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.

Competitive reactions and the cross-sales effects of advertising and promotion.

Abstract: How do competitors react to each other's price-promotion and advertising actions? How do these reactions influence the net sales impact we observe? We answer these questions by performing a large-scale empirical study of the short-run and long-run reactions to promotion and advertising shocks in over 400 consumer product categories, over a four-year time span.Competitive reaction can be passive, accommodating or retaliatory. We first develop a series of expectations on the type and intensity of reaction behavior, and on the moderators of this behavior. These expectations are assessed in two ways. First, vector-autoregressive models quantify the short-run and long-run effect of a promotion or advertising action on competitive sales and on competitive reactions. By cataloging the numerical results, we are able to formulate empirical generalizations of reaction behavior ('how do they react?'). Second, we estimate structural models of reaction intensity, in function of various market and competitive characteristics ('what are the drivers of reaction?'). Finally, by comparing our findings on reaction behavior with those on promotion and advertising effectiveness, we are able to evaluate competitive reaction behavior ('are they reacting as they should?').A major finding is that competitive reaction is predominantly passive. When it is present, it is usually retaliatory in the same instrument, but accommodating or retaliatory in a different instrument. There are very few long-run consequences of any type of reaction behavior. We also report on several moderating effects that are in line with expectations, and that support the presence of a certain amount of rationality in competitive reaction behavior.The net impact of the over-time effects of advertising and price-promotion attacks, competitive reactions and the sales effectiveness of each, is that competitors' sales are generally not affected, and especially not in the long run. We weigh the evidence that this sales neutrality is 'natural' (i.e., due to the nature of consumer response) versus 'managed' (i.e., due to the vigilance and effectiveness of competitors), and conclude in favor of the former.

Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls

We investigate whether surface reconstruction order exists in stationary growing states, at all length scales or only below a crossover length, $l_{\rm rec}$. The later would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale $l_{\rm R}$, but are always rough at large length scales. We investigate this issue in the context of KPZ type dynamics and a checker board type reconstruction, using the restricted solid-on-solid model with negative mono-atomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth, reconstruction order is absent in the thermodynamic limit, but exists below a crossover length $l_{\rm rec}>l_{\rm R}$, and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics

Crossover Scaling Functions in One Dimensional Dynamic Growth Models

The crossover from Edwards-Wilkinson ($s=0$) to KPZ ($s>0$) type growth is studied for the BCSOS model. We calculate the exact numerical values for the $k=0$ and $2\pi/N$ massgap for $N\leq 18$ using the master equation. We predict the structure of the crossover scaling function and confirm numerically that $m_0\simeq 4 (\pi/N)^2 [1+3u^2(s) N/(2\pi^2)]^{0.5}$ and $m_1\simeq 2 (\pi/N)^2 [1+ u^2(s) N/\pi^2]^{0.5}$, with $u(1)=1.03596967$. KPZ type growth is equivalent to a phase transition in meso-scopic metallic rings where attractive interactions destroy the persistent current; and to endpoints of facet-ridges in equilibrium crystal shapes.Comment: 11 pages, TeX, figures upon reques

Muon spin rotation and relaxation in the superconducting ferromagnet UCoGe

We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $\mu^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $\mu$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.Comment: 4 pages, 3 figures, accepted for publication in PR

Line tensions, correlation lengths, and critical exponents in lipid membranes near critical points

Membranes containing a wide variety of ternary mixtures of high chain-melting temperature lipids, low chain-melting temperature lipids, and cholesterol undergo lateral phase separartion into coexisting liquid phases at a miscibility transition. When membranes are prepared from a ternary lipid mixture at a critical composition, they pass through a miscibility critical point at the transition temperature. Since the critical temperature is typically on the order of room temperature, membranes provide an unusual opportunity in which to perform a quantitative study of biophysical systems that exhibit critical phenomena in the two-dimensional Ising universality class. As a critical point is approached from either high or low temperature, the scale of fluctuations in lipid composition, set by the correlation length, diverges. In addition, as a critical point is approached from low temperature, the line tension between coexisting phases decreases to zero. Here we quantitatively evaluate the temperature dependence of line tension between liquid domains and of fluctuation correlation lengths in lipid membranes in order to extract a critical exponent, nu. We obtain nu=1.2 plus or minus 0.2, consistent with the Ising model prediction nu=1. We also evaluate the probability distributions of pixel intensities in fluoresence images of membranes. From the temperature dependence of these distributions above the critical temperature, we extract an independent critical exponent beta=0.124 plus or minus 0.03 which is consistent with the Ising prediction of beta=1/8.Comment: 22 pages, 7 figure

An exact universal amplitude ratio for percolation

The universal amplitude ratio $\tilde{R}_{\xi}$ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to correct error

Temperature Dependence of Facet Ridges in Crystal Surfaces

The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model on a honeycomb lattice is studied numerically. We focus on the facet ridge endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth in the exactly soluble square lattice BCSOS model. In our more general context the transfer matrix is not stochastic at the FRE points, and a more complex structure develops. We observe ridge lines sticking into the rough phase where thesurface orientation jumps inside the rounded part of the crystal. Moreover, the rough-to-faceted edges become first-order with a jump in surface orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical endpoints. The latter display anisotropic scaling with exponent $z=3$ instead of familiar PT value $z=2$.Comment: 12 pages, 19 figure

Quantized Hall Conductance in a Two-Dimensional Periodic Potential

The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential U. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small U/ℏωc