Gaussian processes for choosing laser parameters for driven, dissipative Rydberg aggregates

To facilitate quantum simulation of open quantum systems at finite temperatures, an important ingredient is to achieve thermalization on a given time-scale. We consider a Rydberg aggregate (an arrangement of Rydberg atoms that interact via long-range interactions) embedded in a laser-driven atomic environment. For the smallest aggregate (two atoms), suitable laser parameters can be found by brute force scanning of the four tunable laser parameters. For more atoms, however, such parameter scans are too computationally costly. Here we apply Gaussian processes to predict the thermalization performance as a function of the laser parameters for two-atom and four-atom aggregates. These predictions perform remarkably well using just 1000 simulations, demonstrating the utility of Gaussian processes in an atomic physics setting. Using this approach, we find and present effective laser parameters for generating thermalization, the robustness of these parameters to variation, as well as different thermalization dynamics

Evolution and turnover in scaling systems

Scaling has been discovered in the long tails of size distributions characterizing a variety of diverse systems, many of which evolve in terms of the size of their components through competition. Such time-invariant macro distributions, however, often obscure the micro-dynamics of change, such as continual turnover in the rank order of the constituents. Here we show how a model drawn from evolutionary theory can explain this change, such that the time spent in the top ranked constituents is finite and also characterized by longtailed distributions. To show the broad applicability of this model, we compare typical model runs to real-world examples including US boys’ names, UK Number One for pop albums, journal article keywords, and city sizes

Contracts between Legal Persons

Contract law and the economics of contract have, for the most part, developed independently of each other. In this essay, we briefly review the notion of a contract from the perspective of lawyer, and then use this framework to organize the economics literature on contract. The title, Contracts between Legal Persons, limits the review to that part of contract law that is generic to any legal person. A legal person is any individual, firm or government agency with the right to enter into binding agreements. Our goal is to discuss the role of the law in enforcing these agreements under the hypothesis that the legal persons have well defined goals and objectives.contract law, law and economics, contract breach, contract theory, incomplete contracts

Novel battery model of an all-electric personal rapid transit vehicle to determine state-of-health through subspace parameter estimation and a Kalman Estimator

Abstract--The paper describes a real-time adaptive battery model for use in an all-electric Personal Rapid Transit vehicle. Whilst traditionally, circuit-based models for lead-acid batteries centre on the well-known Randles’ model, here the Randles’ model is mapped to an equivalent circuit, demonstrating improved modelling capabilities and more accurate estimates of circuit parameters when used in Subspace parameter estimation techniques. Combined with Kalman Estimator algorithms, these techniques are demonstrated to correctly identify and converge on voltages associated with the battery State-of-Charge, overcoming problems such as SoC drift (incurred by coulomb-counting methods due to over-charging or ambient temperature fluctuations). Online monitoring of the degradation of these estimated parameters allows battery ageing (State-of-Health) to be assessed and, in safety-critical systems, cell failure may be predicted in time to avoid inconvenience to passenger networks. Due to the adaptive nature of the proposed methodology, this system can be implemented over a wide range of operating environments, applications and battery topologies

Nonlinear observers for predicting state-of-charge and state-of-health of lead-acid batteries for hybrid-electric vehicles

Abstract—This paper describes the application of state-estimation techniques for the real-time prediction of the state-of-charge (SoC) and state-of-health (SoH) of lead-acid cells. Specifically, approaches based on the well-known Kalman Filter (KF) and Extended Kalman Filter (EKF), are presented, using a generic cell model, to provide correction for offset, drift, and long-term state divergence—an unfortunate feature of more traditional coulomb-counting techniques. The underlying dynamic behavior of each cell is modeled using two capacitors (bulk and surface) and three resistors (terminal, surface, and end), from which the SoC is determined from the voltage present on the bulk capacitor. Although the structure of the model has been previously reported for describing the characteristics of lithium-ion cells, here it is shown to also provide an alternative to commonly employed models of lead-acid cells when used in conjunction with a KF to estimate SoC and an EKF to predict state-of-health (SoH). Measurements using real-time road data are used to compare the performance of conventional integration-based methods for estimating SoC with those predicted from the presented state estimation schemes. Results show that the proposed methodologies are superior to more traditional techniques, with accuracy in determining the SoC within 2% being demonstrated. Moreover, by accounting for the nonlinearities present within the dynamic cell model, the application of an EKF is shown to provide verifiable indications of SoH of the cell pack