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.
Many processes in nature occur in the form of rare but important events. Well known examples of such events include conformation changes of biomolecules, chemical reactions, and nucleation events during phase transformation. Rare events do not happen very often on the internal clock of the system (which makes their simulation very challenging), but this clock can be very fast and this leaves plenty of room for the appearance of rare events in our daily life. I will review classical theories for the description of rare events, recent theoretical developments such as Transition Path Theory, concept such as reaction coordinate or free energy of a reaction and I will discuss how to compute the pathway and rate of rare events efficiently using the String Method. As illustrations, I will discuss the hydrophobic collapse of a polymeric chain, phase transitions in the Ising model, and a genetic toggle switch.
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.
The cohesive strength of granular materials is a consequence of either cohesive bonding (capillary bridging, van der Waals forces) between the grains or the action of a binding solid or liquid material in the pore space. I first discuss the constitutive framework of the plastic behavior of granular materials with internal variables pertaining to the granular fabric. Then, I show how cohesive granular systems can be simulated by different methods accounting for capillary or solid bonding and in the presence of a binding solid or liquid. Finally, I focus on two issues: (1) How does local granular disorder affects the scale-up of cohesive interactions? (2) What are the respective roles of adhesion and volume fraction in the case of binding materials?
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.
Zohar Nussinov : The detection of hidden structures in glasses and complex systems by multi-scale clustering- Nonlinear and Complex Systems ( 144 Views )
We will discuss the application of multi-scale graph theory based methods to the detection of general structures in networks, lattices, and amorphous physical systems. These methods enable the detection of the "natural" system structures on all scales. We specifically analyze lattices and spin systems with defects and various glass formers (including an analysis based on experimental data) to ascertain dominant structures at different temperatures. We will discuss general features of the phase diagram related to this analysis.
For centuries, origami, the Japanese art of paper folding, has been a powerful technique for transforming two dimensional sheets into beautiful three dimensional sculptures. Recently, origami has made its foray into a new realm, that of physics and engineering, where it has been revolutionizing our concept of materials design. In this talk I will describe the new design principles we are uncovering for determining the shape, mechanics, and transformations of origami structures along with their usefulness in areas as diverse as solar sail design, architecture, and even fashion. Arguably however, the greatest strength of this new paradigm is the fact that origami is intrinsically scalable. Thus sculptures built at one size can be shrunk down smaller and smaller. This begs the question: what is the smallest fold one can make? Or in other words, how many folded angels can dance on the head of a pin? The rest of this talk will take a deep dive into how origami has been marching smaller and smaller in size. From folding by hand, to self-folding through shape memory alloys and even folding via polymer layers, I will argue that the ultimate limit for scaling down origami is set by folding a sheet of atomic dimensions. I will conclude by showing this vision: realized in the folds of a single sheet of graphene.
The tracking of small, colloidal particles is a common technique for measuring fluid velocities, highly successful at the micro-scale and recently extended to measurements at nano-scales. The Brownian fluctuations of the colloidal tracers are typically isotropic in the bulk; but in the near-wall region, these fluctuations are strongly affected by the hydrodynamic interaction with the wall and by the no-flux condition imposed there. Such wall effects can, under appropriate conditions, bias particle image velocimetry (PIV) measurements based on colloidal tracers, potentially leading to significant overestimation of near-wall velocities. The quantification of the resulting bias is presented in terms of the size of the imaged region and the measurement interval between PIV images. The effect of the steady state particle distribution is additionally explored, and implications for near-wall velocimetry measurements are briefly discussed.
This talk represents collaborative work with Christel Hohenegger, Minami Yoda, Reza Sadr, and Haifeng Li.