Stationary periodic patterns in the 1D Gray–Scott model

Stationary and oscillatory spatial patterns induced by global periodic switching.

We propose a new mechanism for pattern formation based on the global alternation of two dynamics, neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state associated with that dynamics. However, when the two dynamics are globally alternated sufficiently rapidly, the system exhibits stationary spatial patterns. Somew...

Spectrum of 1D quasicrystals near the periodic chain

analyzing patterns of classroom interaction in efl classrooms in iran

با به کار گیری روش گفتما ن شنا سی در تحقیق حا ضر گفتا ر میا ن آموزگا را ن و زبا ن آموزا ن در کلا سهای زبا ن انگلیسی در ایرا ن مورد بررسی قرار گرفت. ا هداف تحقیق عبا رت بودند از: الف) شنا سا ئی سا ختارهای ارتبا ط گفتا ری میا ن معلمین و زبا ن آموزا ن ب) بررسی تا ثیر نقش جنسیت دبیرا ن و زبا ن آموزان بر سا ختا رهای ارتبا ط گفتا ری میا ن آنها پ) مشخص کردن اینکه آ یا آموزگاران غا لب بر این ارتبا ط گف...

Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach

In this work, we analyze the linear stability of singular homoclinic stationary solutions and spatially periodic stationary solutions in the one-dimensional Gray-Scott model. This stability analysis has several implications for understanding the recently discovered phenomena of self-replicating pulses. For each solution constructed in A. Doelman et al. [Nonlinearity 10 (1997) 523-563], we analy...

Periodic minimizers in 1D local mean field theory

Using reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimizers are either periodic, with zero average, or of constant sign. If the local term in the free energy satisfies a convexity condition, then all minimizers are either periodic or constant. Examples of both phenomena ar...