Asymptotic dynamics of attractive-repulsive swarms

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more $\delta$-functions.Comment: 23 pages, 10 figures; revised version updates the analysis in sec. 2.1 and 2.2, and contains enhanced discussion of the admissible class of social interaction force

Nonlocal Aggregation Models: A Primer of Swarm Equilibria

Biological aggregations such as fish schools, bird flocks, bacterial colonies, and insect swarms have characteristic morphologies governed by the group members\u27 intrinsic social interactions with each other and by their interactions with the external environment. Starting from a simple discrete model treating individual organisms as point particles, we derive a nonlocal partial differential equation describing the evolving population density of a continuum aggregation. To study equilibria and their stability, we use tools from the calculus of variations. In one spatial dimension, and for several choices of social forces, external forces, and domains, we find exact analytical expressions for the equilibria. These solutions agree closely with numerical simulations of the underlying discrete model. The analytical solutions provide a sampling of the wide variety of equilibrium configurations possible within our general swarm modeling framework, and include features such as spatial localization with compact support, mass concentrations, and discontinuous density jumps at the edge of the group. We apply our methods to a model of locust swarms, which in nature are observed to consist of a concentrated population on the ground separated from an airborne group. Our model can reproduce this configuration; in this case quasi-two-dimensionality of the locust swarm plays a critical role

Diversity of Artists in Major U.S. Museums

The U.S. art museum sector is grappling with diversity. While previous work has investigated the demographic diversity of museum staffs and visitors, the diversity of artists in their collections has remained unreported. We conduct the first large-scale study of artist diversity in museums. By scraping the public online catalogs of 18 major U.S. museums, deploying a sample of 10,000 artist records comprising over 9,000 unique artists to crowdsourcing, and analyzing 45,000 responses, we infer artist genders, ethnicities, geographic origins, and birth decades. Our results are threefold. First, we provide estimates of gender and ethnic diversity at each museum, and overall, we find that 85% of artists are white and 87% are men. Second, we identify museums that are outliers, having significantly higher or lower representation of certain demographic groups than the rest of the pool. Third, we find that the relationship between museum collection mission and artist diversity is weak, suggesting that a museum wishing to increase diversity might do so without changing its emphases on specific time periods and regions. Our methodology can be used to broadly and efficiently assess diversity in other fields.Comment: 15 pages, 2 figures, minor revisions of and enhancements to tex

Two-frequency forced Faraday waves: Weakly damped modes and pattern selection

Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency parametrically excited surface waves exhibit an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves onset simultaneously, but with different spatial wavenumbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure. Similar patterns have been shown to exist as primary solution branches of a generic 12-dimensional $D_6\dot{+}T^2$-equivariant bifurcation problem, and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities (Silber and Proctor, 1998). Here we use the spatial and temporal symmetries of the problem to argue that weakly damped harmonic waves may be critical to understanding the stabilization of this pattern in the Faraday system. We illustrate this mechanism by considering the equations developed by Zhang and Vinals (1997, J. Fluid Mech. 336) for small amplitude, weakly damped surface waves on a semi-infinite fluid layer. We compute the relevant nonlinear coefficients in the bifurcation equations describing the onset of patterns for excitation frequency ratios of 2/3 and 6/7. For the 2/3 case, we show that there is a fundamental difference in the pattern selection problems for subharmonic and harmonic instabilities near the codimension-two point. Also, we find that the 6/7 case is significantly different from the 2/3 case due to the presence of additional weakly damped harmonic modes. These additional harmonic modes can result in a stabilization of the superpatterns.Comment: 26 pages, 8 figures; minor text revisions, corrected figure 8; this version to appear in a special issue of Physica D in memory of John David Crawfor

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures

Resolved Photon Processes

We review the present level of knowledge of the hadronic structure of the photon, as revealed in interactions involving quarks and gluons ``in" the photon. The concept of photon structure functions is introduced in the description of deep--inelastic $e \gamma$ scattering, and existing parametrizations of the parton densities in the photon are reviewed. We then turn to hard \gamp\ and \gaga\ collisions, where we treat the production of jets, heavy quarks, hard (direct) photons, \jpsi\ mesons, and lepton pairs. We also comment on issues that go beyond perturbation theory, including recent attempts at a comprehensive description of both hard and soft \gamp\ and \gaga\ interactions. We conclude with a list of open problems.Comment: LaTeX with equation.sty, 85 pages, 29 figures (not included). A complete PS file of the paper, including figures, can be obtained via anonymous ftp from ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-898.ps.