Simple Relation Research Articles

The Oxidation States of Iron in Dry and Wet Olivine: A Thermodynamic Model

AbstractThe oxidation state of iron in olivine is an important control on many of its properties but is poorly constrained in mantle conditions. In this work Density Functional Theory is used to build a thermodynamic model of Fe oxidation states and incorporation mechanisms as a function of silica activity (αSiO2), pressure (P), temperature (T), oxygen fugacity (fO2), and the concentrations of Fe, H2O, Ti, and Al. Total Fe3+/∑Fe, Fe oxidation pathways and by‐products of Fe oxidation (such as Mg and Si vacancies) have a complex dependence upon αSiO2, P, T, and fO2, which are difficult to capture using simple Arrhenius relations and experiments over limited ranges. Our model predicts that in the conditions of the upper mantle, depth is the strongest control on Fe3+/∑Fe and that this relationship is strongly nonmonotonic and varies over several orders of magnitude. Fe3+/∑Fe is predicted to always be low reaching a maximum of 0.003 at around 100 km depth under normal mantle conditions though the presence of large amounts of water could increase this value further (0.03 with 500 ppmw water). While the Ferric iron concentration is predicted to be low, the concentration of Mg and Si vacancies—and thus vacancy dependent properties such as diffusion and likely strength—are predicted to be primarily a function of iron oxidation. These properties are predicted to vary by multiple orders of magnitude across the depth range of the upper mantle and thus olivine is predicted to have highly dynamic rather than static properties.

Understanding fusion zone hardness in resistance spot welds for advanced high strength steels: Strengthening mechanisms and data-driven modeling

The fusion zone (FZ) hardness of resistance spot welds is a crucial factor affecting the performance and durability of the welds. Failure mode transition, tendency to fail in interfacial mode, interfacial failure load, and the impact of liquid metal embrittlement cracks on the weld strength are influenced by the FZ hardness. Therefore, accurately predicting the FZ hardness in resistance spot welds made on automotive steels is essential. A simple thermal model is used to calculate the time required for the temperature to drop from 800 °C to 500 °C (Δt85). With the aid of continuous cooling transformation (CCT) diagrams and experimental confirmation, it is shown that in most automotive steels, the FZ exhibits an almost full martensitic microstructure. Generally, the FZ hardness tends to increase in the order of interstitial-free (IF), drawing quality specially killed (DQSK), high strength low alloy (HSLA), ferrite-martensite dual-phase steels, transformation induced plasticity (TRIP), and quench & partitioning (Q&P) steels. To predict the FZ hardness, data-driven regression-based models have been developed based on carbon content, carbon equivalent concept, and the strengthening mechanisms of the martensite. Among these models, the model based on martensite strengthening mechanisms showed the best performance and robustness in estimating the FZ hardness. The assessment of the strengthening mechanism of the FZ showed that most important factors determining the FZ hardness are dislocation hardening due to carbon atoms, interface hardening due to block boundaries, and solid solution hardening due to substitutional alloying elements, respectively. A simple relation is proposed to estimate the load-bearing capacity of automotive steel spot welds during interfacial failure based on the FZ hardness.

Simple Empirical Relation for an Evacuated-Tube Solar Collector Performance Prediction from Solar Intensity

In this paper, the effect of solar intensity on the heat pipe tip temperature in a heat pipe type—evacuated-tube solar collector (HP-ETSC) was investigated. A simple relation was proposed, relating the solar intensity to the heat pipe tip temperature generated from the experimental data. This simple empirical relation was applied in a set of heat transfer equations derived to predict the heating medium temperature at the manifold outlet of the evacuated-tube solar collector. The calculated results corresponding to two types of heating medium, i.e., palm oil and water, were compared with experimental results from the literature. The results show that the average error was 6.41% for the case of palm oil and 4.66% for the case of water. Based on the case of water as a heating medium fluid, it was found that the flow rate of the heating medium fluid affected the accuracy of prediction, as the percentage error increased with the heating medium flow rate. The maximum percentage error increased from only 1.83% for a water inlet flowing at a Reynolds number of about 2.4 × 103 to 15.23% for a water flow rate at a Reynolds number of about 2.6 × 104. The correction factor was added into the correlation to predict the heat transfer coefficients of heating medium fluids. With this correction factor, the maximum error could be reduced from 11.78% to 7.29% for the palm oil case and from 15.23% to 5.57% for the water case. The average errors corresponding to palm oil and water cases could be reduced to 0.74% and 1.26%, respectively.

Travel distance, frequency of return, and the spread of disease

Human mobility is a key driver of infectious disease spread. Recent literature has uncovered a clear pattern underlying the complexity of human mobility in cities: r cdot f, the product of distance traveled r and frequency of return f per user to a given location, is invariant across space. This paper asks whether the invariant rcdot f also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable rcdot f. We use two large-scale datasets of individual human mobility to show that there is in fact a simple relation between r and f and both speed and spatial dispersion of disease spread. This discovery could assist in modeling spread of disease and inform travel policies in future epidemics—based not only on travel distance r but also on frequency of return f.

Width-dependent band gap of arm-chair graphene nanoribbons formed on vicinal SiC substrates by MBE

Formation and electronic states of graphene nanoribbons with arm-chair edges (AGNR) are studied on the SiC(0001) vicinal surfaces toward the [] direction. The surface step and terrace structures of both 4H and 6H-SiC substrates are used as the growth templates of one-dimensional arrays of AGNRs, which are prepared using the carbon molecular beam epitaxy followed by hydrogen intercalation. A band gap is observed above the π-band maximum by angle-resolved photoelectron spectroscopy (ARPES) for the both samples. The average widths of the AGNRs are 6 and 10 nm, and the estimated average band gaps are 0.40 and 0.28 eV for the 4H- and 6H- substrates, respectively. A simple and phenomenological inverse relation between the energy gap and AGNR width works in the analyses of the ARPES data.

Deformation-Induced Surface Roughening of an Aluminum-Magnesium Alloy: Experimental Characterization and Crystal Plasticity Modeling.

The deformation-induced surface roughening of an Al-Mg alloy is analyzed using a combination of experiments and modeling. A mesoscale oligocrystal of AA5052-O, obtained by recrystallization annealing and subsequent thickness reduction by machining, that contains approx. 40 grains is subjected to uniaxial tension. The specimen contains one layer of grains through the thickness. A laser confocal microscope is used to measure the surface topography of the deformed specimen. A finite element model with realistic (non-columnar) shapes of the grains based on a pair of Electron Back-Scatter Diffraction (EBSD) scans of a given specimen is constructed using a custom-developed shape interpolation procedure. A Crystal Plasticity Finite Element (CPFE) framework is then applied to the voxel model of the tension test of the oligocrystal. The unknown material parameters are determined inversely using an efficient, custom-built optimizer. Predictions of the deformed shape of the specimen, surface topography, evolution of the average roughness with straining and texture evolution are compared to experiments. The model reproduces the averaged features of the problem, while missing some local details. As an additional verification of the CPFE model, the statistics of surface roughening are analyzed by simulating uniaxial tension of an AA5052-O polycrystal and comparing it to experiments. The averaged predictions are found to be in good agreement with the experimentally observed trends. Finally, using the same polycrystalline specimen, texture-morphology relations are discovered, using a symbolic Monte Carlo approach. Simple relations between the Schmid factor and roughness can be inferred purely from the experiments. Novelties of this work include: realistic 3D shapes of the grains; efficient and accurate identification of material parameters instead of manual tuning; a fully analytical Jacobian for the crystal plasticity model with quadratic convergence; novel texture-morphology relations for polycrystal.

Conformal dispersion relations for defects and boundaries

We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in \mathcal{N}=4𝒩=4 Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the O(N) critical model. We reproduce the order \epsilon^2ϵ2 result in the \epsilonϵ-expansion using as input a finite number of boundary CFT data.

Monte Carlo simulation of the maximum migration distance of CO[formula omitted] in a sloping aquifer

Carbon capture and storage in saline aquifers is broadly considered a viable technology for reducing anthropogenic impact on the environment. However, a secure CO2 storage can be compromised by the depositional environments of target reservoirs, which can influence the CO2 migration in subsurface. The disposal of CO2 in a sloping aquifer can result in a substantial gas migration in the updip direction from the injection well until all gas becomes trapped. It thus can reach far more than desired regions from the well where the potential leakage paths to the surface can exist. This study aims at understanding the principal parameters that the maximum migration distance in the updip direction depends on, which can be important for estimating the risks of CO2 leakage through old abandoned wells in the regions of intensive subsurface exploration. Using the Monte Carlo method, an extended parametric study is performed by running 3-D reservoir simulations of CO2 storage in random aquifers characterized by various petrophysical and thermobaric parameters, saturation functions and brine salinity, and for the wells operated under different target rates. Herewith, the modeling accounts for such relevant physical phenomena as the phase transitions, the gravity and capillary forces, the hysteresis behavior of the relative permeability, etc. It is shown that the maximum migration distance at the post-injection stage is characterized by just two similarity criteria and the critical gas saturation for the drainage and imbibition processes. It is found that the CO2 plume shape at the moment of the well shut-in influences the subsequent gas transport. A new simple relation parameterizing the revealed dependence is proposed and validated against the sampled maximum migration distances. The relation is useful for an instant estimating the size of the contaminated zone around a projected CO2 well and for ranking the potential storage sites.

