2-Chloro-N-(2,6-dimethyl­phen­yl)acetamide

The crystal structure of the title compound (26DMPCA), C10H12ClNO, is closely related to those of side-chain-unsubstituted N-(2,6-dimethyl­phen­yl)acetamide and side-chain-substituted 2,2,2-trichloro-N-(2,6-dimethyl­phen­yl)­acet­amide and N-(2,6-dimethyl­phen­yl)-2,2,2-trimethylacet­amide, with slightly different bond parameters. The mol­ecules in 26DMPCA are linked into chains through N—H⋯O hydrogen bonding

Early-Warning Signs for Pattern-Formation in Stochastic Partial Differential Equations

There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of mathematical modeling and analysis has been on stochastic ordinary differential equations, where generic statistical early-warning signs can be identified near bifurcation-induced tipping points. In this paper, we outline some basic steps to extend this theory to stochastic partial differential equations with a focus on analytically characterizing basic scaling laws for linear SPDEs and comparing the results to numerical simulations of fully nonlinear problems. In particular, we study stochastic versions of the Swift-Hohenberg and Ginzburg-Landau equations. We derive a scaling law of the covariance operator in a regime where linearization is expected to be a good approximation for the local fluctuations around deterministic steady states. We compare these results to direct numerical simulation, and study the influence of noise level, noise color, distance to bifurcation and domain size on early-warning signs.Comment: Published in Communications in Nonlinear Science and Numerical Simulation (2014

2-Chloro-N-(2,4-dimethyl­phen­yl)acetamide

The conformation of the N—H bond in the structure of the title compound, C10H12ClNO, is syn to the ortho methyl group, similar to that observed with respect to the meta methyl group in 2-chloro-N-(3-methyl­phen­yl)acetamide and the ortho-chloro group in 2-chloro-N-(2-chloro­phen­yl)acetamide. The geometric parameters are similar to those of other acetanilides. The mol­ecules are linked into chains through inter­molecular N—H⋯O hydrogen bonds

N-(2-Methyl­phen­yl)benzene­sulfonamide

In the title compound, C13H13NO2S, the conformation of the N—H bond is anti to the ortho-methyl group on the aniline ring, in contrast to the syn conformation observed with respect to the ortho-chloro group in N-(2-chloro­phen­yl)benzene­sulfonamide. The dihedral angle between the two benzene rings is 61.5 (1)°. Mol­ecules are linked into chains running along the a axis by N—H⋯O hydrogen bonds