Actual Gradient Research Articles

Enhancing the effective temperature model for typical UO2 fuel in criticality calculations

In current neutron transport equation calculations, a common strategy to enhance computational efficiency is approximating the fuel temperature distribution as uniform. This approach defines a uniform temperature, known as the effective temperature (Teff), which preserves the reactivity of the model corresponding to the actual temperature gradient. Based on the actual temperature distributions within the UO2 pellet of the AFA-3G fuel, the present study introduces a weighting coefficient for the volume-averaged temperature to extend the Chabert-Santamarina model. This extended model, as a generalized formulation of both the Rowlands and Chabert-Santamarina models, demonstrates superior performance to the current five effective temperature models in terms of deviation fluctuation and central values. This conclusion is verified through independent simulations, with OpenMC employing the Windowed Multi-Pole (WMP) database and RMC utilizing point-wise ACE library or data derived from Gaussian-Hermite quadrature for online Doppler broadening. Therefore, the present refined effective model enhances the accuracy of effective temperature and the resulting reactivity. Furthermore, the deviation of using a uniform effective temperature across the assembly remains within the acceptable uncertainty range (3 σ).

Target Tracking Two Degrees of Freedom State Feedback Control for Continuous Flow Microfluidic Chips Temperature Controller

Microfluidic chips represent a cutting-edge technology for manipulating fluids within micrometer-scale spaces and are gradually becoming a new favorite platform in life science research. Precise and fast zonal temperature control is essential for accelerating biological experiments. However, current multi-channel temperature controllers typically rely on multiple channel sets to achieve single set-point control, which results in discrepancies between the fluid temperature distribution and sensor temperature due to the distributed temperature field in the fluid channel. To estimate the actual temperature and implement gradient temperature control, this paper introduces an extension of the target tracking (TT) two degrees of freedom (2DOF) state feedback control (SFC) method, followed by a presentation of simulation and experimental results. Through comparisons with an enhanced PID system in both simulation and experimentation, the paper demonstrates an 8.96% reduction in the maximum temperature difference across different regions and a 27.89% decrease in the time taken to reach various temperatures. This solution effectively addresses the existing challenges in temperature control for microfluidic chips, offering a more precise and stable control within the desired temperature range.

Actor Prioritized Experience Replay (Abstract Reprint)

A widely-studied deep reinforcement learning (RL) technique known as Prioritized Experience Replay (PER) allows agents to learn from transitions sampled with non-uniform probability proportional to their temporal-difference (TD) error. Although it has been shown that PER is one of the most crucial components for the overall performance of deep RL methods in discrete action domains, many empirical studies indicate that it considerably underperforms off-policy actor-critic algorithms. We theoretically show that actor networks cannot be effectively trained with transitions that have large TD errors. As a result, the approximate policy gradient computed under the Q-network diverges from the actual gradient computed under the optimal Q-function. Motivated by this, we introduce a novel experience replay sampling framework for actor-critic methods, which also regards issues with stability and recent findings behind the poor empirical performance of PER. The introduced algorithm suggests a new branch of improvements to PER and schedules effective and efficient training for both actor and critic networks. An extensive set of experiments verifies our theoretical findings, showing that our method outperforms competing approaches and achieves state-of-the-art results over the standard off-policy actor-critic algorithms.

A metric for quantitative evaluation of glioma margin changes in magnetic resonance imaging.

Gliomas differ from meningiomas in their margins, most of which are not separated from the surrounding tissue by a distinct interface. To characterize the margins of gliomas quantitatively based on the margin sharpness coefficient (MSC) is significant for clinical judgment and invasive analysis of gliomas. The data for this study used magnetic resonance image (MRI) data from 67 local patients and 15 open patients to quantify the intensity of changes in the glioma margins of the brain using MSC. The accuracy of MSC was assessed by consistency analysis and Bland-Altman test analysis, as well as invasive correlations using receiver operating characteristic (ROC) and Spearman correlation coefficients for subjects. In grading the tumors, the mean MSC values were significantly lower for high-grade gliomas (HGG) than for low-grade gliomas (LGG). The concordance correlation between the measured gradient and the actual gradient was high (HGG: 0.981; LGG: 0.993), and the Bland-Altman mean difference at the 95% confidence interval (HGG: -0.576; LGG: 0.254) and the limits of concordance (HGG: 5.580; LGG: 5.436) indicated no statistical difference. The correlation between MSC and invasion based on the margins of gliomas showed an AUC of 0.903 and 0.911 for HGG and LGG, respectively. The mean Spearman correlation coefficient of the MSC versus the actual distance of invasion was -0.631 in gliomas. The relatively low MSC on the blurred margins and irregular shape of gliomas may help in benign-malignant differentiation and invasion prediction of gliomas and has potential application for clinical judgment.

