Joakim Munkhammar

On the dust abundance gradients in late-type galaxies – I. Effects of destruction and growth of dust in the interstellar medium

We present basic theoretical constraints on the effects of destruction by supernovae (SNe) and growth of dust grains in the interstellar medium (ISM) on the radial distribution of dust in late-type galaxies. The radial gradient of the dust-to-metals ratio is shown to be essentially flat (zero) if interstellar dust is not destroyed by SN shock waves and all dust is produced in stars. If there is net dust destruction by SN shock waves, the dust-to-metals gradient is flatter than or equal to the metallicity gradient (assuming the gradients have the same sign). Similarly, if there is net dust growth in the ISM, then the dust-to-metals gradient is steeper than or equal to the metallicity gradient. The latter result implies that if dust gradients are steeper than metallicity gradients, that is, the dust-to-metals gradients are not flat, then it is unlikely dust destruction by SN shock waves is an efficient process, while dust growth must be a significant mechanism for dust production. Moreover, we conclude that dust-to-metals gradients can be used as a diagnostic for interstellar dust growth in galaxy discs, where a negative slope indicates dust growth.

Chaos in a fractional order logistic map

In this paper we investigate a fractional order logistic map and its discrete time dynamics. After a brief introduction to the discrete-time dynamical systems and fractional dynamics we show some basic properties of the fractional logistic map. We then move on to prove that the special case α = 1/2 exhibits a period doubling route to chaos. A bifurcation diagram for the special case of α = 1/2 is also included. Finally a discussion concerning the results and open problems is given.

A Bernoulli distribution model for plug-in electric vehicle charging based on time-use data for driving patterns

This paper presents a Bernoulli distribution model for plug-in electric vehicle (PEV) charging based on high resolution activity data for Swedish driving patterns. Based on the activity “driving vehicle” from a time diary study a Monte Carlo simulation is made of PEV state of charge which is then condensed down to Bernoulli distributions representing charging for each hour during weekday and weekend day. These distributions are then used as a basis for simulations of PEV charging patterns. Results regarding charging patterns for a number of different PEV parameters are shown along with a comparison with results from a different stochastic model for PEV charging. A convergence test for Monte Carlo simulations of the distributions is also provided. In addition to this we show that multiple PEV charging patterns are represented by Binomial distributions via convolution of Bernoulli distributions. Also the distribution for aggregate charging of many PEVs is shown to be normally distributed. Finally a few remarks regarding the applicability of the model are given along with a discussion on potential extensions.

Polynomial probability distribution estimation using the method of moments

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Autonomous electric vehicle fleet charging in cities: Optimal utility estimates and Monte Carlo simulations

This paper investigates the electricity use of completely autonomous electric vehicle (AEV) fleets in cities. A set of principles for autonomous vehicle fleets in cities is defined, mathematical relations for optimal utility conditions are derived and a Monte Carlo simulation model is developed based on the assumption of central charging. Results show, for example, that accommodation fraction, passenger travel fraction, effective electric fuel economy and mean charging power are essentially independent of battery capacity, given that the initial battery capacity is sufficient for one pickup, delivery and return for charging round trip.

Probabilistic Load Flow for Power Grids With High PV Penetrations Using Copula-Based Modeling of Spatially Correlated Solar Irradiance

This paper presents and applies an improved model for the instantaneous power generation from distributed photovoltaic (PV) systems intended for probabilistic load flow (PLF) simulations. The model combines a probability distribution model for the instantaneous solar irradiance at individual sites with an improved spatial correlation model and uses a Gaussian copula to allow correlated sampling from the distributions for an arbitrary set of distributed PV systems. We show that the model realistically reproduces the spatially distributed clear-sky index over a set of sites, based on comparisons with irradiance sensor network data. We also demonstrate that the probability distributions for system parameters such as customer voltage, substation loading, and power losses, obtained from PLF simulations with the model, differ substantially from those of a nonspatial approach. The results show that spatial irradiance modeling needs to be incorporated in PLF simulations in order not to overestimate the grid impacts of PV systems.