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ON THE BREAKING OF GENERATED WAVES RUNNING IN STILL WATER Kusumawinahyu, W.M. Kusumawinahyu
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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This research is motivated by the requirement of hydrodynamics laboratories to generate extreme waves for testing ships in steep, large amplitude wave fields. For this purpose, finding criteria that determine if wave breaking will occur is important. Different from initial value problems, in this contribution we will consider the signaling problem: a time signal is prescribed to a wave maker in a wave tank that produces propagating waves running in initially still water. The aim is to observe the resulting nonlinear effects on the waves and to study in which cases the waves will or will not break. This also leads to a threshold value for generated waves, and, moreover, to the location in the tank where wave breaking may occur. To study this, we consider Bichromatic waves and Benjamin Feir-waves, and investigate the evolution by using a numerical simulation code HUBRIS developed by Westhuis; the validity of this code has been tested against laboratory experiments. The result of our investigations is that for both classes the parameters of wave breaking are more extreme in the signaling case than in the case of initial value problem.

ANALISIS DINAMIK MODEL RANTAI MAKANAN LIMA UNSUR EKOSISTEM LAUT Hidayatulloh, Muhammad Rifâ€™an; Kusumawinahyu, Wuryasari Muharini
Jurnal Mahasiswa Matematika Vol 1, No 5 (2013)
Publisher : Jurnal Mahasiswa Matematika

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A Dynamical Analysis on a Tumour Virotherapy Model with Standard Incident Rate Ikawati, Deasy Sandhya Elya; Kusumawinahyu, Wuryansari Muharini; Trisilowati, Trisilowati
Journal of Tropical Life Science Vol 7, No 1 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.01.03

This paper discusses a dynamical analysis on a model that governs the growth of tumour cell under a therapy by using oncolytic viruses, on the standard incident rate. The model is a modification of the similar one by replacing the bilinear incident rate with the standard one. The conducted dynamical analysis consists of the determination of equilibrium points and their existence conditions, followed by local as well as global stability analysis of the equilibrium points. The analytical result shows that there are two equilibrium points, namely uninfected and the endemic point, which needs a condition to exist. Stability analysis shows that there is a dimensionless basic reproduction number that marks the existence as well as the stability of equilibrium points. When basic reproduction number is less than one, there is only the uninfected equilibrium, which is global asymptotically stable. On the other hands, both of equilibrium points exist when the basic reproduction number is more than one, but the uninfected point is not stable anymore, while the endemic one is local asymptotically stable under a condition. Some numerical simulations are performed to illustrate the analytical result. Numerically, it can also be demonstrated that there is a set of parameters which indicates that tumour can be fully removed. Â

The Effect of Smoking Behavior in the Human Population Growth of Lung Cancer Patients Lu’luul Wardah; Trisilowati Trisilowati; Wuryansari Muharini Kusumawinahyu
Natural B, Journal of Health and Environmental Sciences Vol 4, No 2 (2017)
Publisher : Natural B, Journal of Health and Environmental Sciences

This article discusses a model of lung cancer as the effect of smoking behavior on both active and passive smoker. There are four subpopulations in this model, namely susceptible subpopulation, active smoker subpopulation, passive smoker subpopulation, and subpopulation of lung cancer. Dynamical analysis is conducted to determine the equilibrium point, existence condition for equilibrium point, and analyze their stability. Based on analysis result, there are three equilibrium points. First equilibrium point shows that all subpopulations extinct. Second equilibrium point shows that only susceptible subpopulation can survive, and the last equilibrium point shows that all subpopulations can survive. First equilibrium point always exists while the others exist under certain condition. The stability of first equilibrium point can be reached when the intrinsic growth rate is less than the death rate. Whereas, the others equilibrium points will be stable under certain condition. Numerical simulation is performed to illustrate the analysis result. It is shown that numerical results are in accordance with analysis result. These numerical simulations also indicate that the rate of passive smoker plays important role in the growth rate of lung cancer.

