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The application of the category-partition method to the test design phase of hardware, software, or system test development is discussed. The method provides a formal framework for reducing the total number of possible test cases to a minimum logical subset for effective testing. An automatic tool and a formal language were developed to implement the method and produce the specification of test cases.
This paper presents a systematic thermodynamic analysis of the effects of temperature and composition on olivine/melt and low-Ca pyroxene/melt partitioning. Experiments were conducted in several synthetic basalts with a wide range of Fe/Mg, determining partition coefficients for Eu, Ca, Mn, Fe, Ni, Sm, Cd, Y, Yb, Sc, Al, Zr, and Ti and modeling accurately the changes in free energy for trace element exchange between crystal and melt as functions of the trace element size and charge. On the basis of this model, partition coefficients for olivine/melt and low-Ca pyroxene/melt can be predicted for a wide range of elements over a variety of basaltic bulk compositions and temperatures. Moreover, variations in partition coeffeicients during crystallization or melting can be modeled on the basis of changes in temperature and major element chemistry.
Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V emb , determined via functional optimization. The optimized effective potential (OEP) process used to optimize V emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO–DFET, namely, H 2 dissociative adsorption on a Cu(111) surface, H 2 O adsorption on a Pt(111) surface, and aqueous [Ca 2+ –SO 4 2– ] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10–70 meV error relative to the original exact-derivative (ED) approach) while accelerating V emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V emb outside the core regions are small, explaining the exceptional agreement between the two approaches. Finally, we anticipate that this more efficient PVO–DFET approximation will be useful whenever computation of V emb is much more expensive than subsequent embedded high-level electron correlation calculations.
Abstract MF-LOGP, a new method for determining a single component octanol–water partition coefficients ( $$LogP$$ LogP ) is presented which uses molecular formula as the only input. Octanol–water partition coefficients are useful in many applications, ranging from environmental fate and drug delivery. Currently, partition coefficients are either experimentally measured or predicted as a function of structural fragments, topological descriptors, or thermodynamic properties known or calculated from precise molecular structures. The MF-LOGP method presented here differs from classical methods as it does not require any structural information and uses molecular formula as the sole model input. MF-LOGP is therefore useful for situations in which the structure is unknown or where the use of a low dimensional, easily automatable, and computationally inexpensive calculations is required. MF-LOGP is a random forest algorithm that is trained and tested on 15,377 data points, using 10 features derived from the molecular formula to make $$LogP$$ LogP predictions. Using an independent validation set of 2713 data points, MF-LOGP was found to have an average $$RMSE$$ RMSE = 0.77 ± 0.007, $$MAE$$ MAE = 0.52 ± 0.003, and $${R}^{2}$$ R 2 = 0.83 ± 0.003. This performance fell within the spectrum of performances reported in the published literature for conventional higher dimensional models ( $$RMSE$$ RMSE = 0.42–1.54, $$MAE$$ MAE = 0.09–1.07, and $${R}^{2}$$ R 2 = 0.32–0.95). Compared with existing models, MF-LOGP requires a maximum of ten features and no structural information, thereby providing a practical and yet predictive tool. The development of MF-LOGP provides the groundwork for development of more physical prediction models leveraging big data analytical methods or complex multicomponent mixtures. Graphical Abstract
An upper bound on the rate-distortion function for discrete ergodic sources with memory is developed by partitioning the source sample space into a finite number of disjoint subsets and bounding the rates for each subset. The bound depends only on the mean vectors and covariance matrices for the subsets and is easy to compute. It is tighter than the Gaussian bound for sources that exhibit clustering of either the values or covariances of successive source outputs. The bound is evaluated for a certain class of pictorial data using both one-dimensional and two-dimensional blocks of picture elements. Two-dimensional blocks yield a tighter bound than one-dimensional blocks; both result in a significantly tighter bound than the Gaussian bound.
The partitioning of major and minor elements between augite and melt was determined as a function of cooling rate for two high-titanium basalt compositions. The results of this study of lunar rock systems 10017 and 75055 were compared with the results of other kinetic studies of augite-liquid partitioning in other rock systems. It was found that the partitioning of major elements (i.e., Ca, Fe, Mg) is essentially rate independent and is insensitive to bulk rock composition and to the nature and order of appearance of coexisting phases for cooling rates of less than 100 C/hr. The partitioning behavior of minor elements (i.e., Al, Cr, Ti) for the same range of cooling rates is complex, being dependent on cooling rate and bulk rock composition. Consideration of these factors is important when augite chemistry and/or partitioning behavior are used in modeling certain magmatic processes or in estimating the thermal history of basaltic rocks.
Apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials, and due to the presence of volatiles within its crystal structure (X-site), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources [i.e., 1]. Experimental studies have investigated the apatite-melt partitioning behavior of F, Cl, and OH in basaltic systems [e.g., 2- 3], reporting that apatite-melt partitioning of volatiles is best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, exchange coefficients may vary as a function of temperature, pressure, melt composition, and/or oxygen fugacity. Furthermore, exchange coefficients may vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite [3]. In these regions of ternary space, we anticipate that crystal chemistry could influence partitioning behavior. Consequently, we conducted experiments to investigate the effect of apatite crystal chemistry on apatite-melt partitioning of F, Cl, and OH.
In situ observations of OH and HO2 from the Airborne Southern Hemisphere Ozone Experiment/Measurements for Assessing the Effects of Stratospheric Aircraft (ASHOE/MAESA), Stratospheric TRacers of Atmospheric Transport (STRAT), and Polar Ozone Loss in the Arctic Region in Summer (POLARIS) NASA ER-2 field campaigns are used to examine the partitioning of HO(x) in the lower stratosphere (tropopause to approx.21 km) and upper troposphere (approx.10 km to tropopause). These measurements span a latitude range from 70degS to 90degN and a variety of atmospheric conditions as a result of seasonal changes and altitude. The response of the observed [HO2]/[OH] to changes in temperature, [03], [CO], [NO], [CIO], and [BrO] is investigated. The measured ratio is accurately described (approx.+/-10%) by a steady-state model constrained by the measured mixing ratios of O3, CO, NO, CIO, and BrO, where the model is valid for conditions of HO(x) cycling much faster than HO(x) production and loss. The concentration of HO2 depends on [OH], which, to first order, has been observed to be a simple function of the solar zenith angle in the lower stratosphere. The partitioning between OH and HO2 is controlled by the local chemistry between the HO, radicals and O3, CO, NO, CIO, and BrO. The response of [HO(x)] to changes in [NO(x)] and [O3] is demonstrated. Further observations are necessary to illustrate the response of HO(x) to changes in halogen concentrations. A quantitative understanding of [HO2]/[OH] is important, since many of the reactions that control this ratio are directly involved in catalytic removal of O3 in the lower stratosphere and production of O3 in the upper troposphere.
In a parallel processing computer system with multiple processing units and shared memory, a method is disclosed for uniformly balancing the aggregate computational load in, and utilizing minimal memory by, a network having identical computations to be executed at each connection therein. Read-only and read-write memory are subdivided into a plurality of process sets, which function like artificial processing units. Said plurality of process sets is iteratively merged and reduced to the number of processing units without exceeding the balance load. Said merger is based upon the value of a partition threshold, which is a measure of the memory utilization. The turnaround time and memory savings of the instant method are functions of the number of processing units available and the number of partitions into which the memory is subdivided. Typical results of the preferred embodiment yielded memory savings of from sixty to seventy five percent.
The surfaces of most metals immersed in aqueous electrolytes have a several-nanometer-thick oxide/hydroxide surface layer. This gives rise to the existence of both metal|oxide and oxide|liquid electrotlyte interfaces, and makes it challenging to correlate atomic length-scale structures with electrochemical properties such the potential-of-zero-charge (PZC). The PZC has been shown to be correlated the onset potential for pitting corrosion. Here, we conduct large-scale Density Functional Theory and ab initio molecular dynamics to calculate the PZC of a Al(111)| γ -Al 2 O 3 (110)| water double-interface model within the context of aluminum corrosion. By partitioning the multiple interfaces involved into binary components with additive contributions to the overall work function and voltage, we predict the PZC to be -1.53 V vs SHE for this model. Furthermore, we calculate the orbital energy levels of defects like oxygen vacancies in the oxide, which are critical parameters in theories associated with pitting corrosion. We predict that the Fermi level at the PZC lies above the impurity defect levels of the oxygen vacancies, which are therefore uncharged at the PZC. From the PZC estimate, we predict the voltage needed to create oxygen vacancies with net positive charges within a flatband approximation.
Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (tau) acting on the surfaces, the surface shear stress on the ground between the elements (tau(sub S)) and the drag force on the elements for each roughness array. The measurements indicated that tau(sub S) quickly reduced near the leading edge of the roughness compared with tau, and a tau(sub S) minimum occurs at a normalized distance (x/h, where h is element height) of approx. -42 (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average tau(sub S): tau values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.
Transcription-coupled repair is essential for the removal of DNA lesions from the transcribed genome. The pathway is initiated by CSB protein binding to stalled RNA polymerase II. Mutations impairing CSB function cause severe genetic disease. Yet, the ATP-dependent mechanism by which CSB powers RNA polymerase to bypass certain lesions while triggering excision of others is incompletely understood. Here we build structural models of RNA polymerase II bound to the yeast CSB ortholog Rad26 in nucleotide-free and bound states. This enables simulations and graph-theoretical analyses to define partitioning of this complex into dynamic communities and delineate how its structural elements function together to remodel DNA. We identify an allosteric pathway coupling motions of the Rad26 ATPase modules to changes in RNA polymerase and DNA to unveil a structural mechanism for CSB-assisted progression past less bulky lesions. Our models allow functional interpretation of the effects of Cockayne syndrome disease mutations.
