לוח שנה משולב

We study cold atomic gases with a contact interaction and confined
into one-dimension. Crossing the confinement induced resonance the
correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We demonstrate the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.

Cell motion is driven by interplay between the actin cytoskeleton and the cell adhesion complexes in the front part of the cell. The actin network undergoes retrograde flow and, at the same time, exhibits a distinctive spatial organization, segregating into lamellipodium and lamellum which are separated from each other by a well-defined boundary of a characteristic shape. The adhesion complexes are non-uniformly distributed such that the newly formed nascent adhesions concentrate underneath the lamellipodium whereas the mature complexes decorate the lamellipodium-lamellum boundary and underlie the lamellum. Here we suggest a physical model for this characteristic organization of the actin-adhesion system. The model is based on the ability of the adhesion complexes to sense mechanical forces, the stick-slip character of the interaction between the adhesions and the moving actin network, and a hypothetical propensity of the actin network to disintegrate upon sufficiently strong stretching stresses. We numerically analyze the system evolution and identify three possible types of its steady-state organization, all observed for different cell types: two states in which the cell edge either remains stationary or moves while the actin networks exhibits segregation into lamellipodium and lamellum, and a state where the actin network does not undergo segregation. The crucial parameter determining the type of the steady state is the rate of generation of new adhesion complexes. Moreover, the model recovers and suggests physical mechanisms of more delicate dynamic features of the cell edge behavior: the asynchronous fluctuations and outward bulging of the edge, and the dependence of the edge protrusion velocity on the rate of the nascent adhesion generation. Finally, the model predicts formation of precursors of the actin stress fibers.

In these introductory lectures I will discuss extreme value statistics (EVS) and its various applications. EVS deals with the statistics of the maximum (or minimum) of a set of random variables which could be either independent or correlated. For independent variables, the theory is well developed and one gets three limiting distributions--Gumbel, Frechet and Weibull. The theory is much less developed for strongly correlated random variables--this arises in a variety of problems in disordered systems, fluctuating interfaces, Brownian motion, and random matrices (just to name a few). I'll discuss some recent advances on the EVS of strongly correlated variables.