Related papers: Optimal Experimental Designs for Estimating Henry'…
A two-step detection strategy is suggested for the precise measurement of the optical phase-shift. In the first step an unsharp, however, unbiased joint measurement of the phase and photon number is performed by heterodyning the signal…
We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…
High harmonic generation (HHG) in solids could enable attosecond and ultraviolet light sources with high compactness, great controllability and rich functions. However, the HHG process is accompanied by a quite large wavevector mismatch…
We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant -…
We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…
Experimental characterization of magnetic components has grown to be increasingly important to understand and model their behaviours in high-frequency PWM converters. The BH loop measurement is the only available approach to separate the…
We define a random measure generated by a real anisotropic harmonizable fractional stable field $Z^H$ with stability parameter $\alpha\in(1,2)$ and Hurst index $H\in(1/2,1)$ and prove that the measure is $\sigma$-additive in probability. An…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
Measurement-based methane inventories, which involve surveying oil and gas facilities and compiling data to estimate methane emissions, are becoming the gold standard for quantifying emissions. However, there is a current lack of…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
In this paper, we did a systematic comparative study on the accuracy of two computational methods of elastic constants combined with the density functional theory (DFT), the stress-strain method and the energy-strain method. We took metal…
This paper develops and analyzes some continuous interior penalty finite element methods (CIP-FEMs) using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in two and three dimensions.…
We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…
Homodyned K (HK) distribution has been widely used to describe the scattering phenomena arising in various research fields, such as ultrasound imaging or optics. In this work, we propose a machine learning based approach to the estimation…
We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of…
We establish a local $\mathcal{O}(k^{-2})$ rate for the gradient update $x^{k+1}=x^k-\nabla f(x^k)/\sqrt{H\|\nabla f(x^k)\|}$ under a $2H$-Hessian--Lipschitz assumption. Regime detection relies on Hessian--vector products, avoiding Hessian…
Phase invariants are important pieces of information about the atomic structures of crystals. There are several mathematical methods in X-ray crystallography to estimate phase invariants. The multi-wave diffraction phenomenon offers a…
If supersymmetry exists at the electroweak scale, then it should be discovered at the LHC. Determining masses, of supersymmetric particles however, is more difficult. In this paper, methods are discussed to determine combinations of masses…