Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds.However,conventional encoding does not include angular information,which is...Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds.However,conventional encoding does not include angular information,which is critical for describing atomic arrangements in disordered systems.In this work,we extend the recently proposed ALIGNN(Atomistic Line Graph Neural Network)encoding,which incorporates bond angles,to also include dihedral angles(ALIGNN-d).This simple extension leads to a memory-efficient graph representation that captures the complete geometry of atomic structures.ALIGNN-d is applied to predict the infrared optical response of dynamically disordered Cu(II)aqua complexes,leveraging the intrinsic interpretability to elucidate the relative contributions of individual structural components.Bond and dihedral angles are found to be critical contributors to the fine structure of the absorption response,with distortions that represent transitions between more common geometries exhibiting the strongest absorption intensity.Future directions for further development of ALIGNN-d are discussed.展开更多
The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the...The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convectionflows, the surface of the cylinder is maintained by the uniform surface temperature(UST)or the uniform heat flux(UHF) condition. The governing equations corresponding to theflow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids(n > 1) than the other fluids(n≤1).The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.展开更多
Storage backends of parallel compute clusters are still based mostly on magnetic disks,while newer and faster storage technologies such as flash-based SSDs or non-volatile random access memory(NVRAM)are deployed withi...Storage backends of parallel compute clusters are still based mostly on magnetic disks,while newer and faster storage technologies such as flash-based SSDs or non-volatile random access memory(NVRAM)are deployed within compute nodes.Including these new storage technologies into scientific workflows is unfortunately today a mostly manual task,and most scientists therefore do not take advantage of the faster storage media.One approach to systematically include nodelocal SSDs or NVRAMs into scientific workflows is to deploy ad hoc file systems over a set of compute nodes,which serve as temporary storage systems for single applications or longer-running campaigns.This paper presents results from the Dagstuhl Seminar 17202"Challenges and Opportunities of User-Level File Systems for HPC"and discusses application scenarios as well as design strategies for ad hoc file systems using node-local storage media.The discussion includes open research questions,such as how to couple ad hoc file systems with the batch scheduling environment and how to schedule stage-in and stage-out processes of data between the storage backend and the ad hoc file systems.Also presented are strategies to build ad hoc file systems by using reusable components for networking and how to improve storage device compatibility.Various interfaces and semantics are presented,for example those used by the three ad hoc file systems BeeOND,GekkoFS,and BurstFS.Their presentation covers a range from file systems running in production to cutting-edge research focusing on reaching the performance limits of the underlying devices.展开更多
The magneto-hydrodynamics(MHD)effect is studied at different inclined angles in Rayleigh-Bénard(RB)convection inside a rectangular enclosure using the lattice Boltzmann method(LBM).The enclosure is filled with el...The magneto-hydrodynamics(MHD)effect is studied at different inclined angles in Rayleigh-Bénard(RB)convection inside a rectangular enclosure using the lattice Boltzmann method(LBM).The enclosure is filled with electrically conducting fluids of different characteristics.These characteristics are defined by Prandtl number,Pr.The considered Pr values for this study are 10 and 70.The influence of other dimensionless parameters Rayleigh numbers Ra=10^(3);10^(4);10^(5);10^(6) and Hartmann numbers Ha=0,10,25,50,100,on fluid flow and heat transfer,are also investigated considering different inclined anglesφof magnetic field by analyzing computed local Nusselt numbers and average Nusselt numbers.The results of the study show the undoubted prediction capability of LBM for the current problem.The simulated results demonstrate that the augmentation in heat transfer is directly related to Ra values,but it is opposite while observing the characteristics of Ha values.However,it is also found thatφhas a significant impact on heat transfer for different fluids.Besides,isotherms are found to be always parallel to the horizontal axis at Ra=10^(3) as conduction overcomes the convection in the heat transfer,but this behaviour is not seen at Ra=10^(4) when Ha>25.Furthermore,at Ra=10^(6),oscillatory instability appears but LBM is still able to provide a complete map of this predicted behavior.An appropriate validation with previous numerical studies demonstrates the accuracy of the present approach.展开更多
A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dim...A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method.The flow was controlled by a range of parameters such as Rayleigh number,length of heat source and nanoparticle volume fraction.The numerical results are represented in terms of isotherms,streamlines,velocity and temperature distribution as well as the local and average rate of heat transfer.A comparative study has been conducted for two different base fluids,ethylene glycol and water as well as for two different solids Cu and Al_(2)O_(3).It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.展开更多
