Low Frequency Domain Research Articles

An Approach for Modelling Harnesses in the Extreme near Field for Low Frequencies

A key part of every space science mission, in the system-level approach, is the detailed study and modeling of the emissions from transmission lines. Harnesses usually emit electromagnetic fields due to the currents (of common and/or differential modes) that flow on their shields. These fields can be identified via conducted emissions measurements. Relying on the operating frequency, any cable can be considered as a dipole or a traveling-wave antenna. Limited work can be found in the literature regarding modeling methodologies for cable topologies, especially in the low frequency (ELF, SLF, VLF, LF) domain. This work intends to provide perceptions for the precise estimation of harness radiated emissions, consider a mission-specific measurement point (where the sensors are placed), and follow ESA’s recent science mission studies for electromagnetic cleanliness applications. For the low frequencies considered herein, any linear cable path is considered as a point source (infinitesimal dipole) and we evaluate its effect on the calculated electric field extremely close to the source. For such distances, it is shown that the dipole representation is not accurate. To remedy this phenomenon, this article proposes a methodology, which can be easily expanded to complex cable geometry cases.

Diffusion–convection impedance for a micro-band electrode under microfluidic conditions

Diffusion–convection impedance for a micro-band electrode placed in a Poiseuille flow was studied experimentally under microfluidic conditions. Electrochemical impedance spectroscopy (EIS) experiments performed with a fast electrochemical system show perfect agreement with a previously published quantitative analytical expression in the low frequency domain.

Detection of periodicity, aperiodicity, and corresponding driving factors of river dissolved oxygen based on high-frequency measurements

Understanding dissolved oxygen (DO) dynamics and corresponding driving factors are essential to improve aquatic environments and protect aquatic organisms. Although several studies have been conducted to investigate DO dynamics on low-frequency scales, high-frequency spectral characteristics of DO and the corresponding connections with hydro-biogeochemical drivers were little known. Accordingly, this study proposed a comprehensive framework to explore the periodic and aperiodic characteristics of DO, and the corresponding hydrological (water temperature) and biogeochemical (pH, ammonia nitrogen (NH3-N), and total phosphorus (TP)) controls in the Pearl River Basin of China based on high-frequency measurements and spectral analysis. The results showed that DO, water temperature, pH, NH3-N and TP all exhibited temporal fractal phenomena, i.e., 1/f fluctuations, in low-frequency domains. The scaling component β of water temperature was larger, implying that the self-similarity of water temperature was stronger. In high-frequency domains, DO exhibited obvious daily and half-day periods. Of the other four elements, water temperature and pH exhibited high-frequency periods, while NH3-N and TP did not. Based on the energy distribution derived from the continuous wavelet transform, three DO transience types, swing, abrupt, and mixed swing and abrupt, were characterized. The first type was characterized by continuous fluctuations, while the second type was characterized by a sudden change with a peak value. The last type had traits of both swing transience and abrupt transience. Through an analysis of maximal information coefficient and correlation coefficient, we found that linear relationships existed between water temperature and DO with correlation coefficient ranging from −0.46 to −0.83. In contrast, pH, NH3-N, and TP generally exhibited nonlinear relationships with DO, and the nonlinear coefficients were above 0.2. On the whole, the driving elements were different for each DO transience type. Hydrological elements mainly corresponded to DO swing transience. In contrast, biogeochemical elements were mainly related to DO abrupt transience. In general, this study provided a new perspective for revealing the high-frequency fluctuations of DO and corresponding drivers. The framework and results summarized in this study broadened our understanding on DO dynamics, and were conducive to river management, such as water quality anomaly detection, water quality prediction and regulation in advance.

Precise Position Adjustment of Automotive Electrohydraulic Coupling System With Parameter Perturbations

Abstract Based on the guaranteed cost theory, this paper proposes a robust controller for the automotive electrohydraulic coupling system. However, parameter perturbation caused by the model linearization is a critical challenge for the nonlinear electrohydraulic coupling system. Generally, the electrical brake booster system (E-booster) can be separated into three parts, a permanent magnet synchronous motor (PMSM), a hydraulic model of the master cylinder, and the transmission mechanism. In this paper, the robust guaranteed cost controller (RGCC) is adopted to achieve an accurate regulation of the pushrod position of the E-booster and has strong robustness against internal uncertainties, and the linear extended state observer (LESO) is utilized to optimize E-booster's dynamic performance. Specifically, the tracking differentiator (TD) and LESO are used to improve the dynamic precision and reduce the hysteresis effect. The overshoot is suppressed by TD, and the disturbance caused by nonlinear uncertainty is restrained by LESO. The experimental results show that RGCC sacrifices a 6% phase lag in the low-frequency domain for a 10% and 40% reduction in first and second-order, respectively, compared with the proportion integration differentiation (PID). Results demonstrate that RGCC has higher precision and stronger robustness in dynamic behavior.

