Equidistribution from Fractals

We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that the sequence x,nx,n^2 x,... equidistributes modulo 1. This condition is robust under C^1 coordinate changes, and it applies also when n is a Pisot number and equidistribution is understood with respect to the beta-map and Parry measure. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host's theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.Comment: 46 pages. v3: minor corrections and elaboration

An Exchange Mechanism to Coordinate Flexibility in Residential Energy Cooperatives

Energy cooperatives (ECs) such as residential and industrial microgrids have the potential to mitigate increasing fluctuations in renewable electricity generation, but only if their joint response is coordinated. However, the coordination and control of independently operated flexible resources (e.g., storage, demand response) imposes critical challenges arising from the heterogeneity of the resources, conflict of interests, and impact on the grid. Correspondingly, overcoming these challenges with a general and fair yet efficient exchange mechanism that coordinates these distributed resources will accommodate renewable fluctuations on a local level, thereby supporting the energy transition. In this paper, we introduce such an exchange mechanism. It incorporates a payment structure that encourages prosumers to participate in the exchange by increasing their utility above baseline alternatives. The allocation from the proposed mechanism increases the system efficiency (utilitarian social welfare) and distributes profits more fairly (measured by Nash social welfare) than individual flexibility activation. A case study analyzing the mechanism performance and resulting payments in numerical experiments over real demand and generation profiles of the Pecan Street dataset elucidates the efficacy to promote cooperation between co-located flexibilities in residential cooperatives through local exchange.Comment: Accepted in IEEE ICIT 201

A spintronic source of circularly polarized single photons

We present a spintronic single photon source which emits circularly polarized light, where the helicity is determined by an applied magnetic field. Photons are emitted from an InGaAs quantum dot inside an electrically operated spin light-emitting diode, which comprises the diluted magnetic semiconductor ZnMnSe. The circular polarization degree of the emitted light is high, reaching 83% at an applied magnetic field of 2T and 96% at 6 T. Autocorrelation traces recorded in pulsed operation mode prove the emitted light to be antibunched. The two circular polarization states could be used for representing quantum states |0> and |1> in quantum cryptography implementations