Prediction of Compound Bioactivities Using Heat-Diffusion Equation

Observation and prediction for the heat equation

Solutions of diffusion equation for point defects

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...

Geometric heat equation and nonlinear diffusion of shapes and images

49, 90]. Witkin proposed that the convolution of a signal Visual tasks often require a hierarchical representation of with a Gaussian removes small-scale features, namely, shapes and images in scales ranging from coarse to fine. A zero-crossings, while retaining the more significant ones variety of linear and nonlinear smoothing techniques, such as [88]. Koenderink showed that among the linear ...

Modeling Diffusion to Thermal Wave Heat Propagation by Using Fractional Heat Conduction Constitutive Model

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

Carleman estimates for the heat equation with discontinuous diffusion coefficients

We consider the heat equation with a diffusion coefficient that is discontinuous at an interface. We give global Carleman estimates for solutions of this equation, even if the jump of the coefficient across the interface has not a constant sign. AMS classification scheme numbers: 35K05, 35K55, 35R05, 35R30