Numerical representation of internal waves propagation

Similar to surface waves propagating at the interface of two fluid of different densities (like air and water), internal waves in the oceanic interior travel along surfaces separating waters of different densities (e.g. at the thermocline). Due to their key role in the global distribution of (physical) diapycnal mixing and mass transport, proper representation of internal wave dynamics in numerical models should be considered a priority since global climate models are now configured with increasingly higher horizontal/vertical resolution. However, in most state-of-the-art oceanic models, important terms involved in the propagation of internal waves (namely the horizontal pressure gradient and horizontal divergence in the continuity equation) are generally discretized using very basic numerics (i.e. second-order approximations) in space and time. In this paper, we investigate the benefits of higher-order approximations in terms of the discrete dispersion relation (in the linear theory) on staggered and nonstaggered computational grids. A fourth-order scheme discretized on a C-grid to approximate both pressure gradient and horizontal divergence terms provides clear improvements but, unlike nonstaggered grids, prevents the use of monotonic or non- oscillatory schemes. Since our study suggests that better numerics is required, second and fourth order direct space-time algorithms are designed, thus paving the way toward the use of efficient high-order discretizations of internal gravity waves in oceanic models, while maintaining good sta- bility properties (those schemes are stable for Courant numbers smaller than 1). Finally, important results obtained at a theoretical level are illustrated at a discrete level using two-dimensional (x,z) idealized experiments

On ordinal utility, cardinal utility, and random utility

Though the Random Utility Model (RUM) was conceived  entirely in terms of ordinal utility, the apparatus throughwhich it is widely practised exhibits properties of  cardinal utility.  The adoption of cardinal utility as a  working operation of ordinal is perfectly valid, provided  interpretations drawn from that operation remain faithful  to ordinal utility.  The paper considers whether the latterrequirement holds true for several measurements commonly  derived from RUM.  In particular it is found that  measurements of consumer surplus change may depart from  ordinal utility, and exploit the cardinality inherent in  the practical apparatus.

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

The Effect of Bankruptcy Laws on the Valuation of Risky Consumer Debt

In a market setting with perfect information, a consumer recognizes that he can influence the state-contingent returns, and hence the pric, of his risky debt by the decision variables that determine the collateral and promised payments. This paper examines the effect of bankruptcy laws on the feasible consumption opportunities of borrowers and lenders in order to determine the necessary requirements for the bilateral debt market to be perfectly competitive.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72017/1/j.1540-6288.1989.tb00348.x.pd

Modeling the impact of ocean circulation on chlorophyll blooms around South Georgia, Southern Ocean.

The northeast periphery of the Scotia Sea hosts one of the largest chlorophyll‐a blooms of the Southern Ocean. This bloom peaks to the northwest of the island of South Georgia, extending eastward for hundreds of kilometers. Although the Southern Ocean has many islands of similar size, South Georgia is ecologically one of the most significant: It not only sustains one of the Southern Ocean's largest and most diverse ecosystems but also constitutes its single most important region for biological carbon sequestration. While the exceptional nature of South Georgia's blooms has been recognized widely, both the physical processes that contribute to their fertilization and the reasons why these blooms are larger than those of other similar regions (e.g., Kerguelen or Crozet Islands) are poorly understood. We use the results of a high‐resolution ocean model to investigate the physical processes that mediate the entrainment of deep, iron‐rich waters into the surface layers of the South Georgia region. We show that the Southern Antarctic Circumpolar Current Front, the southernmost jet of the Antarctic Circumpolar Current (ACC), pumps iron‐enriched waters from the deep ocean onto the bottom layers of South Georgia's shelf. These waters are upwelled along the northern coast of the island and are then exported into the Georgia Basin, where topographically steered circulation shields them from the dispersive effects of local currents and eddies, thus allowing the bloom development

Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved

A relocatable ocean model in support of environmental emergencies

During the Costa Concordia emergency case, regional, subregional, and relocatable ocean models have been used together with the oil spill model, MEDSLIK-II, to provide ocean currents forecasts, possible oil spill scenarios, and drifters trajectories simulations. The models results together with the evaluation of their performances are presented in this paper. In particular, we focused this work on the implementation of the Interactive Relocatable Nested Ocean Model (IRENOM), based on the Harvard Ocean Prediction System (HOPS), for the Costa Concordia emergency and on its validation using drifters released in the area of the accident. It is shown that thanks to the capability of improving easily and quickly its configuration, the IRENOM results are of greater accuracy than the results achieved using regional or subregional model products. The model topography, and to the initialization procedures, and the horizontal resolution are the key model settings to be configured. Furthermore, the IRENOM currents and the MEDSLIK-II simulated trajectories showed to be sensitive to the spatial resolution of the meteorological fields used, providing higher prediction skills with higher resolution wind forcing.MEDESS4MS Project; TESSA Project; MyOcean2 Projectinfo:eu-repo/semantics/publishedVersio