Despite ML’s impressive performance in commercial applications,several unique challenges exist when applying ML in materials science applications.In such a context,the contributions of this work are twofold.First,we ...Despite ML’s impressive performance in commercial applications,several unique challenges exist when applying ML in materials science applications.In such a context,the contributions of this work are twofold.First,we identify common pitfalls of existing ML techniques when learning from underrepresented/imbalanced material data.Specifically,we show that with imbalanced data,standard methods for assessing quality of ML models break down and lead to misleading conclusions.Furthermore,we find that the model’s own confidence score cannot be trusted and model introspection methods(using simpler models)do not help as they result in loss of predictive performance(reliability-explainability trade-off).Second,to overcome these challenges,we propose a general-purpose explainable and reliable machine-learning framework.Specifically,we propose a generic pipeline that employs an ensemble of simpler models to reliably predict material properties.We also propose a transfer learning technique and show that the performance loss due to models’simplicity can be overcome by exploiting correlations among different material properties.A new evaluation metric and a trust score to better quantify the confidence in the predictions are also proposed.To improve the interpretability,we add a rationale generator component to our framework which provides both model-level and decision-level explanations.Finally,we demonstrate the versatility of our technique on two applications:(1)predicting properties of crystalline compounds and(2)identifying potentially stable solar cell materials.We also point to some outstanding issues yet to be resolved for a successful application of ML in material science.展开更多
In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the para...In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu （HX） auxiliary space decomposition [Hiptmair and Xu, SIAM J. Numer. Anal., 45 （2007）, pp. 2483-2509]. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H（curl） problems.展开更多
A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-...A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision.展开更多
Background:Besides maintaining health precautions,vaccination has been the only prevention from SARS-CoV-2,though no clinically proved 100%effective vaccine has been developed till date.At this stage,to withhold the d...Background:Besides maintaining health precautions,vaccination has been the only prevention from SARS-CoV-2,though no clinically proved 100%effective vaccine has been developed till date.At this stage,to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates,the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates.In this article,a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic.Methods:We simulated a five compartment mathematical model to analyze the pandemic scenario in both California,and whole U.S.We considered four vaccines,Pfizer(95%),Moderna(94%),AstraZeneca(79%),and Johnson&Johnson(72%),which are being used rigorously to control the SARS-CoV-2 pandemic,in addition with two special cases:a vaccine with 100%efficacy rate and no vaccine under use.SARS-CoV-2 related data of California,and U.S.were used in this study.Findings:Both the infection and death rates are very high in California.Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine.During this time,six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697%and 98.30%,respectively.However,according to the considered model,this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used.On the other hand,the daily cases and deaths in the U.S.will be under control at the end of 2026 with multiple waves.Although the number of susceptible people will fall down to none in the beginning of 2027,there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100%effective vaccine or Pfizer,and at that case vaccination program must run till the mid of 2028.According to this study,the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028,respectively.Interpretation:The more effective a vaccine is,the less people suffer from this malign infection.Vaccines which are less than 90%effective do not have notable contribution to control the pandemic besides hard immunity.Furthermore,specific groups of people are getting prioritized initially,mass vaccination and quick responses are required to control the spread of this disease.展开更多
Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true ...Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock locations.However,correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is refined.Here we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee(JWL)equation of state.We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations.Furthermore,we demonstrate that under certain conditions,a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.展开更多
