In solar coronal loops, thermal non-equilibrium (TNE) is a phenomenon that can occur when the heating is both highly-stratified and quasi-constant. Unambiguous observational identification of TNE would thus permit to strongly constrain heating scenarios. Up to now, while TNE is the standard interpretation of coronal rain, the long-term periodic evolution predicted by simulations has never been observed yet. However, the detection of long-period intensity pulsations (periods of several hours) has been recently reported with SoHO/EIT, and this phenomenon appears to be very common in loops. Moreover, the three intensity-pulsation events that we recently studied with SDO/AIA show strong evidence for TNE in warm loops. In the present paper, a realistic loop geometry from LFFF extrapolations is used as input to 1D hydrodynamic simulations. Our simulations show that for the present loop geometry, the heating has to be asymmetrical to produce TNE. We analyse in detail one particular simulation that reproduces the average thermal behavior of one of the pulsating loop bundle observed with AIA. We compare the properties of this simulation with the properties deduced from the observations. The magnetic topology of the LFFF extrapolations points to the presence of sites of preferred reconnection at one footpoint, supporting the presence of asymmetric heating. In addition, we can reproduce the temporal large-scale intensity properties of the pulsating loops. This simulation further strengthens the interpretation of the observed pulsations as signatures of TNE. This thus gives important information on the heating localization and time scale for these loops.
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