R5-R19 decreases (p=0.37). TcO2 and SHe changes were negatively correlated (r=-0.47, p=0.01) after LABA, not after LAMA (r=0.10, p=0.65). DLNO/DLCO decreased and Vc increased after LAMA (p=0.04; p=0.01, respectively) but not after LABA (p=0.53; p=0.24). Conclusion LAMA significantly improved tissue oxygenation in COPD patients, while only a trend was observed with LABA. The mechanisms involved may differ between both drugs: LABA increased peripheral ventilation while LAMA increased lung capillary blood volume. Should oxygenation differences persist over time, LAMA could arguably become the first therapeutic choice in COPD.

Frequency dependence of nanorod self-alignment using microfluidic methods

Dielectrophoresis is a potential candidate for aligning nanorods on electrodes, in which the interplay between electric fields and microfluidics is critically associated with its yield. Despite much of previous work on dielectrophoresis, the impact of frequency modulation on dielectrophoresis-driven nanorod self-assembly is insufficiently understood. In this work, we systematically explore the frequency dependence of the self-alignment of silicon nanorod using a microfluidic channel. We vary the frequency from 1kHz to 1000 kHz and analyze the resulting alignments in conjunction with numerical analysis. Our experiment reveals an optimal alignment yield at approximately 100 kHz, followed by a decrease in alignment efficiency. The nanorod self-alignments are influenced by multiple consequences, including the trapping effect, induced electrical double layer, electrohydrodynamic flow, and particle detachment. This study provides insights into the impact of frequency modulation of electric fields on the alignment of silicon nanorods using dielectrophoresis, broadening its use in various future nanotechnology applications.

Direct and indirect switch from semiconductor to metallic behavior defined by the competition between Cation–Anion–Cation and Cation–Cation interactions leading to an important technological aspect of perovskite systems

We discuss in this work the key interactions that explain the possible electrical behaviors in different perovskite systems. Multi-behavior observation characterizes each frequency and temperature dependence of various perovskite systems. We classify such observations according to the temperature regimes. Indeed, a direct switch from semiconductor to metallic feature describes the conductivity evolution indicating the direct change from the localized (cation–anion–cation interactions) to delocalized (cation–cation interactions) state. The metallic character is reached due to the reinforcement of charge delocalization effect at high temperatures and frequencies. An indirect transformation separated by a frequency-independent regime is equally observed and discussed. Subsequently, a mixed regime is described by the conductivity temperature-independence which is explored at a specific frequency. Such investigations lead to demonstrate basic and common rules relevant for oxide-perovskites multi-behavior. Equally, important technological aspects are confirmed for systems that displays such multi-behavior character according to the temperature range.

Parameter identification and NVH characteristic analysis of automotive suspension rubber bushing

Accurate prediction of the dynamic stiffness of rubber bushings is crucial for optimizing vehicle vibration and noise performance. However, this task is highly challenging due to various influencing factors such as frequency and amplitude. Consequently, there has been limited research conducted in this area thus far. This paper presents a novel approach for predicting the dynamic stiffness of rubber bushings. The frequency and amplitude dependencies of rubber bushings were thoroughly investigated through dynamic loading tests. A comprehensive model for rubber bushings, incorporating parallel connections of elastic elements, friction elements, and higher-order fractional derivative viscous elements, was established. The model parameters were accurately identified using the GA-BP method. The results demonstrate that the proposed model exhibits a high level of precision in estimating dynamic stiffness across a frequency range of 0–200 Hz. In comparison to the conventional model, the proposed approach enables more precise computation of interior sound pressure response and enhances vehicle simulation accuracy.

