A bibliography of non-deterministic lot-sizing models

Non-deterministic lot-sizing models are considered which serve for an explicit determination of lot sizes in an uncertain environment. Taxonomy components for such models are suggested and a bibliography structured according to these components is presented. The taxonomy components are numeric characteristics of a lot-sizing problem, names of uncertain parameters and names of approaches to model the uncertainty. The bibliography covers more than 300 publications since the year 2000.     

New predictions of extreme keel depths and scour frequencies for the Beaufort Sea using ice thickness statistics

In 1983 Wadhams proposed a technique for calculating scour return periods and pipeline burial depths for scour avoidance for the coastal Beaufort Sea. The technique combined extreme keel depth predictions based on submarine data with the use of observed distributions of scour widths and incision depths, to calculate the extreme incision depth with a given return period for a pipeline of given length laid across the seabed. The Beaufort Sea submarine dataset used to illustrate the application of the technique was obtained in 1976 from a regime consisting largely of multi-year ice. In recent years first-year ice has come to dominate the southern Beaufort Sea, so we replaced the 1976 statistics with data from a winter 2007 survey of the same region by the submarine HMS “Tireless”. Holding other scour geometry parameters constant, we calculated new return periods and burial depths and found large changes which appear to be reflected in the results of recent resurveys of regions subject to ice scour. We reflect on the likelihood that these more moderate conditions will continue to prevail in the future.     

A new technique for iceberg drift prediction

In this paper we present a preliminary study on a new technique for forecasting iceberg motion. The technique is based on using the past motions of icebergs to generate the currents required by a model for predicting those past observed motions. These currents are then used to forecast the motions of other icebergs passing through the same area at a later time. In addition, consideration — within the limits of our data set — is given the relationship between the currents obtained from the models and the actual currents present in the ocean. Of particular interest is the spatial variability of the derived currents and the implications of this variability for predicting future iceberg motions.     

Local scour at abutments: A review

Failure of bridges due to local scour has motivated many investigators to explore the causes of scouring and to predict the maximum scour depth at abutments. In this paper, a detailed review of the up-to-date work on scour at abutments is presented including all possible aspects, such as flow field, scouring process, parameters affecting scour depth, time-variation of scour and scour depth estimation formulae.     

Model tests of iceberg towing

Icebergs may cause a threat to offshore installations, vessels and operations in a number of Arctic regions. In order to increase the understanding of what happens when an iceberg tow is started in ice covered waters; physical tank model tests have been carried out in various concentrations of sea ice. The objectives with these tests have been to evaluate the practical arrangements for iceberg towing and to collect data regarding tow loads and iceberg behaviour during the tow.The tank model tests were carried out in scale 1:40 in the ice tank at Hamburg Ship Model Basin (HSVA), Germany. Two different iceberg models were used and each towed in four different ice concentrations. From all tests, tow line forces, iceberg displacements and rotations were recorded.It was concluded that towing in 50% ice concentrations and higher were not realistic due to high resistance. During the tows in high concentrations, ice was breaking in flexural mode, crushing, rafting and ridging continuously in front of the iceberg models. With respect to the tow line, the line was fully extended and lifted up from the water/ice. In real operations this may increase the risk for tow line rupture and subsequent “snapping”. In 50% ice concentration, total loads in the tow line will most of the time be lower than maximum bollard pull for powerful diesel electric icebreakers indicating that towing up to this concentration may be feasible. However, tow lines will have to resist even the highest peak loads during a tow and it is unclear whether sufficiently strong tow lines can be produced. With respect to tows in 20% concentration and open water, loads are significantly lower indicating that towing in low ice concentrations should be feasible.Measured loads seem to be reasonable well described by a log-normal distribution. The concentrations of surrounding sea ice are found to be most important for the load magnitude while variations in speed, acceleration, course and iceberg shape seem to be less important.A log-normal distribution, in which the parameters are functions of the sea ice concentration, has been fitted to recorded data. Combined with information regarding expected tow length, this distribution may be applied in order to provide crude estimate on extreme loads during an iceberg tow. By performing additional model tows in different ice conditions and with larger variations in iceberg size, this model may be further developed to be applicable in a wide range of scenarios.     

Statistical prediction of iceberg trajectories

The unpredictability of low frequency currents in the ocean reduces the practicality of iceberg trajectory prediction using deterministic models. However, an optimum statistical model may be developed in which the future velocity of an iceberg (other than the predictable part due to wind, mean flow or tides) is a weighted sum of previous (measured) velocities. The weights are related to the Lagrangian velocity autocorrelation function. The scheme may be used to predict error bars as well as future positions. The theory is outlined in this paper and extended to allow for noise and inertial waves. For appropriate parameter values it is found that there is little value in using more than a one-term predictor, i.e. one based solely on the most recently measured velocity. It is shown how the scheme could also be used to predict, approximately, the probability that a given iceberg will enter a circle of specified radius around a wellsite within a specified time.     

Computer simulation of iceberg instability

The possibility of an iceberg rolling to an orientation of deeper draft and colliding with the sea-bed has important implications for the offshore oil and gas industry on the Grand Banks of Newfoundland. In this paper that possibility is given substance. An interactive computer program was used to study a class of icebergs that increase their draft by as much as 50% on being perturbed from a position of near unstable equilibrium.     

A finite element technique for non-deterministic thermal deformation analyses including temperature dependent material properties

A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.     