We develop an embedded boundary finite difference technique for solving the compressible two-or three-dimensional Euler equations in complex geometries on a Cartesian grid.The method is second order accurate with an e...We develop an embedded boundary finite difference technique for solving the compressible two-or three-dimensional Euler equations in complex geometries on a Cartesian grid.The method is second order accurate with an explicit time step determined by the grid size away from the boundary.Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves.We show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid.Furthermore,we discuss the implementation of the method for thin geometries,and show computed examples of transonic flow past an airfoil.展开更多
In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the f...In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid.In a numerical scheme,there are many ways that velocity-and stress-continuity can be enforced in the discrete approximation.This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes.The analysis shows that depending on the ratio of densities between the solid and the fluid,some numerical interface conditions are stable up to the maximal CFL-limit,while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit.The paper also presents a new interface condition,obtained as a simplified characteristic boundary condition,that is proved to not suffer from any reduction of the stable CFL-limit.Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.展开更多
An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the gr...An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface.Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces.The discretization of singular source terms of point force and point moment tensor type are also studied.Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient,previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces.These source discretization formulas are shown to give second order accuracy in the solution,with the error being essentially independent of the distance between the source and the grid refinement boundary.Several numerical examples are given to illustrate the properties of the proposed method.展开更多
Flows containing steady or nearly steady strong shocks on parts of the flow field,and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing t...Flows containing steady or nearly steady strong shocks on parts of the flow field,and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme,even under the multiblock grid or adaptive grid refinement framework.While sixthorder or higher-order shock-capturing methods are appropriate for unsteady turbulence with shocklets,third-order or lower shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence.In order to minimize the short comings of low order and high order shock-capturing schemes for the subject flows,a multiblock overlapping grid with different types of spatial schemes and orders of accuracy on different blocks is proposed.The recently developed single block high order filter scheme in generalized geometries for Navier Stokes and magnetohydrodynamics systems is extended to multiblock overlapping grid geometries.The first stage in validating the high order overlapping approach with several test cases is included.展开更多
We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed...We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed.We prove stability for a second-order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition.The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials.The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners.The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.展开更多
In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control term.We focus on a time-dependent PDE,and consider both distributed and boundary control.The problems we c...In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control term.We focus on a time-dependent PDE,and consider both distributed and boundary control.The problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle this.We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.展开更多
Machine learning models are increasingly used in materials studies because of their exceptional accuracy.However,the most accurate machine learning models are usually difficult to explain.Remedies to this problem lie ...Machine learning models are increasingly used in materials studies because of their exceptional accuracy.However,the most accurate machine learning models are usually difficult to explain.Remedies to this problem lie in explainable artificial intelligence(XAI),an emerging research field that addresses the explainability of complicated machine learning models like deep neural networks(DNNs).This article attempts to provide an entry point to XAI for materials scientists.Concepts are defined to clarify what explain means in the context of materials science.Example works are reviewed to show how XAI helps materials science research.Challenges and opportunities are also discussed.展开更多
We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the ...We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the far-field boundaries.Mathematically,this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain,where the elastic wave equation is solved numerically on a regular grid.To damp out waves that become poorly resolved because of the coordinate mapping,a high order artificial dissipation operator is added in layers near the boundaries of the computational domain.We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy,which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain.Our spatial discretization is based on a fourth order accurate finite difference method,which satisfies the principle of summation by parts.We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries.Therefore,the coefficients in the finite difference stencils need only be boundary modified near the free surface.This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains.Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer.The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem,where fourth order accuracy is observed with a sixth order artificial dissipation.We then use successive grid refinements to study the numerical accuracy in the more complicated motion due to a point moment tensor source in a regularized layered material.展开更多
We develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation.The material model is a super-imposition of N standard linear solid mechanisms,which commonly is used in seismolo...We develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation.The material model is a super-imposition of N standard linear solid mechanisms,which commonly is used in seismology to model a material with constant quality factor Q.The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables,making it significantly more memory efficient than the commonly used first order velocitystress formulation.The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation[SIAM J.Numer.Anal.,45(2007),pp.1902–1936].Our main result is a proof that the proposed discretization is energy stable,even in the case of variable material properties.The proof relies on the summation-by-parts property of the discretization.The newscheme is implemented with grid refinement with hanging nodes on the interface.Numerical experiments verify the accuracy and stability of the new scheme.Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy.We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.展开更多
Machine-learning(ML)techniques hold the potential of enabling efficient quantitative micrograph analysis,but the robustness of ML models with respect to real-world micrograph quality variations has not been carefully ...Machine-learning(ML)techniques hold the potential of enabling efficient quantitative micrograph analysis,but the robustness of ML models with respect to real-world micrograph quality variations has not been carefully evaluated.We collected thousands of scanning electron microscopy(SEM)micrographs for molecular solid materials,in which image pixel intensities vary due to both the microstructure content and microscope instrument conditions.We then built ML models to predict the ultimate compressive strength(UCS)of consolidated molecular solids,by encoding micrographs with different image feature descriptors and training a random forest regressor,and by training an end-to-end deep-learning(DL)model.Results show that instrument-induced pixel intensity signals can affect ML model predictions in a consistently negative way.As a remedy,we explored intensity normalization techniques.It is seen that intensity normalization helps to improve micrograph data quality and ML model robustness,but microscope-induced intensity variations can be difficult to eliminate.展开更多
基金The authors are partially supported by the Laboratory Directed Research and Development(LDRD)program(20-SI-004)at Lawrence Livermore National LaboratoryThis work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract No.DE-AC52-07NA27344.
文摘Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds.However,conventional encoding does not include angular information,which is critical for describing atomic arrangements in disordered systems.In this work,we extend the recently proposed ALIGNN(Atomistic Line Graph Neural Network)encoding,which incorporates bond angles,to also include dihedral angles(ALIGNN-d).This simple extension leads to a memory-efficient graph representation that captures the complete geometry of atomic structures.ALIGNN-d is applied to predict the infrared optical response of dynamically disordered Cu(II)aqua complexes,leveraging the intrinsic interpretability to elucidate the relative contributions of individual structural components.Bond and dihedral angles are found to be critical contributors to the fine structure of the absorption response,with distortions that represent transitions between more common geometries exhibiting the strongest absorption intensity.Future directions for further development of ALIGNN-d are discussed.
基金Project supported by the North South University,Bangladesh(Nos.NSU-RP-18-067 and CTRG-19/SEPS/15)。
文摘The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convectionflows, the surface of the cylinder is maintained by the uniform surface temperature(UST)or the uniform heat flux(UHF) condition. The governing equations corresponding to theflow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids(n > 1) than the other fluids(n≤1).The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.
基金This work has also been partially funded by the German Research Foundation(DFG)through the German Priority Programme 1648"Software for Exascale Computing"(SPPEXA)and the ADA-FS project,and by the European Union's Horizon 2020 Research and Innovation Program under the NEXTGenIO Project under Grant No.671591the Spanish Ministry of Science and Innovation under Contract No.TIN2015-65316+3 种基金the Generalitat de Catalunya under Contract No.2014-SGR-1051This work was performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract No.DE-AC52-07NA27344(LLNL-JRNL-779789)also supported by the U.S.Department of Energy,Office of Science,Advanced Scientific Computing Research,under Contract No.DE-AC02-06CH11357This work is also supported in part by the National Science Foundation of USA under Grant Nos.1561041,1564647,1744336,1763547,and 1822737.
