A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

The effect of a new drag-law parameterization on ice shelf water plume dynamics

A drag law accounting for Ekman rotation adjacent to a flat, horizontal bou ndary is proposed for use in a plume model that is written in terms of the depth-mean velocity. The drag l aw contains a variable turning angle between the mean velocity and the drag imposed by the turbulent bound ary layer. The effect of the variable turning angle in the drag law is studied for a plume of ice shelf wat er (ISW) ascending and turning beneath an Antarctic ice shelf with draft decreasing away from the groundi ng line. As the ISW plume ascends the sloping ice shelf–ocean boundary, it can melt the ice shelf, wh ich alters the buoyancy forcing driving the plume motion. Under these conditions, the typical turning ang le is of order 10° over most of the plume area for a range of drag coefficients (the minus sign arises for th e Southern Hemisphere). The rotation of the drag with respect to the mean velocity is found to be signifi cant if the drag coefficient exceeds 0.003; in this case the plume body propagates farther along and across the b ase of the ice shelf than a plume with the standard quadratic drag law with no turning angle.

The "value" of property rights in social security law

This article provides a critical examination of the way that property rules are applied judicially in the context of social security law concerned with the assessment of capital, and especially in connection with the determination of ownership and the valuation of assets, which can have a critical bearing on entitlement to various means-tested benefits.

Construction contracts: law and management. 4th edition

This is a fully revised edition of the UK’s leading textbook on the law governing construction contracts and the management and administration of those contracts. Although the legal principles involved are an aspect of general contract law, the practical and commercial complexities of the construction industry have increasingly made this a specialist area. This new edition has been brought up to date with recent cases and developments in the law as it stands at March 2007. The basic approach of the book has been retained. Rather than provide a commentary on standard-form contracts, our approach is to introduce the general principles that underlie contracts in construction, illustrating them by reference to the most important standard forms currently in use. Some of the common standard-form contracts have been revised since the previous edition, and the text has been revised to take account of these changes. Practitioners (consultants, builders, clients and lawyers) will find this an extremely useful source of reference, providing in-depth explanations for all of the features found in contemporary construction contracts, with reasons. A unique feature of this book is the way that it brings together the relevant principles of law with the practical issues arising in construction cases. It is a key text for construction undergraduates and postgraduates as well as for those taking the RIBA Part III and CIOB Part II examinations.

Haworth's Law

The maximum 'Depth to Mate' (DTM(k)) data for k-man chess, k = 3-7, is now available: log(maxDTM(k)) demonstrates quasi-linear behaviour. This note predicts maxDTM for 8- to 10-man chess and the two-sigma distributions around these figures. 'Haworth's Law' is the conjecture that maxDTM will continue to demonstrate this behaviour for some time to come. The supporting datafile is a pgn of maxDTM positions, each having a DTM-minimaxing line of play from it to 'mate'.

SPARC Data Initiative: Comparison of water vapor climatologies from international satellite limb sounders

Within the SPARC Data Initiative, the first comprehensive assessment of the quality of 13 water vapor products from 11 limb-viewing satellite instruments (LIMS, SAGE II, UARS-MLS, HALOE, POAM III, SMR, SAGE III, MIPAS, SCIAMACHY, ACE-FTS, and Aura-MLS) obtained within the time period 1978-2010 has been performed. Each instrument's water vapor profile measurements were compiled into monthly zonal mean time series on a common latitude-pressure grid. These time series serve as basis for the "climatological" validation approach used within the project. The evaluations include comparisons of monthly or annual zonal mean cross sections and seasonal cycles in the tropical and extratropical upper troposphere and lower stratosphere averaged over one or more years, comparisons of interannual variability, and a study of the time evolution of physical features in water vapor such as the tropical tape recorder and polar vortex dehydration. Our knowledge of the atmospheric mean state in water vapor is best in the lower and middle stratosphere of the tropics and midlatitudes, with a relative uncertainty of. 2-6% (as quantified by the standard deviation of the instruments' multiannual means). The uncertainty increases toward the polar regions (+/- 10-15%), the mesosphere (+/- 15%), and the upper troposphere/lower stratosphere below 100 hPa (+/- 30-50%), where sampling issues add uncertainty due to large gradients and high natural variability in water vapor. The minimum found in multiannual (1998-2008) mean water vapor in the tropical lower stratosphere is 3.5 ppmv (+/- 14%), with slightly larger uncertainties for monthly mean values. The frequently used HALOE water vapor data set shows consistently lower values than most other data sets throughout the atmosphere, with increasing deviations from the multi-instrument mean below 100 hPa in both the tropics and extratropics. The knowledge gained from these comparisons and regarding the quality of the individual data sets in different regions of the atmosphere will help to improve model-measurement comparisons (e.g., for diagnostics such as the tropical tape recorder or seasonal cycles), data merging activities, and studies of climate variability.

SPARC Data Initiative: A comparison of ozone climatologies from international satellite limb sounders

A comprehensive quality assessment of the ozone products from 18 limb-viewing satellite instruments is provided by means of a detailed intercomparison. The ozone climatologies in form of monthly zonal mean time series covering the upper troposphere to lower mesosphere are obtained from LIMS, SAGE I/II/III, UARS-MLS, HALOE, POAM II/III, SMR, OSIRIS, MIPAS, GOMOS, SCIAMACHY, ACE-FTS, ACE-MAESTRO, Aura-MLS, HIRDLS, and SMILES within 1978–2010. The intercomparisons focus on mean biases of annual zonal mean fields, interannual variability, and seasonal cycles. Additionally, the physical consistency of the data is tested through diagnostics of the quasi-biennial oscillation and Antarctic ozone hole. The comprehensive evaluations reveal that the uncertainty in our knowledge of the atmospheric ozone mean state is smallest in the tropical and midlatitude middle stratosphere with a 1σ multi-instrument spread of less than ±5%. While the overall agreement among the climatological data sets is very good for large parts of the stratosphere, individual discrepancies have been identified, including unrealistic month-to-month fluctuations, large biases in particular atmospheric regions, or inconsistencies in the seasonal cycle. Notable differences between the data sets exist in the tropical lower stratosphere (with a spread of ±30%) and at high latitudes (±15%). In particular, large relative differences are identified in the Antarctic during the time of the ozone hole, with a spread between the monthly zonal mean fields of ±50%. The evaluations provide guidance on what data sets are the most reliable for applications such as studies of ozone variability, model-measurement comparisons, detection of long-term trends, and data-merging activities.