Gradient Profile Research Articles

Electro-thermo-mechanical multiple fields coupled guided wave in a piezoelectric semiconductor plate

Based on a fully coupled model of electro-thermo-mechanical multiple physical fields, the guided wave in a piezoelectric semiconductor (PSC) plate is studied. The non-Fourier heat conduction (G-N III-type) and non-Fick diffusion are included in the model. By the appropriate definition of the extended displacements and stresses, the system of second-order differential coupled equations degrades to a first-order matrix differential equation. The transfer matrix of the PSC plate is derived from the first-order matrix differential equation. Some combinations of mechanical, electric and carrier boundary conditions are applied to obtain the dispersion relations. The influences of various boundary conditions and typical parameters on the dispersion and attenuation are investigated numerically. The gradient profiles of the inhomogeneous plate are also discussed. Based on the numerical results, it is found that the dispersion characteristics are mainly affected by the mechanical boundary conditions, while the attenuation characteristics are mainly affected by the transport of carrier and heat. In addition, the gradient profiles of inhomogeneous plates affect both dispersion and attenuation characteristics.

Thermal safety considerations for implantable micro-coil design

Micro magnetic stimulation of the brain via implantable micro-coils is a promising novel technology for neuromodulation. Careful consideration of the thermodynamic profile of such devices is necessary for effective and safe designs. Objective. We seek to quantify the thermal profile of bent wire micro-coils in order to understand and mitigate thermal impacts of micro-coil stimulation. Approach. In this study, we use fine wire thermocouples and COMSOL finite element modeling to examine the profile of the thermal gradients generated near bent wire micro-coils submerged in a water bath during stimulation. We tested a range of stimulation parameters previously reported in the literature such as voltage amplitude, stimulus frequency, stimulus repetition rate and coil wire materials. Main results. We found temperature increases ranging from <1 °C to 8.4 °C depending upon the stimulation parameters tested and coil wire materials used. Numerical modeling of the thermodynamics identified hot spots of the highest temperatures along the micro-coil contributing to the thermal gradients and demonstrated that these thermal gradients can be mitigated by the choice of wire conductor material and construction geometry. Significance. ISO standard 14708-1 designates a thermal safety limit of 2 °C temperature increase for active implantable medical devices. By switching the coil wire material from platinum/iridium to gold, our study achieved a 5–6-fold decrease in the thermal impact of coil stimulation. The thermal gradients generated from the gold wire coil were measured below the 2 °C safety limit for all stimulation parameters tested.

Nonlinear control of safety factor gradient in tokamaks using spatially variable electron cyclotron current drives

Active control of plasma properties may be necessary to achieve stable operation of next-generation tokamaks over large time scales. Such control algorithms can regulate the plasma properties to avoid the onset of magnetohydrodynamic (MHD) instabilities. For instance, the global and local properties of the safety factor profile are linked to the onset of neoclassical tearing modes (NTMs). This work proposes a model-based control approach for deterring/delaying NTMs through active modulation of one of the safety factor properties - the gradient of the safety factor profile at a particular rational safety factor surface. In particular, a novel control-oriented model for the local safety factor gradient is developed. The nonlinear control model is governed by a nonautonomous ordinary differential equation that accounts for a given rational safety factor surface’s spatial variation over time. To improve the controllability of the spatially evolving parameter, the control model treats ECH&CD positions, along with noninductive powers, as controllable variables. A nonlinear control algorithm based on feedback linearization with optimization is synthesized to achieve the objective of regulating the safety factor gradient around a given target. The proposed algorithm allocates optimal ECH&CD positions, in addition to auxiliary powers, at each time instant as the rational safety factor surface drifts to locations with a low control authority. Stability guarantees of the proposed control law are also discussed in this work. The proposed algorithm is tested for a DIII-D tokamak scenario in nonlinear simulations carried out using the Control Oriented Transport SIMulator (COTSIM). Both fixed and moving ECH&CD cases are studied, and their outcomes are compared. Simulation results demonstrate that enthusiastic regulation of the safety factor gradient can be achieved during the ramp-up and flat-top phases of tokamak operation in both fixed and moving ECH&CD cases. However, real-time updates of ECH&CD positions can prevent the saturation of auxiliary powers.