Lithospheric and asthenospheric anisotropic gradients along the Eastern North American Margin imaged by frequency dependent quasi-Love wave scattering

The eastern North American margin has experienced a wide array of plate-scale tectonic deformational events, including the breakup of Pangaea. The margin may also host complex patterns of active asthenospheric mantle dynamics. Several studies have observed a strong change in anisotropy across the margin that have been interpreted variously as active asthenospheric flow or past lithospheric deformation. Separating these candidate processes has proven difficult. To constrain the likely source of the change in anisotropy across the margin, we examine scattered quasi-Love waves over three frequency ranges with peak sensitivities in the lithosphere (~75 km), the uppermost mantle (~150 km), and the asthenosphere (~250 km). We observe strong quasi-Love wave scattering along the margin in the lowest two frequency bands but far fewer scatterers in the lithosphere-dominated highest frequency band. The clear frequency dependence suggests a change in anisotropy across the margin is likely located in the asthenosphere and related to active mantle dynamics.

Multi-mechanical frequency locking mechanism and robustness analysis of MDOF coupled resonator

Mechanical frequency locking can overcome the dependence of peak frequency on the driving amplitude and improve the frequency stability in nonlinear resonant systems. Most research focuses on the single mechanical frequency locking phenomenon, but few studies focus on multi-mechanical frequency locking phenomenon. In this study, the multi-mechanical frequency locking mechanism and robustness analysis of the peak frequency is proposed through multi-mode coupled vibration. Firstly, a multi-degree-of-freedom (MDOF) coupled resonator consisting of a low-frequency resonant element and multiple high-frequency resonant elements is designed, and the vibration energy of the resonant system can be transferred from the low-frequency resonant element driven by a harmonic excitation to the high-frequency resonant elements via the 1:3 internal resonance. Through perturbation and bifurcation analysis, the nonlinear dynamic behaviors of MDOF coupled resonator are analyzed in detail. It is found that the peak frequency of the low-frequency resonant element can remain stable in multiple drive intervals, leading to multi-mechanical frequency locking phenomenon. Then, a 3-DOF magnetic coupled resonant system is experimentally designed to demonstrate the physical conditions and influencing factors of the double mechanical frequency locking phenomenon. Typically, introducing external disturbances, the frequency locking is experimentally demonstrated to improve the robustness of peak frequency. The experimental results show that when the mechanical frequency locking phenomenon occurs, the influence of small external noise disturbance on the peak frequency can be ignored, which greatly improves the frequency stability of nonlinear resonant systems.

Effect of hetero-valence ions on structural and electrical properties of La2Ni(Mn0.5Ti0.5)O6 ceramics

The study of powder X-ray diffraction of La2Ni(Mn0.5Ti0.5)O6 (0.5LNMT) confirms a multi-phasic composition. The monoclinic P21/n phase content dominates. Occurrence of minor rhombohedral phase and precipitates of MnO2 and La2MnO4 were detected. The morphology was analyzed using a SEM test and ceramics showed a porous structure and variation in the grain size below 4 μm. Dielectric permittivity of marked magnitude varies from ∼30 to ∼100 000 when temperature increases. Dielectric loss coefficient frequency dependence exhibits well-defined dielectric relaxation peaks, which were found to obey the Arrhenius law with the activation energy of 0.29 eV, below the presumed phase transition. Two sets of relaxation peaks in the imaginary part of electric modulus spectra relate to relaxations of different activation energies of 0.28 eV and 0.38 eV. An optical gap magnitude of 0.8 eV was determined from the diffuse reflectance spectrum in the Vis-NIR range. It compares with the band gap estimated from the X-ray photoelectron spectroscopy test. We also compare the influence of doping ions on the crystal lattice of the surface and the bulk ceramics. Electrical conductivity relaxation processes were attributed to the electron hopping mechanism betwee n multi-valence Mnk+ and Nin+ ions’ states, which were determined from XPS analysis. The dc resistivity shows thermally generated dependence. Activation energy Edc magnitude varies between 0.27-0.37 eV which indicates the occurrence of defects and structural disorder. Such disorder correlates to the variable range hopping of small polarons involved in electrical conductivity. The density of states near Fermi energy was estimated N(EF) = 2.1×1025 eV−1 m−3. The 0.5LNMT application prospects were discussed.