On the Role of ZrN Particles in the Microstructural Development in a Beta Titanium Alloy Processed by Laser Powder Bed Fusion.

Additive manufacturing of titanium alloys usually ends up with large columnar grains due to the steep thermal gradients within melt pools during solidification. In this study, ZrN particles were added into a beta titanium alloy, Ti-10V-2Fe-3Al, with the aim of promoting columnar-to-equiaxed grain transition during laser bed powder fusion (L-PBF). It was found that the addition of ZrN leads to the development of alternate layers of equiaxed grains and refined columnar grains, which is in sharp contrast to the dominant large columnar grains formed in the pure L-PBF-processed titanium alloy. An investigation on single laser melted tracks revealed that the sample with added ZrN showed fine equiaxed grains in the upper regions of solidified melt pools and columnar grains in the lower regions, whereas the solidified melt pools of the pure titanium alloy were dominated by large columnar grains due to epitaxial growth from the previous layer. The formation of equiaxed grains in the former sample is attributed to multiple factors including an increased gradient of liquidus temperature due to the solution of N and a reduced actual melt temperature gradient due to the melting of high-melting-point ZrN particles, which would have expanded constitutional undercooling, a grain growth restriction effect induced by the segregation of N along grain boundaries and the accumulation of unmelted ZrN particles in the upper regions of melt pools. The addition of ZrN also resulted in significant α precipitation, which showed strong variant selection and was found to be driven by laser reheating and the N solution in the matrix.

BART: A transferable liquid chromatography retention time library for bile acids

Identification of unknown bile acids, especially the distinguishment between isomers, requires retention times of a large number of reference standards, which are often not commercially available. Meanwhile, published retention information cannot be directly transferred across labs due to the differences between liquid chromatography (LC) systems, such as different extra column volume and dwell volume. To improve this situation, a transferrable retention time library for bile acids named BART was developed. BART was composed of isocratic retention models of 272 bile acids and a software tool to predict their gradient retention times on various LC systems. The isocratic retention times of bile acids were acquired on a Waters BEH C18 column with mobile phases of acidic ammonium acetate buffer and acetonitrile, and fit to the quadratic solvent strength model (QSSM). Segmented linear gradient retention times were calculated with holdup time (t0), dwell time (tD) and actual gradient profile corrected using 21 bile acid calibration standards. In addition to the reference system where the isocratic retention times were acquired, this approach has been validated on four other LC-MS systems in four labs with two gradient methods. Average root mean square errors (RMSE) between predicted and experimental retention times were 0.052 and 0.054 min for the two gradients tested, which were 9-fold more accurate than referring to a static retention time library. The library is freely available at https://bafinder.github.io/.

ASSESSMENT OF STEC ESTIMATION QUALITY USING GNSS PPP FIXED

Abstract. GNSS (Global Navigation Satellite System) data can be used for geodetic remote sensing, particularly for monitoring the ionosphere in the context of Space Weather. One of the important parameters derived from GNSS measurements for ionospheric analysis is the Slant Total Electron Content (STEC). By utilizing GNSS data from multiple frequencies or even a single frequency, the STEC can be computed using an appropriated linear combination, like geometry free. However, when computing an ionospheric gradient between two IPP (Ionospheric Pierce Point) from the same satellite, the precision of the STEC estimate can become a limiting factor. In some cases, the uncertainty in the estimate may be greater than the actual gradient value itself. This poses challenges, especially for augmentation systems like GBAS (Ground Based Augmentation System), where accurate ionospheric gradients are crucial. An alternative approach to improve these limitations is to estimate the STEC using a different approach, like Precise Point Positioning (PPP). For such case, the coordinates of the GNSS stations are constrained to known values (PPP-Fixed), while other parameters such as clock biases, tropospheric delays, and ionospheric delays (including STEC) can be estimated. The results of an experiment carried out to assess the quality of STEC for such application are presented and have shown good results. Ionospheric gradients are agreed in the mm level.