Enhanced Yb:YAG Active Mirrors for High Power Laser Amplifiers

The work is aimed at the investigation of the influence of nonlinear active ions concentration profiles in Yb:YAG laser elements on temperature distribution and wavefront distortions during amplification using sub-kilowatt level diode pumping. A mathematical model is presented for the theoretical study of the amplification process in crystals with cubic crystal system. A detailed comparison of Yb:YAG active elements with the same thickness and absorbed pumping power, but with various concentration profiles of Yb3+, ions is carried out. It is shown that the use of active elements with an increasing dopant concentration in the pump beam direction allows one to optimize the temperature profile inside the active element and, thus, reduce the thermal-induced wavefront distortions of the amplified radiation. Modeling is carried out for the experimentally grown crystal with linear concentration gradient profile. It is shown that the linear doping profile with a gradient of 0.65 at.%/mm allows increasing the small-signal gain up to 10% and decreasing the thermal-induced wavefront distortions by ~15%.

Heat Soaking for Improving Rollover From S at the Back of CIGSSe Solar Cells

A simple method of low-temperature heat-soaking (HS) treatment on copper indium gallium sulfur selenide (CIGSSe) solar cells is investigated for mitigating the rollover effect. Excessive sulfur accumulation on the backside of the CIGSSe absorber leads to downward valence band bending and forms a Schottky barrier, resulting in the rollover current–voltage characteristic at room temperature. HS treatment effectively reduces current saturation in the first quadrant of the current–voltage curves and improves cell efficiency on average by more than 6%. The depth profile on exfoliated CIGSSe absorbers from the Auger electron spectroscopy analysis demonstrates the elemental redistribution, indicating that HS treatment can change the profile gradient of sulfur. The width of sulfur accumulation is significantly reduced after HS, which enables Fowler–Nordheim tunneling by Schottky barrier width shortening. This study showcases a straightforward process and easy-to-implement strategy to reduce the second reverse diode effect caused from the sulfurization process.

Separation and determination of trace level terbium in gadolinium matrix by ion interaction chromatography

ABSTRACT A gradient elution-based ion interaction chromatography (IIC) method was developed for the determination of trace terbium (Tb) in a gadolinium (Gd) matrix. A reverse-phase column dynamically coated with camphor sulfonic acid (CSA) and α-hydroxybutyric acid (α-HIBA) as the eluent was utilized. Through a comprehensive study, an optimized gradient profile was established, which improved the separation between Tb and Gd. The limit of detection (LOD) for Tb was 2 ng/mL, and the standard deviation was 2% (n = 3) for 0.1 µg/mL Tb in the presence of 1084 µg/mL Gd. With the developed method, trace Tb determination without prior matrix separation was possible.

Hybrid ICHO-HSDC Model For Accurate Covid-19 Detection and Classification From CT Scan And X-Ray Images

The worldwide demand for medical care has increased due to the increasing expansion of Covid-19 cases. Therefore, in this case, prompt and precise identification of this illness is crucial. Health professionals are using additional screening techniques including CT imaging as well as chest Xrays for this. Pre-processing the CT scan pictures to eliminate the areas of areas, normalize image contrast, and minimize image noise, however, receives little attention. The seriousness of the Covid- 19 infection must be assessed in addition to the Covid-19 detection and categorization. An ICHOHYBRID model for Covid-19 identification and classification from X-ray, as well as CT scan images, is offered as a solution to these issues. Histogram and morphological image processing methods are used for CT-scan images. The Improved Chicken Swarm Optimization (ICHO) technique is used to find the input image’s histogram threshold. The extracted areas are categorized using the Convolutional Neural Network method based on a feature vector. When infections are found, the CNN algorithm is used to categorize them as severe, moderate, or extremely severe using Support Vector Machine. To eliminate the noise from the test pictures for X-ray imaging, the Adapted Anisotropic Diffusion Filtering (A2DF) approach is used. Once the preprocessing is completed, features are extracted using an Image profile (IP) and Histogram-oriented gradient (HOG) to create a fused HOG and IP feature. Using the HYBRID method, the FHI characteristics are divided into 3 classes. When compared to SVM and CNN, the study provides the best accuracy, with scores of 94.6 for CT scan pictures and 95.6 for X-ray images.

