Related papers: Fick's Second Law Transformed: One Path to Cloakin…
Dynamic heterogeneity, believed to be one of the hallmarks of the dynamics of supercooled liquids, is expected to affect the diffusion of the particles comprising the liquid. We have carried out extensive molecular dynamics simulations of…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The conventional assumption that the self-diffusion coefficient of a small tracer can be obtained by a local and instantaneous application of Einstein's relation in a temperature field with spatial and temporal heterogeneity is revisited.…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the…
A bio-heat transfer model for biological tissues in a micro-scale and periodical settings is investigated . It is assumed that the model is a two-component system consisting of solid particles representing tissue cells and interconnected…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive…
The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics,…
A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid…
Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
In this work, we investigate the heat flow of two interacting quantum systems on the perspective of noncommutativity phase-space effects and show that by controlling the new constants introduced in the quantum theory, due to a deformed…
Transformation media provide a fundamental paradigm for field regulation, but their tricky anisotropy challenges fabrication. Though optical conformal mapping has been utilized to eliminate anisotropy, two key factors still hinder its…
A normal-diffusion theory for heat transfer in many-body systems via carriers of thermal photons is developed. The thermal conductivity tensor is rigorously derived from fluctuational electrodynamics as a coefficient of diffusion term for…
The classical approach to diffusion processes is based on Fick's law that the flux is proportional to the concentration gradient. Various phenomena occurring during propagation of penetrating liquids in polymers show that this type of…
Based on the generalized kinetic equation for the one-particle distribution function with a small source, the transition from the kinetic to the hydrodynamic description of many-particle systems is performed. The basic feature of this new…