Temperature gradient of ballastless track in large daily temperature difference region and its influence on dynamic responses of vehicle-track-bridge system

Due to the large daily temperature difference on the ultra-high altitude plateau of China, the actual vertical temperature gradient (TG) of ballastless track may exceed the design value in the Code. The temperature monitoring platform of the double-block ballastless track was established to obtain the temperature distribution characteristics of track. The finite element model of the temperature field of the track is developed to study the warping deformation of track, and then the influence of TG on the dynamic responses of the vehicle-track-bridge system (VTBS) are investigated. The results show that the maximum positive temperature gradient (PTG) and negative temperature gradient (NTG) of the track bed slab are 88.875 ℃/m and − 47.159 ℃/m, respectively, and the latter exceeds the design value in the Code. The dynamic responses are positively correlated with the TG, and the influence of the NTG is more significant. The dynamic response of the rail is most sensitive to the TG.

Smooth Lagrangian Crack Band Model Based on Spress-Sprain Relation and Lagrange Multiplier Constraint of Displacement Gradient

Abstract A preceding 2023 study argued that the resistance of a heterogeneous material to the curvature of the displacement field is the most physically realistic localization limiter for softening damage. The curvature was characterized by the second gradient of the displacement vector field, which includes the material rotation gradient, and was named the “sprain” tensor, while the term “spress” is here proposed as the force variable work-conjugate to “sprain.” The partial derivatives of the associated sprain energy density yielded in the preceeding study, sets of curvature resisting self-equilibrated nodal sprain forces. However, the fact that the sprain forces had to be applied on the adjacent nodes of a finite element greatly complicated the programming and extended the simulation time in a commercial code such as abaqus by almost two orders of magnitude. In the present model, Smooth Lagrangian Crack Band Model (slCBM), these computational obstacles are here overcome by using finite elements with linear shape functions for both the displacement vector and for an approximate displacement gradient tensor. A crucial feature is that the nodal values of the approximate gradient tensor are shared by adjacent finite elements. The actual displacement gradient tensor calculated from the nodal displacement vectors is constrained to the approximate displacement gradient tensor by means of a Lagrange multiplier tensor, either one for each element or one for each node. The gradient tensor of the approximate gradient tensor then represents the approximate third-order displacement curvature tensor, or Hessian of the displacement field. Importantly, the Lagrange multiplier behaves as an externally applied generalized moment density that, similar to gravity, does not affect the total strain-plus-sprain energy density of material. The Helmholtz free energy of the finite element and its associated stiffness matrix are formulated and implemented in a user’s element of abaqus. The conditions of stationary values of the total free energy of the structure with respect to the nodal degrees-of-freedom yield the set of equilibrium equations of the structure for each loading step. One- and two-dimensional examples of crack growth in fracture specimens are given. It is demonstrated that the simulation results of the three-point bend test are independent of the orientation of a regular square mesh, capture the width variation of the crack band, the damage strain profile across the band, and converge as the finite element mesh is refined.

Actor Prioritized Experience Replay

A widely-studied deep reinforcement learning (RL) technique known as Prioritized Experience Replay (PER) allows agents to learn from transitions sampled with non-uniform probability proportional to their temporal-difference (TD) error. Although it has been shown that PER is one of the most crucial components for the overall performance of deep RL methods in discrete action domains, many empirical studies indicate that it considerably underperforms off-policy actor-critic algorithms. We theoretically show that actor networks cannot be effectively trained with transitions that have large TD errors. As a result, the approximate policy gradient computed under the Q-network diverges from the actual gradient computed under the optimal Q-function. Motivated by this, we introduce a novel experience replay sampling framework for actor-critic methods, which also regards issues with stability and recent findings behind the poor empirical performance of PER. The introduced algorithm suggests a new branch of improvements to PER and schedules effective and efficient training for both actor and critic networks. An extensive set of experiments verifies our theoretical findings, showing that our method outperforms competing approaches and achieves state-of-the-art results over the standard off-policy actor-critic algorithms.

