24,099 research outputs found
Effects of many-electron jumps in relaxation and conductivity of Coulomb glasses
A numerical study of the energy relaxation and conductivity of the Coulomb
glass is presented. The role of many-electron transitions is studied by two
complementary methods: a kinetic Monte Carlo algorithm and a master equation in
configuration space method. A calculation of the transition rate for
two-electron transitions is presented, and the proper extension of this to
multi-electron transitions is discussed. It is shown that two-electron
transitions are important in bypassing energy barriers which effectively block
sequential one-electron transitions. The effect of two-electron transitions is
also discussed.Comment: 8 pages, 6 figure
2D Lattice Liquid Models
A family of novel models of liquid on a 2D lattice (2D lattice liquid models)
have been proposed as primitive models of soft-material membrane. As a first
step, we have formulated them as single-component, single-layered, classical
particle systems on a two-dimensional surface with no explicit viscosity. Among
the family of the models, we have shown and constructed two stochastic models,
a vicious walk model and a flow model, on an isotropic regular lattice and on
the rectangular honeycomb lattice of various sizes. In both cases, the dynamics
is governed by the nature of the frustration of the particle movements. By
simulations, we have found the approximate functional form of the frustration
probability, and peculiar anomalous diffusions in their time-averaged mean
square displacements in the flow model. The relations to other existing
statistical models and possible extensions of the models are also discussed.Comment: REVTeX4, 14 pages in double colomn, 12 figures; added references with
some comments, typos fixe
A Landscape Analysis of Constraint Satisfaction Problems
We discuss an analysis of Constraint Satisfaction problems, such as Sphere
Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape.
Several intriguing geometrical properties of the solution space become in this
light familiar in terms of the well-studied ones of rugged (glassy) energy
landscapes. A `benchmark' algorithm naturally suggested by this construction
finds solutions in polynomial time up to a point beyond the `clustering' and in
some cases even the `thermodynamic' transitions. This point has a simple
geometric meaning and can be in principle determined with standard Statistical
Mechanical methods, thus pushing the analytic bound up to which problems are
guaranteed to be easy. We illustrate this for the graph three and four-coloring
problem. For Packing problems the present discussion allows to better
characterize the `J-point', proposed as a systematic definition of Random Close
Packing, and to place it in the context of other theories of glasses.Comment: 17 pages, 69 citations, 12 figure
Energy Efficient Scheduling via Partial Shutdown
Motivated by issues of saving energy in data centers we define a collection
of new problems referred to as "machine activation" problems. The central
framework we introduce considers a collection of machines (unrelated or
related) with each machine having an {\em activation cost} of . There
is also a collection of jobs that need to be performed, and is
the processing time of job on machine . We assume that there is an
activation cost budget of -- we would like to {\em select} a subset of
the machines to activate with total cost and {\em find} a schedule
for the jobs on the machines in minimizing the makespan (or any other
metric).
For the general unrelated machine activation problem, our main results are
that if there is a schedule with makespan and activation cost then we
can obtain a schedule with makespan \makespanconstant T and activation cost
\costconstant A, for any . We also consider assignment costs for
jobs as in the generalized assignment problem, and using our framework, provide
algorithms that minimize the machine activation and the assignment cost
simultaneously. In addition, we present a greedy algorithm which only works for
the basic version and yields a makespan of and an activation cost .
For the uniformly related parallel machine scheduling problem, we develop a
polynomial time approximation scheme that outputs a schedule with the property
that the activation cost of the subset of machines is at most and the
makespan is at most for any
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