Reliability of cerebral autoregulation using different measures of perfusion pressure in patients with subarachnoid hemorrhage.

Dynamic cerebral autoregulation to spontaneous fluctuations in cerebral perfusion pressure (CPP) is often assessed by transcranial Doppler (TCD) in the time domain, yielding primarily the mean flow index (Mx), or in the frequency domain using transfer function analysis (TFA), yielding gain and phase. For both domains, the measurement of blood pressure is critical. This study assessed the inter‐method reliability of dynamic cerebral autoregulation using three different methods of pressure measurement. In 39 patients with aneurysmal subarachnoid hemorrhage, non‐invasive arterial blood pressure (ABP), invasive ABP (measured in the radial artery) and CPP were recorded simultaneously with TCD. Intraclass correlation coefficient (ICC) was used to quantify reliability. Mx was higher when calculated using invasive ABP (0.39; 95% confidence interval [95% CI]: 0.33; 0.44) compared to non‐invasive ABP, and CPP. The overall ICC showed poor to good reliability (0.65; 95% CI: 0.11; 0.84; n = 69). In the low frequency domain, the comparison between invasively measured ABP and CPP showed good to excellent (normalized gain, ICC: 0.87, 95CI: 0.81; 0.91; n = 96; non‐normalized gain: 0.89, 95% CI: 0.84; 0.92; n = 96) and moderate to good reliability (phase, ICC: 0.69, 95% CI: 0.55; 0.79; n = 96), respectively. Different methods for pressure measurement in the assessment of dynamic cerebral autoregulation yield different results and cannot be used interchangeably.

Digital H∞ filter design for a low frequency multiple‐input multiple‐output system with multirate measurements

AbstractIn this article, a digital filter is designed for a low frequency multiple‐input multiple‐output (MIMO) system with multirate measurements from multiple samplers. A delay compensation is introduced to reduce estimation errors from the multiple samplers and a zero‐order holder. A single‐rate error system is obtained by converting the low frequency MIMO system using a discrete‐time lifting technique. A digital filter is proposed based on a delay‐partitioning method to guarantee asymptotic stability and performance for the single‐rate error system. A numerical example is provided to show effectiveness and superiority of the digital filter in low frequency domain.

Microfluidic Quantitative Flow Cytometer With Light Modulation

Quantitative detections of proteins for single cells have made great contributions to tumor heterogeneity and immune variance while effective tools of measuring single-cell intracellular proteins are under developments. This study reported a flow cytometer based on constriction microchannel and light modulation, which was capable of quantifying intracellular proteins for single cells with high resolution. Cells tagged with fluorescein labelled antibodies were squeezed into the constriction microchannel as either the calibration or detection structure where a light source with a carrier wave was used for fluorescent modulation, which was further demodulated into the low-frequency domain and translated into numbers of single-cell proteins. In platform characterization, the inclusion of light modulation was shown to effectively improve the detection resolution from &#x007E;1000 intracellular proteins per cell without modulation to &#x007E;100 intracellular proteins per cells with modulation. As demonstrations, expressions of mutant p53 or phosphorylated p53 from tens of thousands of single T47D and/or A431 cells were quantitatively measured by the microfluidic quantitative flow cytometer, which were 1.78 &#x00B1; <inline-formula> <tex-math notation="LaTeX">$0.96 \times10$ </tex-math></inline-formula>⁵ mutant p53 per cell for T47D cells (<inline-formula> <tex-math notation="LaTeX">${N}_{c} =10\,315$ </tex-math></inline-formula>), 1.99 &#x00B1; <inline-formula> <tex-math notation="LaTeX">$1.49\times10$ </tex-math></inline-formula>⁵ mutant p53 per cell for A431 cells (<inline-formula> <tex-math notation="LaTeX">${N}_{c} =15\,665$ </tex-math></inline-formula>), and 6.34 &#x00B1; <inline-formula> <tex-math notation="LaTeX">$7.50\times10$ </tex-math></inline-formula>³ phosphorylated p53 per cell for A431 cells treated with doxorubicin (<inline-formula> <tex-math notation="LaTeX">${N}_{c} =12\,812$ </tex-math></inline-formula>). In conclusion, the inclusion of light modulation can effectively decrease electrical and optical noises and therefore improve detection resolution in microfluidic quantitative flow cytometry.

