Embedded Method Research Articles

New low order Runge–Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction

Embedded Runge–Kutta (RK) methods provide an attractive methodology for solution of initial value problems (IVP) by means of adaptive step size control. According to Fehlbergs suggestion, only one extra function calculation is required to estimate the local error of the embedded method. In the present paper, this methodology is applied to three prominent low order implicit RK-schemes. To this end, new embedded Butcher-tableaus are presented for the implicit Euler-method, the trapezoidal-rule and the midpoint-rule by means of corresponding higher order RK-schemes. In order to account for the global error, an asymptotically exact global error estimator is derived for the so-called reversed embedded RK-method. Moreover, a cause of order reduction is illustrated by aid of a weak discontinuous formulation. It is prevented in a new hybrid integration algorithm by means of a Hermite interpolation for the source term of the IVP, and its implementation renders a convenient “node-to-node” stepping scheme for a laser beam simulation. Two numerical examples are presented with the following main results: The higher order convergence behaviors of the proposed new RK-schemes are verified, its successful performances for asymptotically exact global error estimation of the reversed embedded RK-method are shown, the proposed methodology is illustrated for two different global error functions, and the desired effect of the hybrid algorithm to prevent order reduction is illustrated.

A Novel Embedded Domain Decomposition Method for Electromagnetic Simulation of Structures in Inhomogeneous Medium

A novel embedded domain decomposition method (EDDM) is proposed to simulate electromagnetic scattering from structures in an inhomogeneous medium. In this method, the inhomogeneous medium (e.g., layered substrate) is set as the background subdomain, and the integrated structures (e.g., metallic/dielectric components) with properly defined buffer regions (BRs) are set as the embedded subdomains, where the meshes of two can be completely independent and arbitrarily overlapping. The major contribution of this work lies in the following three aspects. First, to allow for arbitrary inclusion of the embedded subdomains in an inhomogeneous background subdomain, an adaptive BR method is developed. The self-coupling equation is rederived to ensure the consistency of the BR and the inhomogeneous background, and a new mutual-coupling equation is introduced to account for the material and/or conductor differences. Second, the boundary element method (BEM) accelerated by the multilevel fast multipole algorithm (MLFMA) is utilized to truncate the finite-element region so that the computation capability can be enhanced and the extra air box setting of the background subdomain in the original EDDM can be avoided. Third, for structure adjustments such as translations and rotations, we further propose an inherited calculation to avoid mesh regeneration and repeated computation of the self-coupling and preconditioning matrices and also reduce the iteration counts and solution time. Numerical examples have shown the accuracy, robustness, and efficiency of the proposed method.

Contrastive deep embedded clustering

Deep embedded clustering is a popular unsupervised learning method owing to its outstanding performance in data-mining applications. However, existing methods ignore the difficulty in learning discriminative features via clustering due to the lack of supervision, which can be easily obtained in classification tasks. To alleviate this problem, we build a contrastive learning based deep embedded clustering method, i.e., CDEC. Specifically, our model adopts deep auto-encoders to learn a latent discriminative embedded clustering structure. To overcome the problem of lacking label information, the CDEC constructs positive samples and negative samples with the data reconstructed from the data itself and other data, respectively. By maximizing the distance between positive and negative ones, the CDEC can not only obtain the most representative features but also explore the discriminative features. Extensive experiments on several public datasets demonstrate that our method achieves the state-of-the-art clustering effectiveness. Our codes are available at: https://github.com/guoshuaiS/contrastive-deep.

Research on trading strategy based on improved LSTM network model

The economic foundation determines the superstructure of society. Sustainable development of society is inseparable from economic prosperity, and investment has an irreplaceable role as one of the "troika" to promote social economy. Based on this, the modeling in this paper aims to study the trading strategy problem. In this paper, firstly, outliers and missing values are processed by Laiida's rule for the attached data, and then a multi-layer LSTM weighted model is proposed to learn the influencing factors of input time span on output time span by using multi-layer LSTM network, and the model is trained to achieve higher accuracy relative to the LSTM model through the embedded method: superposition of the influence generation cycle sequence. Attention mechanisms are introduced and short and long term forecasts are continuously made. The fluctuations of MACD, RSI indicators, Apriori and other parameters are quantified; then, a risk measurement index is constructed, where the greater the cyclical price fluctuations, the greater the risk. The results show that timely buying and selling maximizes returns, and that a $1,000 investment ends up with a $900,000 return. The model is run again by increasing or decreasing the percentage of transaction costs, setting 0.5%, 1%, 1.5% and 2% points, to test the magnitude of sensitivity (trading decision results) at different transaction costs. The results show that the model is more robust, i.e., the model constructed in this paper has better results under different transaction costs.

