34 research outputs found
The existence and stability of solitons in discrete nonlinear Schrödinger equations
No full textIn this thesis, we investigate analytically and numerically the existence and stability of discrete solitons governed by discrete nonlinear Schrödinger (DNLS) equations with two types of nonlinearity, i.e., cubic and saturable nonlinearities. In the cubic-type model we consider stationary discrete solitons under the effect of parametric driving and combined parametric driving and damping, while in the saturable-type model we examine travelling lattice solitons.
First, we study fundamental bright and dark discrete solitons in the driven cubic DNLS equation. Analytical calculations of the solitons and their stability are carried out for small coupling constant through a perturbation expansion. We observe that the driving can not only destabilise onsite bright and dark solitons, but also stabilise intersite bright and dark solitons. In addition, we also discuss a particular application of our DNLS model in describing microdevices and nanodevices with integrated electrical and mechanical functionality.
By following the idea of the work above, we then consider the cubic DNLS equation with the inclusion of parametric driving and damping. We show that this model admits a number of types of onsite and intersite bright discrete solitons of which some experience saddle-node and pitchfork bifurcations. Most interestingly, we also observe that some solutions undergo Hopf bifurcations from which periodic solitons (limit cycles) emerge. By using the numerical continuation software Matcont, we perform the continuation of the limit cycles and determine the stability of the periodic solitons.
Finally, we investigate travelling discrete solitons in the saturable DNLS equation. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton-Raphson method to find traveling solitons with non-oscillatory tails, i.e., embedded solitons. A variational approximation (VA) is also applied to examine analytically the travelling solitons and their stability, as well as to predict the location of the embedded solitons
The existence and stability of solitons in discrete nonlinear Schrödinger equations
No full textIn this thesis, we investigate analytically and numerically the existence and stability of discrete solitons governed by discrete nonlinear Schrödinger (DNLS) equations with two types of nonlinearity, i.e., cubic and saturable nonlinearities. In the cubic-type model we consider stationary discrete solitons under the effect of parametric driving and combined parametric driving and damping, while in the saturable-type model we examine travelling lattice solitons.
First, we study fundamental bright and dark discrete solitons in the driven cubic DNLS equation. Analytical calculations of the solitons and their stability are carried out for small coupling constant through a perturbation expansion. We observe that the driving can not only destabilise onsite bright and dark solitons, but also stabilise intersite bright and dark solitons. In addition, we also discuss a particular application of our DNLS model in describing microdevices and nanodevices with integrated electrical and mechanical functionality.
By following the idea of the work above, we then consider the cubic DNLS equation with the inclusion of parametric driving and damping. We show that this model admits a number of types of onsite and intersite bright discrete solitons of which some experience saddle-node and pitchfork bifurcations. Most interestingly, we also observe that some solutions undergo Hopf bifurcations from which periodic solitons (limit cycles) emerge. By using the numerical continuation software Matcont, we perform the continuation of the limit cycles and determine the stability of the periodic solitons.
Finally, we investigate travelling discrete solitons in the saturable DNLS equation. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton-Raphson method to find traveling solitons with non-oscillatory tails, i.e., embedded solitons. A variational approximation (VA) is also applied to examine analytically the travelling solitons and their stability, as well as to predict the location of the embedded solitons
Pengembangan Metode Interpolasi Splin Kubik Terapit dan Aplikasinya pada Masalah Pelacakan Trajektori Objek
No full textInterpolasi splin kubik merupakan sebuah metode pencocokan kurva yang sangat populer karena mudah diterapkan dan menghasilkan kurva yang mulus. Pada artikel ini dibahas pengembangan metode interpolasi splin kubik untuk syarat batas terapit yang diambil dari rumus eksplisit beda hingga dengan ketelitian orde lebih tinggi. Pengembangan metode ini diterapkan pada masalah pelacakan trajektori objek (object tracking). Secara khusus, masalah ini diujikan untuk splin kubik terapit orde dua, dan hasil interpolasinya dibandingkan dengan hasil pada splin kubik alami dan splin kubik terapit orde satu. Dari simulasi data trajektori yang dibangkitkan dari kurva spiral Archimedean, diperoleh nilai galat total untuk splin kubik alami, terapit orde satu dan terapit orde dua masing-masing sebagai berikut: , dan . Berdasarkan hasil tersebut, disimpulkan bahwa interpolasi splin kubik terapit orde dua yang dikembangkan pada artikel ini dapat menghasilkan trajektori objek yang lebih akurat dibandingkan splin kubik alami dan splin kubik terapit orde satu. AbstrractCubic spline interpolation is a very popular curve fitting method since it is easy to implement and produces a smooth curve. This article discusses the development of the cubic spline interpolation method for a clamped boundary condition taken from finite-difference explicit formulas with higher-order accuracy. The development of this method is applied to an object tracking problem. In particular, this problem is examined for second-order clamped cubic spline, and the interpolated results are compared with those for natural and first-order clamped cubic splines. From the simulation of trajectory data generated from the Archimedean spiral curve, the total error values for natural, first-order, and second-order clamped cubic splines are respectively , and . Based on these results, it is concluded that the second-order clamped cubic spline interpolation developed in this article can produce a more accurate object trajectory than the natural and first-order clamped cubic splines