The load criteria for ship mechanical noise prediction in low frequencies and experimental validation

The loading method of the external excitations generated by the equipment directly affects the predicted result of the mechanical noise which should be the same under different excitation forms for the given equipment. In this paper, general load criteria are proposed to define forces/moments as the standard form and convert other forms of loads in the low-frequency domain. As the most typical form to characterize equipment excitation, acceleration load loading methods for different conditions are investigated. The equivalent formula between ideal accelerations and generalized forces establishes the first load criterion. The second load criterion is proposed to address the issue of an average acceleration loading, in which the phase and amplitude distribution are both absent, and cannot apply to the load identification. The upper and lower limits of the mechanical noise can be determined by the vibroacoustic transfer function of the three load models, and the energy-averaged value is used to represent the mechanical noise. Furthermore, the third criterion is used to handle the case where the acceleration load is given by the results of a bench test. According to the equipment source descriptor invariance, the conversion method is achieved between the bench test and the real ship based on the transfer function of a load model, and the mechanical noise is predicted by an equivalent energy method. Finally, a three-parameter method to quantitatively evaluate the well-fitting of experimental and numerical results, and the load criteria are well validated by underwater acoustic experiments of an experimental model.

Optical-domain spectral super-resolution via a quantum-memory-based time-frequency processor

Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies to fully exploit information already present in the field is to perform a quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ an optical quantum memory with spin-wave storage and an embedded processing capability to implement a time-inversion interferometer for input light, projecting the optical field in the symmetric-antisymmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.

Imaging biological samples by integrated differential phase contrast (iDPC) STEM technique

Scanning transmission electron microscopy (STEM) is a powerful imaging technique and has been widely used in current material science research. The attempts of applying STEM (annual dark field (ADF)-STEM or annular bright field (ABF)-STEM) into biological research have been going on for decades while applications have still been limited because of the existing bottlenecks in dose efficiency and non-linearity in contrast. Recently, integrated differential phase contrast (iDPC) STEM technique emerged and achieved a linear phase contrast imaging condition, while resolving signals of light elements next to heavy ones even at low electron dose. This enables successful investigation of beam sensitive materials. Here, we investigate iDPC-STEM advantages in biology, in particular, chemically fixed and resin embedded biological tissues. By comparing results to the conventional TEM, we have found that iDPC-STEM not only shows better contrast but also resolves more structural details at molecular level, including conditions of extremely low dose and minimal heavy-atom staining. We also compare iDPC-STEM with ABF-STEM and found that contrast of iDPC-STEM is even further improved, moderately in lower frequency domains while highly with preserving high frequency biological structural details. For thick sample sections, iDPC-STEM is particularly advantageous. It avoids contrast inversion canceling effects, and by adjusting the depth of focus, fully preserves the contrast of structural details along with the sample. In addition, using depth-sectioning, iDPC-STEM enables resolving in-depth structural variation. Our results suggest that iDPC-STEM have the place and advantages within the future biological research.

Wavelet-Attention CNN for image classification

The feature learning methods based on convolutional neural network (CNN) have successfully produced tremendous achievements in image classification tasks. However, the inherent noise and some other factors may weaken the effectiveness of the convolutional feature statistics. In this paper, we investigate Discrete Wavelet Transform (DWT) in the frequency domain and design a new Wavelet-Attention (WA) block to only implement attention in the high-frequency domain. Based on this, we propose a Wavelet-Attention convolutional neural network (WA-CNN) for image classification. Specifically, WA-CNN decomposes the feature maps into low-frequency and high-frequency components for storing the structures of the basic objects, as well as the detailed information and noise, respectively. Then, the WA block is leveraged to capture the detailed information in the high-frequency domain with different attention factors but reserves the basic object structures in the low-frequency domain. Experimental results on CIFAR-10 and CIFAR-100 datasets show that our proposed WA-CNN achieves significant improvements in classification accuracy compared to other related networks. Specifically, based on MobileNetV2 backbones, WA-CNN achieves 1.26% Top-1 accuracy improvement on the CIFAR-10 benchmark and 1.54% Top-1 accuracy improvement on the CIFAR-100 benchmark.

