Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

A simple approach to the supernova progenitor–explosion connection

We present a new approach to understand the landscape of supernova explosion energies, ejected nickel masses, and neutron star birth masses. In contrast to other recent parametric approaches, our model predicts the properties of neutrino-driven explosions based on the pre-collapse stellar structure without the need for hydrodynamic simulations. The model is based on physically motivated scaling laws and simple differential equations describing the shock propagation, the contraction of the neutron star, the neutrino emission, the heating conditions, and the explosion energetics. Using model parameters compatible with multi-D simulations and a fine grid of thousands of supernova progenitors, we obtain a variegated landscape of neutron star and black hole formation similar to other parametrized approaches and find good agreement with semi-empirical measures for the ‘explodability’ of massive stars. Our predicted explosion properties largely conform to observed correlations between the nickel mass and explosion energy. Accounting for the coexistence of outflows and downflows during the explosion phase, we naturally obtain a positive correlation between explosion energy and ejecta mass. These correlations are relatively robust against parameter variations, but our results suggest that there is considerable leeway in parametric models to widen or narrow the mass ranges for black hole and neutron star formation and to scale explosion energies up or down. Our model is currently limited to an all-or-nothing treatment of fallback and there remain some minor discrepancies between model predictions and observational constraints.

Identification of Microturbine Model for Long-term Dynamic Analysis of Distribution Networks

As one of the most successfully commercialized distributed energy resources, the long-term effects of microturbines (MTs) on the distribution network has not been fully investigated due to the complex thermo-fluid-mechanical energy conversion processes. This is further complicated by the fact that the parameter and internal data of MTs are not always available to the electric utility, due to different ownerships and confidentiality concerns. To address this issue, a general modeling approach for MTs is proposed in this paper, which allows for the long-term simulation of the distribution network with multiple MTs. First, the feasibility of deriving a simplified MT model for long-term dynamic analysis of the distribution network is discussed, based on the physical understanding of dynamic processes that occurred within MTs. Then a three-stage identification method is developed in order to obtain a piecewise MT model and predict electro-mechanical system behaviors with saturation. Next, assisted with the electric power flow calculation tool, a fast simulation methodology is proposed to evaluate the long-term impact of multiple MTs on the distribution network. Finally, the model is verified by using Capstone C30 microturbine experiments, and further applied to the dynamic simulation of a modified IEEE 37-node test feeder with promising results.