Phase Diagram for Two Weakly Coupled Oscillatory Chemical Systems

1981 ◽  
Vol 50 (2) ◽  
pp. 687-695 ◽  
Author(s):  
Koji Nakajima ◽  
Yasuji Sawada
Keyword(s):  
Phase Diagram ◽  
Chemical Systems ◽  
Weakly Coupled ◽  
Oscillatory Chemical

Phase diagram of spin-1 quantum Ising models: Applications to systems of weakly coupled classical Ising chains

1981 ◽  
Vol 23 (11) ◽  
pp. 6099-6105 ◽  
Author(s):  
Yuval Gefen ◽  
Yoseph Imry ◽  
David Mukamel
Keyword(s):  
Phase Diagram ◽  
Ising Models ◽  
Weakly Coupled

Vortex dynamics in oscillatory chemical systems

1991 ◽  
Vol 1 (4) ◽  
pp. 421-434 ◽  
Author(s):  
Xiao‐Guang Wu ◽  
Merk‐Na Chee ◽  
Raymond Kapral
Keyword(s):  
Vortex Dynamics ◽  
Chemical Systems ◽  
Oscillatory Chemical

scholarly journals Complex Pacemakers and Wave Sinks in Heterogeneous Oscillatory Chemical Systems

2002 ◽  
Vol 216 (4) ◽  
Author(s):  
Michael Stich ◽  
Alexander S. Mikhailov
Keyword(s):  
Reaction Diffusion ◽  
Frequency Shifts ◽  
Reaction Diffusion Systems ◽  
Sources And Sinks ◽  
Chemical Systems ◽  
Diffusion Systems ◽  
Wave Patterns ◽  
Oscillatory Chemical ◽  
Local Shift ◽  
Phase Slips

We investigate pattern formation in oscillatory reaction-diffusion systems where wave sources and sinks are created by a local shift of the oscillation frequency. General properties of resulting wave patterns in media with positive and negative dispersion are discussed. It is shown that phase slips in the wave patterns develop for strong frequency shifts, indicating the onset of desynchronization in the medium.

scholarly journals Is the Skin an Excitable Medium? Pattern Formation in Erythema Gyratum Repens

2005 ◽  
Vol 6 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Stephen Gilmore ◽  
Kerry A. Landman
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Biochemical Basis ◽  
Bz Reaction ◽  
Chemical Systems ◽  
Inflammatory Dermatosis ◽  
Reaction Diffusion Model ◽  
Oscillatory Chemical ◽  
Spatio Temporal ◽  
Scaly Skin

Erythema gyratum repens (EGR) is a rare, inflammatory dermatosis of unknown aetiology. The morphology of the eruption is striking and displays rapidly evolving circinate and gyrate bands of erythematous and scaly skin. Although the aetiology of the pattern is unknown, it has previously been noted that the eruption shares morphologic features with the patterns of spatio-temporal chemical concentration profiles observed in the Belusov-Zhabotinski (BZ) reaction. Yet this morphologic correspondence has not been investigated further. Here we apply a simple non-linear reaction–diffusion model, previously used to describe the BZ reaction, as a template for pattern formation in EGR, and show how the mechanism may provide a biochemical basis for many of the dynamic and morphologic features of the rash. These results are supported by the results of a cellular automaton simulation approximating the dynamics of oscillatory chemical systems—the Hodgepodge machine—where the spatio-temporal patterns developed show astonishing similarities to the morphology of EGR.

scholarly journals Phase diagram and spin Hamiltonian of weakly-coupled anisotropicS=12chains inCuCl2∙2((CD3)2SO)

2007 ◽  
Vol 75 (21) ◽  
Author(s):  
Y. Chen ◽  
M. B. Stone ◽  
M. Kenzelmann ◽  
C. D. Batista ◽  
D. H. Reich ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Spin Hamiltonian ◽  
Weakly Coupled

scholarly journals A Framework for Quantifying Uncertainty in DFT Energy Corrections

2021 ◽  
Author(s):  
Amanda Wang ◽  
Ryan Kingsbury ◽  
Matthew McDermott ◽  
Matthew Horton ◽  
Anubhav Jain ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Density Functional Theory ◽  
Density Functional ◽  
Enthalpies Of Formation ◽  
Functional Theory ◽  
Chemical Systems ◽  
Correction Scheme ◽  
Derived Properties ◽  
Quantifying Uncertainty ◽  
Formation Phase

In this work, we demonstrate a method to quantify uncertainty in corrections to density functional theory (DFT) energies based on empirical results. Such corrections are commonly used to improve the accuracy of computational enthalpies of formation, phase stability predictions, and other energy-derived properties, for example. We incorporate this method into a new DFT energy correction scheme comprising a mixture of oxidation-state and composition-dependent corrections and show that many chemical systems contain unstable polymorphs that may actually be predicted stable when uncertainty is taken into account. We then illustrate how these uncertainties can be used to estimate the probability that a compound is stable on a compositional phase diagram, thus enabling better-informed assessments of compound stability.

scholarly journals A Framework for Quantifying Uncertainty in DFT Energy Corrections

2021 ◽  
Author(s):  
Amanda Wang ◽  
Ryan Kingsbury ◽  
Matthew McDermott ◽  
Matthew Horton ◽  
Anubhav Jain ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Density Functional Theory ◽  
Density Functional ◽  
Enthalpies Of Formation ◽  
Functional Theory ◽  
Chemical Systems ◽  
Correction Scheme ◽  
Derived Properties ◽  
Quantifying Uncertainty ◽  
Formation Phase

In this work, we demonstrate a method to quantify uncertainty in corrections to density functional theory (DFT) energies based on empirical results. Such corrections are commonly used to improve the accuracy of computational enthalpies of formation, phase stability predictions, and other energy-derived properties, for example. We incorporate this method into a new DFT energy correction scheme comprising a mixture of oxidation-state and composition-dependent corrections and show that many chemical systems contain unstable polymorphs that may actually be predicted stable when uncertainty is taken into account. We then illustrate how these uncertainties can be used to estimate the probability that a compound is stable on a compositional phase diagram, thus enabling better-informed assessments of compound stability.

scholarly journals A framework for quantifying uncertainty in DFT energy corrections

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Amanda Wang ◽  
Ryan Kingsbury ◽  
Matthew McDermott ◽  
Matthew Horton ◽  
Anubhav Jain ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Density Functional Theory ◽  
Density Functional ◽  
Enthalpies Of Formation ◽  
Functional Theory ◽  
Chemical Systems ◽  
Correction Scheme ◽  
Derived Properties ◽  
Quantifying Uncertainty ◽  
Formation Phase

AbstractIn this work, we demonstrate a method to quantify uncertainty in corrections to density functional theory (DFT) energies based on empirical results. Such corrections are commonly used to improve the accuracy of computational enthalpies of formation, phase stability predictions, and other energy-derived properties, for example. We incorporate this method into a new DFT energy correction scheme comprising a mixture of oxidation-state and composition-dependent corrections and show that many chemical systems contain unstable polymorphs that may actually be predicted stable when uncertainty is taken into account. We then illustrate how these uncertainties can be used to estimate the probability that a compound is stable on a compositional phase diagram, thus enabling better-informed assessments of compound stability.

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