Theoretical Study of Potential Manufacturing Insulation Defects in Medium–Voltage Traction Motors

Medium-voltage motors dedicated to the applications of traction operate in an environment with strong multi-physics constraints. Electrical insulation of these engines is a complex multi-layered impregnated system which requires a given number of steps during the manufacturing process. In the present study, we theoretically investigated the potential manufacturing insulation defects of traction motors in low frequency domain. The aim is to assess the theoretical ability of dielectric spectroscopy method for the detection of these defects and the extension of the method to others insulation systems. The theoretical study is based on numerical modelling and simulation achieved by using Comsol Multiphysics software. In our numerical modelling the properties of the main dielectric elementary materials are frequency–dependent. The identification of each potential defect is carried out by comparing its equivalent capacitance and dissipation loss spectra with the characteristics of insulation without defect. As the results, all artificial defects are identifiable with a specific relative deviation. The detection of all the defects analysed will need a measuring device with resolution of 0.4%. Keywords—AC electric motors, Capacitance, dielectric, dissipation factor, composite insulation, numerical modelling.

Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element

In this study, the Absolute Nodal Coordinate Formulation (ANCF) is examined in the framework of the Arbitrary Lagrangian–Eulerian (ALE) formulation for cable simulation. The objective is to determine the stability, efficiency, and accuracy in different frequency domains for two different numerical time integration methods. The methods being compared are the Runge–Kutta method RK4, and the Generalized-α method. For simulations where the lower frequency domain is of interest, the Generalized-α method is stable, accurate and can be used with large time-steps; while where the high frequency domains is of interest, the RK4 procedure can be a more efficient method.The penalty method, the Lagrange multiplier method and linear coupling are tested as constraint methods for connecting ALE-ANCF cable elements. For RK4, the penalty constraint method highly affects the maximum time-step, which again affects the total solution time. For the Generalized-α method, the constraint methods all provide accurate results, and they have similar solution time. ALE-ANCF cable elements can be connected by different constraint techniques without impeding the ability to exhibit large deformations.

Dynamic study of tip-link tension and stereocilia motion in cochlea

Explanation of cochlear active acoustic amplification mechanism has been an unsolved medical problem. This mechanism is closely related to the motion of the stereocilia at the top of the outer hair cells in the cochlea. The motion of stereocilia is regulated by the tip-link tension and the fluid force of the lymph fluid. Therefore, studying the tip-link tension during the motion of stereocilia is an important part of the explanation of the cochlea's active sensory sound amplification mechanism. Most of previous studies regarded the stereocilia as rigid bodies, and ignored the influence of shaft bending when studying the mechanical properties of hair bundle. Most of the researches on elastic stereocilia used the finite element simulation, or simplified the model by ignoring the fluid-solid coupling with lymph fluid, or considered only static loading. Based on the Poiseuille flow combined with the distributed parameter model, the analytical solution of the elastic motion of stereocilia is derived in this work. The dynamic response of the stereocilia under the shear force of the tectorial membrane and the change law of tip-link tension are studied. The shaft bending produces a nonlinear accumulation of displacement at the height of the stereocilia. The higher the stereocilia, the more obvious the accumulation effect is. Under the action of dynamic load, the shaft bending contributes most to the displacement response in the tall stereocilium, and this contribution is easily affected by frequency change. Under low frequency load, the displacement response of tall stereocilium comes mainly from the root deflection. At high frequency, the shaft bending increases significantly, and the displacement response is produced by the combination of shaft bending and root deflection. The change of F-actin content in the cochlea exposed to noise would affect the stereocilia stiffness. In this paper, it is found that the decrease of stereociliary Young's modulus will increase the peak value of normalized tension and reduce its peak frequency, and the amplitude of normalized tension will increase under the low frequency shear load. Since the tip-link is connected to an ion channel, the change of normalized tension will affect the probability of ion channels opening, change the ability of cochlea to perceive the sound of corresponding frequency, and then affect the frequency selectivity of hair bundle. Therefore, previous studies of stereocilia regarded as rigid bodies underestimated the response of the cochlea to low-frequency acoustic signals. This model accurately describes the law of tip-link tension and provides a corresponding theoretical explanation for hearing impairment caused by noise environment. Previous experiments have shown that the lymphatic viscous resistance has little effect on the deflection of stereocilia. In this paper, when the viscous resistance is ignored, the tip-link tension changes very little, and when the pressure between the stereocilia is ignored, the tip-link tension changes significantly and the resonance peak of &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ {f_2} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211105_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211105_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; disappears. Therefore, lymphatic fluid regulates the resonance properties of the tip-link tension by creating the pressure between the stereocilia. The presence of lymphatics is essential for generating the frequency characteristics of the hair bundle. In the low frequency domain, the motion of stereocilia is regulated mainly by tip-link, and in the high frequency domain, it is regulated mainly by lymphatic pressure.