In vivo disentanglement of diffusion frequency-dependence, tensor shape, and relaxation using multidimensional MRI.

Diffusion MRI with free gradient waveforms, combined with simultaneous relaxation encoding, referred to as multidimensional MRI (MD-MRI), offers microstructural specificity in complex biological tissue. This approach delivers intravoxel information about the microstructure, local chemical composition, and importantly, how these properties are coupled within heterogeneous tissue containing multiple microenvironments. Recent theoretical advances incorporated diffusion time dependency and integrated MD-MRI with concepts from oscillating gradients. This framework probes the diffusion frequency, , in addition to the diffusion tensor, , and relaxation, , , correlations. A clinical imaging protocol was then introduced, with limited brain coverage and 3 mm3 voxel size, which hinder brain segmentation and future cohort studies. In this study, we introduce an efficient, sparse in vivo MD-MRI acquisition protocol providing whole brain coverage at 2 mm3 voxel size. We demonstrate its feasibility and robustness using a well-defined phantom and repeated scans of five healthy individuals. Additionally, we test different denoising strategies to address the sparse nature of this protocol, and show that efficient MD-MRI encoding design demands a nuanced denoising approach. The MD-MRI framework provides rich information that allows resolving the diffusion frequency dependence into intravoxel components based on their distribution, enabling the creation of microstructure-specific maps in the human brain. Our results encourage the broader adoption and use of this new imaging approach for characterizing healthy and pathological tissues.

Tailoring the electric, dielectric and optical properties of template-free hydrothermally synthesized CuO nanostructures via Co doping

Facile template-free hydrothermal method was utilized for preparing CuO nanostructures (NSs) doped with Co element (Cu1-xCoxO (x=0.0, 0.02, 0.04, 0.06 and 0.08)). A single-phase monoclinic crystal with changing in morphology from rod- to sphere-like nanoparticles was observed. . The temperature dependency of DC electrical conductivity revealed that the shallow and deep donor levels are responsible for the DC conduction in low and high temperature ranges, respectively. The Ac electrical conductivity, dielectric constant and dielectric loss were also measured as functions in frequency and temperature. The frequency dependence of the AC conductivity was well represented by the Jonscher’s universal power law. The AC conduction was governed by the Correlated Barrier Hopping model where the inter-well and intra-well hopping mechanisms contribute to the electrical conduction in the low and high frequency ranges, respectively. The activation energies and the barrier height decreased while the dielectric constant and dielectric loss increased with increasing the Co content. The relaxation and deformational polarizations predominate and the overall behavior of dielectric constant fits well with the Koops' model. The Cole-Cole plots indicated a decrease in the sample resistance with increasing temperatures and Co concentrations. UV-vis absorption spectra exhibited two peaks at wavelengths 252 and 323 nm. The optical energy gap was calculated using Tauc’s equation and decrease from 2.24 to 2.1 eV with increasing the Co concentrations. The effect of Co-doping on CuO was explored for oxygen evolution reaction (OER) and found a decrease in the overvoltage (μ) about 50 mV at 0.08 ratios, which declares that the doping of Co element enhances the electrical conductivity and feasibility for further electrocatalytic improvement.

Inference of source signatures of merchant ships in shallow ocean environmentsa).

An ocean acoustics experiment in 2017 near a shipping lane on the New England continental shelf in about 75 m of water provided an opportunity to evaluate a methodology to extract source signatures of merchant ships in a bottom-limited environment. The data of interest are the received acoustic levels during approximately 20 min time intervals centered at the closest position of approach (CPA) time for each channel on two 16-element vertical line arrays. At the CPA ranges, the received levels exhibit a frequency-dependent peak and null structure, which possesses information about the geophysical properties of the seabed, such as the porosity and sediment thickness, and the characterization of the source, such as an effective source depth. The modeled seabed is represented by two sediment layers, parameterized with the viscous grain shearing (VGS) model, which satisfies causality, over a fixed deep layered structure. Inferred estimates of the implicit source levels require averaging an error function over the full 20 min time intervals. Within the 200-700 Hz band, the Wales-Heitmeyer model captures the inferred frequency dependence of the source levels.

