public 01:29:47

Marija Vucelja : A glass transition in population genetics: Emergence of clones in populations

  -   Nonlinear and Complex Systems ( 189 Views )

The fields of evolution and population genetics are undergoing a renaissance, due to the abundance of sequencing data. On the other hand, the existing theories are often unable to explain the experimental findings. It is not clear what sets the time scales of evolution, whether for antibiotic resistance, an emergence of new animal species, or the diversification of life. The emerging picture of genetic evolution is that of a strongly interacting stochastic system with large numbers of components far from equilibrium. In this talk, I plan to focus on the clone competition and discuss the diversity of a random population that undergoes selection and recombination (sexual reproduction). Recombination reshuffles genetic material while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, selection can amplify individual genotypes into large clones, and the population reaches the so-called "clonal condensation". I hope to convince you that our work provides a qualitative explanation of clonal condensation. I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions and connections to statistical physics.

public 01:34:44

Luis Bonilla : Bifurcation theory of swarm formation

  -   Nonlinear and Complex Systems ( 157 Views )

In nature, insects, fish, birds and other animals flock. A simple two-dimensional model due to Vicsek et al treats them as self-propelled particles that move with constant speed and, at each time step, tend to align their velocities to an average of those of their neighbors except for an alignment noise (conformist rule). The distribution function of these active particles satisfies a kinetic equation. Flocking appears as a bifurcation from an uniform distribution of particles whose order parameter is the average of the directions of their velocities (polarization). This bifurcation is quite unusual: it is described by a system of partial differential equations that are hyperbolic on the short time scale and parabolic on a longer scale. Uniform solutions provide the usual diagram of a pitchfork bifurcation but disturbances about them obey the Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution, they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. In addition, if the active particles may choose with probability p at each time step to follow the conformist Vicsek rule or to align their velocity contrary or almost contrary to the average one, the bifurcations are of either period doubling or Hopf type and we find stable time dependent solutions. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, non-uniform polarized phases appear as the noise surpasses threshold.

public 01:29:47

John Dolbow : On the Surfactant-Driven Fracture of Particulate Rafts

  -   Nonlinear and Complex Systems ( 146 Views )

Over the past decade, much attention has focused on the behavior of hydrophobic particles at interfaces. These systems are of interest to scientists and engineers, for example, due to their potential for stabilizing drops and emulsions via jamming. This seminar will focus on the behavior of particulate 'rafts' that form when a monolayer of particles are placed at an air- liquid interface. The particles interact with the underlying fluid to form a quasi two-dimensional solid. Such particulate rafts can support both tension and compression, and they buckle under sufficiently large compressive loads. When a drop of surfactant is introduced into the system, fracture networks develop in the rafts. The fracture process exhibits features observed in other elastic systems, such as crack kinking, crack branching, and crack arrest. Moreover, there is a clear coupling between the praft fracture and the diffusion of the surfactant on the surface and through the 'porous' liquid-particle monolayer. As such, one can draw analogies between this system and others where crack growth interacts with fluid flow or mass transport. The seminar will present recent work in modeling the diffusion of surfactant into particle raft systems and the resulting formation of fracture networks. We will present both discrete models that track the motion of individual particles, as well as a new continuum model for poro-chemo-elasticity. Results that reproduce some of the quantitative and qualitative aspects of recent experimental studies of these systems will also be shown.

public 01:39:44

Bob Behringer : TBA

  -   Nonlinear and Complex Systems ( 128 Views )

public 01:17:07

Brian Mann : Nonlinear Energy Harvesting

  -   Nonlinear and Complex Systems ( 121 Views )