Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.

OPTIMAL BOUNDS ON DISPERSION COEFFICIENT IN ONE-DIMENSIONAL PERIODIC MEDIA

In this paper, we consider the macroscopic quantity, namely the dispersion tensor associated with a periodic structure in one dimension (see Refs. 5 and 7). We describe the set in which this quantity lies, as the microstructure varies preserving the volume fraction.

Flow in 2D-Nanotubes by Stochastic Rotation Dynamics Algorithm

We use the Stochastic Rotation Dynamics (SRD) to simulate the fluid flow in 2D Carbon Nanotubes. The SRD algorithm is able to simulate flow in different length scale of the fluids. First of all, we use SRD algorithm to simulate the macroscopic Helium flow as a simple interacting system. Using Green-Kubo formula, viscosity of the system as a macroscopic quantity has been calculated. Then, we apply our algorithm to simulate the Helium flow through the Carbon Nanotube in two dimensions. Finally, we find the effect of interaction of Carbon Nanotube with viscosity as a function of temperature. Also, our simulation shows the viscoelastic effects in 2D flow.

Charge distribution in Adsorbates

The distribution of charges on an adsorbate is important in several respects: It indicates the nature of the adsorption bond, whether it is mainly ionic or covalent, and it affects the dipole potential at the interface. Therefore, a fundamental problem of classical electrochemistry is: What does the current associated with an adsorption reaction tell us about the charge distribution in the adsorption bond? In this chapter we will elaborate this problem, which we have already touched upon in Chapter 4. However, ultimately the answer is a little disappointing: All the quantities that can be measured do not refer to an individual adsorption bond, but involve also the reorientation of solvent molecules and the distribution of the electrostatic potential at the interface. This is not surprising; after all, the current is a macroscopic quantity, which is determined by all rearrangement processes at the interface. An interpretation in terms of microscopic quantities can only be based on a specific model. There is a formal similarity between adsorption and reactions such as metal deposition which gives rise to the concept of electrosorption valence. Consider the deposition of a metal ion of charge number z on an electrode of the same material.