Decision-Based Attack to Speaker Recognition System via Local Low-Frequency Perturbation

Despite neural network-based speaker recognition systems (SRS) have enjoyed significant success, they are proved to be quite vulnerable to adversarial examples. In practice, the SRS model parameters are not always available. Attackers have to probe the model only via querying, and such decision-based attacking merely relies on the output label is quite challenging. This letter proposes a two-step query-efficient decision-based attack based on local low-frequency perturbation. Specifically, instead of imposing perturbation on the entire audio sample, a local attacking region is firstly sought, confining the perturbed distortion to a local region. Second, considering that the majority of energy concentrates on the low-frequency bands, the proposed method suggests performing perturbation generation in the low-frequency domain. Experimental results demonstrate that, compared with the recent methods, our method could implement target attacking to SRS with a higher attacking success rate, at the cost of much lower queries and adversarial perturbation.

Correlation of Heart Rate Variability and Inflammatory Markers in Patients with Depression: A Cross-sectional Study

Introduction: Depression has been found to be associated with cardiovascular morbidity and mortality. Autonomic dysregulation and inflammation have been implicated as the possible mechanisms. A cross-talk between the autonomic nervous system and inflammatory pathways has been observed in different clinical studies. Aim: To examine the inter-relationship between Heart Rate Variability (HRV), a measure of autonomic function, and inflammatory biomarkers measured by high sensitivity C-Reactive Protein (hsCRP) and Interleukin-6 (IL-6) in patients with depression, without any co-morbid conditions. Materials and Methods: This cross-sectional study was conducted in Department of Physiology, in collaboration with the Department of Psychiatry and Biochemistry, Lady Hardinge Medical College, New Delhi, India, from November 2010 to March 2012. Total 30 drug naive cases (without any comorbid diseases) diagnosed with depression (mild, moderate and severe depression) as per International classification of diseases-10 (ICD-10) guidelines, in the age group of 20- 45 years old were included in the study. Heart rate variability measures were recorded and analysed, frequency domain measures Low Frequency (LF), High Frequency (HF) and time domain measures like Standard Deviation of all NN interval (SDNN) and Root Mean Square of Successive differences of NN intervals (RMSSD). The IL-6 and hsCRP levels were also measured and severity of depression by Hamilton Depression Rating Scale (HDRS) was also assessed and correlated. Data was analysed using the Statistical Package for Social Sciences (SPSS) version 16.0. Normality of data was assessed using the Shapiro-Wilk test. Results: The mean age of the cases was 30.33±6.97 years. There were 14 males and 16 females. There was no significant correlation found between the HRV measures and inflammatory biomarkers (LF vs hsCRP: p-value=0.781, HF vs hsCRP: p-value=0.713, SDNN vs hsCRP: p-value=0.262, RMSSD vs hsCRP: p-value=0.50, LF vs IL-6: p-value=0.477, HF vs IL-6: p-value=0.425, SDNN vs IL-6: p-value=0.137, RMSSD vs IL-6: p-value=0.328). Correlation of HDRS with HRV measures or inflammatory markers was not found to be significant. Conclusion: Future studies with larger sample size and wide array of inflammatory biomarkers besides IL-6 and hsCRP is warranted. No significant correlation was observed between

