Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for on...Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.展开更多
Computational catalysis is playing an increasingly significant role in the design of catalysts across a wide range of applications.A common task for many computational methods is the need to accurately compute the ads...Computational catalysis is playing an increasingly significant role in the design of catalysts across a wide range of applications.A common task for many computational methods is the need to accurately compute the adsorption energy for an adsorbate and a catalyst surface of interest.Traditionally,the identification of low-energy adsorbate-surface configurations relies on heuristic methods and researcher intuition.As the desire to perform high-throughput screening increases,it becomes challenging to use heuristics and intuition alone.In this paper,we demonstrate machine learning potentials can be leveraged to identify low-energy adsorbate-surface configurations more accurately and efficiently.Our algorithm provides a spectrum of trade-offs between accuracy and efficiency,with one balanced option finding the lowest energy configuration 87.36%of the time,while achieving a~2000×speedup in computation.To standardize benchmarking,we introduce the Open Catalyst Dense dataset containing nearly 1000 diverse surfaces and~100,000 unique configurations.展开更多
基金supported by the TIFR-CAM Doctoral Fellowship and the NISER Postdoctoral Fellowship(through the project“Basic research in physics and multidisciplinary sciences”with identification#RIN4001)during the preparation of this papersupported by the Raja Ramanna Fellowship.
文摘Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.
文摘Computational catalysis is playing an increasingly significant role in the design of catalysts across a wide range of applications.A common task for many computational methods is the need to accurately compute the adsorption energy for an adsorbate and a catalyst surface of interest.Traditionally,the identification of low-energy adsorbate-surface configurations relies on heuristic methods and researcher intuition.As the desire to perform high-throughput screening increases,it becomes challenging to use heuristics and intuition alone.In this paper,we demonstrate machine learning potentials can be leveraged to identify low-energy adsorbate-surface configurations more accurately and efficiently.Our algorithm provides a spectrum of trade-offs between accuracy and efficiency,with one balanced option finding the lowest energy configuration 87.36%of the time,while achieving a~2000×speedup in computation.To standardize benchmarking,we introduce the Open Catalyst Dense dataset containing nearly 1000 diverse surfaces and~100,000 unique configurations.