Thermodynamics analysis for Darcy model induced by beating waves of cilia under Hall impact

This study conducts the thermodynamics analysis of creeping viscous nanofluid influenced by metachronical waves in an inclined ciliated tube and investigates the effects of magnetic field, porous medium and Hall current. Moreover, heat transport analysis is performed to consider the viscous dissipation phenomena. Thermal conductivity of the fluid is made more effective by adopting water-based titanium dioxide nanoparticles. [Formula: see text] is chosen as it has many remarkable implications in nanobio-sensing, medical implants, drug delivery and antibacterial fields. The governing equations are formulated which are converted into ordinary differential system by taking into account the similarity variables. The analytical solution are obtained for momentum, pressure gradient and energy profiles. It is found that the entropy generation is an increasing function of the Eckert number, Prandtl number and dimensionless temperature difference. Both Darcy and Eckert numbers enhance the energy of flow system. The fluid velocity drops quickly with increasing magnetic parameter.

Capacitively coupled contactless conductivity detection to account for system-induced gradient deformation in liquid chromatography

The time required for method development in gradient-elution liquid chromatography (LC) may be reduced by using an empirical modelling approach to describe and predict analyte retention and peak width. However, prediction accuracy is impaired by system-induced gradient deformation, which can be especially prominent for steep gradients. As the deformation is unique to each LC instrument, it needs to be corrected for if retention modelling for optimization and method transfer is to become generally applicable. Such a correction requires knowledge of the actual gradient profile. The latter has been measured using capacitively coupled “contactless” conductivity detection (C4D), featuring a low detection volume (approximately 0.05 μL) and compatibility with very high pressures (80 MPa or more). Several different solvent gradients, from water to acetonitrile, water to methanol, and acetonitrile to tetrahydrofuran, could be measured directly without the addition of a tracer component to the mobile phase, exemplifying the universal nature of the approach. Gradient profiles were found to be unique for each solvent combination, flowrate, and gradient duration. The profiles could be described by convoluting the programmed gradient with a weighted sum of two distribution functions. Knowledge of the exact profiles was used to improve the inter-system transferability of retention models for toluene, anthracene, phenol, emodin, sudan-I and several polystyrene standards.

Profiling of branched chain and straight chain saturated fatty acids by ultra-high performance liquid chromatography-mass spectrometry

Branched chain fatty acids (BCFAs) are one of the important sub categories of fatty acids (FAs) which have unique functions in nature. They are commonly analyzed by GC–MS after derivatization to methyl esters (FAMEs). On the other hand, there is a lack of isomer-selective LC-MS methods which allow the distinction of different isomers with wide coverage of carbon chain length. In this work, a systematic retention and isomer selectivity study on seven commercially available UHPLC columns (six polysaccharide columns Chiralpak IA-U, IB-U, IC-U, ID-U, IG-U and IH-U; one Acquity UPLC CSH C18 column) was performed. Various experimental factors were evaluated including column temperatures, gradient profiles and flow rates to elucidate their effects on the separation ability of homologous series of BCFAs with distinct chain lengths, different branching types and branching positions. In general, IG-U outperformed the other columns in terms of isomer selectivity especially for the short and medium-chain BCFA isomers while RP C18 showed good potential in terms of selectivity for long-chain BCFA isomers. Furthermore, after the evaluation of the chromatographic retention pattern on the various columns and method optimization, we report a methodology for untargeted isomer-selective BCFA profiling without precolumn derivatization with UHPLC-ESI-MS/MS by quadrupole-time-of-flight instrument with SWATH acquisition. The best method provides selectivity for constitutional isomers of BCFAs covering distinct chain length (C5-C20) with different branching types (methyl or ethyl) and branching positions (2Me, 3Me, 4Me, 6Me, anteiso and iso-BCFAs) with an optimized LC condition on Acquity UPLC CSH C18 column. Finally, the optimized method was applied for the BCFAs profiling in lipid extracts of Staphylococcus aureus samples. Besides, pooled human platelets and pooled human plasma were evaluated as mammalian samples for presence of BCFAs as well. The new method showed strong potential for BCFA profiling in bacterial samples including different isomers anteiso and iso-BCFAs, which could be a useful tool for related subdisciplines in metabolomics and lipidomics in particular in combination with electron-activated dissociation MS. Compared to GC, the presented isomer selective LC methods can be also of great utility for preparative purposes. Equivalent (carbon) chain length numbers were calculated for RP18 and Chiralpak IG-U and compared to those of FAMEs obtained by GC.

