Monte Carlo Simulation of Absorbing Phase Transition in the Models with a Conserved Field on Diluted Lattices

AbstractAn influence of quenched disorder on absorbing phase transitions of the conserved lattice gas (CLG) model and the conserved threshold transfer process (CTTP) was investigated via Monte Carlo simulations. It was found that when the concentration of disordered site is less than the critical concentration, the critical exponents were similar to those of the pure models for both the CLG and the CTTP models. When the concentration becomes critical, the density of active particles showed nonuniversal power-law behavior for all particle densities for the CLG model, whereas the CTTP model exhibited usual critical behavior but with different critical exponents. The nonuniversal power law was attributed to the dead ends on an infinite percolation network. Eliminating those dead ends, it was found that both the CLG model and the CTTP model exhibited usual critical behavior; the estimated exponents were similar for the two models, and they were also similar to those of the CTTP model on an infinite network

Improvements to the RELAP5/MOD3 reflood model and uncertainty quantification of reflood peak clad temperature

Assessment of the original REAP/N4OD3.1 code against the FLECHT SEASET series of experiments has identified some weaknesses of the reflood model, such as the lack of a quenching temperature model, the shortcoming of the Chen transition boiling model, and the incorrect prediction of droplet size and interfacial heat transfer. Also, high temperature spikes during the reflood calculation resulted in high steam flow oscillation and liquid carryover. An effort had been made to improve the code with respect to the above weakness, and the necessary model for the wall heat transfer package and the numerical scheme had been modified. Some important FLECHT-SEASET experiments were assessed using the improved version and standard version. The result from the improved REAP/MOD3.1 shows the weaknesses of REAP/N4OD3.1 were much improved when compared to the standard MOD3.1 code. The prediction of void profile and cladding temperature agreed better with test data, especially for the gravity feed test. The scatter diagram of peak cladding temperatures (PCTs) is made from the comparison of all the calculated PCTs and the corresponding experimental values. The deviation between experimental and calculated PCTs were calculated for 2793 data points. The deviations are shown to be normally distributed, and used to quantify statistically the PCT uncertainty of the code. The upper limit of PCT uncertainty at 95% confidence level is evaluated to be about 99K

Interfacial mixing in heteroepitaxial growth

We investigate the growth of a film of some element B on a substrate made of another substrance A in a model of molecular beam epitaxy. A vertical exchange mechanism allows the A-atoms to stay on the growing surface with a certain probability. Using kinetic Monte Carlo simulations as well as scaling arguments, the incorporation of the A's into the growing B-layer is investigated. Moreover we develop a rate equation theory for this process. In the limit of perfect layer-by-layer growth, the density of A-atoms decays in the B-film like the inverse squared distance from the interface. The power law is cut off exponentially at a characteristic thickness of the interdiffusion zone that depends on the rate of exchange of a B-adatom with an A-atom in the surface and on the system size. Kinetic roughening changes the exponents. Then the thickness of the interdiffusion zone is determined by the diffusion length.Comment: 11 pages, 11 figure

Stationary localized states due to nonlinear impurities described by the modified discrete nonlinear Schr\"odinger equation

The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a perfectly nonlinear chain is also considered. Phase diagrams of localized states for all systems are presented. From the mean square displacement calculation, it is found that all states are not localized even though the system comprises random nonlinear site energies. Stability of the states is discussed.Comment: Six pages including five figure

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Anthocyanidins and anthocyanins: colored pigments as food, pharmaceutical ingredients, and the potential health benefits

