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Central Schemes for Porous Media Flows
We are concerned with central differencing schemes for solving scalar
hyperbolic conservation laws arising in the simulation of multiphase flows in
heterogeneous porous media. We compare the Kurganov-Tadmor, 2000 semi-discrete
central scheme with the Nessyahu-Tadmor, 1990 central scheme. The KT scheme
uses more precise information about the local speeds of propagation together
with integration over nonuniform control volumes, which contain the Riemann
fans. These methods can accurately resolve sharp fronts in the fluid
saturations without introducing spurious oscillations or excessive numerical
diffusion. We first discuss the coupling of these methods with velocity fields
approximated by mixed finite elements. Then, numerical simulations are
presented for two-phase, two-dimensional flow problems in multi-scale
heterogeneous petroleum reservoirs. We find the KT scheme to be considerably
less diffusive, particularly in the presence of high permeability flow
channels, which lead to strong restrictions on the time step selection;
however, the KT scheme may produce incorrect boundary behavior
Steady-state dynamics and effective temperatures of quantum criticality in an open system
We study the thermal and non-thermal steady state scaling functions and the
steady-state dynamics of a model of local quantum criticality. The model we
consider, i.e. the pseudogap Kondo model, allows us to study the concept of
effective temperatures near fully interacting as well as weak-coupling fixed
points. In the vicinity of each fixed point we establish the existence of an
effective temperature --different at each fixed point-- such that the
equilibrium fluctuation-dissipation theorem is recovered. Most notably,
steady-state scaling functions in terms of the effective temperatures coincide
with the equilibrium scaling functions. This result extends to higher
correlation functions as is explicitly demonstrated for the Kondo singlet
strength. The non-linear charge transport is also studied and analyzed in terms
of the effective temperature.Comment: 5 pages, 4 figures; Supplementary Material (7 pages, 1 figure
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