相关论文: Approximation of the modified error function
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered.…
We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called…
Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes.…
In this study we develop a mathematical model that describe the behavior of electromagnetic fields and heat transfer in closed electrical contacts that arises when instantaneous explosion of the micro-asperity which involves vaporization…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
The correlation-driven Mott transition is commonly characterized by a drop in resistivity across the insulator-metal phase boundary; yet, the complex permittivity provides a deeper insight into the microscopic nature. We investigate the…
We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $\beta\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate…
The erasure of a classical bit of information is a dissipative process. The minimum heat produced during this operation has been theorized by Rolf Landauer in 1961 to be equal to $k_B T \ln 2$ and takes the name of Landauer limit, Landauer…
Using experimental data on thermal convection, obtained at a Rayleigh number of 1.5 $\times 10^{11}$, it is shown that the temperature structure functions $<\Delta T_{r}^p>$, where $\Delta T_r$ is the absolute value of the temperature…
We investigate the fluctuation contribution to the specific heat of a two-dimensional superconductor with a non-Fermi normal state described by a Anderson Green's function $G(k,i\omega)=\omega_c^{-\alpha}/(i\omega-\epsilon_k)^{1-\alpha}$.…
The optimized linear $\delta$-expansion is applied to the $\lambda \phi^4$ theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order $\delta^2$. A variational procedure…
Simulated tempering (ST) has attracted a great deal of attention in the last years, due to its capability to allow systems with complex dynamics to escape from regions separated by large entropic barriers. However its performance is…
Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that…
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…
Thermal properties of a two-layered composite conductor are modified in case the interface is damaged. The present paper deals with nondestructive evaluation of perturbations of interface thermal conductance due to the presence of defects.…