We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10 - 500 s in a frequency band of 40 - 1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between $3.4 times 10^{-5}$ - $9.4 times 10^{-4}$ Mpc$^{-3}$ yr$^{-1}$ at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves.
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