Watermarking of a 3D Model based on Wavelet Transform

In the last decade, 3D models gained interest in many applications, such as games, the medical field, and manufacture. It is necessary to protect these models from unauthorized copying, distribution, and editing. Digital watermarking is the best way to solve this problem. This paper introduces a robust watermarking method by embedding the watermark in the low-frequency domain, then selecting the coarsest level for embedding the watermark based on the strength factor. The invisibility of the watermark for the proposed algorithm is tested by using different measurements, such as HD and PSNR. The robustness was tested by using different types of attacks; the correlation coefficient was applied for the evaluation of the extracted watermark. From the results, it is clear that the proposed algorithm achieved good invisibility and robustness against the geometrical attack and the added noise.

Causally-guided acoustic optimization of rigidly-backed micro-perforated partitions: Case studies and experiments

A causal-based optimization criterion has been theoretically derived in an earlier study for a single-layer micro-perforated absorber (MPA) under normal incidence. In this study, it is extended to multiple and parallel MPA systems as well as to general incidence. It is shown that the ultimate wideband performance of multiple (resp. parallel) MPAs scale on their overall (resp. effective) cavity depths, with adverse effect of the incidence angle. The multi-variate constrained optimization process requires maximising the sensitivity of the total reflected intensity, integrated over all wavelengths, with respect to the parameters constitutive of the micro-perforated panels. It leads to perfect absorption and broad bandwidth efficiency at one or several resonant states of the MPAs. As for serial MPA systems, it is a suitable sub-optimal alternative to total absorption and inverse-frequency weighted absorption maximizations. Concerning MPA arrays, the causal-based optimal design brings near-unit absorption over a wide bandwidth in the low-frequency domain due to efficient grouping and merging of cross-coupled resonant states. It brings similar performance to direct maximization of the total inverse-frequency weighted absorption that puts weight on the low frequencies. These optimal performances have been verified through standing wave tube absorption measurements for single and double-layer MPAs and through finite element simulation for MPA arrays.

ИССЛЕДОВАНИЕ КОЛЕБАНИЙ БАЛКИ ИЗ ФУНКЦИОНАЛЬНО-ГРАДИЕНТНОГО МАТЕРИАЛА С УЧЕТОМ ЗАТУХАНИЯ

The problem of oscillations of an inhomogeneous beam made of a functionally gradient material in the framework of various deformation models - the Euler-Bernoulli model and the Timoshenko model in the presence of attenuation, which is described within the framework of the concept of complex modules for a standard viscoelastic body, is considered. The left end of the beam is pinched, and at the right end there is a concentrated moment oscillating with a certain frequency. The solution is built in two ways. In the first of them, on the basis of asymptotic analysis, a solution was constructed in the low-frequency domain, and a complete coincidence of solutions for the models under consideration in the low-frequency domain (up to the first resonance) for any laws of inhomogeneity was shown. In the second case, the influence of rheological factors on the amplitude-frequency characteristics of an inhomogeneous viscoelastic beam in the frequency range up to the third resonance was analyzed using the targeting method. A comparative analysis of the frequency response of two models for different laws of heterogeneity is carried out. Frequency response for various laws of inhomogeneity are presented, the movement of resonant frequencies depending on the dimensionless relaxation time is studied.

Weierstrass function methodology for uncertainty analysis of random media criticality with spectrum range control

Randomized Weierstrass function (RWF) has been under development for evaluating the uncertainty of random media criticality due to the material mixture in disorder. In this work, the modelling capability of RWF is refined so that the spectrum range can be controlled by specifying its lower and upper ends of the frequency domain variable. As a result, it becomes possible to make fair criticality comparison among replicas of random media under inverse power law power spectra. Technically, the infinite sum of trigonometric terms in RWF is formally extended to cover the arbitrarily low frequency domain and then truncated to finite terms for the sole purpose of spectrum range control. This means that the refined RWF is free of the issue of convergence towards a reference fractal characteristic of Weierstrass function and thus termed Incomplete Randomized Weierstrass function (IRWF). As a demonstration, a three-dimensional version of IRWF is applied to the mixture of three fuels with different burnups in a sufficiently water-moderated environment. Monte Carlo criticality calculations are carried out to evaluate the uncertainty of neutron effective multiplication factor (keff) due to the indeterminacy of mixture formation.