Discerning public law concepts in corporate law discourse

Krug, Anita K.

doi:10.1017/cbo9781139856478.013

Cited by 5 publications

(7 citation statements)

References 2 publications

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“…While θ 2 is reliable at all temperatures (unlike θ 1 ), it is less pre- 25) and ( 23) and of Eqs. ( 24) and (22), respectively. The line-tension ratio increases slowly but monotonically to the T =0 limit 2/ √ 3 ≈ 1.15.…”

Section: E Synopsis Of Exact Results and Application To Range Of Brea...mentioning

confidence: 99%

Low-temperature orientation dependence of step stiffness on {111} surfaces

et al. 2005

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For hexagonal nets, descriptive of ͕111͖ fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction, based on the Ising model with nearest-neighbor ͑NN͒ interactions. Our formula agrees well with experimental data for both Ag and Cu͕111͖ surfaces, indicating that NN interactions alone can account for the data in these cases ͑in contrast to results for Cu͕001͖͒. Experimentally significant corollaries of the low-temperature derivation show that the step line tension cannot be extracted from the stiffness and that with plausible assumptions the low-temperature stiffness should have six-fold symmetry, in contrast to the three fold symmetry of the crystal shape. We examine Zia's exact implicit solution in detail, using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high-symmetry directions. From these exact results we rederive our simple result and explore subtle behavior near close-packed directions. To account for the three-fold symmetry in a lattice gas model, we invoke an orientation-dependent trio interaction and examine its consequences.

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Section: E Synopsis Of Exact Results and Application To Range Of Brea...mentioning

confidence: 99%

Low-temperature orientation dependence of step stiffness on {111} surfaces

et al. 2005

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“…(iii) The potential role of a systematically increasing variability on the frequency of records. For the last point, Krug [32] has shown that for an exponential daily temperature distribution whose width is increasing linearly with time, the number of record events after t years grows as (ln t) 2 , intermediate to the ln t growth of a stationary distribution and linear growth when the aver-age temperature systematically increases. (iv) Day/night or high/low asymmetry [33].…”

Section: Discussionmentioning

confidence: 99%

Role of global warming on the statistics of record-breaking temperatures

2006

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We theoretically study the statistics of record-breaking daily temperatures and validate these predictions using both Monte Carlo simulations and 126 years of available data from the city of Philadelphia. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperature distribution in Philadelphia, as a function of the number of years of observation. We then consider the case of global warming, where the mean temperature systematically increases with time. Over the 126-year time range of observations, we argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events, a conclusion that is supported by numerical simulations and by the Philadelphia data. We also study the role of correlations between temperatures on successive days and find that they do not affect the frequency or magnitude of record temperature events.

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“…Both criteria have been met in our simulations. A further criterion which one may invoke [18] is that the interface width itself must be much greater than the effective lattice spacing in the growth direction (here set to O(1) by the noise variance being normalized to unity.) This criterion is not satisfied in our simulations for d = 4, or for very small α, for the simple reason that if the interface fluctuations grow very slowly with time (meaning β is small) then one will never achieve W ≫ 1 on observable time-scales, even though the correlation length of the system is large (since z is generally close to 2).…”

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confidence: 99%

Nonuniversal Exponents in Interface Growth

Newman

Swift

1997

Phys. Rev. Lett.

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We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponent β on the details of the distribution of noise p(ξ). All distributions considered are delta-correlated in space and time, and have finite cumulants. We find that β becomes progressively more sensitive to details of the distribution with increasing dimensionality. We discuss the implications of these results for the universality hypothesis.PACS numbers: 05.40.+j, 68.35.R Typeset using REVT E X 1

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Discerning public law concepts in corporate law discourse

Cited by 5 publications

References 2 publications

Low-temperature orientation dependence of step stiffness on {111} surfaces

Low-temperature orientation dependence of step stiffness on {111} surfaces

Role of global warming on the statistics of record-breaking temperatures

Nonuniversal Exponents in Interface Growth

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