The immiscibility of hydrogen-helium mixture under the temperature and pressure conditions of planetary interiors is crucial for understanding the structures of gas giant planets (e.g., Jupiter and Saturn). While the ...
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Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, a...
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A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In t...
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A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In the MWG finite element method, discontinuous piecewise polynomials of degree k and k-1 are used to approximate the velocity u and the pressure p, respectively. The main idea of the MWG finite element method is to replace the boundary functions by the average of the interior functions. Therefore, the MWG finite element method has fewer degrees of freedom than the WG finite element method without loss of accuracy. The MWG finite element method satisfies the stability conditions for any polynomial with degree no more than k-1. The MWG finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape *** order error estimates are established for the velocity and pressure approximations in H1and L2norms. Some numerical examples are presented to demonstrate the accuracy, convergence and stability of the method.
Heterogeneous catalysts based on sub-nanometer metal clusters often exhibit strongly size-dependent properties, and the addition or removal of a single atom can make all the difference. Identifying the most active spe...
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Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k| → 0;and stealthy hyperuniform systems have S(k) = 0 for the finite range 0 30 for systems sizes more than ...
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We consider the theory of a higher-derivative (HD) real scalar field φ coupled to a complex scalar σ, the coupling of the φ and σ being given by two types, λσφσ†σφ2 and ξσφσ†σ (∂µφ)2. We evaluate ...
Models for the observational appearance of astrophysical black holes rely critically on accurate general-relativistic ray tracing and radiation transport to compute the intensity measured by a distant observer. In thi...
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Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2ve...
Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.
We report on the development of a drone-borne calibration pulser (cal-pulser) for radio observatories detecting ultra-high energy (UHE) cosmic rays and neutrinos. This system allows us to calibrate the radio detector ...
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The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering ...
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