Active matter
The study of active matter constituted of natural or artificial entities able to self-propel is being enormously investigated. For example, self-driven Brownian particles are being considered as minimal models able to provide insight on phase transitions and self-assembly in active matter (which is a non-equilibrium system). Micro- and nano-machines capable of self-propelling inside the human body and used to accomplish certain biomedical applications are already being tested. In addition, efforts for understanding the motion of microorganisms (which are an example of natural self-propelled entities), their wall accumulation, effects of external fields on their motion, and their collective effects, are also being carried out.
Quite recently, it was discovered that active matter generates novel physical quantities like the swim pressure. Physically, this quantity arises from the exchange of extra momentum (due to self-propulsion) that an active particle possesses with its bounding walls. Given its origin, this quantity can exist at different scales, hence microorganisms and larger organisms like fish or birds generate its own swim pressure. The swim pressure has already been used to explain phase separation and self- assembly in a system of interacting active particles. In this sense, it has been identified a very similar active pressure-volume phase diagram to that of a van der Waals fluid, as well as related arguments as those from classical thermodynamics to explain phase transitions in active matter. Moreover, using this active pressure concept, analogous expressions for thermodynamic quantities like the chemical potential, Helmholtz free energy, and spinodal and binodal lines have been introduced and successfully used to understand phase transitions in this new type of matter.
In this work, we computationally and theoretically study the effect of linear/nonlinear external fields (magnetic, electric fields, and flow of fluids) and thermal fluctuations on the diffusion of active Brownian particles (like bacteria or micromachines) moving in two and three dimensions. Additionally, the effect of constraints (that is, particles moving on a given surface) on the diffusion of active matter is also analyzed. We are also working with bulk properties of active matter like the swim and Reynolds pressure.
Quite recently, it was discovered that active matter generates novel physical quantities like the swim pressure. Physically, this quantity arises from the exchange of extra momentum (due to self-propulsion) that an active particle possesses with its bounding walls. Given its origin, this quantity can exist at different scales, hence microorganisms and larger organisms like fish or birds generate its own swim pressure. The swim pressure has already been used to explain phase separation and self- assembly in a system of interacting active particles. In this sense, it has been identified a very similar active pressure-volume phase diagram to that of a van der Waals fluid, as well as related arguments as those from classical thermodynamics to explain phase transitions in active matter. Moreover, using this active pressure concept, analogous expressions for thermodynamic quantities like the chemical potential, Helmholtz free energy, and spinodal and binodal lines have been introduced and successfully used to understand phase transitions in this new type of matter.
In this work, we computationally and theoretically study the effect of linear/nonlinear external fields (magnetic, electric fields, and flow of fluids) and thermal fluctuations on the diffusion of active Brownian particles (like bacteria or micromachines) moving in two and three dimensions. Additionally, the effect of constraints (that is, particles moving on a given surface) on the diffusion of active matter is also analyzed. We are also working with bulk properties of active matter like the swim and Reynolds pressure.
Collective motion
The idea of emergence originates from the fact that global effects emerge from local interactions producing a collective coherent behavior. A particular instance of emergence is illustrated by a flocking model of interacting "boids" encompassing two antagonistic conducts -consensus and frustration- giving rise to highly complex, unpredictable, coherent behavior. The cohesive motion arising from consensus can be described in terms of three ordered dynamic phases. Once frustration is included in the model, local phases for specific groups of flockmates, and transitions among them, replace the global ordered phases. Following the evolution of boids in a single group, we discovered that the boids in this group will alternate among the three phases. When we compare two uncorrelated groups, the second group shows a similar behavior to the first one, but with a different sequence of phases. Besides the visual observation of our animations with marked boids, the result is evident plotting the local order parameters. Rather than adopting one of the consensus ordered phases, the flock motion resembles more an entangled dynamic sequence of phase transitions involving each group of flock.
Fluid Mechanics
HIGH REYNOLDS NUMBER
According to the Prandtl-Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl-Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation. LOW REYNOLDS NUMBER We also study low Reynolds number (Re) problems like the classical swimming sheet moving at low Re, or the solution to the biharmonic equation in two dimensions by using methods from complex variable. |