TRAINING OF MICROSOFT MATHEMATICS TO IMPROVE THE QUALITY OF LEARNING METHODS FOR TEACHERS IN JUNIOR SECONDARY SCHOOLS (SMP AND MTs) AT PONOROGO EAST JAVA INDONESIA Kwardiniya Andawaningtyas; Wuryansari Muharini Kusumawinahyu; Ani Budi Astuti
Journal of Innovation and Applied Technology Vol 3, No 1 (2017)
Publisher : Lembaga Penelitian dan Pengabdian Kepada Masyarakat Universitas Brawijaya

All this time, mathematics has become the scourge for elementary and junior high school students, so that students are not well motivated to learn the material of Mathematics. Along with the development of computer technology, it can be used as one tool that can help the learning process. Mathematics software can be used to explain the difficult concepts in mathematics becomes easily, clearer, more interesting and fun. In Ponorogo, mathematics teachers have a meeting forum called the Subject Teacher Council (MGMP) of Mathematics. The general problems of the council is the less equality in opportunities of MGMP Mathematics teachers in Junior Secondary Schools (SMP and MTs) at Ponorogo to attain trainings for improving students skills in understanding the material of Mathematics and the limited insight of mathematics teachers about mathematics software that can be used as an instructional media of mathematics material. Therefore, the activity of microsoft mathematics training for mathematics teachers in Junior Secondary Schools at Ponorogo has been necessarily and urgently needed to improve the quality of learning methods. These software is open source software with less space requirement in the computer and easy installation.

Tinggi Maksimum Selubung Paket Gelombang Bikromatik Wuryansari Muharini Kusumawinahyu; Andonowati Andonowati
Journal of Mathematical and Fundamental Sciences Vol. 35 No. 1 (2003)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.sci.2003.35.1.4

Previous numerical and experimental investigations found that some envelopes of bichromatics surface water waves show deformation during their propagation along the wave tank in Hydrodinamic Laboratory. In this paper we present investigation on the maximum amplitudes of bichromatics envelopes at every position along the tank, to observe the amplification factor of a signal deformation . As we consider a signaling problem, a spatial Nonlinear Schrodinger (sp-NLS) model is used here. The profiles of waves envelope as a function of time and space are computed numerically from this model. Investigations are done for some different amplitudes and frequencies of bichromatics envelopes at wave generator to show that these two parameters affect the amplification factor and the periode of maximum amplitudes of envelopes.

Pengaruh Amplitudo dan Frekuensi terhadap Fenomena Pemuncakan Wuryansari Muharini Kusumawinahyu
Limits: Journal of Mathematics and Its Applications Vol 3, No 2 (2006)
Publisher : Institut Teknologi Sepuluh Nopember

Telah diketahui bahwa suatu signal bikromatik yang diberikan sebagai masukan di pembangkit gelombang di laboratorium hidrodinamika mengalami fenomena pemuncakan ketika ia merambat di sepanjang kolam pengujian. Dengan memanfaatkan besaran yang disebut Maximal Temporal Amplitude (MTA), dikaji pengaruh amplitudo dan frekuensi selubung signal gugus gelombang di pembangkit gelombang terhadap faktor ampli kasi dan posisi terjadinya elevasi maksimum. Data untuk penyelidikan ini dibangkitkan dengan menggunakan suatu simulasi numerik pembangkitan dan perambatan gelombang di sepanjang kolam pengujian dua dimensi. Hasil yang diperoleh dibandingkan dengan hasil yang diperoleh secara analitik menggunakan aproksimasi orde ke tiga persamaan KdV.

