TY - JOUR

T1 - An optimal scaling to computationally tractable dimensionless models

T2 - Study of latex particles morphology formation

AU - Rusconi, Simone

AU - Dutykh, Denys

AU - Zarnescu, Arghir

AU - Sokolovski, Dmitri

AU - Akhmatskaya, Elena

N1 - Funding Information:
This research is supported by the Spanish Ministry of Science , Innovation and Universities: MTM2016-76329-R (AEI/FEDER, EU), MTM2017-82184-R (DESFLU) and BCAM Severo Ochoa accreditation, Spain SEV-2017-0718 . The Basque Government is acknowledged for support through ELKARTEK Programme, Spain (grants KK-2018/00054 and KK-2019/00068 ) and BERC 2018–2021 program, Spain . The authors thank J.M. Asua and S. Hamzehlou (POLYMAT, Spain) for valuable discussions.
Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2020/2

Y1 - 2020/2

N2 - In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance, the case of the Population Balance Equations (PBE) proposed to model the Latex Particles Morphology formation. The obvious way out of this difficulty is the use of dimensionless scaled quantities, although often the scaling procedure is not unique. In this paper, we introduce a conceptually new general approach, called Optimal Scaling (OS). The method is tested on the known examples from classical and quantum mechanics, and applied to the Latex Particles Morphology model, where it allows us to reduce the variation of the relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then solved by a novel Generalised Method Of Characteristics, and the OS is shown to help reduce numerical error, and avoid unphysical behaviour of the solution. Although inspired by a particular application, the proposed scaling algorithm is expected find application in a wide range of chemical, physical and biological problems.

AB - In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance, the case of the Population Balance Equations (PBE) proposed to model the Latex Particles Morphology formation. The obvious way out of this difficulty is the use of dimensionless scaled quantities, although often the scaling procedure is not unique. In this paper, we introduce a conceptually new general approach, called Optimal Scaling (OS). The method is tested on the known examples from classical and quantum mechanics, and applied to the Latex Particles Morphology model, where it allows us to reduce the variation of the relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then solved by a novel Generalised Method Of Characteristics, and the OS is shown to help reduce numerical error, and avoid unphysical behaviour of the solution. Although inspired by a particular application, the proposed scaling algorithm is expected find application in a wide range of chemical, physical and biological problems.

KW - Dimensionless models

KW - Generalised Method Of Characteristics

KW - Multi-phase polymers

KW - Nondimensionalization

KW - Population Balance Equations

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85073002954&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2019.106944

DO - 10.1016/j.cpc.2019.106944

M3 - Article

AN - SCOPUS:85073002954

SN - 0010-4655

VL - 247

JO - Computer Physics Communications

JF - Computer Physics Communications

M1 - 106944

ER -