Transcription factor IIH (TFIIH) is a protein assembly essential for transcription initiation and nucleotide excision repair (NER). Yet, understanding of the conformational switching underpinning these diverse TFIIH functions remains fragmentary. TFIIH mechanisms critically depend on two translocase subunits, XPB and XPD. To unravel their functions and regulation, we build cryo-EM based TFIIH models in transcription- and NER-competent states. Using simulations and graph-theoretical analysis methods, we reveal TFIIH’s global motions, define TFIIH partitioning into dynamic communities and show how TFIIH reshapes itself and self-regulates depending on functional context. Our study uncovers an internal regulatory mechanism that switches XPB and XPD activities making them mutually exclusive between NER and transcription initiation. By sequentially coordinating the XPB and XPD DNA-unwinding activities, the switch ensures precise DNA incision in NER. Mapping TFIIH disease mutations onto network models reveals clustering into distinct mechanistic classes, affecting translocase functions, protein interactions and interface dynamics.
A concise review is given on the past two decades’ results from laboratory experiments on collisionless magnetic reconnection in direct relation with space measurements, especially by the Magnetospheric Multiscale (MMS) mission. Highlights include spatial structures of electromagnetic fields in ion and electron diffusion regions as a function of upstream symmetry and guide field strength, energy conversion and partitioning from magnetic field to ions and electrons including particle acceleration, electrostatic and electromagnetic kinetic plasma waves with various wavelengths, and plasmoid-mediated multiscale reconnection. Combined with the progress in theoretical, numerical, and observational studies, the physics foundation of fast reconnection in collisionless plasmas has been largely established, at least within the parameter ranges and spatial scales that were studied. Immediate and long-term future opportunities based on multiscale experiments and space missions supported by exascale computation are discussed, including dissipation by kinetic plasma waves, particle heating and acceleration, and multiscale physics across fluid and kinetic scales.
Laser shock-peening (LSP) produces complex gradients in microstructures and residual stresses, which enables fabrication of metallic engineering components with superior mechanical properties. In this work, we use non-destructive and spatially resolved high-energy X-ray diffraction (HE-XRD) to investigate the influences of LSP on microstructure, surface topography, and residual stress for high purity titanium plates. LSP is found to produce large compressive in-plane residual stresses near the peened surface which monotonically decay to zero about 2.5 mm below the surface. These properties were also tracked during in-situ tensile loading, allowing stress partitioning and work-hardening rates to be measured as a function of depth. The surface region is found to have the highest work-hardening rate and remain mechanically stable up to sample failure. In addition, a crystal rigid rotation along a transversal axis of about 27 & nbsp; was observed at large applied strain near the surface region, which is attributed to the formation of denser dispersed shear bands. Furthermore, a sudden drop in tensile stress was observed at a depth of similar to 160 mu m from the LSP surface, indicating the formation of a localized mechanical instability zone (LMIZ). The origin of this LMIZ could be attributed to the increase in shear stress induced by a load transfer from LSP surface due to the formation of denser dispersed shear bands. These observations indicate a localized transition in deformation behavior has occurred from dispersed shear banding to LMIZ and homogeneous deformation.
Many studies over the past few decades have been devoted to addressing the application of diglycolamides (DGAs) for hydrometallurgical-based, f-element separations. Work to date has shown the molecular structure of a DGA derivative can have a significant impact on intra-lanthanide partitioning patterns. More recent studies have pushed towards probing the structure function relationship of the lanthanide-DGA complex to enable the design of more efficient lanthanide separation systems. Spectroscopic techniques, such as UV–Visible, Fourier Transformed Infrared Spectroscopy (FT-IR), Nuclear Magnetic Resonance (NMR), and Extended X-ray Absorption Fine Structure (EXAFS), provide information regarding the inner-sphere coordination of a given lanthanide-DGA complex. Scattering techniques, such as Dynamic Light Scattering (DLS), Small-Angle X-ray Scattering (SAXS), and Small-Angle Neutron Scattering (SANS), address nanoscale structures including aggregate sizes and morphology. Here, this review assesses the current state-of-knowledge regarding lanthanide-DGA hydrometallurgical (i.e., solvent extraction systems) interrogated using spectroscopic and scattering techniques to characterize the extracted Ln 3+ DGA species. Of particular interest to this review is the impact of varied diluents, inclusion and variation of phase modifiers, and DGA derivatization on system characteristics. While there has been extensive literature on the application of DGAs for f-element separations, the literature lacks a collective assessment of the speciation of Ln 3+ in the organic phase. This review provides new insights into the field of DGA separations, explicitly with an application to intra-lanthanide separations. Specifically, this review illustrates the importance of both the co-extraction anion (Cl - , NO 3 - , or ClO 4 - ) as it pertains to both the aggregate size and Ln 3+ distribution coefficient. It is evident the ability of the anion to disrupt the hydrogen bonding network limits both aggregate size and distribution coefficients according to the Hoffmeister series. This suggests the importance of the large, softer anions with a low charge-to-surface area ratio on encouraging hydrogen bond interactions. In addition, the co-extracted cation (H + vs Na + ) is important for mitigating transfer of Ln 3+ from the aqueous to the organic phase through extensive hydrogen bonding networks. These networks are responsible for forming supramolecular aggregates where a change in morphology is observed with increasing concentrations of H + and/or Ln 3+ in the organic phase.
