13,369 research outputs found
Pseudoparticle Multipole Method: A Simple Method to Implement High-Accuracy Treecode
In this letter we describe the pseudoparticle multipole method (P2M2), a new
method to express multipole expansion by a distribution of pseudoparticles. We
can use this distribution of particles to calculate high order terms in both
the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works
on GRAPE. GRAPE is a special-purpose hardware for the calculation of
gravitational force between particles. Although the treecode has been
implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can
calculate forces from point-mass particles only. Thus the calculation cost
grows quickly when high accuracy is required. With P2M2, the multipole
expansion is expressed by particles, and thus GRAPE can calculate high order
terms. Using P2M2, we implemented an arbitrary-order treecode on GRAPE-4.
Timing result shows GRAPE-4 accelerates the calculation by a factor between 10
(for low accuracy) to 150 (for high accuracy). Even on general-purpose
programmable computers, our method offers the advantage that the mathematical
formulae and therefore the actual program is much simpler than that of the
direct implementation of multipole expansion.Comment: 6 pages, 4 figures, latex, submitted to ApJ Letter
Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions
The elliptic genera of two-dimensional N=2 superconformal field theories can
be twisted by the action of the integral Heisenberg group if their U(1) charges
are fractional. The basic properties of the resulting twisted elliptic genera
and the associated twisted Witten indices are investigated with due attention
to their behaviors in orbifoldization. Our findings are illustrated by and
applied to several concrete examples. We give a better understanding of the
duality phenomenon observed long before for certain Landau-Ginzburg models. We
revisit and prove an old conjecture of Witten which states that every ADE
Landau-Ginzburg model and the corresponding minimal model share the same
elliptic genus. Mathematically, we establish ADE generalizations of the
quintuple product identity.Comment: 28 pages; v2 refs adde
Renormalization of 3d quantum gravity from matrix models
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory
of quantum gravity which predicts a positive cosmological constant. Since the
approach is based on a sum over space-time histories, it is perturbatively
non-renormalizable even in three dimensions. By mapping the three-dimensional
theory to a two-matrix model with ABAB interaction we show that both the
cosmological and the (perturbatively) non-renormalizable gravitational coupling
constant undergo additive renormalizations consistent with canonical
quantization.Comment: 14 pages, 3 figure
Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities
Accurate calculations of macroscopic and mesoscopic properties in quantum
electrodynamics require careful treatment of infrared divergences: standard
treatments introduce spurious large-distances effects. A method for computing
these properties was developed in a companion paper. That method depends upon a
result obtained here about the nature of the singularities that produce the
dominant large-distance behaviour. If all particles in a quantum field theory
have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on
the singularities of the scattering functions. These conditions are severely
weakened in quantum electrodynamics by effects of points where photon momenta
vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared
specifically to the pole-decomposition functions that dominate the macroscopic
behaviour in quantum electrodynamics, and leads to strong results for these
functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed,
math_macros.tex can be found on Archive. full postscript available from
http://theorl.lbl.gov/www/theorgroup/papers/35972.p
Tracking Control for FES-Cycling based on Force Direction Efficiency with Antagonistic Bi-Articular Muscles
A functional electrical stimulation (FES)-based tracking controller is
developed to enable cycling based on a strategy to yield force direction
efficiency by exploiting antagonistic bi-articular muscles. Given the input
redundancy naturally occurring among multiple muscle groups, the force
direction at the pedal is explicitly determined as a means to improve the
efficiency of cycling. A model of a stationary cycle and rider is developed as
a closed-chain mechanism. A strategy is then developed to switch between muscle
groups for improved efficiency based on the force direction of each muscle
group. Stability of the developed controller is analyzed through Lyapunov-based
methods.Comment: 8 pages, 4 figures, submitted to ACC201
Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity
A real space renormalization group technique, based on the hierarchical
baby-universe structure of a typical dynamically triangulated manifold, is used
to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the
-function is defined and calculated numerically. An evidence for the
existence of an ultraviolet stable fixed point of the theory is presentedComment: 12 pages Latex + 1 PS fi
Scaling Behavior of Ricci Curvature at Short Distance near Two Dimensions
We study the renormalization of the Ricci curvature as an example of
generally covariant operators in quantum gravity near two dimensions. We find
that it scales with a definite scaling dimension at short distance. The Ricci
curvature singularity at the big bang can be viewed as such a scaling
phenomenon. The problem of the spacetime singularity may be resolved by the
scale invariance of the spacetime at short distance.Comment: 9pages, LaTe
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