Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fraction...Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.展开更多
Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the syste...Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.展开更多
We show that an enslaved phase-separation front moving with diffusive speeds U=C/√T can leave alternating domains of increasing size in their wake.We find the size and spacing of these domains is identical to Liesega...We show that an enslaved phase-separation front moving with diffusive speeds U=C/√T can leave alternating domains of increasing size in their wake.We find the size and spacing of these domains is identical to Liesegang patterns.For equal composition of the components we are able to predict the exact form of the pattern analytically.To our knowledge this is the first fully analytical derivation of the Liesegang laws.We also show that there is a critical value for C below which only two domains are formed.Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.展开更多
The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence t...The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.展开更多
We carry out a chemical treatment(acidization or basification)of typical rock specimens in-situ,and characterize the emerging pattern resulting from the infil-tration-precipitation scenario.Galena and limestone sam-pl...We carry out a chemical treatment(acidization or basification)of typical rock specimens in-situ,and characterize the emerging pattern resulting from the infil-tration-precipitation scenario.Galena and limestone sam-ples were treated with sulfuric acid,while pyrite was reacted with sodium hydroxide.Various infiltration tech-niques were employed,after selection of the most feasible method for each rock separately.The patterns of anglesite(PbSO_(4)),anhydrite(CaSO_(4))and goethite(FeOOH)depo-sition presented different alteration modes of the bare rock textures.Among the three deposited minerals,only the anhydrite(CaSO_(4))displayed a band stratification.The formation of a Liesegang pattern in the rock of highest porosity indicates a plausible correlation between the band formation and a minimum porosity requirement.A banded rock of compact texture could then be formed by a cementation mechanism,governing the long time evolution of the rock.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11205044 and 11405042)the Research Foundation of Education Bureau of Hebei Province,China(Grant Nos.Y2012009 and ZD2015025)+1 种基金the Program for Young Principal Investigators of Hebei Province,Chinathe Midwest Universities Comprehensive Strength Promotion Project
文摘Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.
基金Project supported by the National Nature Science Foundation of China(Grant No.11205044)the Fundamental Research Funds for the Central Universities(Grant No.10ML40)
文摘Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.
基金E.F.acknowledges support by the National Science Foundation under grant DMR-0513393.
文摘We show that an enslaved phase-separation front moving with diffusive speeds U=C/√T can leave alternating domains of increasing size in their wake.We find the size and spacing of these domains is identical to Liesegang patterns.For equal composition of the components we are able to predict the exact form of the pattern analytically.To our knowledge this is the first fully analytical derivation of the Liesegang laws.We also show that there is a critical value for C below which only two domains are formed.Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.
文摘The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.
基金supported by a grant from the University Research Board(URB)of the American University of Beirut(AUB).
文摘We carry out a chemical treatment(acidization or basification)of typical rock specimens in-situ,and characterize the emerging pattern resulting from the infil-tration-precipitation scenario.Galena and limestone sam-ples were treated with sulfuric acid,while pyrite was reacted with sodium hydroxide.Various infiltration tech-niques were employed,after selection of the most feasible method for each rock separately.The patterns of anglesite(PbSO_(4)),anhydrite(CaSO_(4))and goethite(FeOOH)depo-sition presented different alteration modes of the bare rock textures.Among the three deposited minerals,only the anhydrite(CaSO_(4))displayed a band stratification.The formation of a Liesegang pattern in the rock of highest porosity indicates a plausible correlation between the band formation and a minimum porosity requirement.A banded rock of compact texture could then be formed by a cementation mechanism,governing the long time evolution of the rock.
