We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions u and v. We consider a spatial model where individuals migrate up local fitness gradients, seeking out locations where their given traits are more advantageous. The resulting system of...

Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...

We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the str...

Fourier theory of thermal transport considers heat transport as a diffusive process where energy flow is driven by a temperature gradient. However, this is not valid at length scales smaller than the mean free path for the energy carriers in a material, which can be hundreds of nanometres in crystalline materials at room temperature. In this case, heat flow will become 'ballistic'--driven by di...

By using the particle probability density we analyze the spin echo attenuation of particles, diffusing in a bounded region. It provides a means to expand a nonuniform spin phase distribution into a series of waves that characterize the geometry and boundary conditions of confinement. Random motion disrupts the initial phase structure created by applied gradients and consequently discords its st...

We have developed a microfluidic device for on-chip monitoring of cellular reactions. The device consists of two primary analytical functions: control of cell transport and immobilization, and dilution of an analyte solution to generate a concentration gradient. In this device, a dam structure in parallel to the fluid flow was constructed for docking and alignment of biological cells, which all...

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with densitydependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green– Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytica...

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with densitydependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green– Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytica...

Introduction: Crystalline silicates have been detected in a growing number of comets [1] [2] [3]. Since these bodies are presumed to be formed in the cold outer part of the solar nebula, several processes have been invoked in order to explain the origin of their crystalline silicates. It has been suggested that shock waves in the outer solar nebula could anneal the amorphous silicates to crysta...

Water diffusion through OmpF, a porin in the outer membrane of Escherichia coli, is studied by molecular dynamics simulation. A first passage time approach allows characterizing the diffusive properties of a well-defined region of this channel. A carbon nanotube, which is considerably more homogeneous, serves as a model to validate the methodology. Here we find, in addition to the expected regu...