Variational Approach to Regularity of Optimal Transport Maps: General Cost Functions

We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $$\epsilon $$ ϵ -regularity result for optimal transport maps between Hölder continuous densities slightly more quantitative than the result by De Philippis–Figalli. One of the new contributions is the use of almost-minimality: if the cost is quantitatively close to the Euclidean cost function, a minimizer for the optimal transport problem with general cost is an almost-minimizer for the one with quadratic cost. This further highlights the connection between our variational approach and De Giorgi’s strategy for $$\epsilon $$ ϵ -regularity of minimal surfaces.

Dynamic Scheduling of Multiclass Many-Server Queues with Abandonment: The Generalized cμ/h Rule

In “Dynamic Scheduling of Multiclass Many-Server Queues with Abandonment: The Generalized cμ/h Rule,” Long, Shimkin, Zhang, and Zhang propose three scheduling policies to cope with any general cost functions and general patience-time distributions. Their first contribution is to introduce the target-allocation policy, which assigns higher priority to customer classes with larger deviation from the desired allocation of the service capacity and prove its optimality for any general queue-length cost functions and patience-time distributions. The Gcμ/h rule, which extends the well-known Gcμ rule by taking abandonment into account, is shown to be optimal for the case of convex queue-length costs and nonincreasing hazard rates of patience. For the case of concave queue-length costs but nondecreasing hazard rates of patience, it is optimal to apply a fixed-priority policy, and a knapsack-like problem is developed to determine the optimal priority order efficiently.

A Review on Combining Micro Gas Turbines with Organic Rankine Cycles

Current energy conversion machines such as the micro gas turbine can be improved by harvesting the low-grade energy of the exhaust. A prominent option for such is the organic Rankine cycle due to its relatively efficient and reliable design. This manuscript presents a review on the subject and is the first step toward the design of an organic Rankine cycle bottoming a 100 kWe recuperated gas turbine. After introducing and covering the historical development of the technology, appropriate guidelines for defining the cycle arrangement and selecting the fluid are presented. At last, the viability of the cycle is assessed by assuming an appropriate efficiency value and general cost functions. The organic Rankine is expected to generate an additional 16.6 kWe of power, increasing the electrical efficiency from 30 to 35%. However, the capital cost increase was estimated in 48%.