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We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial…
Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled…
Existing learning-based methods effectively reconstruct HDR images from multi-exposure LDR inputs with extended dynamic range and improved detail, but they rely more on empirical design rather than theoretical foundation, which can impact…
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional…
This article presents the convergence analysis of a sequence of piecewise constant and piecewise linear functions obtained by the Rothe method to the solution of the first order evolution partial differential inclusion…
In a Relativistic Diffusion Model (RDM), the evolution of net-proton rapidity spectra with sqrt(s_NN) in heavy systems is proposed as an indicator for local equilibration and longitudinal expansion. The broad midrapidity valley recently…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
The isotropic chemical shifts can be calculated either by full-electron configuration, or by hybrid functionals, which costs a large amount of computational resources. To save the time, DFT+U could be employed to calculate the isotropic…
First principles constrained density functional theory scheme in Wannier functions formalism has been used to calculate Coulomb repulsion U and Hund's exchange J parameters for iron 3d electrons in LaFeAsO. Results strongly depend on the…
The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a…
In this paper, we introduce an efficient, linear algebra-based method for optimizing supercell selection to determine Heisenberg exchange parameters from DFT calculations. A widely used approach for deriving these parameters involves…
We suggest and implement a parallelization scheme based on an efficient multiband eigenvalue solver, called the locally optimal block preconditioned conjugate gradient LOBPCG method, and using an optimized three-dimensional (3D) fast…
Reservoir computing (RC) is attracting attention as a machine-learning technique for edge computing. In time-series classification tasks, the number of features obtained using a reservoir depends on the length of the input series.…
The density functional theory (DFT)+U method based on the linear response (LR) theory was applied to investigate the electronic structures of Co-based ternary full Heusler alloy Co$_2Y$Si for exploring half-metallic (HM) ferromagnets with a…
We analyze the effect of intersite-interaction terms on the stability of the coexisting superconucting-nematic phase (SC+N) within the extended Hubbard and $t$-$J$-$U$ models on the square lattice. In order to take into account the…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
This paper studies the convergence conditions and properties of the distributed adaptive signal fusion (DASF) algorithm, the framework itself having been introduced in a `Part I' companion paper. The DASF algorithm can be used to solve…
Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…
By pretraining on trillions of tokens, an LLM gains the capability of text generation. However, to enhance its utility and reduce potential harm, SFT and alignment are applied sequentially to the pretrained model. Because SFT and alignment…
Density Functional Theory (DFT) stands as a widely used and efficient approach for addressing the many-electron Schr\"odinger equation across various domains such as physics, chemistry, and biology. However, a core challenge that persists…