Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton׳s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton׳s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving

In the production process of polyethylene terephthalate (PET) bottles, the initial temperature of preforms plays a central role on the final thickness, intensity and other structural properties of the bottles. Also, the difference between inside and outside temperature profiles could make a significant impact on the final product quality. The preforms are preheated by infrared heating oven system which is often an open loop system and relies heavily on trial and error approach to adjust the lamp power settings. In this paper, a radial basis function (RBF) neural network model, optimized by a two-stage selection (TSS) algorithm combined with partial swarm optimization (PSO), is developed to model the nonlinear relations between the lamp power settings and the output temperature profile of PET bottles. Then an improved PSO method for lamp setting adjustment using the above model is presented. Simulation results based on experimental data confirm the effectiveness of the modelling and optimization method.

Tailoring the nonlinear frequency coupling between odd harmonics for the optimisation of charged particle dynamics in capacitively coupled oxygen plasmas

The influence of nonlinear frequency coupling in an oxygen plasma excited by two odd harmonics at moderate pressure is investigated using a numerical model. Through variations in the voltage ratio and phase shift between the frequency components changes in ionization dynamics and sheath voltages are demonstrated. Furthermore, a regime in which the voltage drop across the plasma sheath is minimised is identified. This regime provides a significantly higher ion flux than a single frequency discharge driven by the lower of the two frequencies alone. These operating parameters have potential to be exploited for plasma processes requiring low ion bombardment energies but high ion fluxes. 

Nonlinear hydrodynamic Langmuir waves in fully degenerate relativistic plasma

The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p<inf>F</inf>/(m c) (where p<inf>F</inf> is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Optimal day-ahead scheduling of integrated urban energy systems

An optimal day-ahead scheduling method (ODSM) for the integrated urban energy system (IUES) is introduced, which considers the reconfigurable capability of an electric distribution network. The hourly topology of a distribution network, a natural gas network, the energy centers including the combined heat and power (CHP) units, different energy conversion devices and demand responsive loads (DRLs), are optimized to minimize the day-ahead operation cost of the IUES. The hourly reconfigurable capability of the electric distribution network utilizing remotely controlled switches (RCSs) is explored and discussed. The operational constraints from the unbalanced three-phase electric distribution network, the natural gas network, and the energy centers are considered. The interactions between the electric distribution network and the natural gas network take place through conversion of energy among different energy vectors in the energy centers. An energy conversion analysis model for the energy center was developed based on the energy hub model. A hybrid optimization method based on genetic algorithm (GA) and a nonlinear interior point method (IPM) is utilized to solve the ODSM model. Numerical studies demonstrate that the proposed ODSM is able to provide the IUES with an effective and economical day-ahead scheduling scheme and reduce the operational cost of the IUES.

Steps towards fully nonlinear simulations of arrays of OWSC

Abandonment of farming systems on upland areas in southwest Britain during the Late Bronze Age – some 3000 years ago – is widely considered a ‘classic’ demonstration of the impact of deteriorating climate on the vulnerability of populations in such marginal environments. Here we test the hypothesis that climate change drove the abandonment of upland areas by developing new chronologies for human activity on upland areas during the Bronze Age across southwest Britain (Dartmoor, Exmoor and Bodmin Moor). We find Bronze Age activity in these areas spanned 3900–2950 calendar years ago with abandonment by 2900 calendar years ago. Holocene Irish bog and lake oak tree populations provide evidence of major shifts in hydroclimate across western Britain and Ireland, coincident with ice rafted debris layers recognized in North Atlantic marine sediments, indicating significant changes in the latitude and intensity of zonal atmospheric circulation across the region. We observe abandonment of upland areas in southwest Britain coinciding with a sustained period of extreme wet conditions that commenced 3100 calendar years ago. Our results are consistent with the view that climate change increased the vulnerability of these early farming communities and led to a less intensive use of such marginal environments across Britain.