CLASSIFICATION OF TODDLER’S NUTRITIONAL STATUS USING THE ROUGH SET ALGORITHM
No full textThe health and nutrition of children at the age of five are very important aspects in the children’s growth and development. An assessment of the nutritional status of toddlers that is commonly used is anthropometry. This study aims to obtain the decision rules used to classify toddlers into nutritional status groups using the rough set algorithm and determine the level of classification accuracy of the resulting decision rules. The index used in this study is the weight-for-age index. Attributes used in this study were the mother’s education level, mother’s level of knowledge, the status of exclusive breastfeeding, history of illness in the last month, and nutritional status of toddlers. The results of the analysis show that there are 21 decision rules. In this study, the resulting decision rules experience inconsistencies. The selection of decision rules that experience inconsistencies is based on each decision rule’s highest strength value. The rough set algorithm can be used for the classification process with an accuracy rate of 86.36%
Variational Principle for Traveling Waves of a Generalized Benjamin-Bona-Mahony Equation using Semi-Inverse Method
No full textThe semi-inverse method was claimed as an extremely simple method in constructing the variational principles for a wide range of nonlinear problems. In this paper, we apply the method to obtain the variational principle for traveling waves of a generalized Benjamin-Bona-Mahony equation. From the performed calculations, we confirm the effectiveness of the method
Variational Principle for Traveling Waves in a Modified Kuramoto-Sivashinsky Equation
No full textIn this paper, variational principle for traveling waves in a modified Kuramoto-Sivashinsky equation is constructed by the semi-inverse method. We confirm that the method is very effective and gives the results in the concise form of variational functionals
DYNAMICS OF THE RUMOR SPREADING MODEL OF INDONESIA TWITTER CASE
No full textThe study of the spreading of a rumor is significantly important to obtain scientific information and better strategies in reducing its negative impact. Twitter has become a medium for spreading rumors or hoaxes spatially and chronologically because it has a unique community structure. This study demonstrates the model of spreading rumors by considering credibility, correlation, and mass classification based on personality is discussed. The behavior of a model solution around equilibrium points is investigated with the Jacobian matrices. The stability also corresponds to a threshold number indicating the rumor fades away or continues to spread in the population. The analytical results are confirmed by actual data from Twitter in Indonesia with #SahkanRUUPKS. The simulation results show that the free rumor equilibrium point is stable and the threshold number is less than 1. Our study shows that the number of spreaders does not increase and the #SahkanRUUPKS rumor will vanish
Analisis Solusi Persamaan Burger Sebagai Solusi Soliton Menggunakan Transformasi Hopf-Cole
No full textTelah dilakukan penelitian untuk menganalisis solusi persamaan Burger dengan menggunakan transformasi Hopf-Cole. Penelitian ini dilatarbelakangi oleh perbedaan solusi yang diperoleh pada persamaan Burger saat mekanisme penyelesaian persamaan ini menggunakan transformasi Hopf-Cole dilandaskan pada transformasi Fourier dan separasi variabel (deret Fourier). Penelitian ini dilakukan dengan mencari solusi persamaan Burger menggunakan transformasi Hopf-Cole melalui mekanisme penyelesaian yang berlandaskan pada transformasi Fourier dan separasi variabel (deret Fourier). Berdasarkan analisis solusi soliton pada persamaan Burger, hanya mekanisme penyelesaian yang berlandaskan transformasi Fourier yang berhasil menemukan solusi soliton walaupun hanya stabil dalam selang waktu 0.1 s. Mekanisme penyelesaian yang berlandaskan separasi variabel (deret Fourier) menghasilkan solusi periodik berupa gelombang meluruh terhadap waktu.Kata kunci: deret Fourier, persamaan Burger, soliton, transformasi Hopf-Cole, transformasi Fourie
ACE 3-001 Pemodelan Optimasi Evakuasi Tsunami di Kota Padang
No full textPada paper ini dibahas formulasi model optimasi sederhana untuk menentukan skenario terbaik dalam proses evakuasi tsunami.
Model ini kemudian diselesaikandengan mengambil Kota Padang sebagai studi kasus. Dalam hal ini, objek observasi dibatasi pada beberapa kelurahan di Kota Padang yang dinilai memiliki dampak resiko terbesar jika terjadi tsunami. Masalah pemrograman linier yang muncul pada model diselesaikan secara numerik dengan menggunakan metode simpleks. Hasil-hasil perhitungan menunjukkan bahwa waktu evakuasi di kelurahan-kelurahan yang rawan memungkinkan kurang dari 15 menit, dengan asumsi adanya shelter tambahan yang dapat diakses oleh penduduk di Kelurahan Air Tawar Barat, Kelurahan Ulak Karang Utara, dan
Kelurahan Ulak Karang Selatan.
Kata kunci: Pemrograman Linier, Metode Simpleks, Model Evakuasi Tsunam
