Generic two-phase coexistence in the quadratic contact process

This thesis focuses on the demonstration of the existence of and analysis of phenomena related to the discontinuous non-equilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl\u27s second model for autocatalysis. This realization, also known as the Quadratic Contact Process, involves spontaneous annihilation, autocatalytic creation, and diffusion or hopping of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p\u3e0 and is an absorbing particle-free vacuum state. The populated active steady state exists just for p below a critical value, pe. Our initial studies without particle hopping demonstrated a dependence on orientation or slope, S, of the equistability or stationary point p=peq(S) for a planar interface separating active and poisoned states. They also showed that pe = peq(S=1) for diagonal interfaces. This orientation dependence was shown to extend to non-zero hop rates h\u3e0, but to quickly weaken with increasing h. If pf denotes the critical value below which a finite population can survive, then we show that pf =peq(S=0) and that pf \u3c pe. This strict inequality contrasts a postulate of Durrett, and is a direct consequence of the occurrence of coexisting stable active and poisoned states for a finite range pf y p y pe. Although this so-called generic two-phase coexistence (2PC) contrasts behavior in thermodynamic systems. However, one still finds metastability and nucleation phenomena similar to those in discontinuous equilibrium transitions. We also provide a theoretical framework for analysis of such metastability phenomena. Extensions of the basic model are considered to different lattices and to introduce tricritical behavior. Most precise analysis was performed with kinetic Monte Carlo simulation. However, we also developed exact hierarchical master equations and performed approximate truncation analysis of these equations

N-(2,3-Dimeth­oxy­benzyl­idene)naphthalen-1-amine

The title compound, C19H17NO2, represents a trans isomer with respect to the C=N bond. The dihedral angle between the planes of the naphthyl ring system and the benzene ring is 71.70 (3)°. In the crystal, weak C—H⋯O hydrogen bonding is present

Tricriticality in generalized Schloegl models for autocatalysis: Lattice-gas realization with particle diffusion

We analyze lattice–gas reaction–diffusion models which include spontaneous annihilation, autocatalytic creation, and diffusion of particles, and which incorporate the particle creation mechanisms of both Schloegl’s first and second models. For fixed particle diffusion or hop rate, adjusting the relative strength of these creation mechanisms induces a crossover between continuous and discontinuous transitions to a “poisoned” vacuum state. Kinetic Monte Carlo simulations are performed to map out the corresponding tricritical line as a function of hop rate. An analysis is also provided of the tricritical “epidemic exponent” for the case of no hopping. The phase diagram is also recovered qualitatively by applying mean-field and pair-approximations to the exact hierarchical form of the master equation for these models

Using Objective Clustering for Solving Many-Objective Optimization Problems

Many-objective optimization problems involving a large number (more than four) of objectives have attracted considerable attention from the evolutionary multiobjective optimization field recently. With the increasing number of objectives, many-objective optimization problems may lead to stagnation in search process, high computational cost, increased dimensionality of Pareto-optimal front, and difficult visualization of the objective space. In this paper, a special kind of many-objective problems which has redundant objectives and which can be degenerated to a lower dimensional Pareto-optimal front has been investigated. Different from the works in the previous literatures, a novel metric, interdependence coefficient, which represents the nonlinear relationship between pairs of objectives, is introduced in this paper. In order to remove redundant objectives, PAM clustering algorithm is employed to identify redundant objectives by merging the less conflict objectives into the same cluster, and one of the least conflict objectives is removed. Furthermore, the potential of the proposed algorithm is demonstrated by a set of benchmark test problems scaled up to 20 objectives and a practical engineering design problem

Long-Term Exposure to High Altitude Affects Voluntary Spatial Attention at Early and Late Processing Stages

The neurocognitive basis of the effect of long-term high altitude exposure on voluntary attention is unclear. Using event related potentials, the high altitude group (people born in low altitude but who had lived at high altitude for 3 years) and the low altitude group (living in low altitude only) were investigated using a voluntary spatial attention discrimination task under high and low perceptual load conditions. The high altitude group responded slower than the low altitude group, while bilateral N1 activity was found only in the high altitude group. The P3 amplitude was smaller in the high altitude compared to the low altitude group only under high perceptual load. These results suggest that long-term exposure to high altitudes causes hemispheric compensation during discrimination processes at early processing stages and reduces attentional resources at late processing stages. In addition, the effect of altitude during the late stage is affected by perceptual load