1,264 research outputs found
Superfrustration of charge degrees of freedom
We review recent results, obtained with P. Fendley, on frustration of quantum
charges in lattice models for itinerant fermions with strong repulsive
interactions. A judicious tuning of kinetic and interaction terms leads to
models possessing supersymmetry. In such models frustration takes the form of
what we call superfrustration: an extensive degeneracy of supersymmetric ground
states. We present a gallery of examples of superfrustration on a variety of 2D
lattices.Comment: 8 pages, 5 figures, contribution to the proceedings of the XXIII
IUPAP International Conference on Statistical Physics (2007) in Genova, Ital
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
This paper develops a first-order system least-squares (FOSLS) formulation
for equations of two-phase flow. The main goal is to show that this
discretization, along with numerical techniques such as nested iteration,
algebraic multigrid, and adaptive local refinement, can be used to solve these
types of complex fluid flow problems. In addition, from an energetic
variational approach, it can be shown that an important quantity to preserve in
a given simulation is the energy law. We discuss the energy law and inherent
structure for two-phase flow using the Allen-Cahn interface model and indicate
how it is related to other complex fluid models, such as magnetohydrodynamics.
Finally, we show that, using the FOSLS framework, one can still satisfy the
appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic
Stability of general-relativistic accretion disks
Self-gravitating relativistic disks around black holes can form as transient
structures in a number of astrophysical scenarios such as binary neutron star
and black hole-neutron star coalescences, as well as the core-collapse of
massive stars. We explore the stability of such disks against runaway and
non-axisymmetric instabilities using three-dimensional hydrodynamics
simulations in full general relativity using the THOR code. We model the disk
matter using the ideal fluid approximation with a -law equation of
state with . We explore three disk models around non-rotating black
holes with disk-to-black hole mass ratios of 0.24, 0.17 and 0.11. Due to metric
blending in our initial data, all of our initial models contain an initial
axisymmetric perturbation which induces radial disk oscillations. Despite these
oscillations, our models do not develop the runaway instability during the
first several orbital periods. Instead, all of the models develop unstable
non-axisymmetric modes on a dynamical timescale. We observe two distinct types
of instabilities: the Papaloizou-Pringle and the so-called intermediate type
instabilities. The development of the non-axisymmetric mode with azimuthal
number m = 1 is accompanied by an outspiraling motion of the black hole, which
significantly amplifies the growth rate of the m = 1 mode in some cases.
Overall, our simulations show that the properties of the unstable
non-axisymmetric modes in our disk models are qualitatively similar to those in
Newtonian theory.Comment: 30 pages, 21 figure
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