Agus Yodi Gunawan
Industrial & Financial Mathematics Research Group, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia

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Approximate Solutions of Linearized Delay Differential Equations Arising from a Microbial Fermentation Process Using the Matrix Lambert Function Gunawan, Agus Yodi; Kasbawati, Kasbawati; Sidarto, Kuntjoro Adji
Journal of Mathematical and Fundamental Sciences Vol 48, No 1 (2016)
Publisher : ITB Journal Publisher, LPPM ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (285.348 KB) | DOI: 10.5614/j.math.fund.sci.2016.48.1.3

Abstract

In this paper we present approximate solutions of linearized delay differential equations using the matrix Lambert function. The equations arise from a microbial fermentation process in a metabolic system. The delay term appears due to the existence of a rate-limiting step in the fermentation pathway. We find that approximate solutions can be written as a linear combination of the Lambert function solutions in all branches. Simulations are presented for three cases of the ratio of the rate of glucose supply to the maximum reaction rate of the enzyme that experienced delay. The simulations are worked out by taking the principal branch of the matrix Lambert function as the most dominant mode. Our present numerical results show that the zeroth mode approach is quite reliable compared to the results given by classical numerical simulations using the Runge-Kutta method.
UPDATING RESERVOIR MODELS USING ENSEMBLE KALMAN FILTER Darwis, Sutawanir; GUNAWAN, AGUS YODI; WAHYUNINGSIH, SRI; SUNUSI, NURTITI; MUTAQIN, ACENG KOMARUDIN; FITRIYATI, NINA
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 10, No 1 (2010)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v10i1.1007

Abstract

The Ensemble Kalman Filter (EnKF) has gain popularity as a methodology for real time updates ofreservoir models. A sample of models is updated whenever observation data available. Successfulapplication of EnKF to estimate reservoir properties has been reported. A flow modeling is missing inthis research area. This paper presents the applicability of EnKF in flow modeling for three cases:infinite reservoir, bounded reservoir and one dimensional composite reservoir. The solution of flowequation was derived and used as a modeling component of state space modeling of Kalman filterupdating formula. This three reservoir models shows that the EnKF methodology can be used forupdating the reservoir models.
THE EFFECTS OF SURFACTANT ON THE EVOLUTION OF A THIN FILM UNDER A MOVING LIQUID DROP Yulianti, Kartika; Gunawan, Agus Yodi; Soewono, Edy
Indonesian Journal of Science and Technology Vol 5, No 1 (2020): IJOST: VOLUME 5, ISSUE 1, 2020
Publisher : Universitas Pendidikan Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17509/ijost.v5i1.23100

Abstract

The effect of surfactant on the thickness of a thin film bounded by a solid surface and a moving liquid drop was investigated. We proposed a model so that parameters from the liquid drop can be stated in a parameter that acts as normal pressure to the thin film. Using the lubrication approximation, the model was reduced to a set of nonlinear partial differential equations in terms of the film thickness and surfactant concentration. Since we were interested in the role of the surfactant in lifting up the drop, we assumed that the density of the drop is higher than the density of the thin film. Numerically, the results show that the presence of the surfactant tends to delay the decrease of the film thickness insignificantly. However, when the surfactant was added into the system, it tends to significantly increase the film thickness for a certain range value of the normal pressure.