Wave–particle interactions in tokamaks

Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.

Broadband topology optimization of three-dimensional structural-acoustic interaction with reduced order isogeometric FEM/BEM

This paper presents a model order reduction method to accelerate broadband topology optimization of structural-acoustic interaction systems by coupling Finite Element Methods and Boundary Element Methods. The finite element method is used for simulating thin-shell vibration and the boundary element method for exterior acoustic fields. Moreover, the finite element and boundary element methods are implemented in the context of isogeometric analysis, whereby the geometric accuracy and high order continuity of Kirchhoff-Love shells can be guaranteed and meantime no meshing is necessary. The topology optimization method takes continuous material interpolation functions in the density and bulk modulus, and adopts adjoint variable methods for sensitivity analysis. The reduced order model is constructed based on second-order Arnoldi algorithm combined with Taylor's expansions which eliminate the frequency dependence of the system matrices. Numerical results show that the proposed algorithm can significantly improve the efficiency of broadband topology optimization analysis.

Investigation of Morphology, Optical and Electronic Ac Conduction of the Olivine Manganite Compound: NaMnPO4

AbstractThe evolution of multifunctional materials is an outstanding research area, which aims to improve the versatility of materials according to their broad domains of usage. Focus interest was paid here to the orthophosphate compound, in particular, the olivine NaMnPO4 material. This compound was synthesized by a solid‐state method and investigated using numerous techniques. Primary room‐temperature structural analysis evidences the sample synthesized in the orthorhombic structure and its phase purity. The sample‘s average grain size was calculated to be around 420 nm. Further, the band gap for our material was found to be (Eg=4.4 eV) by optical analysis of UV‐visible spectroscopy, revealing that our compound is a potential candidate for optoelectronic applications. The electrical behavior study‘s main results confirm the ferroelectric character of the sample and support the aim of deepening the knowledge of the material according to its thermally stimulated conduction processes through impedance spectroscopy. Electrical studies revealed the dominant transport processes across various temperature and frequency ranges, leading to the NSPT model. The frequency dependency relates to frequency‐dispersive dielectric spectra, conduction mechanisms, and relaxation phenomena. The obtained results show perspective and suggest that the material under study has a wide range of potential electronic applications.

Enhancing the Electrical, Dielectric, and Structural Properties of CeO2-ZrO2 Nanocomposites

For enhancing the breakdown strength and increase the capacity of high voltage power supply with high oxidation stability and good electric properties, Ceramic nanomaterials like zirconia (ZrO2) and Ceria (CeO2) preferred due to their strong insulating property and high relative permittivity. In this article, we have reported the synthesis of CeO2/ZrO2 nanocomposite by chemical method. The use of surfactants during synthesis have an adverse effect on the catalytic activity of CeO2 with different morphologies like nanorods, nanocubes, and nano-octahedra. In addition, zirconia can be synthesized via a variety of techniques, including sol-gel, hydrothermal, and precipitation procedures, and combined with other metal oxide nanoparticles. The synthesized nanocomposites were analyzed by X-ray diffraction (XRD), scanning electron microscope (SEM). The crystalline nature and mixed phase of CeO2/ZrO2 nanoparticles have been confirmed by the findings of XRD and SEM analysis. At various frequencies and temperatures, the dielectric constant and dielectric loss of the synthesized nanoparticles were determined. The conductivity and dielectric characteristics of the synthesized samples exhibited temperature and frequency dependency, indicating that the dopant concentration had a significant impact. As frequency increased, the nanoparticles' tangent loss and dielectric constant dropped sharply. These nano-composites can be used as a metal oxide semiconductor for memory devices as well as fuel cells.