Analisis Dinamik Model Hepatitis B dengan Sirosis Hati Muna Afdi Muniroh; Trisilowati Trisilowati; Wuryansari Muharini Kusumawinahyu
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v19i1.11060

Hepatitis B adalah suatu penyakit peradangan pada organ hati yang memiliki dua fase infeksi yaitu akut dan kronis. Sirosis hati terjadi akibat terbentuknya jaringan parut pada individu hepatitis B berkepanjangan (kronis). Oleh karena itu, pada penelitian ini dibentuk model penyebaran penyakit hepatitis B dengan sirosis hati. Selain itu, pada model diasumsikan virus hepatitis B (HBV) dapat ditularkan baik secara vertikal maupun horizontal. Analisis dinamik dilakukan untuk menentukan eksistensi dan kestabilan titik kesetimbangan. Berdasarkan hasil analisis dinamik, diperoleh dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Angka reproduksi dasar (R0) didapatkan dengan menggunakan matriks generasi selanjutnya. Titik kesetimbangan bebas penyakit eksis tanpa syarat, sedangkan titik kesetimbangan endemik eksis ketika R0>1. Hasil analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit dan endemik bersifat stabil asimtotik lokal jika kriteria Routh-Hurwitz terpenuhi. Selain itu, titik kesetimbangan bebas penyakit bersifat stabil asimtotik global jika R0<1 dan titik kesetimbangan endemik bersifat stabil asimtotik global jika memenuhi kondisi tertentu. Simulasi numerik mendukung hasil analisis yang telah diperoleh.

A Dynamical Analysis on a Tumour Virotherapy Model with Standard Incident Rate Deasy Sandhya Elya Ikawati; Wuryansari Muharini Kusumawinahyu; Trisilowati Trisilowati
Journal of Tropical Life Science Vol. 7 No. 1 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.01.03

This paper discusses a dynamical analysis on a model that governs the growth of tumour cell under a therapy by using oncolytic viruses, on the standard incident rate. The model is a modification of the similar one by replacing the bilinear incident rate with the standard one. The conducted dynamical analysis consists of the determination of equilibrium points and their existence conditions, followed by local as well as global stability analysis of the equilibrium points. The analytical result shows that there are two equilibrium points, namely uninfected and the endemic point, which needs a condition to exist. Stability analysis shows that there is a dimensionless basic reproduction number that marks the existence as well as the stability of equilibrium points. When basic reproduction number is less than one, there is only the uninfected equilibrium, which is global asymptotically stable. On the other hands, both of equilibrium points exist when the basic reproduction number is more than one, but the uninfected point is not stable anymore, while the endemic one is local asymptotically stable under a condition. Some numerical simulations are performed to illustrate the analytical result. Numerically, it can also be demonstrated that there is a set of parameters which indicates that tumour can be fully removed. Â

Dynamical Analysis and Parameter Estimation of Hepatitis B Disease Model in Malang Fitroh Aulani; Wuryansari Muharini Kusumawinahyu; Isnani Darti
The Journal of Experimental Life Science Vol. 11 No. 3 (2021)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2021.011.03.03

In this article, a model representing the spread of Hepatitis B disease is constructed as a nonlinear autonomous system. The model divides the considered human population into three classes, namely susceptible, infected, and recovered class. The dynamical analysis shows that there are two equilibrium points in the model, namely a disease-free equilibrium point and an endemic equilibrium point. The existence and stability of the equilibrium points depend on the basic reproduction number (R_0). The disease-free equilibrium point is local asymptotically stable when R_0<1 while the endemic equilibrium point exists and is local asymptotically stable if R_0>1. The five parameters of the model are estimated by applying Downhill Simplex (Nelder-Mead) Algorithm and by using the infected data cases taken from such a hospital in Malang. The estimated parameters are the transmission of infection rate, the saturation rate, the vaccination rate, the recovery rate, and the immunity loss rate. The resulting parameter estimation supports the analytical result and is used to illustrate the analytical results numerically. Based on the considered model and the result of the parameters estimation, it can be concluded that the Hepatitis B spread in Malang is controllable. Keywords: downhill simplex (Nelder-mead) algorithm, dynamical analysis, hepatitis B model, parameter estimation.

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