Arterial spin labeling MRI using spiral acquisitions and concurrent field monitoring

Perfusion MRI based on arterial spin labeling (ASL) has intrinsically very low signal-to-noise ratio (SNR). Signal acquisition at shorter echo times (TE) is necessary to boost the SNR of the ASL images. Spiral trajectories provide substantially shorter TE yielding increased SNR and are among the fastest k-space sampling schemes to encode a given field of view and resolution. Moreover, they provide approximately isotropic point-spread functions and inherent refocusing of motion- and flow-induced phase errors. However, the efficiency of the spiral acquisitions in ASL-MRI has been limited because these advantages are counterbalanced by practical technical challenges. This is because spiral acquisitions are highly sensitive to encoding deficiencies such as static off-resonance in the main magnetic field manifested as blurring artifacts in the image. Moreover, deviation of the gradient fields from the nominal waveforms due to the imperfection of the employed hardware critically limits the practical utilization of spiral trajectories. In this work, I provide single- and multiple-shot spiral ASL images that are robust against typical spiral encoding drawbacks enabled by deploying a comprehensive signal model involving static off-resonance and coil sensitivity maps and actual B0 and gradient field dynamics up to third order in space. The spiral ASL signal acquisition was concurrently monitored using a 3rd order dynamic field camera based on NMR field probes. The reconstructed ASL images at 3 mm and 2 mm in-plane resolution associating with the monitored field dynamics and the static off-resonances exhibited strongly reduced blurring- and aliasing artifacts and distortion. Concurrent field monitoring also enables to account for quasi-static B0 drifts by encompassing the parametric input data with consistent encoding geometry and physiological field fluctuations. In conclusion, concurrent field monitoring in spiral ASL acquisition largely overcomes traditional vulnerability of spiral trajectories in practice providing high quality ASL images with increased SNR, speed and motion robustness.

Reflector Design for Simulating Varying Heat Flux on Nose Cap of a Re-entry Module

For thermo-structural tests of a nose cap for a re-entry module accurate simulation of time and space varying heat flux is essential for generating the actual temperature gradients as expected in flight. Temperature gradient simulations along with simulated structural loads are essential for testing the structural integrity of the C-C nose cap.
 Contoured reflectors are essential for obtaining spatial distribution of incident heat flux. For realizing the reflector for thermo-structural testing, it is important to design radiation reflectors that will generate required heat flux envelope along the nose cap geometry. Reflector design for simulating varying heat flux on re-entry nose cap has been carried out by estimating view factor between nose cap and for different geometries of reflector.
 Design could be accomplished by making use of view factor algebra. Elemental heat flux values were validated with literature data and methodology for reflector heat flux design was validated against test data. With single flat reflectors and multiple flat reflectors, the required spatial variation of incident radiative heat flux could be realized efficiently. View factor variation is compared with heat flux variation along the nose cap. It is recommended practice to have multiple reflectors for simulating required varying heat flux on the nose cap due to better flexibility.