Anthocyanins are colored water-soluble pigments belonging to the phenolic group. The pigments are in glycosylated forms. Anthocyanins responsible for the colors, red, purple, and blue, are in fruits and vegetables. Berries, currants, grapes, and some tropical fruits have high anthocyanins content. Red to purplish blue-colored leafy vegetables, grains, roots, and tubers are the edible vegetables that contain a high level of anthocyanins. Among the anthocyanin pigments, cyanidin-3-glucoside is the major anthocyanin found in most of the plants. The colored anthocyanin pigments have been traditionally used as a natural food colorant. The color and stability of these pigments are influenced by pH, light, temperature, and structure. In acidic condition, anthocyanins appear as red but turn blue when the pH increases. Chromatography has been largely applied in extraction, separation, and quantification of anthocyanins. Besides the use of anthocyanidins and anthocyanins as natural dyes, these colored pigments are potential pharmaceutical ingredients that give various beneficial health effects. Scientific studies, such as cell culture studies, animal models, and human clinical trials, show that anthocyanidins and anthocyanins possess antioxidative and antimicrobial activities, improve visual and neurological health, and protect against various non-communicable diseases. These studies confer the health effects of anthocyanidins and anthocyanins, which are due to their potent antioxidant properties. Different mechanisms and pathways are involved in the protective effects, including free-radical scavenging pathway, cyclooxygenase pathway, mitogen-activated protein kinase pathway, and inflammatory cytokines signaling. Therefore, this review focuses on the role of anthocyanidins and anthocyanins as natural food colorants and their nutraceutical properties for health. Abbreviations: CVD: Cardiovascular disease VEGF: Vascular endothelial growth factor

Statistics of anisotropic random walks

We discuss the three different types of anisotropic random walks based on Monte Carlo simulations and real space renormalization group transformations. Our work for biased self-avoiding walks using Monte Carlo simulation coupled with scaling analyses suggests qualitative differences in the effect of excluded volume on the chain conformation in the stiff limit between two and three dimensions in a manner similar to a suggestion made by Petschek. In the limit of gauche weight p $\to$ 0 and contour length N $\to$ $\infty$, we find scaling for the mean square end-to-end distance $\langle$R\sp2\rangle\u3e with the crossover exponent one as before; however, the scaling function in three dimensions closely matches the random stiff chain results with no excluded volume while that in two dimensions exhibits marked deviations. Our cell renormalization approach also confirms the crossover exponent to be exactly one in any dimensions and for all cell sizes. Our work also shows, by use of renormalization flows, a substantial difference in the crossover between two and three dimensions in the limit of N $\to\infty$ for fixed p. In three dimensions a crossover seems to occur first to random walk limit and then to self-avoiding walk limit, while in two dimensions, it seems to occur directly to self-avoiding walk limit in agreement with our observations based on Monte Carlo simulation. We also study self-avoiding Levy flights in one dimension by Monte Carlo simulation. We find very large corrections to scaling in the node-avoiding Levy flights for a wide range of $\mu$ and also, surprisingly, that the moments of the end-to-end distance of the node-avoiding Levy flights are greater than those of path-avoiding Levy flight when they both exist and are finite. Based on these observations we conclude that the morphology of the node-avoiding Levy flights is far more complex than that of the path-avoiding Levy flights or the random Levy flights, and that the node-avoiding and path-avoiding Levy flights are certainly in different universality classes in one dimension. We also present new results of Monte Carlo simulation for self-avoiding walks on randomly diluted square and simple cubic lattices performed for p very close to the percolation thresholds. The asymptotic behavior obtained is very different from the only previous work of this kind by Kremer for the diamond lattice. While the previous work reported a large increase of Flory exponent compared to the undiluted lattice, our results indicate a behavior rather similar to the ordinary self-avoiding walks

Monomer concentration profile in the depletion region

We study by Monte Carlo simulation the monomer concentration profile of the dilute solution of linear chain polymers in the depletion region near an impenetrable but otherwise non-interacting wall. Only the case of a good solvent is treated here but we allow both for flexible and semi-flexible chains. Our results on the simple cubic lattice indicate a profile exponent of 5/3 in agreement with the scaling theories of Joanny et al. and of de Gennes. Moreover, the results for the semi-flexible case suggest that the simple blob picture proposed by Ausserré and coworkers is reasonably accurate if a modification is made in the offset of the effective location of the surface.On étudie par des simulations de Monte Carlo le profil de concentration, près d'une paroi impénétrable mais non répulsive, des monomères de polymères linéaires en solution diluée. On traite seulement le cas de polymères en bon solvant, soit flexibles, soit semi-flexibles. Les résultats obtenus sur un réseau cubique simple donnent un profil défini par un exposant 5/3 en accord avec les théories d'échelle proposées par Joanny et al. et par de Gennes. D'autre part, les résultats pour les chaînes semi-flexibles suggèrent que l'image de blobs proposée par Ausserré et al. est assez correcte à condition de décaler la position effective de la surface