Related papers: Solid-State Diffusion: An Introduction
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…
Transition and separation are difficult but important problems in the field of fluid mechanics. Hitherto, separation and transition problems have not been described accurately in mathematical terms, leading to design errors and prediction…
During the last decade, an increasing importance has been given to the feedback of mechanical stresses on the chemical diffusion and, further, on corrosion. Many works point the active role of stresses on the material ageing especially on…
A recent study has demonstrated that phase separation in binary liquid mixtures is arrested in the presence of elastic networks and can lead to a nearly uniformly-sized distribution of the dilute-phase droplets. At longer timescales, these…
We report on a particle-based numerical study of sheared amorphous solids in the dense slow flow regime. In this framework, deformation and flow are accompanied by critical fluctuation patterns associated with the macroscopic plastic…
The diffusion of tungsten in {\alpha}-iron is important for the application of ferritic-iron alloys to thermal power plants. These data, over a wide temperature range across the Curie temperature, have been recently reported. We show that…
The moisture absorption in granulated materials used in foundry technologies is analyzed. The absorption process has a diffusive behavior mainly. A simple experimental technique, in which the wet weight increment was recorded as the…
The propagation of incoherent elastic energy in a three-dimensional solid due to the scattering by many, randomly placed and oriented, pinned dislocation segments, is considered in a continuum mechanics framework. The scattering mechanism…
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…
Drying of colloidal dispersion and their consolidation into a particulate deposit is a common phenomenon. This process involves various physical processes such as diffusion of liquid molecules into the ambient atmosphere and advection of…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
A model is presented allowing calculation of energy and matter distribution in the Universe after expansion from singularity without introduction of expansion energy. Beginning with Fick's law of diffusion, we solve the Bessel function for…
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…
Steels, and in particular stainless steels, play a crucial role in the construction of large particle accelerators and high-energy physics experiments, of fusion reactors and their superconducting magnet structures. Such projects face…
Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…
Solid state material at high pressure is prevalent throughout the Universe, and an understanding of the structure of matter under such extreme conditions, gleaned from x-ray diffraction, has been pursued for the best part of a century. The…
Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly…
Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as…
This paper develops an input-to-state stability (ISS) analysis of the Stefan problem with respect to an unknown heat loss. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a…