TY - JOUR
T1 - Continuous description of lattice discreteness effects in front propagation
AU - Clerc, Marcel G.
AU - Elías, Ricardo G.
AU - Rojas, René G.
PY - 2011/1/28
Y1 - 2011/1/28
N2 - Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description. This journal is
AB - Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description. This journal is
KW - Front propagation
KW - Fronts interaction
KW - Nonlinear waves
UR - http://www.scopus.com/inward/record.url?scp=79251497368&partnerID=8YFLogxK
U2 - 10.1098/rsta.2010.0255
DO - 10.1098/rsta.2010.0255
M3 - Article
C2 - 21149380
AN - SCOPUS:79251497368
VL - 369
SP - 412
EP - 424
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 1364-503X
IS - 1935
ER -