Prospects for future binary black hole gravitational wave studies in light of PTA measurements

NANOGrav and other Pulsar Timing Arrays (PTAs) have discovered a common-spectrum process in the nHz range that may be due to gravitational waves (GWs): if so, they are likely to have been generated by black hole (BH) binaries with total masses > 109 M⊙. Using the Extended Press-Schechter formalism to model the galactic halo mass function and a simple relation between the halo and BH masses suggests that these binaries have redshifts z = 𝒪(1) and mass ratios ≳10, and that the GW signal at frequencies above 𝒪(10) nHz may be dominated by relatively few binaries that could be distinguished experimentally and would yield observable circular polarization. Extrapolating the model to higher frequencies indicates that future GW detectors such as LISA and AEDGE could extend the PTA observations to lower BH masses ≳103 M⊙.

Physical Evolution of Dark Matter Halo around the Depletion Boundary

We investigate the buildup of the halo profile out to large scale in a cosmological simulation, focusing on the roles played by the recently proposed depletion radii. We explicitly show that halo growth is accompanied by the depletion of the environment, with the inner depletion radius demarcating the two. This evolution process is also observed via the formation of a trough in the bias profile, with the two depletion radii identifying key scales in the evolution. The ratio between the inner depletion radius and the virial radius is approximately a constant factor of 2 across redshifts and halo masses. The ratio between their enclosed densities is also close to a constant of 0.18. These simple scaling relations reflect the largely universal scaled mass profile on these scales, which only evolves weakly with redshift. The overall picture of the boundary evolution can be broadly divided into three stages according to the maturity of the depletion process, with cluster halos lagging behind low-mass ones in the evolution. We also show that the traditional slow and fast accretion dichotomy of halo growth can be identified as accelerated and decelerated depletion phases, respectively.

The GAPS programme at TNG

Context. The leading spectrographs used for exoplanets’ search and characterization offer online data reduction softwares (DRS) that yield, as an ancillary result, the full-width at half-maximum (FWHM) of the cross-correlation function (CCF) that is used to estimate the radial velocity of the host star. The FWHM also contains information on the stellar projected rotational velocity veq sin i★, if appropriately calibrated. Aims. We wanted to establish a simple relationship to derive the veq sin i★ directly from the FWHM computed by the HARPS-N DRS in the case of slow-rotating solar-like stars. This may also help to recover the stellar inclination i★, which in turn affects the exoplanets’ parameters. Methods. We selected stars with an inclination of the spin axis compatible with 90 deg by looking at exoplanetary transiting systems with known small sky-projected obliquity: for these calibrators, we can presume that veq sin i★ is equal to stellar equatorial velocity veq. We derived their rotational periods from photometric and spectroscopic time series and their radii from the spectral energy distribution (SED) fitting. This allowed us to recover their veq, which could be compared to the FWHM values of the CCFs obtained both with G2 and K5 spectral-type masks. Results. We obtained an empirical relation for each mask: this can be used to derive veq sin i★ directly from FWHM values for slow rotators (FWHM < 20 km s−1). We applied our relations to 273 exoplanet-host stars observed with HARPS-N, obtaining homogeneous veqsin i★ measurements. When possible, we compared our results with the literature ones to confirm the reliability of our work. We were also able to recover or constrain i★ for 12 objects with no prior veq sin i★ estimation. Conclusions. We provide two simple empirical relations to directly convert the HARPS-N FWHM obtained with the G2 and K5 mask to a veq sin i★ value. We tested our results on a statistically significant sample, and we found a good agreement with literature values found with more sophisticated methods for stars with log ɡ > 3.5. We also tried our relation on HARPS and SOPHIE data, and we conclude that it can be used as it is also on FWHM derived by HARPS DRS with the G2 and K5 mask, and it may be adapted to the SOPHIE data as long as the spectra are taken in high-resolution mode.