Excellent removal performance of 4,4'-biphenyldicarboxaldehyde m-phenylenediamine Schiff base magnetic polymer towards phenanthrene and 9-phenanthrol: Experimental, modeling and DFT calculations studies

Phenanthrene (PTH) and 9-phenanthrol (9-PTH) exhibited severe health threats and ecological hazards, for this reason, exploring a high-efficient removing strategy for PTH and 9-PTH could be considered of great urgency. Herein the 4,4'-biphenyldicarboxaldehyde m-phenylenediamine Schiff base magnetic polymer (magnetic BIPH-PHEN) was successfully fabricated via Schiff base polycondensation reaction and the subsequently one-pot embedded method. The mutual aromatic nucleus of BIPH-PHEN polymer and PTH/9-PTH could form π–π interaction, thus improving the capture ability, the embedded Fe3O4 nanoparticles provided the possibility for rapid separation. The physical and chemical properties of the magnetic BIPH-PHEN were systematically characterized. The removal rate of magnetic BIPH-PHEN towards PTH and 9-PTH was 85.65 % and 98.52 %, respectively (PTH or 9-PTH: 8 mg/L; Adsorbent: 0.2 g/L). The DFT calculations including energy calculations and electrostatic potential distribution analyzed the different bonding modes and proposed the most possible bonding modes in the adsorbent/adsorbate system. Moreover, the LUMO and HOMO orbits combined with energy gaps analysis proved the existence and specific types of the π–π interaction. The monolayer adsorption occurred on the homogeneous magnetic BIPH-PHEN surface, simultaneously the chemisorption was dominant. This work not only proposed new sights on assembling magnetic Schiff base polymer for removing polycyclic aromatic hydrocarbons, but also provided a deeper understanding of intramolecular interactions.

Simple enhanced charge density of chitosan film by the embedded ion method for the flexible triboelectric nanogenerator

This research proposed a simple ionic embedded method to improve electrical output performance by adding surface charges of cationic chitosan (CS) biopolymer for compatible utilization of the triboelectric nanogenerator (TENG). By simply embedding cationic salts, the TENG performance was enhanced by over four times more than that with pristine CS. Moreover, by modifying roughness on the film surface, the optimized condition of R-CS/3 %CaCl2 reached the highest VOC and ISC of ~149 V and ~15 μA, respectively, thus exceeding the output from pristine R-CS TENG by four- and three times of ⁓38 V and ⁓5.1 μA. The maximum power output of 400 μW/cm2 can be observed at the 10 MΩ external load resistance. Finally, by integrating an automatic self-charge pumping (ASCP) module, the ASCP/CS-TENG provided highly efficient VOC and ISC output power by over 1.3 times more than the R-CS/3 %CaCl2 TENG and could light up 72 light emitting diodes (LEDs) easily.

Frequency-domain acoustic full waveform inversion with an embedded boundary method for irregular topography

In the implementation of full waveform inversion (FWI) to identify subsurface velocity distributions with land seismic data, which are often acquired in regions with irregular topography, wave equation-based modelling requires caution. In particular, when using the finite difference method (FDM), unwanted scattered waves are generated because irregular surfaces crossing a rectangular grid are discretized via a staircase approximation; hence, if the problems caused by this staircase approximation are disregarded, FDM-based FWI may fail due to the presence of undesirable wavefields. To resolve this problem, this study develops a 2D frequency-domain acoustic FWI technique using a 9-point FDM-based modelling scheme that includes an embedded boundary method (EBM). This study suggests a workflow for the whole EBM-based FWI process from the calculation of coefficients for the EBM-based 9-point FDM modelling to applying it to FWI for proper velocity updates. In numerical examples, using velocity models with a tilted surface and an arbitrarily fluctuating surface, we synthesize seismic data and verify the accuracy of EBM-based 9-point FDM modelling and its superiority over the conventional FDM by comparing it with wavefields derived from the spectral element method. Then, we show that our EBM-based FWI is able to estimate subsurface velocity distributions even though the model has irregular topography, which spoils the result of the conventional FWI.