Собственные колебания упругой прямоугольной CFCF-пластинки при одноосном растяжении-сжатии ее плоскости

The influence of a uniaxial distributed load in the plane of a thin rectangular plate on the value of the first natural frequency of its oscillations has been studied. We considered a plate, two opposite faces of which are clamped, and the other two are free (CFCF-plate, C-clamped edge, F-free edge). The load is applied to the clamped edges. The main differential equation for the coordinate component of the deflection function and all the boundary conditions of the problem are fulfilled exactly using two hyperbolic-trigonometric series in two coordinates and an additional function depending on one variable x. The problem was reduced to an infinite system of linear algebraic equations with respect to one sequence of uncertain coefficients, containing as parameters the magnitude of the load and the frequency of oscillations. For a number of load values, the natural frequencies of oscillations were found by enumerating frequency values in combination with the method of successive approximations when solving a reduced system of linear algebraic equations. To ensure acceptable accuracy of calculations, the number of terms in the series (the size of the reduced system), the number of iterations and the number of significant digits in the mantissa when calculating non-trivial coefficients of the system were changed. A square plate was considered as an example. Based on the calculation results, a graph was constructed of the dependence of the first natural frequency of oscillations on the magnitude of tension-compression forces, which is a curve close to a parabola. Under Eulerian compressive load, the oscillations stop. The shapes of natural vibrations changed slightly and were similar to the shape of the curved surface of a plate under the action of a uniform transverse load. The purpose of this study is to create an effective algorithm for calculating the natural frequencies of oscillations of a CFCF-plate when the uniaxial tensile-compression load of its clamped faces changes.

On the Frequency Dependence of the PDIV in Twisted Pair Magnet Wire Analogy in Humid Air

Abstract The partial discharge inception voltage (PDIV) of low-voltage induction motor turn-turn insulation analogy is investigated for variable relative humidity of the surrounding air (temperature and pressure are kept constant close to their ambient values). Three materials, perfluoralkoxy alkane, sealed and unsealed alumina, are employed as the dielectric coating (insulation) of test samples. Each material’s dielectric properties change differently with relative humidity—of these, relative permittivity is regarded as the most crucial, as it was previously proven to be, along with the coating’s thickness, the key factor in determining the PDIV in dry air conditions. To further vary the value of permittivity and thus provide larger data sets for the verification study, the frequency of the excitation voltage is also varied between 1 Hz and 50 kHz. The obtained experimental data are compared against the PDIV predictions obtained by a breakdown model based on the reduced thickness of the coating (ratio of the coating thickness to its relative permittivity).Satisfying agreement between the measured and predicted PDIV are obtained for the first two materials, whereas significant discrepancies are seen for the unsealed alumina material. For this case, surface conductivity is introduced into the prediction model and much better fits to the experimental data are obtained for a suitable value of surface resistance. It is hence demonstrated that the model is able to satisfactorily predict the PDIV for three substantially different materials when the relative humidity of the surrounding air is varied between 10% to 80 %.

The NANOGrav 12.5-Year Data Set: Dispersion Measure Misestimations with Varying Bandwidths

Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from misestimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to misestimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643−1224, a pulsar with unusual chromatic timing behavior. We artificially restricted these observations to a narrowband frequency range, then used both the broad- and narrowband data sets to calculate residuals with a timing model that does not account for time variations in the dispersion. By fitting the resulting residuals to a dispersion model and comparing the fits, we quantify the error introduced in the timing parameters due to using a reduced frequency range. Moreover, by calculating the autocovariance function of the parameters, we obtained a characteristic timescale over which the dispersion misestimates are correlated. For PSR J1643−1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ∼22 μs due to incomplete frequency sampling, with correlations over about one month. For lower-DM pulsars, the offset is ∼7 μs. This error quantification can be used to provide more robust noise modeling in the NANOGrav data, thereby increasing the sensitivity and improving the parameter estimation in gravitational wave searches.