Dynamic Competitive Persuasion

We examine a dynamic game of competitive persuasion played between two long-lived sellers over $T \leq \infty$ periods. Each period, each seller provides information via a Blackwell experiment to a single short-lived buyer, who buys from the seller whose product has the highest expected quality. We solve for the unique subgame perfect equilibrium of this game, and conduct comparative statics: in particular we find that long horizons lead to less information

Population Processes with Immigration

The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or non-stationary ones. We also study the branching random walk on $Z^d$ with immigration and prove the existence of the limits for the first two correlation functions

EcoBlock: Grid Impacts, Scaling, and Resilience

Widespread deployment of EcoBlocks has the potential to transform today's electricity system into one that is more resilient, flexible, efficient and sustainable. In this vision, the system will consist of self- su cient, renewable-powered, block-scale entities that can deliberately adjust their net power exchange and can optimize performance, maintain stability, support each other, or disconnect entirely from the grid as needed. This report is intended as an independent analysis of the potential relationships, both constructive and adverse, between EcoBlocks and the grid

Kirigami-inspired, highly stretchable micro-supercapacitor patches fabricated by laser conversion and cutting.

The recent developments in material sciences and rational structural designs have advanced the field of compliant and deformable electronics systems. However, many of these systems are limited in either overall stretchability or areal coverage of functional components. Here, we design a construct inspired by Kirigami for highly deformable micro-supercapacitor patches with high areal coverages of electrode and electrolyte materials. These patches can be fabricated in simple and efficient steps by laser-assisted graphitic conversion and cutting. Because the Kirigami cuts significantly increase structural compliance, segments in the patches can buckle, rotate, bend and twist to accommodate large overall deformations with only a small strain (<3%) in active electrode areas. Electrochemical testing results have proved that electrical and electrochemical performances are preserved under large deformation, with less than 2% change in capacitance when the patch is elongated to 382.5% of its initial length. The high design flexibility can enable various types of electrical connections among an array of supercapacitors residing in one patch, by using different Kirigami designs