Gravitational lensing in modified Newtonian dynamics

Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes no definite predictions about gravitational lensing. The most obvious form that MONDian lensing might take is that photons experience twice the deflection of massive particles moving at the speed of light, as in general relativity (GR). In such a theory there is no general thin-lens approximation (although one can be made for spherically-symmetric deflectors), but the three-dimensional acceleration of photons is in the same direction as the relativistic acceleration would be. In regimes where the deflector can reasonably be approximated as a single point-mass (specifically low-optical depth microlensing and weak galaxy-galaxy lensing), this naive formulation is consistent with observations. Forthcoming galaxy-galaxy lensing data and the possibility of cosmological microlensing have the potential to distinguish unambiguously between GR and MOND. Some tests can also be performed with extended deflectors, for example by using surface brightness measurements of lens galaxies to model quasar lenses, although the breakdown of the thin-lens approximation allows an extra degree of freedom. Nonetheless, it seems unlikely that simple ellipsoidal galaxies can explain both constraints. Further, the low-density universe implied by MOND must be completely dominated by the cosmological constant (to fit microwave background observations), and such models are at odds with the low frequency of quasar lenses. These conflicts might be resolved by a fully consistent relativistic extension to MOND; the alternative is that MOND is not an accurate description of the universe.Comment: MNRAS, in press; 11 pages, 10 figure

Constraint interface preconditioning for topology optimization problems

The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size. In this work we propose a methodology which brings together existing fast algorithms, namely, interior-point for the optimization problem and a novel substructuring domain decomposition method for the ensuing large-scale linear systems. The main contribution is the choice of interface preconditioner which allows for the acceleration of the domain decomposition method, leading to performance independent of problem size.Comment: To be published in SIAM J. Sci. Com

Nashbots: How Political Scientists have Underestimated Human Rationality, and How to Fix It

Political scientists use experiments to test the predictions of game-theoretic models. In a typical experiment, each subject makes choices that determine her own earnings and the earnings of other subjects, with payments corresponding to the utility payoffs of a theoretical game. But social preferences distort the correspondence between a subject’s cash earnings and her subjective utility, and since social preferences vary, anonymously matched subjects cannot know their opponents’ preferences between outcomes, turning many laboratory tasks into games of incomplete information. We reduce the distortion of social preferences by pitting subjects against algorithmic agents (“Nashbots”). Across 11 experimental tasks, subjects facing human opponents played rationally only 36% of the time, but those facing algorithmic agents did so 60% of the time. We conclude that experimentalists have underestimated the economic rationality of laboratory subjects by designing tasks that are poor analogies to the games they purport to test

Labor in the New Urban Battlegrounds: Local Solidarity in a Global Economy

[Excerpt] Labor in the New Urban Battlegrounds is an energizing, optimistic book. By using the contemporary metropolis as a comparative laboratory to see what contexts and strategies contribute best to labor revitalization, Lowell Turner, Daniel Cornfield, and their collaborators generate a fresh sense of positive possibilities for labor and new insights as to how creative actors can best take advantage of those possibilities. Energizing optimism should not be confused with seeing things through rose-colored glasses. The book fully acknowledges the odds against labor revitalization and the structural obstacles to a more equitable society. Optimism is generated by pairing obstacles with possibilities, often brought to light by another city in which similar obstacles have been overcome with innovative strategies. This book builds on a new tradition of recent analyses of U.S. labor that compellingly contests previous premature obituaries of the labor movement while making a distinctive contribution. Its power is rooted in the comparative metropolis analytical theme and the editors\u27 skill in bringing a diverse baker\u27s dozen of substantive studies to bear on it. The individual chapters are empirically diverse, complementing a gamut of metropolitan areas in the United States with comparative cases from Europe. They employ varied methodological approaches to look at the social infrastructure and strategic choices that underlie urban successes and failures. Many chapters are in-depth case studies of individual cities, while others (e.g., Greer, Byrd, and Fleron; Hauptmeier and Turner) are paired comparisons. Still others (Applegate; Luce; Reynolds) draw their evidence from larger numbers of cities. One (Sellers) employs an ingenious analysis of cross-national data to draw inferences about differences in urban strategic possibilities. The result is much more powerful analytically than it would have been had the editors collected thirteen metropolitan case studies and then tried to figure out their comparative implications. Empirical range and methodological diversity augment the power of the volume, but the overarching focus on comparative metropolitan analysis is what gives the book its distinctive analytical punch. Even though a variety of organizations and social actors populate the stage—campaigns, nongovernmental organizations, individual unions, and ethnic communities—defining the urban area as the stage on which the dramas occur was a critical decision. From this decision flows the book\u27s special contribution to refocusing contemporary labor debates

Density regulation in strictly metric-free swarms

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition

Gravitational lensing and modified Newtonian dynamics

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe.Comment: PASA (OzLens edition), in press; 5 pages, 1 figur

Gravitational lensing and modified Newtonian dynamics

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe.Comment: PASA (OzLens edition), in press; 5 pages, 1 figur

The distance to the young open cluster Westerlund 2

Evidence is presented indicating that the young star cluster Westerlund~2 lies $d_{\odot}\sim3.0$ kpc in the direction of Carina. The distance is tied partly to new $UBVRI_c$ photometry and revised spectral classifications for cluster stars, which imply that dust in the direction of Carina is characterized by an anomalous extinction law ($R_V\sim3.8$). That result was determined from a multi-faceted approach relying on the variable-extinction and color excess methods.Comment: 4 pages, 4 eps figure, proceedings of IAU Symposium 289, Beijing, August 201