Flocking with discrete symmetry: the 2d Active Ising Model

We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a 2d lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density/velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density/temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.Comment: 20 pages, 25 figure

Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.Comment: 32 pages, 6 figure

Optimal paths on the road network as directed polymers

We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly proportional to the absolute distance between them. This motivates comparisons to universal features of directed polymers in random media. There are similarities in scalings of fluctuations in length/time and transverse wanderings, but also important distinctions in the scaling exponents, likely due to long-range correlations in geographic and man-made features. At short scales the optimal paths are not directed due to circuitous excursions governed by a fat-tailed (power-law) probability distribution.Comment: 5 pages, 7 figure

Historic Barns of Iowa State

On March 22, 1858, Governor of Iowa Ralph P. Lowe signed the legislative bill establishing the State Agricultural College and Model Farm. The bill provided for a board of trustees to manage the model farm and college to be developed. Residents of Story and Boone counties presented an attractive proposal to locate the new institution at a site west of Squaw Creek and downtown Ames. The proposal included significant gifts of land and funding to assist in developing the College site. The Story County site was selected by the trustees on June 21, 1859. The first concern was establishing the model farm specified in the legislation. Priority was given to two buildings. A farmhouse and livestock barn were both considered essential as a beginning, and construction of these two started in 1860

UC-400 Electric Vehicle Team

The KSU Electric Vehicle Team is developing a fully autonomous electric go-kart to compete in the Autonomous Karting Series (AKS). Our team will be making two programs for the kart’s software stack. These programs include a race line optimizer, which can take the centerline of a track and generate a minimum curvature path for it to follow to get around the track faster, as well as a race controller which can switch navigation algorithms automatically based on the current conditions of the race