An Outcomes-based Evaluation of the Mindfulness for Safe Schools Program

Objectives. The objective of this evaluation was to assess the effectiveness of Mindfulness for Safe Schools, a mindfulness-based intervention adapted for sexual abuse prevention during peer-to-peer dating among Filipino public school children in Grades 7 and 8. It was hoped that through the intervention, children would be able to regulate their emotions so that they do not react impulsively to emotionally stimulating events, especially during peer dating. The study consists of four levels of evaluation: reaction, learnings, and behaviors of teachers toward the program, as well as effect of the intervention on emotion regulation and peer conformity among students.
 Methods. This study utilized a mixed methods design using a concurrent embedded method. For teachers, quantitative surveys and focused group discussions were conducted to determine their reactions to the training, their learnings, and behaviors after the program, as well as their observations of students’ responses to the intervention. Focused group discussions were analyzed through thematic analysis. Effect of the program on emotion regulation and peer conformity among students were determined mainly through a pre and post-test survey and analyzed through paired samples t-test. Video content analysis of the classroom delivery was also conducted to determine student engagement during the program.
 Results. Teachers reacted favorably to the training workshops and were able to use what they learned from the workshops to increase their patience and understanding towards themselves, their job, and their students. Students also reacted favorably to the Mindfulness for Safe Schools modules and were observed to use the skills taught in the modules to regulate their emotions. Emotion regulation improved (t=3.47, significant with p=0.00) and susceptibility to peer pressure decreased (t=8.94, significant with p=0.00) for Grade 8 students (n=950) after the modules were delivered. However, teachers reported implementation issues, such as conflicting requirements of the program with their official workload, which may have affected program effects.
 Conclusion. Our findings indicate that Mindfulness for Safe Schools was associated with improvements in emotional awareness, management of negative emotions, and showing care and respect for student peers. It also suggests that integrating mindfulness interventions in schools requires close coordination with all stakeholders: teachers, schools, and appropriate government divisions to ensure fidelity and reaching desired effects.

Atomic level simulations of the phase stability and stacking fault energy of FeCoCrMnSi high entropy alloy

High entropy alloys (HEAs) have many promising properties beneficial to advanced technologies. However, their underlying deformation mechanisms are largely unclear. So, as a first step, we have developed a modified embedded atom method potential for FeCoCrMnSi alloys to study such mechanisms. We predict the phase stability, chemical short-range ordering (CSRO), and stacking fault energy (SFE) of a specific alloy system using molecular dynamics (MD) and hybrid Monte-Carlo and molecular dynamics (MC/MD) simulation techniques. Room temperature MD simulations showed that both the potential energy and free energy of the single phase ε-hcp alloy is marginally more stable than the γ-fcc phase alloy, which resulted in a large, negative SFE. However, the room temperature MC/MD simulation showed an opposite trend where the γ-fcc phase was found to be more stable than the ε-hcp phase, and this resulted in a small, positive SFE. The prediction of the lower energy γ-fcc phase and resultant SFE agreed well with the experimentally reported SFE and phase stability for the Fe40Co20Cr15Mn20Si5 HEA, illustrating the importance of CSRO. Also, the calculated basal SFE of the hcp phase was close to that of the fcc phase. Therefore, the MC/MD implementation is crucial for the proper prediction of the phase stability and structural evolution in this HEA system. Many previous studies showed the ability of hybrid MC/MD technique to obtain consistent structural and configurational information of different alloy systems. The current work illustrates the potential of accelerating HEA materials development by utilizing computational methods based on the MC/MD technique which can reduce time and cost associated with experimental methods.

Tensile properties dependency on crystal size and direction of single crystal Ag3Sn intermetallic compound: a molecular dynamics study

The necessities of lead-free solder alloys have been expanded by the advent of eco-friendly technologies of microelectronic packaging industry. Mostly lead-free solder alloys are SAC, which is the alloy of tin, silver and copper metal. Ag3Sn, Cu3Sn and Cu6Sn5 inter-metallic compounds are formed during microelectronic packaging, which reduce the properties of SAC solder joints adversely. The present study explores direction dependent tensile properties of various sized single crystal anisotropic Ag3Sn. Molecular dynamics simulation platform LAMMPS is used to examine the elastic behavior of these crystals by modified embedded atom method (MEAM) potential parameters. The atomistic investigation is performed for four crystal sizes of 30×30×30, 60×60×60, 90×90×90 and 120×120×120 Å3 at a temperature of 298 K and a strain rate of 1010 s−1. A comprehensive insight from this work is that the tensile properties fluctuations due to direction are within 13–25% at any distinct crystal size, whereas fluctuations at any specific direction are within 5–17% for mentioned interest of crystal sizes. An optimum crystal size of 60×60×60 Å3, exhibits maximum tensile properties. However, the fracture initiation patterns are quite similar for all sizes and directions where the natures are investigated as ductile.

Implementation Supplementary Feeding Program and Infant and Young Child Feeding Counseling as a Stunting Prevention Program During Pandemic

Large-Scale Social Restrictions (PSBB) as an effort to reduce the transmission of COVID-19 pandemic and COVID-19 pandemic itself hasan impact on stunting prevention program carried out by Public Health Centers (Puskesmas), including the Supplementary Feeding Program (PMT) and Infant and Young Child Feeding Counseling (PMBA) and this condition occurs in various regions in Indonesia, including Bandung. This study aimed to examine the implementation of PMT and PMBA counseling program during the COVID-19 pandemic in the working area of the Buahbatu Public Health Center as one of the public health centers with the highest stunting number in Bandung. This study using the mixed methods concurrent embedded method, in this study quantitative data were used to determine percentage of PMT and PMBA counseling coverage before the COVID-19 pandemic (2017-2019) and during the COVID-19 pandemic (in 2020) as supporting qualitative data done with in-depth interviews. The results showed that the stunting rate increased every year especially during the COVID-19 pandemic, PMT and PMBA counseling continued to be carried out during the COVID-19 Pandemic even though at the beginning of the COVID-19 pandemic the program was hampered, so several adjustments and innovation were made by the public health center officers and cadres to made percentage of stunting children in 2020 is 23,20%, percentage of PMT coverage in 2020 is 100% but percentage for PMBA counseling coverage in 2020 is only 9%. PMT runs smoothly so that all children get PMT, while PMBA counseling runs but is only given to a few stunted children because of some obstacles.

Teacher's Perception of the Online Learning Process at SD Inpres Tinggimae, Gowa Regency

The main problems in this study are the teacher's perception of the online learning process at SD Inpres Tinggimae, problems faced by teachers during the online learning process at SD Inpres Tinggimae, and solutions to problems faced by teachers at SD Inpres Tinggimae. The type of research used in this study is a qualitative research using the mixed method concurrent embedded method. Data collection techniques carried out include: Observation, interviews, documents, and documentation. Data analysis techniques used are data collection, data reduction, data presentation, and drawing conclusions. The results of this study indicate that: (1) online learning is not going well because it has many obstacles and is also ineffective. Problems or obstacles faced by teachers during the online learning process are the absence of supporting facilities such as mobile phones, quotas, and internet networks. The solution to the problem is that students come to school to take assignments or learning materials, study with teachers, seek good network access, also use appropriate learning methods and create discussion forums for parents and teachers. Based on the results of this study, it can be concluded that online learning is not suitable for use at the elementary school level because basically the learning of elementary school children is still teacher-centered. Online learning makes learning objectives not achieved. In addition, there are many obstacles so that learning does not run well and is also effective.

An embedded method: Improve the relevance of text and face image with enhanced face attributes

To solve the problem of low quality and lack of specific attributes in the text-to-face synthesis task, this paper proposes EFA, a general embedding method for strengthening face attributes in the text-to-image synthesis models. First, we re-encode the irregular word-level descriptions scattered in sentences to form word encoding. Then, we design the embedded local feature extraction layer for discriminators of different models to learn more specific information related to face attributes. Next, we associate the word encoding with the extracted face image feature regions to obtain face attribute domain classification loss of the real image and the generated image. Finally, in the training process, we adopt the loss function to constrain the generator and discriminator to improve their performance. This method can improve the quality of text-to-face synthesis and enhance the semantic correlation between the generated image and text description. A large number of experimental results on the newly released Multi-Modal CelebA-HQ dataset verify the validity of our method, and the experimental results are competitive compared with state of the art. Especially, our approach boosts the FID by 47.75% over AttnGAN, by 33.68% over ControlGAN, by 10.05% over DM-GAN, and by 12.52% over DF-GAN. Code is available at https://github.com/cookie-ke/EFA.