文摘Storage backends of parallel compute clusters are still based mostly on magnetic disks,while newer and faster storage technologies such as flash-based SSDs or non-volatile random access memory(NVRAM)are deployed within compute nodes.Including these new storage technologies into scientific workflows is unfortunately today a mostly manual task,and most scientists therefore do not take advantage of the faster storage media.One approach to systematically include nodelocal SSDs or NVRAMs into scientific workflows is to deploy ad hoc file systems over a set of compute nodes,which serve as temporary storage systems for single applications or longer-running campaigns.This paper presents results from the Dagstuhl Seminar 17202"Challenges and Opportunities of User-Level File Systems for HPC"and discusses application scenarios as well as design strategies for ad hoc file systems using node-local storage media.The discussion includes open research questions,such as how to couple ad hoc file systems with the batch scheduling environment and how to schedule stage-in and stage-out processes of data between the storage backend and the ad hoc file systems.Also presented are strategies to build ad hoc file systems by using reusable components for networking and how to improve storage device compatibility.Various interfaces and semantics are presented,for example those used by the three ad hoc file systems BeeOND,GekkoFS,and BurstFS.Their presentation covers a range from file systems running in production to cutting-edge research focusing on reaching the performance limits of the underlying devices.
基金The second author would like to acknowledge to the North South University for the partial support as a Research Assistant(Grant No.NSU-RP-18-067)。
文摘The magneto-hydrodynamics(MHD)effect is studied at different inclined angles in Rayleigh-Bénard(RB)convection inside a rectangular enclosure using the lattice Boltzmann method(LBM).The enclosure is filled with electrically conducting fluids of different characteristics.These characteristics are defined by Prandtl number,Pr.The considered Pr values for this study are 10 and 70.The influence of other dimensionless parameters Rayleigh numbers Ra=10^(3);10^(4);10^(5);10^(6) and Hartmann numbers Ha=0,10,25,50,100,on fluid flow and heat transfer,are also investigated considering different inclined anglesφof magnetic field by analyzing computed local Nusselt numbers and average Nusselt numbers.The results of the study show the undoubted prediction capability of LBM for the current problem.The simulated results demonstrate that the augmentation in heat transfer is directly related to Ra values,but it is opposite while observing the characteristics of Ha values.However,it is also found thatφhas a significant impact on heat transfer for different fluids.Besides,isotherms are found to be always parallel to the horizontal axis at Ra=10^(3) as conduction overcomes the convection in the heat transfer,but this behaviour is not seen at Ra=10^(4) when Ha>25.Furthermore,at Ra=10^(6),oscillatory instability appears but LBM is still able to provide a complete map of this predicted behavior.An appropriate validation with previous numerical studies demonstrates the accuracy of the present approach.
基金The third author acknowledges the Ministry of Science and Technology(MOST),the People’s Republic of Bangladesh(https://most.gov.bd/),for providing the financial support for this research gratefully(Grant No.441-EAS)The third author also acknowledges gratefully to the North South University for the financial support as a Faculty Research Grant(CTRG-20-SEPS-15)(http://www.northsouth.edu/research-office/).
文摘A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method.The flow was controlled by a range of parameters such as Rayleigh number,length of heat source and nanoparticle volume fraction.The numerical results are represented in terms of isotherms,streamlines,velocity and temperature distribution as well as the local and average rate of heat transfer.A comparative study has been conducted for two different base fluids,ethylene glycol and water as well as for two different solids Cu and Al_(2)O_(3).It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.
基金This work was performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344was supported by the LLNL-LDRD Program under Project No.16-ERD-019 and 19-SI-001(LLNL-JRNL-764864).
文摘Despite ML’s impressive performance in commercial applications,several unique challenges exist when applying ML in materials science applications.In such a context,the contributions of this work are twofold.First,we identify common pitfalls of existing ML techniques when learning from underrepresented/imbalanced material data.Specifically,we show that with imbalanced data,standard methods for assessing quality of ML models break down and lead to misleading conclusions.Furthermore,we find that the model’s own confidence score cannot be trusted and model introspection methods(using simpler models)do not help as they result in loss of predictive performance(reliability-explainability trade-off).Second,to overcome these challenges,we propose a general-purpose explainable and reliable machine-learning framework.Specifically,we propose a generic pipeline that employs an ensemble of simpler models to reliably predict material properties.We also propose a transfer learning technique and show that the performance loss due to models’simplicity can be overcome by exploiting correlations among different material properties.A new evaluation metric and a trust score to better quantify the confidence in the predictions are also proposed.To improve the interpretability,we add a rationale generator component to our framework which provides both model-level and decision-level explanations.Finally,we demonstrate the versatility of our technique on two applications:(1)predicting properties of crystalline compounds and(2)identifying potentially stable solar cell materials.We also point to some outstanding issues yet to be resolved for a successful application of ML in material science.
