86,007 research outputs found
Alternative Implementations of Expanding Algorithm for Multi-Commodity Spatial Price Equilibrium
This thesis presents an algorithm based on the expanding algorithm to solve spatial price equilibrium problems for three different models: perfect competition, monopoly, oligopoly. The expanding algorithm is used to solve the linear single commodity spatial price equilibrium problem for perfectly competitive markets. In this thesis, we consider the general multi-commodity spatial price equilibrium problems with all nonlinear functions, and variable shipping cost. We also show that more commodities in total are shipped, and there is more congestion, especially in oligopoly model
A fully relativistic lattice Boltzmann algorithm
Starting from the Maxwell-Juettner equilibrium distribution, we develop a
relativistic lattice Boltzmann (LB) algorithm capable of handling
ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm
is validated through simulations of quark-gluon plasma, yielding excellent
agreement with hydrodynamic simulations. The present scheme opens the
possibility of transferring the recognized computational advantages of lattice
kinetic theory to the context of both weakly and ultra-relativistic systems.Comment: 12 pages, 8 figure
Monte Carlo study of the random-field Ising model
Using a cluster-flipping Monte Carlo algorithm combined with a generalization
of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied
the equilibrium properties of the thermal random-field Ising model on a cubic
lattice in three dimensions. We have equilibrated systems of LxLxL spins, with
values of L up to 32, and for these systems the cluster-flipping method appears
to a large extent to overcome the slow equilibration seen in single-spin-flip
methods. From the results of our simulations we have extracted values for the
critical exponents and the critical temperature and randomness of the model by
finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06
+/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.Comment: 12 pages, 6 figures, self-expanding uuencoded compressed PostScript
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Estimating Relevant Portion of Stability Region using Lyapunov Approach and Sum of Squares
Traditional Lyapunov based transient stability assessment approaches focus on
identifying the stability region (SR) of the equilibrium point under study.
When trying to estimate this region using Lyapunov functions, the shape of the
final estimate is often limited by the degree of the function chosen, a
limitation that results in conservativeness in the estimate of the SR. More
conservative the estimate is in a particular region of state space, smaller is
the estimate of the critical clearing time for disturbances that drive the
system towards that region. In order to reduce this conservativeness, we
propose a methodology that uses the disturbance trajectory data to skew the
shape of the final Lyapunov based SR estimate. We exploit the advances made in
the theory of sum of squares decomposition to algorithmically estimate this
region. The effectiveness of this technique is demonstrated on a power systems
classical model.Comment: Under review as a conference paper at IEEE PESGM 201
An elementary way to rigorously estimate convergence to equilibrium and escape rates
We show an elementary method to have (finite time and asymptotic) computer
assisted explicit upper bounds on convergence to equilibrium (decay of
correlations) and escape rate for systems satisfying a Lasota Yorke inequality.
The bounds are deduced by the ones of suitable approximations of the system's
transfer operator. We also present some rigorous experiment showing the
approach and some concrete result.Comment: 14 pages, 6 figure
Non equilibrium effects in fragmentation
We study, using molecular dynamics techniques, how boundary conditions affect
the process of fragmentation of finite, highly excited, Lennard-Jones systems.
We analyze the behavior of the caloric curves (CC), the associated thermal
response functions (TRF) and cluster mass distributions for constrained and
unconstrained hot drops. It is shown that the resulting CC's for the
constrained case differ from the one in the unconstrained case, mainly in the
presence of a ``vapor branch''. This branch is absent in the free expanding
case even at high energies . This effect is traced to the role played by the
collective expansion motion. On the other hand, we found that the recently
proposed characteristic features of a first order phase transition taking place
in a finite isolated system, i.e. abnormally large kinetic energy fluctuations
and a negative branch in the TRF, are present for the constrained (dilute) as
well the unconstrained case. The microscopic origin of this behavior is also
analyzed.Comment: 21 pages, 11 figure
Smoothing Method for Approximate Extensive-Form Perfect Equilibrium
Nash equilibrium is a popular solution concept for solving
imperfect-information games in practice. However, it has a major drawback: it
does not preclude suboptimal play in branches of the game tree that are not
reached in equilibrium. Equilibrium refinements can mend this issue, but have
experienced little practical adoption. This is largely due to a lack of
scalable algorithms.
Sparse iterative methods, in particular first-order methods, are known to be
among the most effective algorithms for computing Nash equilibria in
large-scale two-player zero-sum extensive-form games. In this paper, we
provide, to our knowledge, the first extension of these methods to equilibrium
refinements. We develop a smoothing approach for behavioral perturbations of
the convex polytope that encompasses the strategy spaces of players in an
extensive-form game. This enables one to compute an approximate variant of
extensive-form perfect equilibria. Experiments show that our smoothing approach
leads to solutions with dramatically stronger strategies at information sets
that are reached with low probability in approximate Nash equilibria, while
retaining the overall convergence rate associated with fast algorithms for Nash
equilibrium. This has benefits both in approximate equilibrium finding (such
approximation is necessary in practice in large games) where some probabilities
are low while possibly heading toward zero in the limit, and exact equilibrium
computation where the low probabilities are actually zero.Comment: Published at IJCAI 1
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