In this study,insights into the effect of interfacial anisotropy on a complex hexagonal close-packed(hcp) dendritic growth during alloy solidification were gained by graphics processing unit(GPU)-accelerated three-dim...In this study,insights into the effect of interfacial anisotropy on a complex hexagonal close-packed(hcp) dendritic growth during alloy solidification were gained by graphics processing unit(GPU)-accelerated three-dimensional(3D) phase-field simulations,as demonstrated for a Mg-Gd alloy.An anisotropic phasefield model with finite interface dissipation was developed by incorporating the contribution of the anisotropy of interfacial energy into the total free energy functional.The modified spherical harmonic anisotropy function was then chosen for the hcp crystal.The GPU parallel computing algorithm was implemented in the present phase-field model,and a corresponding code was developed in the compute unified device architecture parallel computing platform.Benchmark tests indicated that the calculation efficiency of a single TESLA V100 GPU could be~80times that of open multi-processing(OpenMP) with eight central processing unit cores.By coupling the phase-field model with reliable thermodynamic and interfacial energy descriptions,the 3D phase-field simulation of α-Mg dendritic growth in the Mg-6Gd(in wt%) alloy during solidification was performed.Various two-dimensional dendrite morphologies were revealed by cutting the simulated 3D dendrite along different crystallographic planes.Typical sixfold equiaxed and butterflied microstructures observed in experiments were well reproduced.展开更多
Electricity prices in liberalized markets are determined by the supply and demand for electric power,which are in turn driven by various external influences that vary strongly in time.In perfect competition,the merit ...Electricity prices in liberalized markets are determined by the supply and demand for electric power,which are in turn driven by various external influences that vary strongly in time.In perfect competition,the merit order principle describes that dispatchable power plants enter the market in the order of their marginal costs to meet the residual load,i.e.the difference of load and renewable generation.Various market models are based on this principle when attempting to predict electricity prices,yet the principle is fraught with assumptions and simplifications and thus is limited in accurately predicting prices.In this article,we present an explainable machine learning model for the electricity prices on the German day-ahead market which foregoes of the aforementioned assumptions of the merit order principle.Our model is designed for an ex-post analysis of prices and builds on various external features.Using SHapley Additive exPlanation(SHAP)values we disentangle the role of the different features and quantify their importance from empiric data,and therein circumvent the limitations inherent to the merit order principle.We show that load,wind and solar generation are the central external features driving prices,as expected,wherein wind generation affects prices more than solar generation.Similarly,fuel prices also highly affect prices,and do so in a nontrivial manner.Moreover,large generation ramps are correlated with high prices due to the limited flexibility of nuclear and lignite plants.Overall,we offer a model that describes the influence of the main drivers of electricity prices in Germany,taking us a step beyond the limited merit order principle in explaining the drivers of electricity prices and their relation to each other.展开更多
By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ionsare recombined into neutral molecules and atoms of hydrogen isotopes. These speciesrecycle back into the plasma volume and pa...By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ionsare recombined into neutral molecules and atoms of hydrogen isotopes. These speciesrecycle back into the plasma volume and participate, in particular, in charge–exchange(cx) collisions with ions. As a result, hot atoms with chaotically directed velocities aregenerated and some of them hit the wall. Statistical Monte Carlo methods often usedto model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kineticequation2 has been significantly accelerated, by a factor of 30–50, by applying a passmethod to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation,describing the transport of cx atoms in the vicinity of an opening in the wall, e.g.,the entrance of a duct guiding to a diagnostic installation. To assess the erosion rateand lifetime of the installation, one need to know the energy spectrum of hot cx atomsescaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The resultsof kinetic modeling are compared with those found by using a diffusion approximation5relevant for cx atoms if the time between cx collisions with ions is much smaller thanthe time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximatediffusion approach.展开更多
基金supported by the Natural Science Foundation of Hunan Province for Distinguished Young Scholars (No. 2021JJ10062)National Key Research and Development Program of China (No. 2016YFB0301101)+2 种基金Science and Technology Program of Guangxi province, China (No. AB21220028)the financial support from the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts050)Postgraduate Scientific Research Innovation Project of Hunan Province (No. CX20190106)。
文摘In this study,insights into the effect of interfacial anisotropy on a complex hexagonal close-packed(hcp) dendritic growth during alloy solidification were gained by graphics processing unit(GPU)-accelerated three-dimensional(3D) phase-field simulations,as demonstrated for a Mg-Gd alloy.An anisotropic phasefield model with finite interface dissipation was developed by incorporating the contribution of the anisotropy of interfacial energy into the total free energy functional.The modified spherical harmonic anisotropy function was then chosen for the hcp crystal.The GPU parallel computing algorithm was implemented in the present phase-field model,and a corresponding code was developed in the compute unified device architecture parallel computing platform.Benchmark tests indicated that the calculation efficiency of a single TESLA V100 GPU could be~80times that of open multi-processing(OpenMP) with eight central processing unit cores.By coupling the phase-field model with reliable thermodynamic and interfacial energy descriptions,the 3D phase-field simulation of α-Mg dendritic growth in the Mg-6Gd(in wt%) alloy during solidification was performed.Various two-dimensional dendrite morphologies were revealed by cutting the simulated 3D dendrite along different crystallographic planes.Typical sixfold equiaxed and butterflied microstructures observed in experiments were well reproduced.
文摘Electricity prices in liberalized markets are determined by the supply and demand for electric power,which are in turn driven by various external influences that vary strongly in time.In perfect competition,the merit order principle describes that dispatchable power plants enter the market in the order of their marginal costs to meet the residual load,i.e.the difference of load and renewable generation.Various market models are based on this principle when attempting to predict electricity prices,yet the principle is fraught with assumptions and simplifications and thus is limited in accurately predicting prices.In this article,we present an explainable machine learning model for the electricity prices on the German day-ahead market which foregoes of the aforementioned assumptions of the merit order principle.Our model is designed for an ex-post analysis of prices and builds on various external features.Using SHapley Additive exPlanation(SHAP)values we disentangle the role of the different features and quantify their importance from empiric data,and therein circumvent the limitations inherent to the merit order principle.We show that load,wind and solar generation are the central external features driving prices,as expected,wherein wind generation affects prices more than solar generation.Similarly,fuel prices also highly affect prices,and do so in a nontrivial manner.Moreover,large generation ramps are correlated with high prices due to the limited flexibility of nuclear and lignite plants.Overall,we offer a model that describes the influence of the main drivers of electricity prices in Germany,taking us a step beyond the limited merit order principle in explaining the drivers of electricity prices and their relation to each other.
文摘By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ionsare recombined into neutral molecules and atoms of hydrogen isotopes. These speciesrecycle back into the plasma volume and participate, in particular, in charge–exchange(cx) collisions with ions. As a result, hot atoms with chaotically directed velocities aregenerated and some of them hit the wall. Statistical Monte Carlo methods often usedto model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kineticequation2 has been significantly accelerated, by a factor of 30–50, by applying a passmethod to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation,describing the transport of cx atoms in the vicinity of an opening in the wall, e.g.,the entrance of a duct guiding to a diagnostic installation. To assess the erosion rateand lifetime of the installation, one need to know the energy spectrum of hot cx atomsescaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The resultsof kinetic modeling are compared with those found by using a diffusion approximation5relevant for cx atoms if the time between cx collisions with ions is much smaller thanthe time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximatediffusion approach.