Indian practice on estimation of scour around bridge piers—A comment

Well-laid foundation is mostly provided in road and railway bridges in India over large and medium-sized rivers. The age-old Lacey-Inglis method is used for estimation of the design scour depth around bridge elements such as pier, abutment, guide bank, spur and groyene. Codal provisions are seen to produce too large a scour depth around bridge elements resulting in bridge sub-structures that lead to increased construction costs. Limitations that exist in the codes of practice are illustrated in this paper using examples. The methods recently developed for estimation of the scour are described. New railway and road bridges are required to be built in large numbers in the near future across several rivers to strengthen such infrastructure in the country. It is strongly felt that provisions in the existing codes of practice for determination of design scour depth require immediate review. The present paper provides a critical note on the practices followed in India for estimating the design scour depth.     

A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU⁺ cells are expected to divide into BrdU⁺ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU⁺ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU⁺ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU⁺ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.     

Effect of pressure on the vacuum cooling of iceberg lettuce

Vacuum cooling is known as a rapid evaporative cooling technique for any porous product which has free water. The aim of this paper is to apply vacuum cooling technique to the cooling of the iceberg lettuce and show the pressure effect on the cooling time and temperature decrease. The results of vacuum cooling are also compared with conventional cooling (cooling in refrigerator) for different temperatures. Vacuum cooling of iceberg lettuce at 0.7 kPa is about 13 times faster than conventional cooling of iceberg lettuce at 6 °C. It has been also found that it is not possible to decrease the iceberg lettuce temperature below 10 °C if vacuum cooling method is used and vacuum pressure is set to 1.5 kPa.     

A semi-empirical method for predicting hardened case depths in laser heat treating

Some predictions on the hardness and hardening depths on laser heat treatment of steels can be obtained when specific characteristics of both laser processes (heating and cooling rates) and laser heat treated steels (microhardness profiles) are taken into account. Some controlled surface temperature laser heat treatments have been carried out with a medium power c.w. CO₂ laser on a medium carbon steel (AISI/SAE1045), allowing these predictions to be tested. In particular, knowing the surface temperature has enabled an analytical algorithm to be used to describe thermal processes and a simple exponential expression to be employed to carefully predict the hardened case depth.     

Determination of the optical properties of a two-layer tissue model by detecting photons migrating at progressively increasing depths

We have investigated a method for solving the inverse problem of determining the optical properties of a two-layer turbid model. The method is based on deducing the optical properties (OPs) of the top layer from the absolute spatially resolved reflectance that results from photon migration within only the top layer by use of a multivariate calibration model. Then the OPs of the bottom layer are deduced from relative frequency-domain (FD) reflectance measurements by use of the two-layer FD diffusion model. The method was validated with Monte Carlo FD reflectance profiles and experimental measurements of two-layer phantoms. The results showed that the method is useful for two-layer models with interface depths of >5 mm; the OPs were estimated, within a relatively short time (<1 min), with a mean error of <10% for the Monte Carlo reflectance profiles and with errors of <25% for the phantom measurements.     

Monte Carlo calculations of iceberg draft changes caused by roll

Draft changes in iceberg roll have been investigated using a Monte Carlo technique for generating iceberg shapes of constant, polygonal cross section. Stability is assessed from the potential energy curves calculated assuming vertical but not rotational hydrostatic equilibrium. No modelling of the roll dynamics has been included. The draft changes are approximately normally distributed, with increases almost as probable as decreases. Extreme draft changes (defined to be those in excess of 20%) are not uncommon. The mean draft change, standard deviation, skewness and kurtosis depend on the number of sides in the berg model, and on the ratio of berg ice density to seawater density. In particular the fraction of extreme draft changes is a sensitive function of this ratio.     

A new tip area function for instrumented nanoindentation at extremely small contact depths

The accuracy of measurement of mechanical properties of a material using instrumented nanoindentation at extremely small penetration depths heavily relies on the determination of the contact area of the indenter. Our experiments have demonstrated that the conventional area function could lead to a significant error when the contact depth was below 40 nm, due to the singularity in the first derivation of the function in this region and thus, the resultant unreasonable sharp peak on the function curve. In this paper, we proposed a new area function that was used to calculate the contact area for the indentations where the contact depths varied from 10 to 40 nm. The experimental results have shown that the new area function has produced better results than the conventional function.     

Import-export of knowledge between scientific subject categories: The iceberg hypothesis

The capacity to attract citations from other disciplines — or knowledge export — has always been taken into account in evaluating the quality of scientific papers or journals. Some of the JCR’s (ISI’s Journal Citation Report) Subject Categories have a greater exporting character than others because they are less isolated. This influences the rank/JIF (ISI’s Journal Impact Factor) distribution of the category. While all the categories fit a negative power law fairly well, those with a greater External JIF give distributions with a more sharply defined peak and a longer tail — something like an iceberg. One also observes a major relationship between the rates of export and import of knowledge.     

Gain of parabolic mesh reflector antennas with arbitrary depths

Analytical expressions for calculating the gain of a parabolic mesh reflector with arbitrary ratio of the focal length to aperture diameter have been derived using the method of averaged boundary conditions. The results are obtained for a dense thin-wire mesh with square cells and ideal electric contacts between conductors at junctions. Specific features of the influence of mesh topology on the gain of reflectors with various depths are considered.