Màster universitari en Física Computacional i Aplicada (Pla 2009)
http://hdl.handle.net/2099.1/5721
2024-03-28T22:08:39ZVariational mechanics and numerical methods for structural analysis
http://hdl.handle.net/2099.1/16710
Variational mechanics and numerical methods for structural analysis
Andújar, Rabindranath
This work focuses on the particular application of the variational principles of Lagrange and Hamilton for structural
analysis. Different numerical methods are compared in their computation of the elastic energy through time.
According to variational mechanics, the difference between the stored elastic energy and the applied work should be
null on each time step, so by computing this difference we can account for the level of accuracy of each combination of
numerical methods. Moreover, in some situations when numerical instabilities are difficult to perceive due to high
complexities, this procedure allows for the control and straightforward visualization of them, being an excellent source
of hindsight on the behaviour of the analysed system.
The purpose of this dissertation is to present a scheme where the current numerical methods can be benchmarked in a
qualitative as well as in a quantitative manner. It is shown how different combinations of methods, even for a simple
model, can give very different results, particularly in the field of dynamics, where often also instabilites arise.
The first half of the thesis is a thorough explanation of these concepts and their application in terms of structural
analysis. In the second part, a review on the numerical methods in general and of those implemented for our
experiments is provided, followed by the experimental results and their interpretation. The model of choice, for
simplicity and availability of analytical results is one cantilever column. Bending elastic energy of the column is
monitored under transient regimes of different shapes, computing the total action of the system as its integral through
time.
2013-01-07T14:01:31ZAndújar, RabindranathThis work focuses on the particular application of the variational principles of Lagrange and Hamilton for structural
analysis. Different numerical methods are compared in their computation of the elastic energy through time.
According to variational mechanics, the difference between the stored elastic energy and the applied work should be
null on each time step, so by computing this difference we can account for the level of accuracy of each combination of
numerical methods. Moreover, in some situations when numerical instabilities are difficult to perceive due to high
complexities, this procedure allows for the control and straightforward visualization of them, being an excellent source
of hindsight on the behaviour of the analysed system.
The purpose of this dissertation is to present a scheme where the current numerical methods can be benchmarked in a
qualitative as well as in a quantitative manner. It is shown how different combinations of methods, even for a simple
model, can give very different results, particularly in the field of dynamics, where often also instabilites arise.
The first half of the thesis is a thorough explanation of these concepts and their application in terms of structural
analysis. In the second part, a review on the numerical methods in general and of those implemented for our
experiments is provided, followed by the experimental results and their interpretation. The model of choice, for
simplicity and availability of analytical results is one cantilever column. Bending elastic energy of the column is
monitored under transient regimes of different shapes, computing the total action of the system as its integral through
time.Structural study of C2Cl6 by molecular dynamics
http://hdl.handle.net/2099.1/13139
Structural study of C2Cl6 by molecular dynamics
Henao Aristizábal, Andrés
English: A Molecular Dynamics study of hexachloroethane C2Cl6 was done in order to study the structure at different temperatures, varying from 300K to 480K. The system at 480K showed a liquid phase, as reported in the literature. A comparison with an experimental neutron scattering structure factor was made obtaining good agreement. A simulated annealing was carried out in a range of 300 to 480K. The radial distribution functions were compared studying the thermal dependence of the structure, the mean square displacements and self diffusion coefficients were also analyzed to complete an image of the structural changes. The transition to the liquid phase is observed above 450K, this is in agreement with the reported melting temperature for this system of 458K.
2011-10-14T07:48:41ZHenao Aristizábal, AndrésEnglish: A Molecular Dynamics study of hexachloroethane C2Cl6 was done in order to study the structure at different temperatures, varying from 300K to 480K. The system at 480K showed a liquid phase, as reported in the literature. A comparison with an experimental neutron scattering structure factor was made obtaining good agreement. A simulated annealing was carried out in a range of 300 to 480K. The radial distribution functions were compared studying the thermal dependence of the structure, the mean square displacements and self diffusion coefficients were also analyzed to complete an image of the structural changes. The transition to the liquid phase is observed above 450K, this is in agreement with the reported melting temperature for this system of 458K.Smoothed Particle Hydrodynamics simulations of white dwarf close encounters in dense stellar systems
http://hdl.handle.net/2099.1/13138
Smoothed Particle Hydrodynamics simulations of white dwarf close encounters in dense stellar systems
Aznar Siguan, Gabriela
English: In old dense stellar systems collisions of white dwarfs are a rather frequent phenomenon. Here we present the results of several Smoothed Particle Hydrodynamics simulations of close encounters of white dwarfs to explore under which conditions collisions occur and which are the final remnants of the interaction. Depending on the initial conditions, three different outcomes are possible. Specifically, the outcome of the interaction can be either a direct or a lateral collision or the interaction can result in the formation of an eccentric binary system. The large number of simulations performed has allowed us to identify the key parameters to parametrize the outcome of the interaction as a function of the initial conditions. We find that the outcome of the interaction mostly depends on the periastron distance and the reduced mass of the system. Finally, we discuss the influence of the masses and chemical compositions of the interacting white dwarfs in the properties of the remnants.
2011-10-14T07:44:47ZAznar Siguan, GabrielaEnglish: In old dense stellar systems collisions of white dwarfs are a rather frequent phenomenon. Here we present the results of several Smoothed Particle Hydrodynamics simulations of close encounters of white dwarfs to explore under which conditions collisions occur and which are the final remnants of the interaction. Depending on the initial conditions, three different outcomes are possible. Specifically, the outcome of the interaction can be either a direct or a lateral collision or the interaction can result in the formation of an eccentric binary system. The large number of simulations performed has allowed us to identify the key parameters to parametrize the outcome of the interaction as a function of the initial conditions. We find that the outcome of the interaction mostly depends on the periastron distance and the reduced mass of the system. Finally, we discuss the influence of the masses and chemical compositions of the interacting white dwarfs in the properties of the remnants.Multivariate Curve Resolution applied to Ion Mobility Spectra
http://hdl.handle.net/2099.1/13137
Multivariate Curve Resolution applied to Ion Mobility Spectra
Oller Moreno, Sergio
English: In this work, a Multivariate Curve Resolution (MCR) with Alternating Least Squares (ALS) method is described and used to identify the concentrations of a two-component (ethanol and acetone) mixture analysed with an Ion Mobility Spectrometer. Results allow us to distinguish qualitatively both components at lower concentrations, whereas fail to detect ethanol at higher concentrations. The impossibility of detecting etanol at higher concentrations is caused by higher acetone’s proton affinity.
Projecte final de Màster Oficial realitzat en col.laboració amb Universitat de Barcelona. Departament d’Electrònica.
2011-10-14T07:39:01ZOller Moreno, SergioEnglish: In this work, a Multivariate Curve Resolution (MCR) with Alternating Least Squares (ALS) method is described and used to identify the concentrations of a two-component (ethanol and acetone) mixture analysed with an Ion Mobility Spectrometer. Results allow us to distinguish qualitatively both components at lower concentrations, whereas fail to detect ethanol at higher concentrations. The impossibility of detecting etanol at higher concentrations is caused by higher acetone’s proton affinity.Maximum Likelihood Approach for Stochastic Volatility Models
http://hdl.handle.net/2099.1/13136
Maximum Likelihood Approach for Stochastic Volatility Models
Camprodon Masnou, Jordi
English: Volatility is a measure of the amplitude of price return fluctuations. Despite it is one of the most important quantities in finance, volatility is a hidden quantity because it is not directly observable. Here we apply a known maximum likelihood process which assumes that volatility is a time-dependent diffusions coefficient of the random walk of the price return and that it is a Markov process. We use this method using the expOU, the OU and the Heston models which are previously imposed. We find an estimator of the volatility for each model and we observe that it works reasonably well for the three models. Using these estimators, we reach a way of forecasting absolute values of future returns with current volatilities. During all the process, no-correlation is introduced and at the end, we see that volatility has non-zero autocorrelation for hundreds of days and we observe a significant correlation between volatility and price return called leverage effect. We finally apply this methodology to different market indexes and we conclude that its properties are universal.
Projecte final de Màster Oficial fet en col.laboració amb Universitat de Barcelona. Departament de Física Fonamental
2011-10-14T07:26:02ZCamprodon Masnou, JordiEnglish: Volatility is a measure of the amplitude of price return fluctuations. Despite it is one of the most important quantities in finance, volatility is a hidden quantity because it is not directly observable. Here we apply a known maximum likelihood process which assumes that volatility is a time-dependent diffusions coefficient of the random walk of the price return and that it is a Markov process. We use this method using the expOU, the OU and the Heston models which are previously imposed. We find an estimator of the volatility for each model and we observe that it works reasonably well for the three models. Using these estimators, we reach a way of forecasting absolute values of future returns with current volatilities. During all the process, no-correlation is introduced and at the end, we see that volatility has non-zero autocorrelation for hundreds of days and we observe a significant correlation between volatility and price return called leverage effect. We finally apply this methodology to different market indexes and we conclude that its properties are universal.Swimmers’ Collective Dynamics Modelization
http://hdl.handle.net/2099.1/13135
Swimmers’ Collective Dynamics Modelization
Ferré Porta, Guillem
English: We describe a new model in order to study the properties of collections of self-propelled particles swimming in a two-dimensional fluid. Our model consist in two types of particles, the first interacting with each other with a soft potential and thus representing the fluid while the second type are self-propelled particles of biological nature capable of changing its orientation following the velocity field of the fluid. The results of the simulations show how a super-diffusive regime arises at large times for biological particles, in addition to having higher velocity correlation. Also, it is show how the biological particles have a tendency to form clusters and how these particles tend to look for the same orientation.
2011-10-14T07:19:10ZFerré Porta, GuillemEnglish: We describe a new model in order to study the properties of collections of self-propelled particles swimming in a two-dimensional fluid. Our model consist in two types of particles, the first interacting with each other with a soft potential and thus representing the fluid while the second type are self-propelled particles of biological nature capable of changing its orientation following the velocity field of the fluid. The results of the simulations show how a super-diffusive regime arises at large times for biological particles, in addition to having higher velocity correlation. Also, it is show how the biological particles have a tendency to form clusters and how these particles tend to look for the same orientation.Statistical Complex Analysis of Taxi Mobility in San Francisco
http://hdl.handle.net/2099.1/13134
Statistical Complex Analysis of Taxi Mobility in San Francisco
Sagarra Pascual, Oleguer
English: The recent developments in technology of movement tracking devices such as Global Positioning (GPS), together with the increasing availability of consistent data bases, have lately given rise to the study of human mobility patterns in different environments. In this work a statistical characterization of real mobility GPS high-frequency data from taxis in San Francisco is performed. The di_erent patterns taxi drivers and customers follow are shown through comparing behavior when cabs are empty or full and the information is presented using a weighted directed complex network metric, from which the author obtains some topological information such as correlations between nodes, assortativity and clustering. Some adapted measurements to weighted nets are presented together with some remarks to support the need for new tools for assortativity classification.
Projecte final de Màster Oficial realitzat en col.laboració amb Universitat de Barcelona, Departament de Física Fonamental.
2011-10-14T07:15:16ZSagarra Pascual, OleguerEnglish: The recent developments in technology of movement tracking devices such as Global Positioning (GPS), together with the increasing availability of consistent data bases, have lately given rise to the study of human mobility patterns in different environments. In this work a statistical characterization of real mobility GPS high-frequency data from taxis in San Francisco is performed. The di_erent patterns taxi drivers and customers follow are shown through comparing behavior when cabs are empty or full and the information is presented using a weighted directed complex network metric, from which the author obtains some topological information such as correlations between nodes, assortativity and clustering. Some adapted measurements to weighted nets are presented together with some remarks to support the need for new tools for assortativity classification.Global epidemic spreading processes in coupled networks
http://hdl.handle.net/2099.1/13120
Global epidemic spreading processes in coupled networks
Saumell Mendiola, Anna
English: We study the effect of coupling two random networks where an epidemic process propagates. A theoretical SIS model is applied and a new critical threshold for the existence of an endemic state is analytically calculated for the two coupled networks, under the assumption that there is total correlation between the outer degree and the inner degree of each node. Our main result is that a global endemic state can exist in the coupled networks, even though the epidemics does not propagate on each network separately. Finally, we checked these results by running large scale computer simulations.
Projecte final de Màster Oficial fet en col.laborció amb Universitat de Barcelona. Departament de Física Fonamental i Departament de Química Física.
2011-10-13T11:48:40ZSaumell Mendiola, AnnaEnglish: We study the effect of coupling two random networks where an epidemic process propagates. A theoretical SIS model is applied and a new critical threshold for the existence of an endemic state is analytically calculated for the two coupled networks, under the assumption that there is total correlation between the outer degree and the inner degree of each node. Our main result is that a global endemic state can exist in the coupled networks, even though the epidemics does not propagate on each network separately. Finally, we checked these results by running large scale computer simulations.Characterization of the clustering phase transition of a complex network embedded in a hyperbolic plane
http://hdl.handle.net/2099.1/13119
Characterization of the clustering phase transition of a complex network embedded in a hyperbolic plane
Colomer de Simón, Pol
English: If we distribute nodes homogeneously in an hyperbolic plane and connect each possible pair of nodes with a probability that depends on the hyperbolic distance among them, heterogeneous degree distributions and strong clustering emerge naturally. Both metrics are key properties observed in real complex networks but are rarely seen together in standard network models. Our model considers edges in a network as noninteracting fermions whose energies are equal to the hyperbolic distances between nodes. This interpretation allows us to use statistical mechanics methods, like the Metropolis Hastings algorithm, in order to perform numerical simulations and to get precise measurements of the network properties. In this master thesis, we focus on the study of clustering, which undergoes a phase transition at a certain critical temperature. We develop an analytical framework to obtain the critical exponents of this phase transition and compare them with numerical simulations. Finally, we check whether the Finite Size Scaling (FSS) assumption holds in this case or not.
Projecte final de Màster Oficial reaizat en col.laboració amb Universitat de Barcelona. Departament de Física Fonamental.
2011-10-13T11:41:05ZColomer de Simón, PolEnglish: If we distribute nodes homogeneously in an hyperbolic plane and connect each possible pair of nodes with a probability that depends on the hyperbolic distance among them, heterogeneous degree distributions and strong clustering emerge naturally. Both metrics are key properties observed in real complex networks but are rarely seen together in standard network models. Our model considers edges in a network as noninteracting fermions whose energies are equal to the hyperbolic distances between nodes. This interpretation allows us to use statistical mechanics methods, like the Metropolis Hastings algorithm, in order to perform numerical simulations and to get precise measurements of the network properties. In this master thesis, we focus on the study of clustering, which undergoes a phase transition at a certain critical temperature. We develop an analytical framework to obtain the critical exponents of this phase transition and compare them with numerical simulations. Finally, we check whether the Finite Size Scaling (FSS) assumption holds in this case or not.Infinite period bifurcation due to imperfections in rotating thermal convection
http://hdl.handle.net/2099.1/12666
Infinite period bifurcation due to imperfections in rotating thermal convection
López Alonso, Jose Manuel
A pinning area is a band of finite width where rotating waves with precession frequences near zero turn into steady non-axisymmetric solutions. Dynamical systems theory suggests that any imperfection breaking the SO(2) invariance of a problem must result in the formation of such a region. Numerical simulations of rotating convection in a finite cylinder have been made breaking the symmetry by imposing a linear profile of
temperature at the top lid in order to find the aforementioned steady solutions region.
2011-07-15T11:49:30ZLópez Alonso, Jose ManuelA pinning area is a band of finite width where rotating waves with precession frequences near zero turn into steady non-axisymmetric solutions. Dynamical systems theory suggests that any imperfection breaking the SO(2) invariance of a problem must result in the formation of such a region. Numerical simulations of rotating convection in a finite cylinder have been made breaking the symmetry by imposing a linear profile of
temperature at the top lid in order to find the aforementioned steady solutions region.