13C NMR Chemical Shifts of Saccharides in the Solid State: A Density Functional Theory Study

In this work we present a systematic, theoretical investigation of the 13C NMR chemical shifts for several mono-, di- and trisaccharides in the solid state. The chemical shifts have been calculated using density functional theory (DFT) together with the gauge including the projector augmented wave (GIPAW) method as implemented in the CASTEP program. We studied the changes in the 13C NMR chemical shifts in particular due to the formation of one or two glycosidic linkages and due to crystal water. The largest changes, up to 14 ppm, are observed between the mono- and disaccharides and typically for the glycosidic linkage atoms, but not in all cases. An analysis of the bond angles at the glycosidic linkage and the observed changes in chemical shifts displays no direct correlation between them. Somewhat smaller changes in the range of 2 to 5 ppm are observed when single crystal water molecules are close to some of the atoms. Relating the changes in the chemical shifts of the carbon atoms closest to the crystal water to the distance between them does, however, not lead to a simple relation between them.

Impact force reconstruction and localization using Distance-assisted Graph Neural Network

In this paper, a novel impact force identification method named Distance-assisted Graph Neural Network (DAGNN) is proposed for simultaneous force localization and force history reconstruction. The DAGNN model is a graph-based supervised learning method. A graph is formed by treating the sensors as nodes and the connections between them as edges. The relationships of the nodes and edges contained in the graph are mathematically characterized into two matrices, an adjacency matrix and a degree matrix, that form the basis of the Graph Neural Network (GNN). Meanwhile, in order to improve the learning of the DAGNN model and realize impact force localization, physical distances between the position of the impact force and sensors are infused into the training process as physics-informed constraints. An experiment on a metal plate is conducted to verify the effectiveness and practicability of DAGNN. A sparse grid is arranged on the plate to collect the force and response signals to form a dataset for the DAGNN model. The results indicate that the accuracy of time history reconstruction of DAGNN is higher than a conventional GNN model, a typical Graph Convolutional Network (GCN) model and an ANN model, and also remain high accuracy with different locations of impact. In addition, due to the infused distance information, a simple relation regarding the distances between the impact location and the sensor location can be constructed to realize localization of the impact with good accuracy.

A condition for the reduction of couplings in the [formula omitted] supersymmetric theories

We demonstrate that in the P=13Q supersymmetric theories the renormalization group invariance of the ratio λijk/e (of the Yukawa couplings to the gauge coupling) is equivalent to a simple relation between the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields, which should be valid in each order of the perturbation theory. In the one- and two-loop approximations it is verified explicitly. Presumably, in higher orders this relation can be satisfied for the planar supergraphs under a certain renormalization prescription. Assuming that it is valid we rewrite the exact equation for the (corresponding contribution to the) anomalous dimension of the matter superfields in the theories under consideration in a different (but equivalent) form.

Robust table structure recognition with dynamic queries enhanced detection transformer

We present a new table structure recognition (TSR) approach, called TSRFormer, to robustly recognize the structures of complex tables with geometrical distortions from various table images. Unlike previous methods, we formulate table separation line prediction as a line regression problem instead of an image segmentation problem and propose a new two-stage dynamic queries enhanced DETR based separation line regression approach, named DQ-DETR, to predict separation lines from table images directly. Compared to Vallina DETR, we propose three improvements in DQ-DETR to make the two-stage DETR framework work efficiently and effectively for the separation line prediction task: 1) A new query design, named Dynamic Query, to decouple single line query into separable point queries which could intuitively improve the localization accuracy for regression tasks; 2) A dynamic queries based progressive line regression approach to progressively regressing points on the line which further enhances localization accuracy for distorted tables; 3) A prior-enhanced matching strategy to solve the slow convergence issue of DETR. After separation line prediction, a simple relation network based cell merging module is used to recover spanning cells. With these new techniques, our TSRFormer achieves state-of-the-art performance on several benchmark datasets, including SciTSR, PubTabNet, WTW, FinTabNet, and cTDaR TrackB2-Modern. Furthermore, we have validated the robustness and high localization accuracy of our approach to tables with complex structures, borderless cells, large blank spaces, empty or spanning cells as well as distorted or even curved shapes on a more challenging real-world in-house dataset.

Development of a model to investigate the effect of the bias in SNIa measurements related to the inhomogeneity of space

It has been suggested recently that the apparent accelerated expansion of the universe could be explained by a bias in the SNIa measurements. Such events indeed occur mainly in overdense regions, where matter is located, and whose dynamics can perhaps not been considered as representative of the one of the universe. In this article, we develop a model to investigate in more detail the effect of this bias. This model depends on one single parameter, related to the void fraction of space, and leads to simple analytical relations. We determine in particular the average metric tensor in overdense regions, and deduce that the scale factor and the rate at which proper time progresses in such regions differ significantly from the corresponding values expected on the average space. We then quantitatively deduce how redshift and luminosity distance measurements are affected by the bias, taking into account the perturbation of the metric tensor. Using a value for the void fraction corresponding to the order of magnitude found in the literature, we show that the model is able to predict a distance modulus versus redshift relation being in excellent agreement with the one corresponding to a universe characterized by Omega _{m,0} = 0.3 and Omega _{Lambda ,0} = 0.7.