Computational Fluid Dynamics Analysis of a Hollow Fiber Membrane Module for Binary Gas Mixture

The membrane gas separation process has gained significant attention using the computational fluid dynamics (CFD) technique. This study considered the CFD method to find gas concentration profiles in a hollow fiber membrane (HFM) module to separate the binary gas mixture. The membrane was considered with a fiber thickness where each component’s mass fluxes could be obtained based on the local partial pressures, solubility, diffusion, and the membrane’s selectivity. COMSOL Multiphysics was used to solve the numerical solution at corresponding operating conditions and results were compared to experimental data. The two different mixtures, CO2/CH4 and N2/O2, were investigated to obtain concentration gradient and mass flux profiles of CO2 and O2 species in an axial direction. This study allows assessing the feed pressure’s impact on the HFM system’s overall performance. These results demonstrate that the increment in feed pressures decreased the membrane system’s separation performance. The impact of hollow fiber length indicates that increasing the active fiber length has a higher effective mass transfer region but dilutes the permeate-side purities of O2 (46% to 28%) and CO2 (93% to 73%). The results show that increasing inlet pressure and a higher concentration gradient resulted in higher flux through the membrane.

Examining effect of super-resolution on AVIRIS-NG data: A precursor to generation of large-scale urban material and natural cover maps

The two-phase Airborne Visible InfraRed Imaging Spectrometer – Next Generation (AVIRIS-NG) campaign over India has generated datasets of numerous natural and artificial surroundings with high signal-to-noise ratios and higher spatial and spectral consistencies. However, the first phase AVIRIS-NG datasets of urban areas have 8.1 m spatial resolution, which is insufficient for producing level-4 urban material and natural cover maps required to model Earth’s processes at the micro-scale or constantly monitor urban processes. The current work addresses this drawback by demonstrating a part of the proposed proof-of-concept approach on the AVIRIS-NG dataset of Ahmedabad, India, wherein super-resolution (SR) is proposed to enhance the hyperspectral image’s spatial resolution and preserve its rich spectral content at the targeted spatial scale before utilizing it for producing detailed urban land cover maps. A step-wise account of the SR process has been provided herein to aid the reader in reproducing these experiments. Super-resolved products generated using four SR algorithms have been compared and validated using a composite framework based on processing time, qualitative visual investigation of selected image patches and spectral profiles, re-interpretation of Wald’s reduced resolution protocol and full-reference image quality metrics. Results suggest the AVIRIS-NG dataset’s successful spectral and spatial fidelity at a larger spatial scale, albeit varying in each super-resolved output. Sparse regression and natural prior (SRP), and anchored neighbourhood regression (ANR) produce the best and poorest super-resolved outputs among the tested SR algorithms. Although gradient profile prior (GPP) generated super-resolved product is the second best, it is also the most computationally expensive algorithm. An additional yardstick in the form of a spectral similarity analysis of randomly selected unknown spectral signatures on super-resolved output against a reference spectral library has been proposed to ascertain spectral content preservation further before utilizing the super-resolved product for urban information extraction. This exercise’s findings reveal the presence of the target urban land cover feature at the unknown pixels with matching scores of greater than 0.5 in both best and worst super-resolved products, thereby advocating the extension of the proposed proof-of-concept to recently launched spaceborne hyperspectral missions’ datasets.

Transient velocity field prediction and uncertainty quantification of pump-jet propulsor using variational Bayesian neural networks

The study provides a fast and accurate variational Bayesian convolution neural network (VB–CNN) framework to obtain the pump-jet propulsor (PJP) transient velocity field. In practical engineering or experiments, it can obtain the transient velocity field of PJP only by discrete pressure points for different times conditions. Compared with the computational fluid dynamics (CFD) method, it can save a lot of computing time and computing resources. This study also uses the VB-CNN method to solve the problem of poor performance of CNN in small data-sets, VB-CNN method can consider the prior knowledge of PJP transient data to improve the prediction accuracy. The predicted values, errors and variances of the PJP transient wake velocity field and stator domain at different times and different rotating speed conditions are investigated. The uncertainty of the transient flow field is analyzed using 95% confidence intervals. It also uses GPU technology to improve training speed. The research results show that VB-CNN and CNN methods can better predict the PJP transient flow field, while the VB-CNN method has higher accuracy than CNN method. The velocity gradient and velocity profile of the PJP transient velocity field are predicted accurately, the predicted velocity field is in good agreement with the CFD flow field. All linear correlation coefficients exceeds 0.99. The value of structural similarity index (SSIM) at different times exceeds 0.95.