基金This work performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.UCRL-JRNL-237306
文摘In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu （HX） auxiliary space decomposition [Hiptmair and Xu, SIAM J. Numer. Anal., 45 （2007）, pp. 2483-2509]. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H（curl） problems.
基金This work performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
文摘A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision.
基金M.Kamrujjaman is grateful to the centennial research program,Dhaka UniversityThe research by M.Kamrujjaman was partially supported by a TWAS grant 2019_19-169 RG/MATHS/AS_I.
文摘Background:Besides maintaining health precautions,vaccination has been the only prevention from SARS-CoV-2,though no clinically proved 100%effective vaccine has been developed till date.At this stage,to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates,the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates.In this article,a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic.Methods:We simulated a five compartment mathematical model to analyze the pandemic scenario in both California,and whole U.S.We considered four vaccines,Pfizer(95%),Moderna(94%),AstraZeneca(79%),and Johnson&Johnson(72%),which are being used rigorously to control the SARS-CoV-2 pandemic,in addition with two special cases:a vaccine with 100%efficacy rate and no vaccine under use.SARS-CoV-2 related data of California,and U.S.were used in this study.Findings:Both the infection and death rates are very high in California.Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine.During this time,six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697%and 98.30%,respectively.However,according to the considered model,this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used.On the other hand,the daily cases and deaths in the U.S.will be under control at the end of 2026 with multiple waves.Although the number of susceptible people will fall down to none in the beginning of 2027,there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100%effective vaccine or Pfizer,and at that case vaccination program must run till the mid of 2028.According to this study,the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028,respectively.Interpretation:The more effective a vaccine is,the less people suffer from this malign infection.Vaccines which are less than 90%effective do not have notable contribution to control the pandemic besides hard immunity.Furthermore,specific groups of people are getting prioritized initially,mass vaccination and quick responses are required to control the spread of this disease.
基金supported by Lawrence Livermore National Laboratory under the auspices of the U.S.Department of Energy through contract number DE-AC52-07NA27344.
文摘Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock locations.However,correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is refined.Here we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee(JWL)equation of state.We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations.Furthermore,we demonstrate that under certain conditions,a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.
基金performed under the auspices of the U.S.Department of Energy by University of California Lawrence Livermore National Laboratory under contract No.W7405-Eng-48.
文摘We develop an embedded boundary finite difference technique for solving the compressible two-or three-dimensional Euler equations in complex geometries on a Cartesian grid.The method is second order accurate with an explicit time step determined by the grid size away from the boundary.Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves.We show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid.Furthermore,we discuss the implementation of the method for thin geometries,and show computed examples of transonic flow past an airfoil.
基金supported by Lawrence Livermore National Laboratory under the auspices of the U.S.Department of Energy through contract number DE-AC52-07NA27344.
文摘In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid.In a numerical scheme,there are many ways that velocity-and stress-continuity can be enforced in the discrete approximation.This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes.The analysis shows that depending on the ratio of densities between the solid and the fluid,some numerical interface conditions are stable up to the maximal CFL-limit,while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit.The paper also presents a new interface condition,obtained as a simplified characteristic boundary condition,that is proved to not suffer from any reduction of the stable CFL-limit.Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.
基金the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344contribution LLNL-JRNL-419382.
文摘An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface.Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces.The discretization of singular source terms of point force and point moment tensor type are also studied.Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient,previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces.These source discretization formulas are shown to give second order accuracy in the solution,with the error being essentially independent of the distance between the source and the grid refinement boundary.Several numerical examples are given to illustrate the properties of the proposed method.