Study of a vertical gravity gradient at the MUT area

Any object on the globe, in addition to the gravitational force, is affected by the force associated with the rotation of the Earth, i.e., the centrifugal force, which together define the force of gravity. Due to various factors, both external (the influence of other celestial bodies) and internal (the inhomogeneous internal structure of the Earth), the gravity depends on the location and time of observation. The study on gravity is made possible by using extremely sensitive measuring devices called gravimeters, which are a branch of physical geodesy called geodetic gravimetry. Geodetic gravimetry is widely used in geodesy to study the shape of the geoid and the realisation of gravimetric control networks or in geophysics to detect mineral deposits, underground watercourses or caves. However, in order to obtain reliable results, it is necessary not only to measure the gravity accurately, but also to reduce these measurements adequately. This is possible by determining, among other things, the vertical gravity gradients (VGG), which are used to reduce the measured gravity values to any reference level. In our research, we focused on analysing the change in the value of VGGs in the closed area of the Military University of Technology (MUT). We used 33 points of the existing vertical and horizontal networks of the MUT for measurements. We performed the observations using ZLS Burris model B-67 spring gravimeter at several heights in the range of 0.1 m to 1.3 m using a specially constructed tripod. We showed that the values of the vertical gradients vary over the selected area from ‒0.2534 mGal/m to ‒0.3917 mGal/m. The obtained results show consistency with the spatial distribution of changes of the topography of the terrain, the density of the Earth’s crust, and the type of geological formations present beneath the surface. In the study, we also showed the relevance of using the actual (measured) values of gradients to analyse geoid-to-quasigeoid separation. We have shown that taking the actual gradient values instead of their average (or modelled) values results in deviations in modelling the separation of both geodetic reference surfaces of up to 2 mm in the study area.Keywords: gravity, vertical gravity gradient, gravimetry, geoid-quasigeoid separation

Effect of composition gradient design on microstructure and mechanical properties of dual-wire plasma arc additively manufactured 316L/IN625 functionally graded materials

Wire and arc additive manufacturing (WAAM) is a promising technology for the preparation of refractory metal functional gradient materials (FGMs) due to its high material utilization, high deposition efficiency and ability to create large-sized parts. In the present work, 316L/IN625 FGM with chemical composition gradients of 25 wt% and 100 wt% were fabricated using dual-wire plasma arc additive manufacturing (DW-PAAM) by changing the wire feeding speeds (WFSs) layer by layer. The phase evolution, microstructure, chemical composition and mechanical properties of the FGM were analyzed. The results demonstrated that the microstructure in all regions was predominantly the austenite phase, and no cracks or defects were observed. The microstructure of the 100 wt% 316L zone was composed of the austenite phase (face-centered cubic, FCC) and a small amount of ferrite phase (body-centered cubic, BCC), whereas mainly FCC structure was observed in the other chemical composition regions. There was a certain error between the actual composition gradient and the designed gradient. The microhardness transition of S1 was smoother and wider, while the tensile test results of S2 were better. In addition, the position of the tensile fracture was different for S1 and S2. In conclusion, the DW-PAAM process shows great potential for manufacturing FGM with desirable properties for various industrial applications. Further studies are warranted to optimize process parameters and develop new design strategies to enhance the performance of FGM in various industrial applications.

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.

Adaptive slope and CPSO-based energy management strategy of hybrid energy storage system for electric logistics vehicles

Energy management strategy play a crucial role in the optimal control of energy in pure electric logistics vehicles with hybrid energy storage system (HESS). Aiming at the problem that the energy management strategy of HESS cannot be reasonably allocated according to different slope conditions, this paper adds the road slope coefficient to the input of fuzzy control and designs a fuzzy controller that automatically adjusts the output power of ultracapacitor based on different road slope coefficients. Then, a chaotic particle swarm optimization (CPSO) method is used to optimize the designed fuzzy controller. Finally, the simulation test is carried out under urban dynamometer driving schedule (UDDS) urban road driving cycle by using Matlab/Simulink. The results show that the improved control strategy can increase the energy utilization by 3.63\% and reduce the battery power consumption by 3.97%. Furthermore, the proposed strategy can improve 30.66% energy utilization and 18.70% ultracapacitor power storage at the downhill situation, and can reduce the energy consumption of the whole vehicle by 5.23%, the average current by 6.19%, and the lithium-ion battery power consumption by 2.20% under the actual urban road gradient.

How do the skin barrier and microbiome adapt to the extra-uterine environment after birth? Implications for the clinical practice.

