Active fluids are an interesting new class of non-equilibrium systems in physics. In such fluids, the system is forced out of equilibrium by the individual active particles - in contrast to driven systems where the system is forced out of equilibrium by some external forces. Some biological examples of active fluids are bacterial suspensions and actomyosin solutions inside eukaryotic cells. In the case of bacterial suspensions, the fluid is stirred internally by the swimming bacteria and as a consequence of this, active fluids can have some interesting physics of their own such as hydrodynamic instabilities and spontaneous symmetry breaking. Here, in particular, we study how such instabilities may arise and how they may lead to a non-equilibrium steady state. We also study numerically a droplet of active matter as a simple representation of cell extract comprising actomyosin solution bounded by a cell membrane. It is widely believed that cell motility is driven only by actin polymerization pushing against the cell membrane. However, we show that even in the absence of actin polymerization, actin-myosin contraction alone can also generate a unidirectional motion. This happens due to the spontaneous breakdown of a discrete symmetry at large enough activity (i.e. actomyosin contraction). This non-equilibrium phase transition from stationary to motile state is somewhat similar to the second order phase transition in equilibrium thermodynamics. Finally, we studied the behaviour of an active droplet on a two-dimensional surface to mimic cell crawling. Whereas cell migration in 3D environment maybe driven mainly by actin-myosin contraction (described above), cell crawling on a 2D surface is driven mainly by actin polymerisation. Here we find that localised actin polymerisation can cause protrusion in the cell membrane which is qualitatively similar to lamellipodium formation in cell crawling.

We study the phase diagram of an interacting lattice gas of two species of particles and holes, driven out of equilibrium by a local hopping bias (denoted by `E'). Particles interact by excluded volume and nearest-neighbor attractions. We present a detailed Monte Carlo investigation of the phase diagram. Three phases are found, with a homogenous phase at high temperatures and two distinct ordered phases at lower temperatures. Which ordered phase is observed depends on the parameter f, which controls the ratio of the two types of particles. At small f, there is nearly a single species, and a transition is observed into a KLS-type ordered phase. At larger f, the minority species are sufficiently dense to form a transverse blockage, and a sequence of two transitions are observed as the temperature is lowered. First, a continuous boundary is crossed into an SHZ-type ordered phase, then at a lower temperature a first-order boundary is crossed into the KLS-type ordered phase. At some critical value of f is a bicritical point, where the first-order line branches from the two continuous boundaries. We also consider correlations in the homogenous phase, by constructing a continuum description and comparing to the results of simulations. Long range correlations are present in both the theoretical results and the simulations, though certain details of the theory do not fit the observations very well. Finally, we examine the beahvior of three-point correlations in the single-species (KLS) limit. Nontrivial three-point correlations are directly related to the nonzero bias E. We therefore consider the behavior of the three-point correlations as a function of E. We find that the three-point signal saturates very rapidly with E. There are some difficulties interpreting the data at small E. / Ph. D.

coordenadoria de aperfeiÃoamento de pessoal de ensino superior / Estudamos por meio de simulaÃÃes de Monte Carlo e anÃlises de escala de tamanho finito as transiÃÃes de fase que os modelos do votante majoritÃrio e do processo de contato descrevem em redes de Kleinberg. Tais estruturas sÃo construÃdas a partir de uma rede regular onde conexÃes de longo alcance sÃo adicionadas aleatoriamente seguindo a probabilidade Pij ~ r&#945;, sendo rij a distÃncia Manhattan entre dois nÃs i e j e o expoente &#945; um parÃmetro de controle [J. M. Kleinberg, Nature 406, 845 (2000)]. Nossos resultados mostram que o comportamento coletivo desses sistemas exibe uma transiÃÃo de fase contÃnua, do tipo ordem-desordem para o votante majoritÃrio e ativo absorvente para o processo de contato, no parÃmetro crÃtico correspondente. Tal parÃmetro à monotÃnico com o expoente &#945;, sendo crescente para o votante majoritÃrio e decrescente para o processo de contato. O comportamento crÃtico dos modelos apresenta uma dependÃncia nÃo trivial com o expoente &#945;. Precisamente, considerando as funÃÃes de escala e os expoentes crÃticos, concluÃmos que os sistemas passam pelo fenÃmeno de crossover entre duas classes de universalidade. Para &#945; &#8804; 3, o comportamento crÃtico à descrito pelos expoentes de campo mÃdio enquanto que para &#945; &#8805; 4 os expoentes pertencem à classe de universalidade de Ising 2D, para o modelo do votante majoritÃrio, e à classe da percolaÃÃo direcionada no caso do processode contato. Finalmente, na regiÃo 3< &#945; <4 os expoentes crÃticos variam continuamente com o parÃmetro &#945;. Revisamos o processo de contato simbiÃtico aplicando um mÃtodo alternativo para gerarmos estados quase estacionÃrios. Desta forma, realizamos simulaÃÃes de Monte Carlo em grafos completos, aleatÃrios, redes espacialmente incorporadas e em redes regulares. Observamos que os resultados para o grafo completo e redes aleatÃrias concordam com as soluÃÃes das equaÃÃes de campo mÃdio, com a presenÃa de ciclos de histerese e biestabilidade entre as fases ativa e absorvente. Para redes regulares, comprovamos a ausÃncia de biestabilidade e comportamento histerÃtico, implicando em uma transiÃÃo de fase contÃnua para qualquer valor do parÃmetro que controla a interaÃÃo simbiÃtica. E por fim, conjecturamos que a transiÃÃo de fase descrita pelo processo de contato simbiÃtico serà contÃnua ou descontÃnua se a topologia de interesse estiver abaixo ou acima da dimensÃo crÃtica superior, respectivamente. / We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model and the contact process taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which long-range connections are randomly added according to the probability, Pij ~ r&#945; , where rij is the Manhattan distance between nodes i and j, and the exponent &#945; is a controlling parameter [J. M. Kleinberg, Nature 406, 845 (2000)]. Our results show that the collective behavior of those systems exhibits a continuous phase transition, order-disorder for the majority-vote model and active-absorbing for the contact process, at a critical parameter, which is a monotonous function of the exponent &#945;. The critical behavior of the models has a non-trivial dependence on the exponent &#945;. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the systems undergoes a crossover between distinct universality classes. For &#945; &#8804; 3 the critical behavior in both systems is described by mean-field exponents, while for &#945; &#8805; 4 it belongs to the 2D Ising universality class for majority-vote model and to Directed Percolation universality class for contact process. Finally, in the region where the crossover occurs, 3< &#945; <4, the critical exponents vary continuously with the exponent &#945;. We revisit the symbiotic contact process considering a proper method to generate the quasistatiorary state. We perform Monte Carlo simulations on complete and random graphs that are in accordance with the mean-field solutions. Moreover, it is observed hysteresis cycles between the absorbing and active phases with the presence of bistable regions. For regular square lattice, we show that bistability and hysteretic behavior are absence, implying that model undergone a continuous phase transition for any value of the parameter that controlled the symbiotic interaction. Finally, we conjecture that the phase transition undergone by the symbiotic contact process will be continuous or discontinuous if the topology considered is below or above of the upper critical dimension, respectively.