Predicting Maximum Effective Temperatures and Thermal Gradients for Steel I-Girder in Canadian Climate Regions

The constant fluctuation of thermal loads on steel members, especially during construction, causes non-uniform distributions of temperatures, resulting in possible constructional and structural defects leading to unfavorable thermally induced responses and potential safety risks. The Canadian Highway Bridge Design Code (CHBDC) provides one thermal gradient variation profile without accounting for the differences in the geometrical parameters of the steel members and the variations in the climate regions of Canada. Therefore, in this study, three-dimensional finite element (FE) thermal simulations were conducted to investigate the maximum effective temperatures and positive vertical thermal gradients for different Canadian climate regions. Parametric studies were performed to conduct the FE thermal analysis using the thermal model validated in ANSYS. The comprehensive study results showed that Canada could be divided into two main zones for vertical thermal gradient calculations, meaning that one stationary thermal gradient profile cannot be applicable to all climate regions of Canada, as recommended by the CHBDC. Based on the FE thermal analysis results, empirical formulas as a function of the significant parameters were proposed to predict the maximum effective temperature and thermal gradient variations of the steel I-girder. The predicted maximum effective temperature and thermal gradient variation values were found to be highly correlated with the FE values with coefficients of determination R2 of approximately 0.97 and 0.98, respectively.

Flexible combinatorial ionic/electronic thermoelectric converters to efficiently harvest heat from both temperature gradient and temperature fluctuation

It is of great significance to develop novel heat-harvesting technology due to abundant waste heat on earth. Although thermoelectric generators (TEGs) based on the Seebeck effect under temperature gradient has been studied for more than 200 years, their thermoelectric (TE) performance is still not good enough for large-scale practical application. Ionic TE materials can exhibit much higher thermovoltage than electronic conductors, but they can be used to harvest heat merely from temperature fluctuation. In order to take the advantages of these two types of TE materials, we developed flexible combinatorial TE converters (CTECs) with an ionic TE capacitor (ITEC) made of an ionogel and a TEG consisted of poly (3,4-ethylenedioxythiophene):polystyrenesulfonate (PEDOT:PSS), which were connected in parallel, that is, the electrodes of the ITEC and TEG at the hot end are wired together, while those at the cold end are connected. These CTECs can harvest heat from both temperature gradient by the TEG and temperature fluctuation by the ITEC. Their TE performances are sensitive to the factors like heating/cooling rates, temperature gradient profile and internal resistance of the TEG. The specific average power supplied by the CTEC can be up to 4.7 times as that of the control TEG with PEDOT:PSS. Moreover, the TE performance can be further improved by combining an ITEC with a TEG consisted of both p- and n-type legs in series, which can generate a specific average power as 5.8 times as the CTECs with the TEG of only one p-type leg.

Hybrid PIC–fluid simulations for fast electron transport in a silicon target

Ultra-intense laser-driven fast electron beam propagation in a silicon target is studied by three-dimensional hybrid particle-in-cell–fluid simulations. It is found that the transverse spatial profile of the fast electron beam has a significant influence on the propagation of the fast electrons. In the case of a steep spatial profile (e.g., a super-Gaussian profile), a tight fast electron beam is produced, and this excites more intense resistive magnetic fields, which pinch the electron beam strongly, leading to strong filamentation of the beam. By contrast, as the gradient of the spatial profile becomes more gentle (e.g., in the case of a Lorentzian profile), the resistive magnetic field and filamentation become weaker. This indicates that fast electron propagation in a solid target can be controlled by modulating the spatial gradient of the laser pulse edge.

