Triviality of the prolongation algebra of the Kuramoto-Sivashinsky equation

The authors apply the well known Wahlquist-Estabrook prolongation technique to the Kuramoto-Sivashinsky equation. The prolongation algebra turns out to be trivial in the sense that it is commutative. This supports nonintegrability of the equation

Preroughening transitions in a model for Si and Ge (001) type crystal surfaces

The uniaxial structure of Si and Ge (001) facets leads to nontrivial topological properties of steps and hence to interesting equilibrium phase transitions. The disordered flat phase and the preroughening transition can be stabilized without the need for step-step interactions. A model describing this is studied numerically by transfer matrix type finite-size-scaling of interface free energies. Its phase diagram contains a flat, rough, and disordered flat phase, separated by roughening and preroughening transition lines. Our estimate for the location of the multicritical point where the preroughening line merges with the roughening line, predicts that Si and Ge (001) undergo preroughening induced simultaneous deconstruction transitions.Comment: 13 pages, RevTex, 7 Postscript Figures, submitted to J. Phys.

Advertising spending patterns and competitor impact

In most industries, brand managers do not advertise continuously. Instead, advertising is switched on and off systematically, a phenomenon often referred to as pulsing. Moreover, spending levels vary considerably across periods when brands do advertise. Surprisingly, this variety in advertising spending patterns as observed in practice, as well as competitor impact on these patterns and their sales outcomes, have received relatively little empirical attention. In this paper we focus on two core aspects of observed advertising patterns: incidence and magnitude. Insights are based on the analysis of advertising spending for 370 CPG brands in 71 product categories over a four-year period. We also collected feedback from practitioners dealing with advertising across a wide range of firms. We first empirically establish that pulsing is the dominant form of advertising scheduling. Observed patterns, in turn, are largely driven by television and print advertising. Next, we show that, after accounting for a wide range of other possible drivers, advertising in-sync with competitors is more common than out-of-sync. However, the results suggest that competitive reasoning plays only a relatively minor role in advertising decisions. Finally, we show that, across a wide range of real-world scenarios, investing in top-of-mind awareness through maintenance advertising insulates brands from competitors' actions and boosts sales

Critical Exponents of the Four-State Potts Model

The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page

Mineralogical composition and origin of marine clays in the Poitou coastal plain (France)

The mineralogical composition of a well-chosen set of Holocene marine clay samples from the Marais Poitevin, tbe most important coastal marsh of France, consists of well-crystallized illite and kaolinite, and an important amount of beidellite. Chlorite, vermiculite and other interstratified clay minerals only occur in small amount.There is a clear qualitative parenthood between this composition and that of the recent alluvium of the local rivers, which makes a far origin of the marine clay superfluous. Quantitatively however, the alluvium shows a lower illite content and a dominance of (mostly interstratified) illite weathering products. As a matter of fact, the mineralogical composition of the alluvium has been inherited from the soils of the region (developed in Jurassic marls), characterized by pedogenetical degradation of illite into open illite, vermiculite, beidellite ánd a large range of interstratified minerals. In marine environment agradation into illite of the alluvial minerals, in which the illite framework was still rather well preserved, probably took place; hence the marine clay shows a lower content of interstratified minerals and a better crystallinity . Finally, an important part of the enormous “bri”-masses must consist of remobilized sediments stored close to the shore on he continental shelf and accumulated there as a detritical product of Jurassic marls during the pleistocene periods with a low sea-level and characterized by strong erosion on the land.Consequently, the origin of the bulk of the marine clay or “bri” in the Poitou coastal plain may be considered as (merely undirectly) continental and local