基金This work performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344。
文摘Flows containing steady or nearly steady strong shocks on parts of the flow field,and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme,even under the multiblock grid or adaptive grid refinement framework.While sixthorder or higher-order shock-capturing methods are appropriate for unsteady turbulence with shocklets,third-order or lower shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence.In order to minimize the short comings of low order and high order shock-capturing schemes for the subject flows,a multiblock overlapping grid with different types of spatial schemes and orders of accuracy on different blocks is proposed.The recently developed single block high order filter scheme in generalized geometries for Navier Stokes and magnetohydrodynamics systems is extended to multiblock overlapping grid geometries.The first stage in validating the high order overlapping approach with several test cases is included.
文摘We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed.We prove stability for a second-order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition.The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials.The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners.The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
文摘In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control term.We focus on a time-dependent PDE,and consider both distributed and boundary control.The problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle this.We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
基金This work was performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344supported by the LLNL-LDRD Program under Project No.19-SI-001.
文摘Machine learning models are increasingly used in materials studies because of their exceptional accuracy.However,the most accurate machine learning models are usually difficult to explain.Remedies to this problem lie in explainable artificial intelligence(XAI),an emerging research field that addresses the explainability of complicated machine learning models like deep neural networks(DNNs).This article attempts to provide an entry point to XAI for materials scientists.Concepts are defined to clarify what explain means in the context of materials science.Example works are reviewed to show how XAI helps materials science research.Challenges and opportunities are also discussed.
基金the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.This is contribution LLNL-JRNL-610212.
文摘We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the far-field boundaries.Mathematically,this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain,where the elastic wave equation is solved numerically on a regular grid.To damp out waves that become poorly resolved because of the coordinate mapping,a high order artificial dissipation operator is added in layers near the boundaries of the computational domain.We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy,which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain.Our spatial discretization is based on a fourth order accurate finite difference method,which satisfies the principle of summation by parts.We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries.Therefore,the coefficients in the finite difference stencils need only be boundary modified near the free surface.This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains.Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer.The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem,where fourth order accuracy is observed with a sixth order artificial dissipation.We then use successive grid refinements to study the numerical accuracy in the more complicated motion due to a point moment tensor source in a regularized layered material.
文摘We develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation.The material model is a super-imposition of N standard linear solid mechanisms,which commonly is used in seismology to model a material with constant quality factor Q.The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables,making it significantly more memory efficient than the commonly used first order velocitystress formulation.The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation[SIAM J.Numer.Anal.,45(2007),pp.1902–1936].Our main result is a proof that the proposed discretization is energy stable,even in the case of variable material properties.The proof relies on the summation-by-parts property of the discretization.The newscheme is implemented with grid refinement with hanging nodes on the interface.Numerical experiments verify the accuracy and stability of the new scheme.Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy.We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.
基金The authors would like to thank Donald Loveland,Jize Zhang,and Piyush Karande for prototype codes and helpful discussions.This work was performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344was supported by the LLNL-LDRD Program under Project No.19-SI-001。
文摘Machine-learning(ML)techniques hold the potential of enabling efficient quantitative micrograph analysis,but the robustness of ML models with respect to real-world micrograph quality variations has not been carefully evaluated.We collected thousands of scanning electron microscopy(SEM)micrographs for molecular solid materials,in which image pixel intensities vary due to both the microstructure content and microscope instrument conditions.We then built ML models to predict the ultimate compressive strength(UCS)of consolidated molecular solids,by encoding micrographs with different image feature descriptors and training a random forest regressor,and by training an end-to-end deep-learning(DL)model.Results show that instrument-induced pixel intensity signals can affect ML model predictions in a consistently negative way.As a remedy,we explored intensity normalization techniques.It is seen that intensity normalization helps to improve micrograph data quality and ML model robustness,but microscope-induced intensity variations can be difficult to eliminate.
