相关论文: Approximation of the modified error function
We address the existence and uniqueness of the so-called modified error function that arises in the study of phase-change problems with specific heat and thermal conductivity given by linear functions of the material temperature. This…
We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density…
Considering high-temperature heating, the equations of transient heat conduction model require an adaptation, i.e. the dependence of thermophysical parameters of the model on the temperature is to be identified for each specific material to…
Thermal rectification which is a diode-like behavior of heat flux has been studied over a long time. However, a universal and systematic physical description is still lacking. In this letter, a perturbation theory of thermal rectification…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
In this paper we show how to obtain the exact value of the global error of a conforming mixed approximation of the reaction-convection-diffusion problem. We operate in the framework of functional type a posteriori error control. The error…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
In the low temperature phase of the square Ising model, we describe the inverse temperature beta as the function of a squared mass M and study the critical behavior of beta(M) via the large M expansion. Using the delta-expansion by which…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
Previous first-principles calculations of the melting properties of Si, based on the local-density approximation (LDA) for electronic exchange-correlation energy, under-predict the melting temperature by ~ 20%. We present new…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…
In this work we present a general method, commonly applied to the numerical analysis of stochastic models, to interpolate AC-DC differences (usually denoted by the greek letter $\delta$) between calibration points in thermal transfer…
We present efficient approximation of the error function obtained by Fourier expansion of the exponential function $\exp [{- {(t - 2 \sigma)^2}/4}]$. The error analysis reveals that it is highly accurate and can generate numbers that match…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural…
We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between…
We decompose the energy error of any variational DFT calculation into a contribution due to the approximate functional and that due to the approximate density. Typically, the functional error dominates, but in many interesting situations,…
A new transformation involving the error function $\textup{erf}(z)$, the imaginary error function $\textup{erfi}(z)$, and an integral analogue of a partial theta function is given along with its character analogues. Another complementary…
In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan problem. The present result is an improvement of the recent full state feedback backstepping controller…