Fabrication and integration of functional stretchable circuit based on liquid metal

A liquid metal patterning method and a fabrication process for liquid metal stretchable circuits are described. The initial resistance of the wire-electrode unit is only about 1.4 Ω, and the maximum applied strain is up to 260%. Static stretching and dynamic fatigue tests both reflect the excellent resistance stability. Two types of integrated packaging processes for liquid metal stretchable circuits, surface mount and embedded, are presented. The LED-wire unit manufactured by the embedded method can work normally under a strain of 260%. Through the integration process of surface mounting, the electronic devices are integrated onto the flexible substrate, and the flexible circuit system demonstration of a flash LED is realized. The circuit can work normally under 100% strain. The integration process for liquid metal based flexible electronics provides potential applications in flexible micro-systems.

Characteristics of [formula omitted] screw dislocations and their slip on prismatic and pyramidal planes in pure [formula omitted] titanium from atomistic simulations

Molecular statics and dynamics simulations were carried out to characterize the core structure and calculate the critical resolved shear stress (CRSS) of an 〈a〉 screw dislocation in pure α-Ti using a recent modified embedded atom method spline like potential developed for Ti-Nb alloys. Firstly, it is shown that the generalized stacking fault energy (GSFE) curves calculated using this potential agree well with density functional theory (DFT) and nudged elastic band + DFT computations for the basal, prismatic-I and pyramidal-I planes. In particular, this potential predicts that the 〈a〉 prismatic stacking fault (SF) is lower in energy than the basal intrinsic I2 SF. Two stable core structures for the 〈a〉 screw dislocations were identified by this potential, one dissociates on the pyramidal-I plane, and the other on the prismatic-I plane. The pyramidal-I core is found to be the ground state core structure, while the prismatic-I core is metastable with an excess energy of 18.8 meV/b, which is in good agreement with published DFT calculations. Also, it is shown that the basal dissociation of the 〈a〉 screw dislocation is not stable and upon relaxation this core reconstructs directly to the pyramidal-I ground state structure. Finally, the CRSS for the slip of a prismatic 〈a〉 screw dislocation core on the prismatic-I plane is computed as a function of temperature between 0 and 300 K. It is found that screw dislocations glide by kink-pair mechanism on the prismatic-I planes, and the calculated CRSSs are in good agreement with experimental measurements.

Molecular dynamics study on wetting characteristics of lead droplet on iron surface at high temperatures

The wetting characteristics of a lead (Pb) droplet on an iron (Fe) surface at high temperatures are vital in reactor-related applications. The wetting characteristics of the lead droplet on the iron surface at different temperatures have been investigated by molecular dynamics with the generalized embedded atom method. The spreading process of the lead droplet can be divided into stages dominated by momentum and surface tension, respectively. For the two stages, the spreading radius R of the precursor film (PF) of the lead droplet increases with time t, but the increase of the latter stage is significantly smaller than that of the former one, and the equations of R vs. t are R~t0.5092 and R~t0.2078, respectively. The contact angle of the lead droplet on the iron surface decreases with the increase of the temperature at the same time. In the stage dominated by momentum, the velocity field of the lead droplet presents an overall trend of downward flow. In the stage dominated by surface tension, the flow velocity in the region near the liquid-vapor interface of the lead droplet is significantly higher than that in its internal region, and the velocity of the PF is extremely small. The atoms of the PF of the lead droplet are regularly distributed in the interstitial positions on the iron surface during the spreading process, and its diffusion mechanism on the iron surface is the surface near-neighbor interstice hopping mechanism. Furthermore, the iron substrate is corroded by the liquid lead during the wetting process, and the corrosion is aggravated with both the increase of the time and the temperature.

Sentiment Analysis of Tourism Objects on Trip Advisor Using LSTM Method

This study developed a sentiment analysis application for comments on tourist sites. It is used to help people who want to know about tourist attractions information to get positive or negative information. The method used to analyze the sentiment was LSTM. The determination of LSTM architecture consists of scraping data, manual labelling, preprocessing (case folding, removing punctuation, removing stopwords, tokenization, and lemmatization), word2index, word embedding, and LSTM layer. In order to achieve optimal accuracy, it is necessary to determine the right embedded method, the total number of layers for the dropout layer, and LSTM. The performance of this study showed that the accuracy and loss from sentiment analysis using the LSTM method were 96.71% and 14.22%.

