Coupling climate and economic models in a cost-benefit framework: A convex optimisation approach

In this paper, we present a general method, based on a convex optimisation technique, that facilitates the coupling of climate and economic models in a cost-benefit framework. As a demonstration of the method, we couple an economic growth model à la Ramsey adapted from DICE-99 with an efficient intermediate complexity climate model, C-GOLDSTEIN, which has highly simplified physics, but fully 3-D ocean dynamics. As in DICE-99, we assume that an economic cost is associated with global temperature change: this change is obtained from the climate model, which is driven by the GHG concentrations computed from the economic growth path. The work extends a previous paper in which these models were coupled in cost-effectiveness mode. Here we consider the more intricate cost-benefit coupling in which the climate impact is not fixed a priori. We implement the coupled model using an oracle-based optimisation technique. Each model is contained in an oracle, which supplies model output and information on its sensitivity to a master program. The algorithm Proximal-ACCPM guarantees the convergence of the procedure under sufficient convexity assumptions. Our results demonstrate the possibility of a consistent, cost-benefit, climate-damage optimisation analysis with a 3-D climate mode

Control of singularly perturbed hybrid stochastic systems

In this paper, we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental “ergodicity” property for a class of “infinitesimal control systems” associated with the fast mode, we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system. Both the finite- and infinite-discounted horizon cases are considered. We show how an approximate optimal control law can be constructed from the solution of the limit control problem. In the particular case where the infinitesimal control systems possess the so-called turnpike property, i.e., are characterized by the existence of global attractors, the limit control problem can be given an interpretation related to a decomposition approach

Control of singularly perturbed hybrid stochastic systems

In this paper we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental ”ergodicity” property for a class of ”infinitesimal control systems” associated with the fast mode, we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system. Both the finite and infinite discounted horizon cases are considered. We show how an approximate optimal control law can be constructed from the solution of the limit control problem. In the particular case where the infinitesimal control systems possess the so-called turnpike property, i.e. are characterized by the existence of global attractors, the limit control problem can be given an interpretation related to a decomposition approach

Oscillations in a maturation model of blood cell production.

We present a mathematical model of blood cell production which describes both the development of cells through the cell cycle, and the maturation of these cells as they differentiate to form the various mature blood cell types. The model differs from earlier similar ones by considering primitive stem cells as a separate population from the differentiating cells, and this formulation removes an apparent inconsistency in these earlier models. Three different controls are included in the model: proliferative control of stem cells, proliferative control of differentiating cells, and peripheral control of stem cell committal rate. It is shown that an increase in sensitivity of these controls can cause oscillations to occur through their interaction with time delays associated with proliferation and differentiation, respectively. We show that the characters of these oscillations are quite distinct and suggest that the model may explain an apparent superposition of fast and slow oscillations which can occur in cyclical neutropenia. © 2006 Society for Industrial and Applied Mathematics

Oracle-based optimization applied to climate model calibration

In this paper, we show how oracle-based optimization can be effectively used for the calibration of an intermediate complexity climate model. In a fully developed example, we estimate the 12 principal parameters of the C-GOLDSTEIN climate model by using an oracle-based optimization tool, Proximal-ACCPM. The oracle is a procedure that finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradient. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex. The method converges to a ‘best fit' estimate over 10 times faster than a comparable test using the ensemble Kalman filter. The approach is simple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily availabl

Decomposition and parallel processing techniques for two-time scale controlled Markov chains

This paper deals with a class of ergodic control problems for systems described by Markov chains with strong and weak interactions. These systems are composed of a set of m subchains that are weakly coupled. Using results recently established by Abbad et al. one formulates a limit control problem the solution of which can be obtained via an associated non-differentiable convex programming (NDCP) problem. The technique used to solve the NDCP problem is the Analytic Center Cutting Plane Method (ACCPM) which implements a dialogue between, on one hand, a master program computing the analytical center of a localization set containing the solution and, on the other hand, an oracle proposing cutting planes that reduce the size of the localization set at each main iteration. The interesting aspect of this implementation comes from two characteristics: (i) the oracle proposes cutting planes by solving reduced sized Markov Decision Problems (MDP) via a linear program (LP) or a policy iteration method; (ii) several cutting planes can be proposed simultaneously through a parallel implementation on m processors. The paper concentrates on these two aspects and shows, on a large scale MDP obtained from the numerical approximation "a la Kushner-Dupuis” of a singularly perturbed hybrid stochastic control problem, the important computational speed-up obtained

Thermo-physical properties of paraffin wax with iron oxide nanoparticles as phase change material for heat storage applications

Phase change materials (PCMs) are growing in importance in many thermal applications as heat storage or to smooth the energy peak demand in many technological fields in industrial as well as in civil applications. Conductive nanoparticles can be added to phase change material to improve their thermo-physical properties. In this work, Iron oxide nanoparticles (IOx-NPs) were synthesized using a simple and green synthesis method, free of toxic and harmful solvents, using the extract of a plant as a reducer and stabilizer at two different temperatures of calcination 500°C and 750°C. The metallic oxide was used as an additive with 2% wt. compositions to paraffin wax to prepare a nanocomposite. The variation in thermal properties of paraffin wax in the composite was experimentally investigated. The biosynthesized IOx-NPs were characterized by X-ray diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR) and Scanning Electron Microscope (SEM) and Thermal Gravimetric Analysis (TGA) techniques. The thermal properties of the synthesized nanocomposites were characterized by a thermal conductivity analyzer and differential scanning calorimetry (DSC). The FTIR spectra showed a bond at 535 cm-1, which confirms the Fe-O vibration. The XRD powder analysis revealed the formation of the cubic phase of Fe3O4 with an average particle size of 11 nm at 500°C and the presence of the phase α-Fe2O3 with Fe3O4 at 750°C. Scanning Electron Microscopy (SEM) showed that the obtained oxide was made up of particles of nanoscale size. Experimental measurements showed that the presence of nanoparticles can improve the latent heat capacity by a maximum of 16.16 % and the thermal conductivity of the nanocomposites by a maximum of 16.99%

RUVBL1 (RuvB-like 1 (E. coli))

Review on RUVBL1 (RuvB-like 1 (E. coli)), with data on DNA, on the protein encoded, and where the gene is implicated

One-Parameter GHG Emission Policy with R&D-based Growth

This document examines the GHG emission policy of regions which use land, labor and emitting inputs in production and enhance their productivity by devoting labor to R&D, but with different endowments and technology. The regions also have different impacts on global pollution. The problem is to organize common emission policy, if the regions cannot form a federation with a common budget and the policy parameters must be uniform for all regions. The results are the following. If a self-interested central planner allocate emission caps in fixed proportion to past emissions (i.e. grandfathering), then it establishes the Pareto optimum, decreasing emissions and promoting R&D and economic growth