Vera Halfiani

Deformation of bichromatic wave groups based on third order side band solution of Benjamin-Bona-Mahony equation

This paper concerns on propagation of Benjamin Bona Mahony (BBM) wave groups. The previous results, experimental, analytical and numerical, show that nonlinear effects will deform wave groups and may lead to large waves with wave heights larger than twice the original input; the deformation may show itself as peaking and splitting. To investigate this, especially at which location the waves will achieve their maximum amplitude, and to determine the amplitude amplification factor, a concept called Maximal Temporal Amplitude (MTA) is applied. This quantity is a tool that can be used to measure the maximum amplitude of the waves over time. In this paper we will use Benjamin-Bona-Mahony (BBM) model and third order side band approximation theory to investigate the peaking and splitting phenomena of the wave groups which is initially in bichromatic signal. The bichromatic signal here is a signal that is described by superposition of two monochromatic signals with the same value in amplitude but slightly different in frequencies. We present that the waves undergo deformation in their propagation.

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

This article discusses the evolution of Benjamin-Bona-Mahony (BBM) wave packet’s envelope. The envelope equation is derived by applying the asymptotic series up to the third order and choosing appropriate fast-to-slow variable transformations which eliminate the resonance terms that occurred. It is obtained that the envelope evolves satisfying the Nonlinear Schrodinger (NLS) equation. The evolution of NLS envelope is investigated through its exact solution, Soliton on Finite Background, which undergoes modulational instability during its propagation. The resulting wave may experience phase singularity indicated by wave splitting and merging and causing amplification on its amplitude. Some parameter values take part in triggering this phenomenon. The amplitude amplification can be analyzed by employing Maximal Temporal Amplitude (MTA) which is a quantity measuring the maximum wave elevation at each spatial position during the observation time. Wavenumber value affects the extreme position of the wave but not the amplitude amplification. Meanwhile, modulational frequency value affects both terms. Comparison of the evolution of the BBM wave packet to the previous results obtained from KdV equation gives interesting outputs regarding the extreme position and the maximum wave peaking.

The epidemic of Tuberculosis on vaccinated population

Tuberculosis is an infectious disease which has caused a large number of mortality in Indonesia. This disease is caused by Mycrobacterium tuberculosis. Besides affecting lung, this disease also affects other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. This article discusses the epidemic of tuberculosis through employing the SEIR model. Here, the population is divided into four compartments which are susceptible, exposed, infected and recovered. The susceptible population is further grouped into two which are vaccinated group and unvaccinated group. The behavior of the epidemic is investigated through analysing the equilibrium of the model. The result shows that administering vaccine to the susceptible population contributes to the reduction of the tuberculosis epidemic rate.

Mathematical model of tuberculosis epidemic with recovery time delay

Tuberculosis (TB) is a contagious disease which can cause death. The disease is caused by Mycobacterium Tuberculosis which generally affects lungs and other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. The spread of TB occurs through the bacteria-contaminated air which is inhaled into the lungs. The symptoms of the TB patients are cough, chest pain, shortness of breath, appetite lose, weight lose, fever, cold, and fatigue. World Health Organization (WHO) reported that Indonesia placed the second in term of the most TB cases after India which has 23 % cases while China is reported to have 10 % cases in global. TB has become one of the greatest death threats in global. One way to countermeasure TB disease is by administering vaccination. However, a medication is needed when one has already infected. The medication can generally take 6 months of time which consists of two phases, inpatient and outpatient. Mathematical models to analyze the spread of TB have been widely developed. One of them is the SEIR type model. In this model the population is divided into four groups, which are suspectible (S), exposed (S), infected (I), recovered (R). In fact, a TB patient needs to undergo medication with a period of time in order to recover. This article discusses a model of TB spread with considering the term of recovery (time delay). The model is developed in SIR type where the population is divided into three groups, suspectible (S), infected (I), and recovered (R). Here, the vaccine is given to the susceptible group and the time delay is considered in the group undergoing the medication.Tuberculosis (TB) is a contagious disease which can cause death. The disease is caused by Mycobacterium Tuberculosis which generally affects lungs and other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. The spread of TB occurs through the bacteria-contaminated air which is inhaled into the lungs. The symptoms of the TB patients are cough, chest pain, shortness of breath, appetite lose, weight lose, fever, cold, and fatigue. World Health Organization (WHO) reported that Indonesia placed the second in term of the most TB cases after India which has 23 % cases while China is reported to have 10 % cases in global. TB has become one of the greatest death threats in global. One way to countermeasure TB disease is by administering vaccination. However, a medication is needed when one has already infected. The medication can generally take 6 months of time which consists of two phases, inpatient and outpatient. Mathematical models to analyze the spread of TB have been widely developed. ...

Soliton solution of Benjamin-Bona-Mahony equation and modified regularized long wave equation

This article discusses about solutions of Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation. BBM equation is a model describing the propagation of long wave with small amplitude on one directional space. This equation was developed to resolve the shortcoming of classic Korteweg-de-Vries (KdV) equation which fails to model the wave when the wavenumbers value is high. Meanwhile, MRLW equation represents the dispersed wave phenomenon such as shallow water and phonon packet on nonlinear crystal. The solutions of these equations are known as a solitary wave (soliton). This solution can be determined by various methods. Here, we apply the sine-cosine function method and analyze in detail the resulting solitary waves.

Optimization model of parking charge and income using Lagrange multiplier method

This paper discusses about developing optimization models for parking space unit (PSU) and maximum parking charge and income. The models are applied at the parking lot of Hermes Palace Mall of Banda Aceh. The models of parking space unit are governed by using the Integer Linear Programming (ILP) approach which maximizes PSU based on the parking angle. The result shows that the parking area for vehicles (cars and motorcycles) can maximally accommodate 54 PSUs for car and 760 PSUs for motorcycle. This maximum PSU then becomes a constraint in modeling the parking charge and income’s mathematical system. Lagrange multiplier is employed to find the maximum charge and income. The result shows that the maximum income is earned from the parking of cars an motorcycles giving Rp. 66.622.500 and Rp 60.909.000 in total, respectively.

Modified formula for velocity and acceleration setting in Obstacle Avoidance problem

This paper concerns on an optimal control problem of a robot movement from an initial point to another target point while avoiding obstacles. Previous study had generated a trajectory that should be taken by the robot to minimized the consumed energy while moving with constant velocity. Here, we find the optimal performance index value which minimizes the trajectory length as well as the energy usage of the robot. We also consider nonconstant velocity which changes over time as the robot moves. The solution is generated numerically by using software package TOMLAB/PROPT. The results show that there is different route taken by the robot yet it is shorter in distance. Also, the optimum energy and trajectory length can be obtained by setting the right penalty values at both measures.