The Korteweg-De Vries Equation of a New Lattice Model with a Consideration of the Next-Nearest-Neighbor Site and its Numerical Simulation

Based on Nagatanis model, a new lattice hydrodynamic model of traffic flow with a consideration of the next-nearest-neighbor site is proposed. Using nonlinear analysis, we derive the Korteweg-de Vries (KdV, for short) equation near the neutral stability curve to describe the density waves. Numerical simulations are consonant with the analytical results and shows that the consideration of the next-nearest-neighbor interaction helps suppress traffic jam.

Oxygen vacancy migration in CSZ using density functional theory

We studied oxygen migration in calcia-stabilized cubic zirconia (CSZ) using density functional theory. A Ca atom was substituted for a Zr atom in a 2×2×2 ZrO2 cubic supercell, and an oxygen vacancy was produced to satisfy the charge neutrality condition. We found that the formation energies of an oxygen vacancy, as a function of its location with respect to the Ca atom, were varied. The relative formation energies of the oxygen vacancies located at the first-, second-, third-, and fourth-nearest-neighbors were 0.0, −0.07, 0.19, and 0.19 eV, respectively. Therefore, the oxygen vacancy located at the second-nearest-neighbor site of the Ca atom was the most favorable, the oxygen vacancy located at the first-nearest-neighbor site was the second most favorable, and the oxygen vacancies at the third- and fourth-nearest-neighbor sites were the least favorable. We also calculated the energy barriers for the oxygen vacancy migration between oxygen sites. The energy barriers between the first and the second nearest sites, the second and third nearest sites, and the third and fourth nearest sites were 0.11, 0.46, and 0.23 eV, respectively. Therefore, the oxygen vacancies favored the first- and second-nearest-neighbor oxygen sites when they drifted under an electric field.

A 2-DIMENSIONAL CELLULAR AUTOMATON FOR AGENTS MOVING FROM ORIGINS TO DESTINATIONS

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise (p) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter "μ" is also introduced to control the probability that movement of all involved agents to the same site (conflict) is denied at each time step. This model displays two states; namely the freely moving and the jamming state. If μ is large and p is low, the system is in the jamming state even if the density is low. However, if μ is large and p is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state, while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if μ is large and p is low (jamming state); but long travel times are suppressed if p becomes large (freely moving state).

FROM NEXT NEAREST NEIGHBOR SITE PERCOLATION TO CONTINUUM PERCOLATION: APPLICATION TO HIGH-Tc SUPERCONDUCTORS

In high-Tc superconductors dopant atoms supply holes or excess electrons, and electric conduction is established in the neighborhood of the dopant. We propose that percolation of these conducting areas leads to global electric conduction. To investigate these processes numerical procedures to simulate continuum percolation are developed. The relation between the concentration of connecting discs and the fraction of the area of the plane covered by all discs is computed in the whole range between next nearest neighbor site percolation and continuum percolation. This method is applied to investigate underdoped copper oxides where small hole or excess electron concentrations are insufficient to establish electric conduction. The results of this study are applied to the model of mobile charge carriers which consist of or are accompanied by diffusing d-electrons. Our investigations show that with increasing doping the Neel temperature of the antiferromagnetism vanishes and spin glass states appear in accordance with experiments. Furthermore, the peaks in the specific heat become very broad. This broadening due to randomness and loss of translation invariance has been observed in nuclear magnetic resonance peaks of doped superconducting cuprates.

EFFECTS OF FINITE REACTION RATES ON THE KINETIC PHASE TRANSITIONS IN THE CATALYTIC OXIDATION OF CARBON MONOXIDE

Oxidation of carbon monoxide is one of the most extensively studied heterogeneous catalysis reactions, being important among other applications in automobile-emission control. Catalytic oxidation of carbon monoxide on platinum (111) surface was simulated by the Monte Carlo technique following an extended version of the model proposed by Ziff, Gulari and Barshad (ZGB). In the simulation, a simple square two-dimensional lattice of active sites replaces the surface of the catalyst. Finite reaction rates for (i) diffusion of the reactive species on the surface, (ii) reaction of a CO molecule with an oxygen atom in a nearest neighbor site, and (iii) desorption of unreacted CO molecules, have been taken into account. The produced CO 2 desorbs instantly. The average coverage of O, CO and the CO 2 production rate for a steady state configuration, as a function of the normalized CO partial pressure (P CO ), shows two kinetic phase transitions. In the ZGB model these transitions occur at P CO ≈ 0.39 and P CO ≈ 0.53. For 0.39 < P CO < 0.53 a reactive ( CO 2 production) steady state is found. Outside of the interval, the only steady state is a poisoned catalyst of pure CO or pure O. Our results show that finite reaction rates shift the values in which these phase transitions occur.