Modified extended Finnis Sinclair potential for cubic crystal metal

Unlike the modified embedded atom method (MEAM), which requires consideration of the bond angles, the embedded atom method (EAM) and Finnis Sinclair (FS) potential have achieved a wide range of applications in molecular dynamics simulations of amorphous alloys and disordered systems. In this paper, the potential functions of 10 cubic crystalline metals are reconstructed using the extended Finnis Sinclair (EFS) potential to improve the FS potential in terms of defects, surface energy and thermal properties. First of all, for the BCC crystal structure and FCC crystal structure, the fitted physical quantity expressions suitable for EAM potential and FS potential are deduced, including pressure, bulk modulus, shear elastic modulus elastic constant, vacancy formation energy and surface energy. Then, based on these physical quantities and the Rose equation of state, the least-squares method is used to fit the new potential parameters. Finally, using the current potential, the cohesive energy, elastic constants (C11, C12 and C44), vacancy formation energy, self-interstitial formation energy, surface energy, coefficient of thermal expansion, specific heat capacity and the melting point of 10 kinds of cubic crystals are calculated by molecular dynamics simulation. The reliability of the current potential is verified by comparing with other potential functions, experimental values and first-principles calculations. The results show that the current potential can well reproduce the characteristics of physical quantities such as lattice constant, cohesive energy and elastic constants (C11, C12 and C44). Compared with the previous EFS potential, the current potential is closer to the Rose equation of state. The calculated surface energy is more accurate, and the performance of defects and thermal properties shows the reliability of the current potential function, and these improvements are due to the improvement of the fitting method.

A Novel Method for Survival Prediction of Hepatocellular Carcinoma Using Feature-Selection Techniques

The World Health Organization (WHO) predicted that 10 million people would have died of cancer by 2020. According to recent studies, liver cancer is the most prevalent cancer worldwide. Hepatocellular carcinoma (HCC) is the leading cause of early-stage liver cancer. However, HCC occurs most frequently in patients with chronic liver conditions (such as cirrhosis). Therefore, it is important to predict liver cancer more explicitly by using machine learning. This study examines the survival prediction of a dataset of HCC based on three strategies. Originally, missing values are estimated using mean, mode, and k-Nearest Neighbor (k-NN). We then compare the different select features using the wrapper and embedded methods. The embedded method employs Least Absolute Shrinkage and Selection Operator (LASSO) and ridge regression in conjunction with Logistic Regression (LR). In the wrapper method, gradient boosting and random forests eliminate features recursively. Classification algorithms for predicting results include k-NN, Random Forest (RF), and Logistic Regression. The experimental results indicate that Recursive Feature Elimination with Gradient Boosting (RFE-GB) produces better results, with a 96.66% accuracy rate and a 95.66% F1-score.

Computational analysis of mechanical behavior and potential energy of thermoresponsive copper-tantalum nanoalloy.

Temperature, strain rate, and defects are important considerations in determining the mechanical properties of materials. The mechanical properties of nanocrystalline copper-tantalum (Cu-Ta) alloy are investigated using classical molecular dynamics simulation approach in which embedded atom method of potential with periodic boundary conditions in all directions has been adopted. Numerical simulation has been performed to predict the mechanical properties of nanocrystalline copper-tantalum alloy. The virtual tensile test has been conducted at a fixed strain rate and increasing temperature where the discreet change in temperature from 50 to 1600K has been used as a controlling parameter. The strain rate is fixed in the direction of the principal crystallographic planes and has not been affected by the change in temperature. The mechanical properties of the Cu-Ta nanocrystalline alloy such as yield strength, ultimate strength, and Young's modulus are observed. Further, simulations are carried out to analyze the vacancy formation energy with vacancy concentration and potential energy response at discrete temperatures. Nanocrystalline Cu-Ta alloy is observed to be more susceptible to failure at high temperatures. Particularly at 300K, the strength of nanocrystalline Cu-Ta is 6 GPa which decreases to 4 GPa at 1200K.