On string vibrations influenced by a smooth obstacle at one of the endpoints

In this paper, the vibrations of a string are considered. At one end of the string, a smooth obstacle is placed and the other end of the string is attached to a fixed point. The contact between the string and the obstacle varies in time, and leads to a linear, moving boundary value problem for the string vibrations. By applying a boundary...

On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact...

On the multiple time-scales perturbation method for differential-delay equations

In this paper, we present a new approach on how the multiple time-scales perturbation method can be applied to differential-delay equations such that approximations of the solutions can be obtained which are accurate on long time-scales. It will be shown how approximations can be constructed which branch off from solutions of differential...

Multi-time scale energy management framework for smart PV systems mixing fast and slow dynamics

We propose a multi-time scale energy management framework for a smart photovoltaic (PV) system that can calculate optimized schedules for battery operation, power purchases, and appliance usage. A smart PV system is a local energy community that includes several buildings and households equipped with PV panels and batteries. However, due to...

Hierarchical model predictive control for energy management of power-to-X systems

This paper presents the application of Hierarchical Model Predictive Control (HMPC) as an energy management framework for a multi-timescale mixed-energy system, i.e., Power-to-X (PtX). The goal of the energy managing controller is to minimize an economic objective by determining the energy flows within the system. HMPC enables a long-term...

Long-term effects of dam operations for water supply to irrigation on downstream river reaches. The case of the Ribb River, Ethiopia

This work investigates the applicability of an analytical method for quick assessments of the long-term morphological effects of different dam operations on downstream river reaches with the idea to apply the method in feasibility studies to identify the least morphologic-impacting operation scenario. The Ribb River (Ethiopia) is used as a...

Epidemic mitigation via awareness propagation in communication networks: The role of time scales

The participation of individuals in multi-layer networks allows for feedback between network layers, opening new possibilities to mitigate epidemic spreading. For instance, the spread of a biological disease such as Ebola in a physical contact network may trigger the propagation of the information related to this disease in a communication...

Multi-scale modelling of bioreactor–separator system for wastewater treatment with two-dimensional activated sludge floc dynamics

A simple “first generation” multi-scale computational model of the formation of activated sludge flocs at micro-scale and reactor performance at macro-scale is proposed. The model couples mass balances for substrates and biomass at reactor scale with an individual-based approach for the floc morphology, shape and micro-colony development. Among...

Quantifying nearshore morphological recovery time scales using argus video imaging: Palm Beach, Sydney and Duck, North Carolina

Time scales of post-storm nearshore morphological recovery and physical processes governing these time scales are poorly understood at present. The ability to predict nearshore morphological recovery time scales based on pre-, during- or post-resetting storm conditions is an essential requirement for building and validating scale aggregated...

On the scaling and unsteadiness of shock induced separation

Shock wave boundary layer interactions (SWBLI) are a common phenomenon in transonic and supersonic flows. The presence of shock waves, induced by specific geometrical configurations, causes a rapid increase of the pressure, which can lead to flow separation. Examples of such interactions are found in amongst others rocket engine nozzles and on...

Adaptive image interrogation for PIV: Application to compressible flows and interfaces

As an experimental tool, Particle Image Velocimetry has quickly superseded traditional point-wise measurements. The inherent image processing has become standardized though the performances are strongly dependent on user experience. Moreover, the arduously selected image interrogation parameters are applied uniformly throughout the image...

A mathematical analysis of a belt system with a low and time-varying velocity

In this thesis a mathematical analysis has been given for model which describes the transversal vibrations of belt systems. The belt speed is assumed to be time-varying and to be small compared to the wave speed. Not only linear string-like or beam-like models but also nonlinear models have been studied. In all cases initial-boundary value...