Calculation of the incremental stress-strain relation of a polygonal packing

The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure surface, that shows a power law dependence on the pressure. Below the failure surface, non linear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results shows that the stiffness tensor can be directly related to the micro-contact rearrangements. The plasticity obeys a non-associated flow rule, with a plastic limit surface that does not agree with the failure surface.Comment: 11 pages, 20 figur

Equilibrium spin-glass transition of magnetic dipoles with random anisotropy axes on a site diluted lattice

We study partially occupied lattice systems of classical magnetic dipoles which point along randomly oriented axes. Only dipolar interactions are taken into account. The aim of the model is to mimic collective effects in disordered assemblies of magnetic nanoparticles. From tempered Monte Carlo simulations, we obtain the following equilibrium results. The zero temperature entropy approximately vanishes. Below a temperature T_c, given by k_B T_c= (0.95 +- 0.1)x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy and x is the site occupancy rate, we find a spin glass phase. In it, (1) the mean value , where q is the spin overlap, decreases algebraically with system size N as N increases, and (2) D|q| = 0.5 (T/x)^1/2, independently of N, where D|q| is the root mean square deviation of |q|.Comment: 7 LaTeX pages, 7 eps figures. Submitted to PRB on 30 December 200

Cost Efficient Distributed Load Frequency Control in Power Systems

The introduction of new technologies and increased penetration of renewable resources is altering the power distribution landscape which now includes a larger numbers of micro-generators. The centralized strategies currently employed for performing frequency control in a cost efficient way need to be revisited and decentralized to conform with the increase of distributed generation in the grid. In this paper, the use of Multi-Agent and Multi-Objective Reinforcement Learning techniques to train models to perform cost efficient frequency control through decentralized decision making is proposed. More specifically, we cast the frequency control problem as a Markov Decision Process and propose the use of reward composition and action composition multi-objective techniques and compare the results between the two. Reward composition is achieved by increasing the dimensionality of the reward function, while action composition is achieved through linear combination of actions produced by multiple single objective models. The proposed framework is validated through comparing the observed dynamics with the acceptable limits enforced in the industry and the cost optimal setups

Multi-ion sensing of dipolar noise sources in ion traps

Trapped-ion quantum platforms are subject to `anomalous' heating due to interactions with electric-field noise sources of nature not yet completely known. There is ample experimental evidence that this noise originates at the surfaces of the trap electrodes, and models assuming fluctuating point-like dipoles are consistent with observations, but the exact microscopic mechanisms behind anomalous heating remain undetermined. Here we show how a two-ion probe displays a transition in its dissipation properties, enabling experimental access to the mean orientation of the dipoles and the spatial extent of dipole-dipole correlations. This information can be used to test the validity of candidate microscopic models, which predict correlation lengths spanning several orders of mag- nitude. Furthermore, we propose an experiment to measure these effects with currently-available traps and techniques

Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model

By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L^3 sites of a simple cubic lattice, and point along a given crystalline axis. For x_c< x<=1, where x_c = 0.65, we find an antiferromagnetic phase below a temperature which vanishes as x tends to x_c from above. At lower values of x, we find an equilibrium spin-glass (SG) phase below a temperature given by k_B T_{sg} = x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy. We study (a) the relative mean square deviation D_q^2 of |q|, where q is the SG overlap parameter, and (b) xi_L/L, where xi_L is a correlation length. From their variation with temperature and system size, we determine T_{sg}. In the SG phase, we find (i) the mean values and decrease algebraically with L as L increases, (ii) double peaked, but wide, distributions of q/ appear to be independent of L, and (iii) xi_L/L rises with L at constant T, but extrapolations to 1/L -> 0 give finite values. All of this is consistent with quasi-long-range order in the SG phase.Comment: 15 LaTeX pages, 15 figures, 3 tables. (typos fixed in Appendix A