Damage Model and the Influence Factors of Mitigation Engineering against Glacial Debris Flow in the Parlung River Basin, SE Tibetan Plateau

Understanding the damage mechanism of glacial debris flow mitigation systems is crucial for the risk prevention and assessment of the 200 km traffic corridor in the Southeast of the Tibetan Plateau, where the Sichuan-Tibet railway and expressway have been planned. Based on the phenomena, position and residual efficiency of damaged engineering, our analysis of satellite imagery and field investigation in multitype spatial reveals the damage types and influencing factors of glacial debris flow mitigation engineering. An evaluation model which can be used to estimate the engineering damage grade is established by using the relationship between mono engineering works and mitigation systems. In the new model, the engineering damage is divided into five grades: undamaged, slightly damaged, relatively damaged, seriously damaged, and totally damaged. For glacial debris flow in the Parlung river basin, the five grades of damage of mitigation works account for 8.70%, 34.78%, 21.74%, 13.04% and 21.74%, respectively. Furthermore, the soil source type and channel profile gradient are the key factors in engineering damage. Design defect of profile gradient is the controlling factor of damage in drainage channel engineering. Based on those results, an engineering damage model is established, which can provide an important reference for risk reduction and prevention of hazards due to the increasing development of traffic engineering.

Entropy generation phenomenon for ciliated pumping flow of aluminum oxide and silver nanoparticles with Hall device significances

The study of hybrid nanomaterials subject to the magnetic force and Hall device applications presents many novel applications in the chemical engineering and biomedical domains. This study theoretically investigates the physical features of two-dimensional flow of hybrid fluid via ciliated pumping through a micro-tube. This investigation deals with the performance of aluminum oxide and silver nanoparticles in viscous (water) flow enclosed in a complex ciliated tube. Physical effects of Hartmann number, Hall parameter, volumetric concentration of nanoparticles, ciliated length parameter, Brinkman number, and temperature difference parameter. The impacts of embedded parameters in the velocity profile, pressure gradient, heat transfer, entropy generation, and Bejan number are explored. The larger strength of Hall parameter overcomes the physical impacts of the magnetic device. The absorption of nanoparticles has a remarkable role in the flow features. Additionally, the ciliated length parameter has a significant role in the enhancement of the velocity profile, pressure gradient, and temperature profile. The comprehensive investigation has dynamic applications in the thermos-electric cells, transportation of biological liquids through uniform and non-uniform vessels, nanotechnologies, chemical processes, and mobility of the red blood cells.

Sedimentation of magnetorheological fluids measured using an automated vertical axis inductance monitoring system

Stable magnetorheological fluids (MRFs) are inevitably required to develop reliable MRF-based applications. Suspension stability of MRFs can be studied using an automated vertical axis inductance monitoring system (AVAIMS), where an inductance sensor is translated vertically along a column of MRF to measure particle concentration as a function of column height and time. The AVAIMS allows for tracking the particle concentration discontinuities due to the sedimentation of MRFs including the mud-line, the gel-line, and the cake-line. The sedimentation progress of MRFs can be evaluated by analyzing these boundaries. In this study, the AVAIMS design was improved to better identify the sedimentation zone boundaries by using an optimized inductance sensor that measures the concentration gradient as a function of time. The inductance sensor design, material selection, and geometry were optimized to improve the sensor sensitivity. The calibration curve of the sensor was obtained by measuring samples with different particle volume fractions. The sensor design was validated by examining an MRF sample with a particle concentration of 20% volume fraction for seven consecutive days. These tests show the effectiveness of the AVAIMS optimized to better localize the sedimentation zone boundaries using the concentration gradient profile method.

On the Ratio of Full-Resonance to Square-Root-Impedance Amplifications for Shear-Wave Velocity Profiles That Are a Continuous Function of Depth

ABSTRACT Amplifications of seismic waves traveling upward through a continuous, interface-free velocity profile are consistently smaller when computed using the square-root-impedance (SRI) method than when computed using full-resonance (FR) calculations. This was found for a wide range of velocity profiles. For realistic profiles, for which the gradient of velocity decreases with depth, the differences are not large, with the ratio of FR/SRI amplifications ranging from about 1.05 to 1.3. Comparisons of the amplifications from a continuous velocity profile with those from approximations to that profile using a stack of constant-velocity layers give some support to the hypothesis that the difference between FR and SRI amplifications for gradient profiles is because the former is controlled by the ratio of seismic impedances, whereas the latter is based on the square root of the seismic impedance ratios. This implies that gradient profiles will always have FR amplifications greater than SRI amplifications. A model-independent, easy-to-implement modification of the SRI amplifications is proposed that shows promise in bringing the SRI amplifications closer to the FR amplifications.