The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.
The availability of formaldehyde (HCHO) (a proxy for volatile organic compound reactivity) and nitrogen dioxide (NO 2 ) (a proxy for nitrogen oxides) tropospheric columns from ultraviolet–visible (UV–Vis) satellites has motivated many to use their ratios to gain some insights into the near-surface ozone sensitivity. Strong emphasis has been placed on the challenges that come with transforming what is being observed in the tropospheric column to what is actually in the planetary boundary layer (PBL) and near the surface; however, little attention has been paid to other sources of error such as chemistry, spatial representation, and retrieval uncertainties. Here we leverage a wide spectrum of tools and data to quantify those errors carefully. Concerning the chemistry error, a well-characterized box model constrained by more than 500 h of aircraft data from NASA's air quality campaigns is used to simulate the ratio of the chemical loss of HO 2 + RO 2 (LRO x ) to the chemical loss of NO x (LNO x ). Subsequently, we challenge the predictive power of HCHO/NO 2 ratios (FNRs), which are commonly applied in current research, in detecting the underlying ozone regimes by comparing them to LRO x /LNO x . FNRs show a strongly linear (R 2 =0.94) relationship with LRO x /LNO x , but only on the logarithmic scale. Following the baseline (i.e., ln(LRO x /LNO x ) = −1.0 ± 0.2) with the model and mechanism (CB06, r2) used for segregating NO x -sensitive from VOC-sensitive regimes, we observe a broad range of FNR thresholds ranging from 1 to 4. The transitioning ratios strictly follow a Gaussian distribution with a mean and standard deviation of 1.8 and 0.4, respectively. This implies that the FNR has an inherent 20 % standard error (1σ) resulting from not accurately describing the RO x –HO x cycle. We calculate high ozone production rates (PO 3 ) dominated by large HCHO × NO 2 concentration levels, a new proxy for the abundance of ozone precursors. The relationship between PO 3 and HCHO × NO 2 becomes more pronounced when moving towards NO x -sensitive regions due to nonlinear chemistry; our results indicate that there is fruitful information in the HCHO × NO 2 metric that has not been utilized in ozone studies. The vast amount of vertical information on HCHO and NO 2 concentrations from the air quality campaigns enables us to parameterize the vertical shapes of FNRs using a second-order rational function permitting an analytical solution for an altitude adjustment factor to partition the tropospheric columns into the PBL region. We propose a mathematical solution to the spatial representation error based on modeling isotropic semivariograms. Based on summertime-averaged data, the Ozone Monitoring Instrument (OMI) loses 12 % of its spatial information at its native resolution with respect to a high-resolution sensor like the TROPOspheric Monitoring Instrument (TROPOMI) (> 5.5 × 3.5 km 2 ). A pixel with a grid size of 216 km 2 fails at capturing ∼ 65 % of the spatial information in FNRs at a 50 km length scale comparable to the size of a large urban center (e.g., Los Angeles). We ultimately leverage a large suite of in situ and ground-based remote sensing measurements to draw the error distributions of daily TROPOMI and OMI tropospheric NO 2 and HCHO columns. At a 68 % confidence interval (1σ), errors pertaining to daily TROPOMI observations, either HCHO or tropospheric NO 2 columns, should be above 1.2–1.5 × 10 16 molec. cm −2 to attain a 20 %–30 % standard error in the ratio. This level of error is almost non-achievable with the OMI given its large error in HCHO. The satellite column retrieval error is the largest contributor to the total error (40 %–90 %) in the FNRs. Due to a stronger signal in cities, the total relative error (< 50 %) tends to be mild, whereas areas with low vegetation and anthropogenic sources (e.g., the Rocky Mountains) are markedly uncertain (> 100 %). Our study suggests that continuing development in the retrieval algorithm and sensor design and calibration is essential to be able to advance the application of FNRs beyond a qualitative metric.