DSpace Collection:http://hdl.handle.net/10174/3062024-03-29T07:21:02Z2024-03-29T07:21:02ZBurgers' Equation and Some ApplicationsCorreia, Joaquimda Costa, FernandoSirisack, SackmoneVongsavang, Khankhamhttp://hdl.handle.net/10174/266152020-01-24T11:51:05Z2017-07-09T23:00:00ZTitle: Burgers' Equation and Some Applications
Authors: Correia, Joaquim; da Costa, Fernando; Sirisack, Sackmone; Vongsavang, Khankham
Abstract: In this thesis, I present Burgers' equation and some of its applications. I consider the inviscid and the viscid Burgers' equations and present different analytical methods for their study: the Method of Characteristics for the inviscid case, and the Cole-Hopf Transformation for theviscid one.
Two applications of Burgers' equations are given: one in simple models of Traffic Flow (which have been introduced independently by Lighthill-Whitham and Richards) and another in Coagulation theory (in which we use Laplace Transform to obtain Burgers' equations from the original coagulation integro-differential equation). In both applications we consider only analytical methods.2017-07-09T23:00:00ZTraffic Modelling and Some Inequalities in Banach SpacesBedjaoui, NabilCorreia, JoaquimSirisack, SackmoneDoungsavanh, Bouasyhttp://hdl.handle.net/10174/265752020-01-23T16:33:01Z2017-07-09T23:00:00ZTitle: Traffic Modelling and Some Inequalities in Banach Spaces
Authors: Bedjaoui, Nabil; Correia, Joaquim; Sirisack, Sackmone; Doungsavanh, Bouasy
Abstract: Modelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can
correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the
flow in crucial areas can maximize the overall throughput of traffic along a stretch of road.
We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes.
The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t.
The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t.
An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions.
Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes.2017-07-09T23:00:00ZMathematical Study of Schistosoma Mekongi Models: Application to LaosCorreia, JoaquimMammeri, YoucefSouksomvang, PhouiTounsavathdy, Souksadahttp://hdl.handle.net/10174/265692020-01-23T15:34:32Z2018-07-16T23:00:00ZTitle: Mathematical Study of Schistosoma Mekongi Models: Application to Laos
Authors: Correia, Joaquim; Mammeri, Youcef; Souksomvang, Phoui; Tounsavathdy, Souksada
Abstract: We study different models of Schistosomiasis transmission a water borne disease. Modeling tools as well as analysis of differential equations are presented and various scenarios are simulated (with Python).2018-07-16T23:00:00ZModelo Adaptativo de Partilha de Largura de Banda em Cenário de Auto-estradaJacinto, Gonçalohttp://hdl.handle.net/10174/58492014-01-02T09:44:48Z2004-01-01T00:00:00ZTitle: Modelo Adaptativo de Partilha de Largura de Banda em Cenário de Auto-estrada
Authors: Jacinto, Gonçalo
Abstract: As redes móveis sem os multimédia são vistas hoje em dia como um dos
factores chave para o desenvolvimento da infra-estrutura de comunicação global. Neste
trabalho é proposto um modelo de previsão e de empréstimo de largura de banda entre
células, de forma a manter a qualidade de serviço das chamadas durante os períodos de
congestão.
É generalizado o modelo proposto por Antunes, Pacheco e Rocha (2000) para um
cenário de auto-estrada em que o processo de chegadas de móveis é um processo de Poisson
não homogéneo. Prova-se que as distribuições espaciais do número de móveis por tipo de
chamada num instante xo são processos de Poisson não homogéneos independentes. Com
base neste resultado são obtidas estimativas da capacidade requerida e da probabilidade de
bloqueio em cada célula, para actualização da estratégia de empréstimo. Para validar os
resultados analíticos e aferir o desempenho da estratégia de empréstimo são apresentados
resultados de simulações.2004-01-01T00:00:00Z