The multiple protective functions of the skin derive from the interactions between epithelial skin and immune cells as well as the commensal microbiota. Developed in the last trimester of intra-uterine life, the skin barrier adapts dynamically after birth. Specific differences in the structure and physiology have been disclosed between infant and adult skin. The stratum corneum of infants is thinner and structured by thicker corneocytes with a more anisotropic surface in comparison to adult skin. Lower levels of the natural moisturizing factor and its constituents, together with the increased protease activity in the epidermis result in dry baby skin and ongoing adaptation of the desquamation to the extra-uterine environment. Infant epidermis is characterized by an accelerated proliferation rate and clinically competent permeability barrier in term neonates, despite the higher baseline values of transepidermal water loss in infants. The skin surface of newborns is less acidic, which could increase susceptibility to diaper and atopic dermatitis. Immediately after birth, skin is colonized by commensal bacteria-a process dependent on the mode of delivery and of major importance for the maturation of the immune system. Skin bacterial diversity and dysbiosis have been related to different pathology such as atopic and seborrheic dermatitis. This paper focuses on the ongoing structural, functional and biochemical adaptation of the human skin barrier after birth. We discuss the interactions on the 'skin barrier/ microbiota/ immune system' axis and their role in the development of competent functional integrity of the epidermal barrier.

Shear and filtration strength of foundation of channel type hydropower plant building

The purpose of the study was to analyze the foundation's filtration strength and the HPP building's shear stability after 38 years of operation as part of the Tuyamuyun hydroelectric complex on the Amudarya River. The analysis was carried out based on field data obtained with the help of 16 piezometers installed in two alignments within the block of the HPP building and vertical drainages in the grassland. The constructed graphs of water pressure fluctuations in piezometers coincide with the nature of the change in the water level in the upper and lower pools. The actual gradients did not exceed the allowable gradient for the shaly sand interlayer and limestone bedding fracture filler. Comparison of the maximum natural gradients and those calculated from model studies using electrohydrodynamic analogies. The stability of the HPP building block is estimated by the maximum piezometric pressure and compared with analytical calculations, and the safety factor is 2.303. In this way, the base's filtration strength and the structure's shear stability are ensured in the entire range of changes in the operating mode of the pressure front of the HPP building block.

Model Based Prediction of the Heat Affected Zone in a Steel Workpiece Induced by an EDM Single Discharge

Setting a determined microstructure within the rim zone of a manufactured workpiece without cost-intensive trial and error experiments is essential to meet the increasing requirements of the industry. The most promising approach to predict the final functional properties is to simulate the microstructure evolution and to build an inverse approach of the manufacturing process. Thermal load based microstructure evolution models with an artificial initial structure and temperature gradients up to 1·106 K/s have been published in previous works presented by the authors. In this work, an existing heat transfer model was extended to predict the actual temperature gradients for a single discharge during electrical discharge machining (EDM). These calculated temperature gradients were then used to simulate the microstructure evolution of a 42CrMo4 steel. The initial structure was derived from a cross sectional SEM image. Therefore, the presented model is able to simulate the actual microstructure evolution within the heat affected zone of an EDM'ed workpiece.

An experimental crystallization of the Macusani obsidian in a thermal gradient with applications to lithium-rich granitic pegmatites

Abstract Drilled cores of Macusani green obsidian pebbles from Peru were hydrated and melted above their liquidus temperatures at 200 MPa to a single column ~4 cm in length and then undercooled in a thermal gradient >150 °C along the length of the cores. Despite thousands of hours at subliquidus temperatures, the crystallinity of the products ranged from ~30 to ~5 vol%. Mineral assemblages varied along the length of the cores but not in relation to the thermal gradients in all cases. Oscillations in the abundances of plagioclase, K-feldspar, and quartz were observed across the crystallization fronts and along the lengths of the cores. The originally homogeneous melts became heterogeneous in response to crystallization and to thermal gradients. Chemical gradients in the glasses included sharp boundary layer pile-up of F and B adjacent to the crystallization fronts, as well as linear gradients among several of the elements spanning the entire lengths of the melt columns. Values of molar K/(K+Na) in the glasses, plotted as K*, varied positively with Si, inversely with Al and F, and positively with the domains of K-feldspar that formed at maximum distance from the plagioclase-rich regions. Overall, the results are marked by sharply bounded textural domains, by the spatial segregation of mineral assemblages, by oscillations in mineral assemblages at multiple scales, and by monomineralic crystal aggregates that are hallmarks of pegmatite bodies. Temperatures recorded by feldspars closely approached the actual temperature gradient down to ~500 °C, and the solvus on the alkali feldspar join has been delineated for the first time by the simultaneous crystallization of feldspars from an undercooled melt.