Efficient and flexible mediation analysis with time-varying mediators, treatments, and confounders

AbstractUnderstanding the mechanisms of action of interventions is a major general goal of scientific inquiry. The collection of statistical methods that use data to achieve this goal is referred to asmediation analysis. Natural direct and indirect effects provide a definition of mediation that matches scientific intuition, but they are not identified in the presence of time-varying confounding. Interventional effects have been proposed as a solution to this problem, but existing estimation methods are limited to assuming simple (e.g., linear) and unrealistic relations between the mediators, treatments, and confounders. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator, and mediator-outcome relationships. Identification is achieved under the standard no-unmeasured-confounders and positivity assumptions. In this article, we study semi-parametric efficiency theory for the functional identifying the mediation parameter, including the non-parametric efficiency bound, and was used to propose non-parametrically efficient estimators. Implementation of our estimators only relies on the availability of regression algorithms, and the estimators in a general framework that allows the analyst to use arbitrary regression machinery were developed. The estimators are doubly robust,n\sqrt{n}-consistent, asymptotically Gaussian, under slow convergence rates for the regression algorithms used. This allows the use of flexible machine learning for regression while permitting uncertainty quantification through confidence intervals andpp-values. A free and open-sourceRpackage implementing the methods is available on GitHub. The proposed estimator to a motivating example from a trial of two medications for opioid-use disorder was applied, where we estimate the extent to which differences between the two treatments on risk of opioid use are mediated by craving symptoms.

Correlations and projective measurements in maximally entangled multipartite states

Multipartite quantum states constitute the key resource for quantum computation. The understanding of their internal structure is thus of great importance in the field of quantum information. This paper aims at examining the structure of multipartite maximally entangled pure states, using tools with a simple and intuitive physical meaning, namely, projective measurements and correlations. We first show how, in such states, a very simple relation arises between post-measurement expectation values and pre-measurement correlations. We then infer the consequences of this relation on the structure of the recently introduced entanglement metric, allowing us to provide an upper bound for the persistency of entanglement. The dependence of these features on the chosen measurement axis is underlined, and two simple optimization procedures are proposed, to find those maximizing the correlations. Finally, we apply our procedures onto some prototypical examples.

Prediction of the monotonic load–displacement curve of slender RC beams with corroded transverse and longitudinal reinforcements

AbstractThe present paper proposes a mechanical model for the prediction of the response of slender reinforced concrete beams with corroded transverse and longitudinal reinforcements. The proposed model is based on the Modified Compression Field Theory and is able to predict the load–displacement curve of members subjected to monotonic displacement‐controlled tests up to their peak load. The corrosion‐damage effects are considered by means of an effective width of the beam and by means of reduced values of both cross‐sectional area and strain capacity of steel bars. The accuracy of the model is evaluated by comparison with results of tests reported in the literature. Moreover, a simple relation is suggested for the estimate of the shear strength of reinforced concrete beams with low values of the effective geometric percentage of (corroded) stirrups.

Three-dimensional modelling of blur property for conventional optical microscopes

Intensity diffusion caused by optical diffraction limits the imaging resolution of conventional optical microscopes, therefore modelling and measuring the intensity transmission and distribution property of the light sources is a significant research topic in system development and pattern recognition. However, the complicated wave propagation process in optical imaging makes it difficult to provide a direct, analytical and simple mathematical model to measure the relationship between the blur degree and various camera parameters. In this study, an improved intensity transmission and distribution calculation method for conventional optical microscopes was proposed; furthermore, a simple mathematical relation between the blur degree and camera parameters was achieved based on the proposed method. First, the light intensity distribution and propagation characteristics of a conventional optical microscope were modeled based on the property of the Fresnel circular hole diffraction combined with the practical optical parameters. Second, by analyzing the property of intensity distribution and blurring imaging, a quantitative simplified mathematical relationship between the blur degree and camera parameters in optical microscope imaging was obtained, and the three-dimensional (3D) blur property in the optical imaging process was analyzed under different conditions. Third, the connection between diffractive optics and geometric optics was obtained by summarizing and generalizing the 3D blur property curve of each monochromatic light source. Finally, the proposed method was verified through a series of simulations and experiments.