Mechanism for the thermal dependence of the Cr to Nd energytransfer in garnets

The temperature dependence of the Cr-Nd energy transfer is found to be due to the thermal variation of the radiative decay probability of Cr. The validity of this conjecture is checked in the Gd₃Sc ₂Ga₃O₁₂ and CaMg₂Y₂ Ge₃O₁₂ crystals. It is also found that above 200 K, the nonradiative energy transfer rate from Cr to Nd is greater in Gd₃Sc₂Ga₃O₁₂ than in CaMg ₂Y₂Ge₃O₁₂     

Stochastic Constraint Programming: A Scenario-Based Approach

To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (non-stochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Van Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.