Identification of a response amplitude operator for ships

At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations

Identification of a Response Amplitude Operator for Ships

At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations

A comparison of tube model predictions of the linear viscoelastic behavior of symmetric star polymer melts

We present a modified version of the time-marching algorithm (TMA) [van Ruymbeke et al., 2005, 2010] for predicting the linear viscoelasticity of monodisperse symmetric star polymer melts. Several new elements were added to the original TMA model. In particular, the remaining fraction of the initial tube segments is considered as a function of time, while taking into account the past relaxation history of each molecular segment. We validate the TMA model and, for the first time, compare it with the so-called BoB model [Das et al., 2006]. The predictions obtained with the two models are compared to a large set of experimental data, which cover a broad range of arm molecular weights (from 1.5 to 55 entanglements per arm) of different chemistries (polystyrene, polybutadiene, and polyisoprene). We indicate the significant differences between the two approaches, which mainly affect the choice of material parameters of the models. We then point out a systematic deviation of the TMA model in accurately predicting the intermediate regime of relatively short star chains, while the BoB model fails in correctly describing the plateau modulus of these short chains. From our point of view, both disparities have the same origin and, in the case of the TMA, can be solved by removing the high-frequency mode contribution to the contour length fluctuation of the primitive path. An excellent agreement between data and theory is then obtained for all molecular weights of the arms, which indicates the capability of the TMA to provide a quantitative prediction of the rheology of monodisperse star-shaped polymers. A very good agreement is also obtained with the BoB model, despite the expected discrepancy observed with short star chains. This proves the fact that current tube-based models are successful in quantitative predictions of linear rheology of monodisperse star-shaped polymers

Dynamic Dilution Effect in Binary Blends of Linear Polymers with Well-Separated Molecular Weights

We investigate and model the viscoelastic properties of binary blends composed of linear chains. These systems are indeed very suitable to test the validity and the limit of the constraint release (CR) process and dynamic tube dilution and to determine the value of the dynamic dilution exponent α. We first focus on binary blends containing barely entangled short chains. In such a case, we show that the tension re-equilibration process previously observed [van Ruymbeke Macromolecules 2012, 45, 2085] can be correctly described as a CR-activated contour length fluctuation (CLF) process, which takes place along the fully dilated tube and is governed by the intrinsic Rouse time of a long–long entanglement segment. In addition, reptation is considered to take place along the fully dilated tube. We also show that this CR-activated CLF process speeds up the relaxation of the long chains, which naturally leads to an effective dilution exponent α equal to 4/3, despite the fact that the modeling is based on α = 1. This result is in agreement with the experimental data. Then, we analyze the rheological behavior of binary blends containing entangled short chains. In such a case, we show that the CR-activated CLF also takes place, but with a delay time being necessary for the long chain to explore the dilated tube. This approach is tested for several binary blends, showing an improved quality of the predictions compared to previous tube modeling on the same blends. Indeed, by considering the chain motions on two different length scales, a larger fraction of the long chains relax at intermediate frequencies (through the tension re-equilibration) before their reptation, leading to an effective dilution exponent larger than 1 as determined from the low-frequency plateau modulus

Comparative analysis of different tube models for linear rheology of monodisperse linear entangled polymers

\u3cp\u3eThe aim of the present paper is to analyse the differences between tube-based models which are widely used for predicting the linear viscoelasticity of monodisperse linear polymers, in comparison to a large set of experimental data. The following models are examined: Milner-McLeish, Likhtman-McLeish, the Hierarchical model proposed by the group of Larson, the BoB model of Das and Read, and the TMA model proposed by the group of van Ruymbeke. This comparison allows us to highlight and discuss important questions related to the relaxation of entangled polymers, such as the importance of the contour-length fluctuations (CLF) process and how it affects the reptation mechanism, or the contribution of the constraint release (CR) process on the motion of the chains. In particular, it allows us to point out important approximations, inherent in some models, which result in an overestimation of the effect of CLF on the reptation time. On the contrary, by validating the TMA model against experimental data, we show that this effect is underestimated in TMA. Therefore, in order to obtain accurate predictions, a novel modification to the TMA model is proposed. Our current work is a continuation of earlier research (Shchetnikava et al., 2014), where a similar analysis is performed on well-defined star polymers.\u3c/p\u3

Identification of a response amplitude operator for ships Citation for published version (APA): Identification of a Response Amplitude Operator for Ships

Abstract At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations