MA311exam 1999 pdf

Exam questions and solutions in PDF

MA311exam 1998 pdf

Exam questions and solutions in PDF

MA311exam 2000

Exam questions and solutions in LaTex

Numerical simulation of the liquid phase in SnO(2) thin film deposition by sol-gel-dip-coating

The fluid flow of the liquid phase in the sol-gel-dip-coating process for SnO(2) thin film deposition is numerically simulated. This calculation yields useful information on the velocity distribution close to the substrate, where the film is deposited. The fluid modeling is done by assuming Newtonian behavior, since the linear relation between shear stress and velocity gradient is observed. Besides, very low viscosities are used. The fluid governing equations are the Navier-Stokes in the two dimensional form, discretized by the finite difference technique. Results of optical transmittance and X-ray diffraction on films obtained from colloidal suspensions with regular viscosity, confirm the substrate base as the thickest part of the film, as inferred from the numerical simulation. In addition, as the viscosity increases, the fluid acquires more uniform velocity distribution close to the substrate, leading to more homogenous and uniform films.

Numerical simulation of the liquid phase in SnO2 thin film deposition by sol-gel-dip-coating

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mean-field equations for cigar- and disc-shaped Bose and Fermi superfluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Abordagem matemática de roll waves em escoamentos hiperconcentrados com superfície livre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelagem do fluxo sanguíneo na aorta abdominal utilizando interação fluido-estrutura

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método numérico-analítico generalizado para estimação do campo eletromagnético de linhas de transmissão de energia elétrica utilizando a teoria dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estabilidade de métodos numéricos LCR para a simulação de escoamento

Pós-graduação em Matematica Aplicada e Computacional - FCT

Uso das ondas de Lamb e Scholte para caracterização de líquidos

Pós-graduação em Engenharia Elétrica - FEIS

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

Simulazione numerica di fenomeni aeroelastici con applicazione alle strutture civili

Il presente lavoro tratta lo studio dei fenomeni aeroelastici di interazione fra fluido e struttura, con il fine di provare a simularli mediante l’ausilio di un codice agli elementi finiti. Nel primo capitolo sono fornite alcune nozioni di fluidodinamica, in modo da rendere chiari i passaggi teorici fondamentali che portano alle equazioni di Navier-Stokes governanti il moto dei fluidi viscosi. Inoltre è illustrato il fenomeno della formazione di vortici a valle dei corpi tozzi dovuto alla separazione dello strato limite laminare, con descrizione anche di alcuni risultati ottenuti dalle simulazioni numeriche. Nel secondo capitolo vengono presi in rassegna i principali fenomeni di interazione fra fluido e struttura, cercando di metterne in luce le fondamenta della trattazione analitica e le ipotesi sotto le quali tale trattazione è valida. Chiaramente si tratta solo di una panoramica che non entra in merito degli sviluppi della ricerca più recente ma fornisce le basi per affrontare i vari problemi di instabilità strutturale dovuti a un particolare fenomeno di interazione con il vento. Il terzo capitolo contiene una trattazione più approfondita del fenomeno di instabilità per flutter. Tra tutti i fenomeni di instabilità aeroelastica delle strutture il flutter risulta il più temibile, soprattutto per i ponti di grande luce. Per questo si è ritenuto opportuno dedicargli un capitolo, in modo da illustrare i vari procedimenti con cui si riesce a determinare analiticamente la velocità critica di flutter di un impalcato da ponte, a partire dalle funzioni sperimentali denominate derivate di flutter. Al termine del capitolo è illustrato il procedimento con cui si ricavano sperimentalmente le derivate di flutter di un impalcato da ponte. Nel quarto capitolo è presentato l’esempio di studio dell’impalcato del ponte Tsing Ma ad Hong Kong. Sono riportati i risultati analitici dei calcoli della velocità di flutter e di divergenza torsionale dell’impalcato e i risultati delle simulazioni numeriche effettuate per stimare i coefficienti aerodinamici statici e il comportamento dinamico della struttura soggetta all’azione del vento. Considerazioni e commenti sui risultati ottenuti e sui metodi di modellazione numerica adottati completano l’elaborato.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.